calculation rules of lightweight steel … · ... more and more lightweight steel structures are...

* CTICM – Domaine de Saint-Paul – 102 Route de Limours – 78471 SAINT-REMY-LES-CHEVREUSE CEDEX – FRANCE Tel : + 33 1 30 85 20 73 / Fax : + 33 1 30 85 25 30 E-Mail : [email protected] / www.cticm.com

CALCULATION RULES OF LIGHTWEIGHT STEEL

SECTIONS IN FIRE SITUATION

ECSC PROJECT N° 7210 PR 254

From 1st July 2000 to 31st December 2003

Authors Contractors

ZHAO B., KRUPPA J. and RENAUD C. - CTICM* – Coordinator - France

O’CONNOR M. - CORUS – United Kingdom

MECOZZI E. - CSM - Italy

AZPIAZU W. - LABEIN - Spain

DEMARCO T. - PROFILARBED - Luxembourg

KARLSTROM P. - SBI - Sweden

JUMPPANEN U., KAITILA O., OKSANEN T. and SALMI P. - VTT - Finland

FINAL REPORT

/250

SUMMARY

Due to a number of specific advantages, more and more lightweight steel structures are used in constructions as both non load-bearing and load-bearing members. This has led to the development of relevant design rules for room temperature application in different standards, such as part 1.3 of Eurocode 3 [1]. However, as far as design for the fire limit state is concerned, the knowledge remains still quite poor in this field due to lack of sufficient research. As a consequence of this, the present project aims:

• to provide available data on the basis of an extensive experimental investigation and a series of parametric studies using validated advanced calculation models;

• to develop relevant simple design rules for load-bearing capacity of lightweight structures under different conditions;

• to elaborate a simple extrapolation method for high non load-bearing partition walls exposed to fire.

In order to achieve above objectives, within the scope of this project, the following items have been studied:

• material mechanical properties of lightweight steels at elevated temperatures; • behaviour of lightweight steel members under normal utilisation condition (room

temperature); • behaviour of isolated lightweight steel members engulfed in fire; • fire behaviour of lightweight steel members maintained by boards; • fire performance of lightweight steel structure assemblies; • an assessment method to extend test results of small size partition walls to very high

non load-bearing partition walls. From the extensive amount of work carried out by all the partners involved in the project, the main outcomes were:

• the development of a mathematical material model for two types of cold-formed lightweight steels at elevated temperatures in accordance with part 1.2 of Eurocode 3 [2];

• an investigation of the design rules of lightweight steel members at room temperature by means of both tests and numerical analysis;

• the development of design rules for isolated lightweight steel members under compression at elevated temperatures;

• the development of design rules for maintained lightweight steel members under different heating regimes at elevated temperatures;

• the establishment of a simple extrapolation method for high non load-bearing partition walls made of lightweight steel stud members and plasterboards.

/250

ABSTRACT

The main motivation of this research project on the fire behaviour of cold formed steel member is increasing the use of such components for both load-bearing and non load-bearing elements. The load-bearing elements are used in houses, low rise official or residential buildings as well as high storage constructions. Non load-bearing elements are widely used for partitions, for example with plasterboards, and often reach 10 or 15 metres in height in some constructions. Currently in the design of lightweight steel frames used in load-bearing and non load-bearing partitions, the contribution of non-structural items such as plasterboard and glazing to the overall stiffness of the structure is generally ignored in engineering codes. However, in fire it is known that the panels contribute significantly to the overall performance of the sub-frame such as through the development of membrane action. This contribution will depend upon the construction of the sub-frame – spacing, size and shape of the individual struts, the type and spacing of the connections, the material used for the panels and the level of protection provided to the steel members. Additionally the performance of the frame will depend upon whether it is designed to be load-bearing or non load-bearing at room temperature. All these aspects are not covered in existing fire design codes. In order to improve design efficiency and take advantage of economic benefits that may be accrued by considering the overall performance of sub-frames in fire, it is necessary to understand the fundamental engineering parameters that influence their behaviour and the interaction that is obtained by considering the frame as a whole rather than as individual components or elements. The objectives of this research programme are, therefore: 1) To increase the understanding in fire of the performance of lightweight steel frames to

improve design efficiency, for example by quantifying the structural benefits that are obtained from including board or glazing elements.

2) To develop numerical analytical calculation methods that are capable of predicting the behaviour of lightweight steel frames under load and non-load bearing conditions taking into account infill panels.

3) To develop design rules that can be used in practice and that are harmonised across Europe for implementation into the European standards.

In order to cover the field of application of cold formed lightweight steel members, as extensively as possible,, the research project was divided into the following parts:

• evaluation of the mechanical performance of cold formed steel at elevated temperatures, • confirmation of the behaviour of cold formed steel members and assemblies, at room

temperature conditions, • assessment of the fire behaviour of fully engulfed lightweight steel studs, • assessment of the fire behaviour of steel studs maintained by boards with fire on one

side of the partition, • verification of the fire behaviour of floors and wall-floor assemblies. For most of project parts, the research work was handled in the following way:

• analysis of existing knowledge, • definition and performance of tests, • analysis and numerical simulations with advanced calculation tools of test results, • parametrical study, • comparison with existing simple calculation methods and/or development of them.

/250

The above methodology allowed concentration of the experimental study on a number of key specimens. Nevertheless, overall, 135 different tests - from tensile tests on specimen of 100 mm length up to full scale wall-floor assembly fire resistance tests. These results were supplemented with the help of numerical modelling with approximately a 1000 further "virtual" test results being produced. This provides more confidence in the simple calculation methods developed, since they are validated for a wider scope of application. A brief summary of the work undertaken for each part is outlined below. Mechanical properties of lightweight steel at elevated temperatures (see chapter 2) Steels from four types of steel sections were investigated: one small C-section (100 x 50 x 0.6 [mm] in grade S280) mainly used for non load-bearing partitions, two other, medium and large, C-sections (150 x 57 x 1.2 and 250 x 80 x 2.5 in grade S 350) and lastly, a section with a special shape (AWS) with perforations in web in grade S 350. For each steel section, tensile tests were performed at room and elevated temperatures. More than 40 tensile tests were done. Elevated temperature Tests were carried out in steady state, at temperatures of 400°C, 600°C and 800°C, and as anisothermal transient tests, where load is maintained constant and temperature increased continuously. It was shown that the mechanical properties at elevated temperatures for the steel from medium and large C-sections, in steel grade S 350, are comparable, but the properties of small C-section, in steel grade S 280, differs significantly. Consequently, two sets of stress-strain relationships were produced. Analytical formulae are provided and these were used within the numerical simulation and for the development of simple calculation methods. Behaviour at room temperature (see chapter 3) It was not the purpose of carrying out a research project on the behaviour at normal temperature of these cold formed steel members, the aim of this static testing programme was to provide a series of control tests at room temperature for specimens to be tested in fire situation and to establish accurate information on the load-bearing capacity and deformations of lightweight steel members in common design situations. The results were also used to calibrate advanced calculation models and to examine the conservatism, if any, within existing design rules for load-bearing elements at room temperature condition. Overall, 31 different tests were performed on the four types of sections mentioned previously studying the effects of various parameters on static behaviour. The various effects studied included:

• local buckling stub column tests), • overall buckling (2.85 m tall stud tests), • different boundary conditions, • load eccentricity, • steel studs alone, • steel studs maintained by plasterboards on one or both sides, • steel studs maintained by plasterboards and a steel sheet.

/250

The comparison of test results with advanced calculation model results shows a quite good agreement. Therefore, it was concluded that numerical models are capable of accurately predicting room temperature behaviour. The comparison with simple calculation methods as given in Eurocode 3 part 1.3 [1], found that the results were acceptably conservative for most sections. However, some underestimation of the load-bearing capacity did exist for larger C-section when unsupported by plasterboard. In addition, one test was performed on floor-wall assembly with a Finnish building system and another one with a UK building system, with identical specimens as used for further fire resistance test. Fully fire engulfed studs (see chapter 4) Overall, 8 short stub column tests (height of 600 mm to 1000 mm) and 7 “tall” stud tests (height of 3.5 m) were performed at elevated temperatures were performed with applied load varying from 15 to 60 kN. In comparison with numerical modelling results, satisfactory agreement in behaviour was obtained for the prediction of deformation as a function of heating, for load-bearing capacity and for the failure mode. These numerical simulations were based on the use of shell and plate elements within finite element method for close prediction of local buckling effects. Beam type elements cannot be used to predict such effects. From test results and an extensive parametric study carried out with the validated computer models, a simple calculation method for the load-bearing capacity in fire situation is provided. This simple calculation method deals with lightweight steel studs with uniform or linear temperature distribution over the cross-section and uniform temperature field over the height under either axial or eccentric loading. Fire behaviour of steel studs maintained by boards (see chapter 5 and 7) Since the fire behaviour of lightweight steel members, when connected to boards in walls or floors differs largely from the behaviour of isolated steel members, a very extensive testing programme was carried out, in which 32 different specimens were tested. All these specimens had a size of 1200 mm in width and 2800 mm in height and consisted of two studs spaced of 600 mm apart from each other with plasterboards connected on one or both sides of steel studs. Of course the purpose of this part was not to provide ready-to-use fire resistance classifications of separating elements, as the number of possible parameters would be huge, but only to concentrate on the mechanical behaviour of steel sections in real end-use conditions. The different parameters taken into account were:

• load level, • axial or eccentric load, on the fire exposed or unexposed side, • restrained elongation or not, • insulation in the cavity within the plaster boards or not, • regular of "fire resistant" plaster boards, • plaster boards fixed on one or both sides of studs,

/250

• plain or perforated steel sections, • single or double steel sections, • plasterboards with and without steel sheet. The temperatures and deformations recorded during the tests, the failure modes obtained and comparison between test results have provided interesting insight into the behaviour of cold formed steel studs connected with plasterboards in fire situation. Advanced calculation models were found to be capable of simulating the experimental results with fair agreement. Further parametric calculation have been performed and, with a little further work, will lead to the possibility of developing a simple calculation method for assessing load-bearing capacity of the full range of steel studs maintained by boards when subjected to the full variety of thermal gradient over the cross section, under either axial or eccentric load. In order to allow the assessment of much taller partition walls than those which can be currently tested with existing European testing facilities (maximum height of 5 m), a simple extended application rule was developed. This extended application method is considering results of a given fire resistance test to be performed for the specific foreseen design. It provides rules for assessing the fire performance of this design, by only changing the cross-section of the steel studs and the partition height (up to 3 times of the tested one). Fire behaviour of floors, walls and floor-wall assemblies (see chapter 6) To complete the understanding of cold formed steel members in fire situation, both full scale walls (3000 mm x 2800 mm) and floors (2990 mm x 5500 mm) were tested. Firstly, the specimens were tested individually and, secondly, they were tested as an assembly including a realistic floor to wall connection. Overall, 7 tests were performed. These test results have provided interesting information on possible failure modes for such kind of elements or assemblies in a more realistic situation. Good agreement was obtained between numerical simulation and test results as far as lightweight steel members under bending are concerned. This confirms that the emphasis of the project on lightweight steel members under compressive loading conditions was correct.

/250

LIST OF CONTENTS

SUMMARY .............................................................................................................................................. 3

ABSTRACT............................................................................................................................................. 5

LIST OF CONTENTS.............................................................................................................................. 9

LIST OF TABLES ................................................................................................................................. 13

LIST OF FIGURES................................................................................................................................ 15

1. INTRODUCTION............................................................................................................................... 21

1.1 BACKGROUND OF THE PROJECT .........................................................................................21 1.2 OBJECTIVES ......................................................................................................................21 1.3 SUMMARY OF TECHNICAL CONTENT AND ITS MANAGEMENT .................................................22

2. MATERIAL MECHANICAL PROPERTIES OF COLD FORMED STEEL AT ELEVATED TEMPERATURES............................................................................................................................. 27

2.1 GENERAL...........................................................................................................................27 2.2 TESTING METHODOLOGY ....................................................................................................27 2.2.1 TENSILE TESTS – ROOM TEMPERATURE ...........................................................................27 2.2.2 TENSILE STEADY STATE TESTS - HIGH TEMPERATURE .......................................................27 2.2.3 TENSILE ANISOTHERMAL TRANSIENT TESTS ......................................................................28 2.3 CHARACTERISTICS OF INVESTIGATED COLD FORMED STEELS ..............................................31 2.4 DETAILED EXAMPLES OF TESTS RESULTS............................................................................32 2.4.1 TENSILE TESTS AT ROOM TEMPERATURE ..........................................................................32 2.4.2 TENSILE STEADY STATE TESTS - HIGH TEMPERATURE .......................................................32 2.4.3 TENSILE ANISOTHERMAL TRANSIENT TESTS ......................................................................33 2.5 SUMMARY OF TESTS RESULTS ............................................................................................35 2.5.1 TENSILE TESTS AT ROOM TEMPERATURE ..........................................................................35 2.5.2 TENSILE STEADY STATE TESTS - HIGH TEMPERATURE .......................................................36 2.5.3 TENSILE ANISOTHERMAL TRANSIENT TESTS ......................................................................36 2.6 PROPOSAL FOR STRESS–STRAIN RELATIONSHIPS AT ELEVATED TEMPERATURES.................38 2.6.1 ANALYSIS OF TENSILE ANISOTHERMAL TRANSIENT TESTS..................................................38 2.6.2 MATHEMATICAL MODEL FOR STRESS-STRAIN RELATIONSHIP OF COLD FORMED STEELS AT

ELEVATED TEMPERATURES..............................................................................................40 2.6.3 REDUCTION FACTORS OF COLD FORMED LIGHTWEIGHT STEELS USED FOR MATHEMATICAL

MODEL............................................................................................................................42 2.6.3.1 Steel of Type A: Grade S280-Small C1......................................................................42 2.6.3.2 Steel of Type B...........................................................................................................45 2.6.4 COMPARISON BETWEEN MATHEMATICAL MODEL AND TEST RESULTS..................................49 2.6.4.1 Type A steel ...............................................................................................................49 2.6.4.2 Type B steel ...............................................................................................................50 2-7 COMPARISON BETWEEN TWO TYPES OF STEEL ....................................................................54 2-8 CONCLUSIONS ...................................................................................................................55

/250

3. MECHANICAL BEHAVIOUR OF LIGHTWEIGHT STEEL MEMBERS AND ASSEMBLIES AT ROOM TEMPERATURE................................................................................................................... 59

3.1 GENERAL...........................................................................................................................59 3.2 STATIC TEST PROGRAMME..................................................................................................59 3.2.1 STUB COLUMN TESTS......................................................................................................59 3.2.2 DOUBLE STUD TESTS ......................................................................................................59 3.2.3 FLOOR & WALL ASSEMBLY TESTS....................................................................................60 3.3 TESTING METHODOLOGY ....................................................................................................60 3.3.1 STUB COLUMN TESTS......................................................................................................60 3.3.2 DOUBLE STUD TESTS ......................................................................................................61 3.3.3 FLOOR & WALL ASSEMBLY TESTS....................................................................................63 3.4 TEST RESULTS ...................................................................................................................64 3.4.1 STUB COLUMN TESTS......................................................................................................64 3.4.2 DOUBLE STUD TESTS ......................................................................................................65 3.4.2.1 Tall stud tests .............................................................................................................66 3.4.2.2 Boundary condition tests ............................................................................................68 3.4.2.3 Load eccentricity tests................................................................................................70 3.4.2.4 Specimens supported with plasterboard on one side only .........................................74 3.4.2.5 Effect of including steel sheet.....................................................................................75 3.4.2.6 Comparison of test results across test series.............................................................77 3.4.3 FLOOR & WALL ASSEMBLY TESTS....................................................................................79 3.4.3.1 Test on Rannila Floor and Wall assembly (Finnish system) ......................................79 3.4.3.2 Test on the Metsec Floor and Wall assembly (UK system)........................................81 3.5 NUMERICAL MODELING OF TESTS........................................................................................82 3.5.1 NUMERICAL SIMULATION OF STUB COLUMN TESTS.............................................................82 3.5.2 NUMERICAL SIMULATION OF TALL STUD TESTS ..................................................................85 3.5.2.1 Assumption for numerical simulations........................................................................86 3.5.2.2 Example Analysis .......................................................................................................89 3.5.2.3 Parametric study with end restrain and imperfection conditions ................................93 3.5.2.4 Comparison with numerical modelling results ............................................................95 3.5.2.5 Additional numerical modelling on floor and wall assemblies ....................................97 3.6 COMPARISON OF TEST RESULTS WITH SIMPLE CALCULATION RULES ..................................100 3.7 CONCLUSIONS .................................................................................................................103

4. MECHANICAL BEHAVIOUR OF INDEPENDENT LIGHTWEIGHT STEEL MEMBERS ENGULFED IN FIRE............................................................................................................................................ 105

4.1 GENERAL.........................................................................................................................105 4.2 EXPERIMENTAL WORK......................................................................................................105 4.2.1 TESTS ON SHORT STUB COLUMNS..................................................................................105 4.2.1.1 Testing methodology ..............................................................................................105 4.2.1.2 Test results .............................................................................................................109 4.2.1.3 Summary of test results..........................................................................................112 4.2.2 TEST ON TALL STUDS ....................................................................................................114 4.2.2.1 Testing methodology ..............................................................................................114 4.2.2.2 Test results .............................................................................................................116 4.2.2.3 Comparison between the results of tests on short and tall columns ......................122 4.3 NUMERICAL SIMULATIONS OF FIRE TESTS .........................................................................123 4.3.1 GENERAL .....................................................................................................................123 4.3.2 NUMERICAL MODELLING OF STUB COLUMN TESTS...........................................................124 4.3.2.1 Description of numerical modelling.........................................................................124

/250

4.3.2.2 Numerical results....................................................................................................125 4.3.2.3 Evaluation of proposed reduction factors ...............................................................126 4.3.3 NUMERICAL MODELLING OF HIGH STUDS ENGULFED IN FIRE ............................................127 4.3.3.1 Elevated temperature simulations with C-type section tall studs............................127 4.3.3.2 Numerical modelling of AWS-type cross section tall studs.....................................129 4.4 DEVELOPMENT OF SIMPLE CALCULATION MODEL ..............................................................135 4.4.1 GENERAL .....................................................................................................................135 4.4.2 NUMERICAL PARAMETRIC STUDY WITH HIGH STUDS ENGULFED IN FIRE............................135 4.4.3 GENERAL PRINCIPLES OF SIMPLE CALCULATION MODEL ..................................................137 4.4.3.1 Buckling with uniform temperature distribution and centric load ............................137 4.4.3.2 Buckling with uniform temperature distribution and eccentric load.........................139 4.4.3.3 Flexural or torsional flexural buckling with temperature gradient ...........................140 4.4.3.4 Cross sectional resistance......................................................................................141 4.4.4 COMPARISON OF MECHANICAL PERFORMANCE OF STUDS ENGULFED IN FIRE BETWEEN

SIMPLE CALCULATION MODEL AND ADVANCED NUMERICAL MODEL ...................................142 4.5 CONCLUSIONS .................................................................................................................145

5 MECHANICAL BEHAVIOUR OF LIGHTWEIGHT STEEL MEMBERS MAINTAINED BY BOARDS AT ELEVATED TEMPERATURES................................................................................................. 147

5.1 GENERAL.........................................................................................................................147 5.2 EXPERIMENTAL INVESTIGATION ........................................................................................147 5.2.1 TESTING METHODOLOGY...............................................................................................147 5.2.2 SUMMARY OF ALL TEST RESULTS ...................................................................................153 5.2.3 EXAMPLES OF DETAILED TEST RESULTS .........................................................................159 5.3 ANALYSIS OF FIRE BEHAVIOUR OF STEEL STUDS MAINTAINED BY BOARDS WITH ADVANCED

CALCULATION MODELS .....................................................................................................162 5.3.1 NUMERICAL MODELLING OF HEATING REGIME OF STEEL STUDS WITH PLASTERBOARDS.....162 5.3.2 BENCHMARK NUMERICAL STUDY OF MECHANICAL BEHAVIOUR OF STEEL STUDS MAINTAINED

BY PLASTERBOARDS USING DIFFERENT COMPUTER CODES .............................................166 5.3.3 NUMERICAL MODELLING OF FIRE TESTS ON STEEL STUDS MAINTAINED BY PLASTERBOARDS

....................................................................................................................................168 5.3.3.1 Assumptions for numerical simulations ....................................................................168 5.3.3.2 Results of numerical modelling ................................................................................171 5.3.4 FULL COMPARISON BETWEEN TESTS AND NUMERICAL MODELLING ...................................181 5.4 DEVELOPMENT OF SIMPLE CALCULATION METHOD FOR LIGHTWEIGHT STEEL STUDS

MAINTAINED BY BOARDS...................................................................................................183 5.4.1 PARAMETRIC STUDY ......................................................................................................183 5.4.1.1 Calculation assumptions ..........................................................................................183 5.4.1.2 Results of parametric calculations............................................................................184 5.4.2 PROPOSAL OF A SIMPLE CALCULATIONS RULE FOR ASSESSING FIRE RESISTANCE OF

LIGHTWEIGHT STEEL STUDS MAINTAINED BY BOARDS......................................................185 5.4.2.1 Simplified design method for studs under flexural buckling .....................................185 5.4.2.2 Simplified design method for studs under bending and axial compression..............187 5.4.3 COMPARISON BETWEEN NUMERICAL MODEL AND SIMPLIFIED METHOD .............................189 5.5 CONCLUSIONS .................................................................................................................191

6 FIRE BEHAVIOUR OF LOAD-BEARING WALLS, FLOORS AND THEIR ASSEMBLIES .......... 193

6.1 GENERAL.........................................................................................................................193 6.2 EXPERIMENTAL WORK......................................................................................................194 6.2.1 TESTING METHODOLOGY ...............................................................................................194

/250

6.2.2 SUMMARY OF TEST RESULTS .........................................................................................194 6.2.3 EXAMPLES OF DETAILED TEST RESULTS .........................................................................198 6.2.3.1 Experimental results of floor element test (VTT) ......................................................198 6.2.3.2 Experimental results of wall element test (VTT).......................................................199 6.2.3.3 Experimental results of floor-wall assembly test (CTICM)........................................202 6.2.4 COMPARISON OF FIRE BEHAVIOUR BETWEEN ELEMENTS AND ASSEMBLIES.......................205 6.3 NUMERICAL INVESTIGATION OF FIRE BEHAVIOUR OF JOISTS IN FLOOR................................211 6.3.1 ASSUMPTION OF NUMERICAL MODELLING .......................................................................211 6.3.2 COMPARISON OF NUMERICAL MODELLING WITH TEST RESULTS........................................212 6.4 CONCLUSIONS .................................................................................................................213

7 FIRE RESISTANCE ASSESSMENT OF HIGH NON LOAD-BEARING PARTITION WALLS BUILT WITH COLD FORMED LIGHTWEIGHT STEEL MEMBERS......................................................... 215

7.1 GENERAL.........................................................................................................................215 7.2 TESTING CONFIGURATION AND SAFIR SIMULATIONS.........................................................215 7.3 SIMPLIFIED METHODOLOGY ..............................................................................................217 7.3.1 GENERAL FEATURES .....................................................................................................217 7.3.2 ASSUMPTIONS CONCERNING THE NEW METHODOLOGY ...................................................218 7.3.2.1 Background ..............................................................................................................218 7.3.2.2 Working steps for the determination of the curvature radius ρ .................................219 7.3.2.3 Working steps for the determination of the elongation ε ..........................................220 7.3.2.4 Reference values for the test ...................................................................................220 7.3.2.5 Assumptions concerning the deformations of extended partitions ...........................221 7.3.3 SIMPLIFIED METHODOLOGY RESULTS .............................................................................228 7.4 DEVELOPED TOOL GUIDANCE ...........................................................................................232 7.5 SUPPLEMENTARY VALIDATION TEST..................................................................................234 7.5.1 TESTING CONFIGURATION AND SAFIR SIMULATIONS FOR THE TEST 2..............................234 7.5.2 REFERENCE VALUES FOR THE TEST 2.............................................................................236 7.5.3 SIMPLIFIED METHODOLOGY RESULTS FOR THE TEST 2 ....................................................236 7.5 CONCLUSIONS .................................................................................................................239

8 GENERAL CONCLUSIONS ........................................................................................................... 245

9 REFERENCES................................................................................................................................ 249

/250

LIST OF TABLES Table 1-1 : Technical management of the project................................................................................. 25 Table 2-1 : Investigated materials ......................................................................................................... 31 Table 2-2: CSM tensile tests results – Room temperature ................................................................... 35 Table 2-3: CORUS Measured yield stress of test sections ................................................................... 35 Table 2-4: VTT Measured yield stress of test sections ......................................................................... 35 Table 2-5: Tensile steady state tests results – High temperature......................................................... 36 Table 2-6: Stress – strain relationship recommended in Eurocode3 Part 1.2....................................... 41 Table 2-7: Reduction factors recommended in part 1.2 of Eurocode 3 ................................................ 41 Table 2-8: Classification of tested cold formed steels........................................................................... 42 Table 2-9: Proposed reduction factors for Type A steel........................................................................ 45 Table 2-10: Proposed reduction factors for Type B steel...................................................................... 49 Table 2-11: Reduction factors for steel non load bearing elements at high temperatures ................... 56 Table 2-12: Reduction factors for steel load bearing elements at high temperatures .......................... 57 Table 3-1: Section sizes used in Test Programme ............................................................................... 59 Table 3-2: Summary of stub column test results ................................................................................... 65 Table 3-3: Summary of tall stud test results .......................................................................................... 67 Table 3-4: Summary of boundary condition test results........................................................................ 69 Table 3-5: Summary of load eccentricity test results ............................................................................ 71 Table 3-6: Summary of test results of specimens supported on one side only..................................... 74 Table 3-7: Summary of test results of specimens with additional steel sheet....................................... 76 Table 3-8: Compression resistance of the steel stud for different magnitudes of global and local

imperfections (b is the height of the web) ............................................................................ 84 Table 3-9: Critical stresses from numerical calculations ....................................................................... 84 Table 3-10: Ultimate compression resistance Nu considering local buckling according to part 1-3 of

Eurocode 3 [1], comparison with tests results and numerical calculations – room temperature calculations.................................................................................................... 85

Table 3-11: Comparison of numerical simulation with tests. The characteristic resistance according to part 1-3 of Eurocode 3 [1] is 46.5 kN with end boundary conditions similar to FEA_2 ..... 95

Table 3-12: Comparison of failure loads of test specimens .................................................................. 97 Table 3-13: Comparison with design rules for stub column test results.............................................. 102 Table 3-14: Comparison with design rules for tall stud test results..................................................... 102 Table 3-15: Comparison with design rules for boundary condition test results................................... 102 Table 3-16: Comparison with design rules for load eccentricity test results ....................................... 102 Table 3-17: Comparison with design rules for test results with additional steel sheet........................ 103 Table 4-1: Short stub column specimens ............................................................................................ 105 Table 4-2: The results of short stub column tests performed at room temperature and at elevated

temperatures...................................................................................................................... 109 Table 4-3: Summary of fire tests on tall studs..................................................................................... 116 Table 4-4: Geometric data for the tested stub columns - nominal values (mm) ................................. 124 Table 4-5: Measured geometric data for core thickness and corner radius used in the numerical

calculations (mm)............................................................................................................... 124 Table 4-6: Comparison between different reduction factors and numerical calculations on small section

(Type A steel)..................................................................................................................... 127 Table 4-7: Comparison between different reduction factors and numerical calculations on medium and

large sections (Type B steel) ............................................................................................. 127 Table 4-8: Comparison of failure temperature of studs engulfed in fire between numerical calculation

and fire test ........................................................................................................................ 129 Table 4-9: Basic nominal geometry for the AWS section.................................................................... 130 Table 4-10: Symbols used for applying boundary conditions.............................................................. 131 Table 4-11: End boundary conditions for the different numerical models........................................... 131 Table 4-12: Summary of failure temperatures from test and numerical simulations........................... 133 Table 4-13: Numerical compression resistance of steel studs at room temperature.......................... 136 Table 4-14: Critical temperatures for the C-250x2.5 section – load level of 0.3 ................................. 137 Table 4-15: Comparison between simple calculation method and numerical calculations for medium

section (Uniform temperature, eccentric loading)............................................................ 142

/250

Table 4-16: Comparison between simple calculation method and numerical calculations for medium section (Uniform temperature, centric loading)................................................................ 142

Table 5-1: Summary of fire tests performed on small steel stud (100x50x0.6)................................... 148 Table 5-2: Summary of fire tests performed on medium section (150x57x1.2) .................................. 149 Table 5-3: Summary of fire tests performed on TC-section (150x1.2)................................................ 149 Table 5-4: Summary of fire tests performed on large steel stud (250x80x2.5) ................................... 150 Table 5-5: Summary of fire tests performed on AWS steel stud (150x1.2)......................................... 150 Table 5-6: Summary of first series of fire tests carried out at CTIM.................................................... 155 Table 5-7: Summary of additional fire tests carried out at CTIM......................................................... 155 Table 5-8: Summary of tests carried out at VTT ................................................................................. 156 Table 5-9: Summary of four of fire tests on lightweight steel studs maintained by plasterboards with or

without internal insulation................................................................................................... 160 Table 5-10: Results of fire tests CTICM 2, CTICM 5, VTT3 and VTT5............................................... 161 Table 5-11: Summary of main results of different codes..................................................................... 168 Table 5-12: Comparison of failure times of steel studs between tests and numerical modelling ....... 181 Table 5-13: Observation about deflection at mid-height between test and numerical simulation....... 181 Table 5-14: Calculated failure times of fire test specimens................................................................. 182 Table 6-1: Summary of tests with Finnish system............................................................................... 196 Table 6-2: Summary of tests with UK system ..................................................................................... 197 Table 6-3: Comparison of testing conditions for UK construction system........................................... 208 Table 7-1: Failure time in function of length ........................................................................................ 241 Table 7-2: Failure time in function of length ........................................................................................ 243

/250

LIST OF FIGURES Figure 2-1: Tensile tests – Specimen sketch ........................................................................................ 27 Figure 2-2: Temperature and applied load versus time in steady state tests ....................................... 28 Figure 2-3:Temperature and applied load versus time in anisothermal tests ....................................... 28 Figure 2-4: Testing equipment – MAYES.............................................................................................. 29 Figure 2-5: Testing equipment – Frame................................................................................................ 29 Figure 2-6: Thermocouples location...................................................................................................... 30 Figure 2-7: Temperature vs Time curve ................................................................................................ 30 Figure 2-8: Tensile test specimen ......................................................................................................... 30 Figure 2-9: Example of the evaluation of the collapse temperature...................................................... 31 Figure 2-10: Large C3 steel grade S350 - Stress – Strain curve .......................................................... 32 Figure 2-11: Large C3 steel grade S350 - Stress – Strain curves ........................................................ 33 Figure 2-12: Parasite strain recorded - Steel grade S350 Large C3..................................................... 34 Figure 2-13: Tensile anisothermal transient tests results – Steel grade S350 Large C3...................... 34 Figure 2-14: Tensile anisothermal transient tests results – Steel grade S280 Small C1...................... 37 Figure 2-15: Tensile anisothermal transient tests results – Steel grade S350 Medium C2 .................. 37 Figure 2-16: Tensile anisothermal transient tests results – Steel grade S350 Large C3...................... 38 Figure 2-17: Stress – Strain curve derived from anisothermal transient tests - Steel grade S280 Small

C1...................................................................................................................................... 39 Figure 2-18: Stress – Strain curve derived from anisothermal transient tests - Steel grade S350

Medium C2........................................................................................................................ 39 Figure 2-19: Stress – Strain curve derived from anisothermal transient tests - Steel grade S350 Large

C3...................................................................................................................................... 40 Figure 2-20: Stress – strain relationship proposed in Eurocode 3 Part 1.2 .......................................... 41 Figure 2-21: Reduction factors proposed for 2% effective strength ky,θ of Type A steel ..................... 43 Figure 2-22: Reduction factors proposed for E ..................................................................................... 44 Figure 2-23: Reduction factors proposed for proportional limit ............................................................. 44 Figure 2-24: Reduction factors proposed for effective yield strength – Medium section ...................... 46 Figure 2-25: Reduction factors proposed for effective yield strength – Large section.......................... 46 Figure 2-26: Reduction factors proposed for effective yield strength-Medium and Large section........ 47 Figure 2-27: Reduction factors proposed for E ..................................................................................... 48 Figure 2-28: Reduction factors proposed for proportional limit ............................................................. 48 Figure 2-29: Comparison between test and mathematical model......................................................... 50 Figure 2-30: Comparison between test and mathematical model – T=200°C ...................................... 51 Figure 2-31: Comparison between test and mathematical model – T=300°C ...................................... 51 Figure 2-32: Comparison between test and mathematical model – T=400°C ...................................... 52 Figure 2-33: Comparison between test and mathematical model – T=500°C ...................................... 52 Figure 2-34: Comparison between test and mathematical model – T=600°C ...................................... 53 Figure 2-35: Comparison between test and mathematical model – T=700°C ...................................... 53 Figure 2-36: Comparison between test and mathematical model – T=800°C ...................................... 54 Figure 2-37: Comparison between the model for load and non load bearing sections steels .............. 54 Figure 3-1: Floor/wall assembly test setup............................................................................................ 60 Figure 3-2: Stub Column Test Setup..................................................................................................... 61 Figure 3-3: Building specimen in test rig ............................................................................................... 62 Figure 3-4: View of test setup................................................................................................................ 62 Figure 3-5: View of lateral measurement devices ................................................................................. 63 Figure 3-6: View of test rig for floor/wall assembly................................................................................ 64 Figure 3-7: View of load introduction on floor system ........................................................................... 64 Figure 3-8: Stub Column failure models................................................................................................ 65 Figure 3-9: Basic failure modes – local ................................................................................................. 66 Figure 3-10: Basic failure modes - global.............................................................................................. 66 Figure 3-11: Comparison of medium and large specimen failures in tall stud tests.............................. 67 Figure 3-12: Comparison of AWS specimen tall stud tests under centric and eccentric loading.......... 68 Figure 3-13: Comparison of load-deflection curves of specimens with different boundary conditions . 69 Figure 3-14: Comparison of failure modes of specimens with different boundary conditions............... 70 Figure 3-15: Typical elastic local buckles in web of specimen.............................................................. 71

/250

Figure 3-16: Comparison of failure modes of centric and eccentric loaded medium specimens supported on both sides ................................................................................................... 72

Figure 3-17: Comparison of failure modes of centric and eccentric loaded large specimens supported on both sides..................................................................................................................... 72

Figure 3-18: Comparison of failure modes of centric and eccentric loaded AWS specimens supported on both sides..................................................................................................................... 73

Figure 3-19: Problems with AWS testing............................................................................................... 73 Figure 3-20: Comparison of large and medium section failure modes for specimens supported on one

side only............................................................................................................................ 75 Figure 3-21: AWS section failure modes for specimens supported on one side only........................... 75 Figure 3-22: Effect of including steel sheet on medium section failure modes ..................................... 76 Figure 3-23: Effect of including steel sheet on AWS section failure modes.......................................... 77 Figure 3-24: Comparison of load-deflection curves of small specimens............................................... 77 Figure 3-25: Comparison of load-deflection curves of medium specimens .......................................... 78 Figure 3-26: Comparison of load-deflection curves of large specimens ............................................... 78 Figure 3-27: Comparison of load-deflection curves of AWS specimens............................................... 79 Figure 3-28: Load –Displacement of Rannila Wall Assembly ............................................................... 80 Figure 3-29: Final buckled shape of Rannila Wall Assembly ............................................................... 80 Figure 3-30: Load –Displacement of Metsec Wall Assembly................................................................ 81 Figure 3-31: Final buckled shape of Metsec Wall Assembly................................................................ 82 Figure 3-32: Modelling principles of C-type cross-sections - stub column............................................ 83 Figure 3-33: Comparison between test results, numerical calculations and EC3 (FEA (3) is similar to

FEA (2)) ............................................................................................................................ 85 Figure 3-34: Modelling of steel studs with shell element....................................................................... 86 Figure 3-35: Position of screws along the steel stud............................................................................. 87 Figure 3-36: Example of boundary conditions adopted for steel suds .................................................. 88 Figure 3-37: Applied load conditions (pressure on free end surface parallel to Z axis)........................ 88 Figure 3-38: Lateral displacement of specimen of test n°3 assuming .................................................. 90 Figure 3-39: Lateral displacement of specimen of test n°3 assuming .................................................. 90 Figure 3-40: Lateral displacement of specimen of test n°7 assuming .................................................. 91 Figure 3-41: Lateral displacement of specimen of test n°7 assuming .................................................. 91 Figure 3-42: Deformed shape of the specimen assumed as fixed at one end...................................... 92 Figure 3-43: Deformed shape of the specimen assumed as fixed at both ends................................... 92 Figure 3-44: View of specimen after test number 7 .............................................................................. 93 Figure 3-45: Modelling features of high studs at room temperature ..................................................... 94 Figure 3-46: Numerical failure mode governed by distortional buckling of flange but also by torsional-

flexural buckling. ............................................................................................................... 95 Figure 3-47: Comparison of failure loads between numerical modelling and tests............................... 96 Figure 3-48: Finite element model of stub column test ......................................................................... 98 Figure 3-49: Final deformed shape and stress state of column stub model ......................................... 99 Figure 3-50: Finite element model of stud/floor assembly .................................................................... 99 Figure 3-51: Detail of finite element model – joint area....................................................................... 100 Figure 3-52: Deformed shape and stress state at failure .................................................................... 100 Figure 3-51: Comparison of test and design failure loads................................................................... 103 Figure 4-1: Test arrangement in the furnace; horizontal and vertical sections. .................................. 107 Figure 4-2: Support conditions of the steel stud.................................................................................. 107 Figure 4-3: Position of the measuring points C-sections..................................................................... 108 Figure 4-4: Average temperature of the furnace in Test 3 .................................................................. 109 Figure 4-5: Specimen temperatures at different levels in Test 3......................................................... 110 Figure 4-6: Mounting of the specimen (AWS–section)........................................................................ 110 Figure 4-7: Test specimens 1–4 after the fire tests............................................................................. 111 Figure 4-8: Test specimens 4–7 after the fire tests............................................................................. 111 Figure 4-9: Test specimen 8 after fire test........................................................................................... 112 Figure 4-10: Failure load level (NTest.fi / NTest.ref) as a function of the temperature for different steel

sections (Load level 1.0 corresponds to reference load Ntest.ref) ..................................... 113 Figure 4-11: Strain (∆L/L) as a function of temperature for different steel sections and load levels .. 113 Figure 4-12: Boundary condition of AWS section stud test................................................................. 114 Figure 4-13: Location of the temperature measurement points in the C-sections .............................. 115

/250

Figure 4-14: Location of the temperature measurement points AWS section .................................... 115 Figure 4-15: Location of the displacement measurement points in AWS section............................... 116 Figure 4-16: Temperatures measured on section N1 versus time in the test on AWS section .......... 117 Figure 4-17: Temperatures measured on section N2 versus time in the test on AWS section .......... 117 Figure 4-18: Temperatures measured on section N3 versus time in the test on AWS section .......... 118 Figure 4-19: Temperatures measured on section N4 versus time in the test on AWS section .......... 118 Figure 4-20: Lateral displacements measured along strong axis versus time .................................... 119 Figure 4-21: Lateral displacements measured along weak axis versus time in the test on AWS section............................................................................................................................................................. 119 Figure 4-22: Measured vertical displacement versus time in the test on AWS section ...................... 120 Figure 4-23: Measured applied force versus time in the test on AWS section ................................... 120 Figure 4-24: C-sections specimens after the fire tests (C 250)........................................................... 121 Figure 4-25: C-sections specimens after the fire tests (C 250)........................................................... 121 Figure 4-26: AWS-section specimen after the fire test........................................................................ 122 Figure 4-27: Failure temperatures of different steel sections in function of load level in fire tests on

short short and tall columns............................................................................................ 123 Figure 4-28: Temperature evolution in numerical modelling for medium section with load levels 0.07,

0.02, 0.4 and 0.6 ............................................................................................................. 125 Figure 4-29: Comparison of failure temperatures for the different tested steel studs with numerical

calculations ..................................................................................................................... 126 Figure 4-30: Example of boundary conditions adopted for steel suds ................................................ 128 Figure 4-31: Comparison of lateral displacement of steel stud about weak axis between numerical

simulation and fire test .................................................................................................... 129 Figure 4-32: Basic nominal geometry of the tested AWS section....................................................... 130 Figure 4-33: Modelled AWS steel stud................................................................................................ 130 Figure 4-34: The endplate and the section was connected with the keyword TIE.............................. 131 Figure 4-35: The load and the end boundary conditions were applied at the reference point at each

end of the stud ................................................................................................................ 131 Figure 4-36: Basic geometry showing mesh and axis convention ...................................................... 132 Figure 4-37: Local buckling mode shape used for local initial imperfections ...................................... 132 Figure 4-38: Temperature evolution at different levels used in the numerical simulation................... 133 Figure 4-39: Lateral displacement along strong axis versus time for numerical model FEA_1 compared

to test results................................................................................................................... 134 Figure 4-40: Lateral displacement along strong axis versus time for numerical model FEA_2 compared

to test results................................................................................................................... 134 Figure 4-41: Critical temperature results of the numerical calculations (large section, centric load and

load level of 0.3).............................................................................................................. 136 Figure 4-42: Critical temperature results of the numerical calculations (large section, eccentric load

and load level of 0.3)....................................................................................................... 136 Figure 4-43: Coefficient of κ for different end restraint conditions ...................................................... 140 Figure 4-44: Comparison of buckling resistance between numerical results and simplified calculation

method for the small, medium and large section. Relationship between numerical results (FEA) and simplified method. Centric load with uniform temperature over the section. 143

Figure 4-45: Comparison of buckling resistance between numerical results and simplified calculation method for the small, medium and large section. Relationship between numerical results (FEA) and simplified method. Eccentric load with uniform temperature over the section........................................................................................................................................ 143

Figure 4-46: Comparison between numerical results and simplified calculation method for the small, medium and large section. Centric load with temperature gradient. .............................. 144

Figure 4-47: Comparison between numerical results and simplified calculation method for the small, medium and large section. Eccentric load on fire side with temperature gradient. ........ 144

Figure 4-48: Comparison between numerical results and simplified calculation method for the small, medium and large section. Eccentric load on cold side with temperature gradient. ...... 145

Figure 5-1: Schematic view of lightweight steel sections maintained by plasterboards...................... 148 Figure 5-2: Test arrangement of lightweight steel studs ..................................................................... 151 Figure 5-3: Example of measuring points of temperature in some specimens ................................... 152 Figure 5-4: Location of the measurement sections along all specimens ............................................ 153 Figure 5-5: Effect of the connection condition between steel stud and plasterboard on failure modes of

studs.................................................................................................................................. 158

/250

Figure 5-6: Effect of eccentricity of the applied load on failure modes of studs.................................. 158 Figure 5-7: Effect of internal insulation on the test failure modes ....................................................... 159 Figure 5-8: Failure mode of AWS steel stud section........................................................................... 159 Figure 5-9: Measured temperatures in test VTT 3 .............................................................................. 160 Figure 5-10: Measured temperatures in test VTT 5 ............................................................................ 160 Figure 5-11: Measured temperatures in test CTICM 2........................................................................ 161 Figure 5-12: Measured temperatures in test CTICM 5........................................................................ 161 Figure 5-13: Lateral displacement measured at mid height of steel stud for test CTICM 5................ 162 Figure 5-14: Lateral displacement measured at mid height of steel stud for test VTT 3 .................... 162 Figure 5-15: Cases used for validation study of heat transfer............................................................. 163 Figure 5-16: Details of studied specimens .......................................................................................... 163 Figure 5-17: Section mesh of studied specimens ............................................................................... 164 Figure 5-18: Comparison between ANSYS and SAFIR for case 3a ................................................... 164 Figure 5-19: Comparison between ANSYS and ABAQUS for case 4................................................. 164 Figure 5-20: Temperature comparison of stud heating between calculation and test for non insulated

specimen......................................................................................................................... 165 Figure 5-21: Temperature comparison of stud heating between calculation and test for insulated

specimen......................................................................................................................... 165 Figure 5-22: Temperatures calculated for chambers without internal insulation and 6m height as

function of chambers width ............................................................................................. 166 Figure 5-23: Temperatures calculated for chambers with internal insulation as function of chambers

width................................................................................................................................ 166 Figure 5-24: Cases used for validation study of mechanical behaviour.............................................. 167 Figure 5-25: Reaction force curves for Case 2 between codes .......................................................... 167 Figure 5-26: Axial displacements calculated for Case 3 between codes............................................ 167 Figure 5-27: Modelling of steel studs with shell element..................................................................... 168 Figure 5-28: Position of screws along the steel stud........................................................................... 169 Figure 5-29: Applied load conditions (pressure on free end surface parallel to Z axis)...................... 169 Figure 5-30: Example of boundary conditions adopted for steel suds ................................................ 169 Figure 5-31: Temperature gradient along the steel stud in numerical modelling ................................ 170 Figure 5-32: Section temperature distribution on steel stud in numerical modelling .......................... 170 Figure 5-33: Section temperature distribution assumed for test VTT 3 .............................................. 171 Figure 5-34: Lateral displacement of steel stud calculated at mid-height of test VTT 3 ..................... 171 Figure 5-35: Failure modes obtained in test VTT 3............................................................................. 172 Figure 5-36: Failure modes predicted in numerical analysis for test VTT 3........................................ 173 Figure 5-37: Assumed section temperature distributions for test VTT5.............................................. 174 Figure 5-38: Lateral displacement of steel stud calculated at mid-height of test VTT5 ...................... 174 Figure 5-39: Failure modes obtained in VTT analysis for test VTT 5 assuming steel stud as hinged at

both ends ........................................................................................................................ 174 Figure 5-40: Failure modes obtained in CTICM analysis for test VTT 5 ............................................. 175 Figure 5-41: Failure modes obtained in test VTT 5............................................................................. 175 Figure 5-42: Assumed section temperature distributions in numerical simulations of test CTICM 2.. 176 Figure 5-43: Lateral displacement calculated at mid-height of steel stud for test CTICM 2 ............... 176 Figure 5-44: Deformed shape predicted for steel stud of test CTICM 2 in VTT numerical analysis ... 176 Figure 5-45: Deformed shape predicted for steel stud of test CTICM 2 in CTICM numerical analysis............................................................................................................................................................. 176 Figure 5-46: Failure modes obtained in test CTICM 2 ........................................................................ 177 Figure 5-47: Assumed section temperature distributions in numerical simulations of test CTICM 5.. 178 Figure 5-48: Lateral displacement calculated at mid height of steel stud for test CTICM 5................ 178 Figure 5-49:Vertical displacement measured at the bottom end of test specimen CTICM 5.............. 178 Figure 5-50: Failure modes predicted in VTT analysis for test CTICM 5 ............................................ 178 Figure 5-51: Deformed shape predicted for steel stud of test CTICM 5 in CTICM analysis ............... 178 Figure 5-52: Deformed state of studs in test CTICM 5........................................................................ 179 Figure 5-53: Assumed section temperature distributions in numerical simulations of test VTT 11 .... 179 Figure 5-54: Lateral displacement calculated at mid height of steel stud for test VTT 11 .................. 179 Figure 5-55: Axial displacement measured at the bottom end of test specimen VTT 11 ................... 180 Figure 5-56: Failure mode obtained in VTT analysis .......................................................................... 180 Figure 5-57: Deformed state of studs in test VTT 11 .......................................................................... 180 Figure 5-58: Comparisons of failure times between numerical calculations and tests ....................... 182

/250

Figure 5-59: Uniform heating condition of steel studs for parametric studies ..................................... 184 Figure 5-60: Heating condition of steel studs with temperature gradient for parametric studies ........ 184 Figure 5-61: Temperatures calculated for the small section and a load level of 0.1 (as function of

heating conditions) assuming a centric loading.............................................................. 184 Figure 5-62: Temperatures calculated for the medium section and a load level of 0.3 (as function of

heating conditions) assuming an eccentric loading at unexposed side.......................... 184 Figure 5-63: Temperatures calculated for the large section and a load level of 0.5 (as function of

heating conditions) assuming a eccentric loading at exposed side................................ 185 Figure 5-64: Temperatures calculated for the AWS section and a load level of 0.3 (as function of

heating conditions) assuming an centric loading............................................................ 185 Figure 5-65: Shift of neutral axis due to temperature effects .............................................................. 189 Figure 5-66: Comparison of temperatures calculated for the small section under centric load and a

load level of 0.1 (as function of heating conditions)........................................................ 190 Figure 5-67: Comparison of critical temperatures calculated for the medium section under centric load

and a load level of 0.3 (as function of heating conditions).............................................. 190 Figure 5-68: Comparison of critical temperatures calculated for the medium section under eccentric

load on the unexposed side and a load level of 0.3 (as function of heating conditions) 190 Figure 5-69: Comparison of critical temperatures calculated for the large section under eccentric load

on the exposed side and a load level of 0.5 (as function of heating conditions) ............ 190 Figure 5-70: Failure mode of stud column with medium section subjected to a centric load (load level

of 0.3) with higher temperature gradient (T2=100) ......................................................... 191 Figure 5-71: Failure mode of stud column with large section subjected to an eccentric load located at

the unexposed side (load level of 0.3) with higher temperature gradient (T2=100) ....... 191 Figure 6-1: Building assembly of cold formed lightweight members................................................... 193 Figure 6-2: Different types of test with load-bearing lightweight steel members................................. 194 Figure 6-3: The test set up of floor element ........................................................................................ 198 Figure 6-4: Some representative experimental results ....................................................................... 199 Figure 6-5: Test set up of wall element ............................................................................................... 201 Figure 6-6: Typical experimental results of wall element test ............................................................. 202 Figure 6-7: Test set up of floor-wall assembly using UK system ........................................................ 204 Figure 6-8: Typical experimental results of UK floor-wall assembly test............................................. 205 Figure 6-9: Comparison of test results with Finnish construction system ........................................... 207 Figure 6-10: Failure mode of assembly test with Finnish construction system................................... 208 Figure 6-11: Comparison of test results with UK construction system................................................ 209 Figure 6-12: Failure mode of second assembly test with UK construction ......................................... 210 Figure 6-13: Heating of steel joist as well as applied load in second assembly test with UK

construction system ........................................................................................................ 211 Figure 6-14: Boundary conditions as well as loading condition of joist in numerical modelling.......... 212 Figure 6-15: Initial geometry imperfection and temperature field attributed to steel joists.................. 212 Figure 6-16: Comparison of floor deflection between numerical modelling and test .......................... 213 Figure 7-1: Test configuration, system and section geometry ............................................................ 215 Figure 7-2: Imposed temperature distribution according to test results .............................................. 216 Figure 7-3: Comparison between measured and calculated displacements at different heights of studs............................................................................................................................................................. 216 Figure 7-4: Boundary conditions of lightweight steel stud in partition walls ........................................ 217 Figure 7-5: Comparison between measured and calculated displacements with different systems... 218 Figure 7-6: Lagrange formula.............................................................................................................. 219 Figure 7-7: Discretization steps........................................................................................................... 219 Figure 7-8: Discretization steps........................................................................................................... 220 Figure 7-9: Young Modulus in function of temperature ....................................................................... 221 Figure 7-10: Strength reduction factor for Type A steel ...................................................................... 222 Figure 7-11: Strength reduction factor for Type B steel ...................................................................... 222 Figure 7-12: Definition of deformations ............................................................................................... 224 Figure 7-13: Comparison between SAFIR results and simplified methodology.................................. 226 Figure 7-14: Excel sheet for the determination of the horizontal displacements at mid height........... 227 Figure 7-15: Comparison between SAFIR results and simplified methodology (L=3m) ..................... 228 Figure 7-16: Comparison between SAFIR results and simplified methodology (L=4m) ..................... 228 Figure 7-17: Comparison between SAFIR results and simplified methodology (L=5m) ..................... 229 Figure 7-18: Comparison between SAFIR results and simplified methodology (L=6m) ..................... 229

/250

Figure 7-19: Comparison between SAFIR results and simplified methodology (L=7m) ..................... 230 Figure 7-20: Comparison between SAFIR results and ARCELOR simplified (L=8m) ........................ 230 Figure 7-21: Comparison between SAFIR results and ARCELOR simplified (L=9m) ........................ 231 Figure 7-22: Comparison between SAFIR results and ARCELOR simplified (L=10m) ...................... 231 Figure 7-23: Failure time for extended partitions in function of the curvature radius ρ....................... 232 Figure 7-24: Failure time for extended partitions in function of the elongation ε ................................ 232 Figure 7-25: Excel sheet for calculation of reference criteria .............................................................. 233 Figure 7-26: Excel sheet for calculation of extended sections ............................................................ 233 Figure 7-27: Test configuration, system and section geometry .......................................................... 234 Figure 7-28: Imposed temperature distribution following test ............................................................. 235 Figure 7-29: Comparison between measured and calculated displacement at mid height ................ 235 Figure 7-30: Comparison between SAFIR results and simplified methodology (L=6m) ..................... 236 Figure 7-31: Comparison between SAFIR results and simplified methodology (L=8m) ..................... 237 Figure 7-32: Comparison between SAFIR results and simplified methodology (L=10m) ................... 237 Figure 7-33: Comparison between SAFIR results and simplified methodology (L=12m) ................... 238 Figure 7-34: Failure time for extended partitions in function of the curvature radius ρ....................... 238 Figure 7-35: Failure time for extended partitions in function of the elongation ε ................................ 239 Figure 7-36: Comparison between calculated and measured failure time following reference criteria............................................................................................................................................................. 240 Figure 7-37: Comparison between calculated and measured failure time following reference criteria............................................................................................................................................................. 242

/250

1. INTRODUCTION

1.1 BACKGROUND OF THE PROJECT

Nowadays, lightweight steel frames are more and more widely used in construction, either as load-bearing elements such as in residential, office buildings as well as in industrial buildings or as non load-bearing elements in partition walls and suspended ceilings. This development tendency is largely due to several advantages offered by this type of building system, namely:

• rapid construction and building flexibility, using well engineered and industrially produced components

• easy to assemble as a kit of parts • easy to dismantle if required

However, in many cases, the steel structure built with this type of elements needs to provide a certain level of fire resistance in order to fulfil fire safety requirement for the relevant whole building. As a consequence, it is necessary for engineers to have design rules available to assess the behaviour of these lightweight steel frames in case of fire. Unfortunately, few research works have been carried out in this field so that the knowledge is still too poor to lead to the establishment of an operational design rules for fire assessment of lightweight steel elements. For both load-bearing and non load-bearing separating elements using cold formed lightweight steel frames, this situation creates an important handicap in enlarging their application since they will require systematically either heavier protection measures with significant additional cost or to perform expensive fire resistance tests. In addition, when used in load-bearing condition, a wide range of shapes and dimensions are used for cold formed lightweight elements so that it is impossible to fully cover their fire assessment by means of testing. Another special feature related to partition walls is that the height limit in testing is in general up to 3 meters and maximum to 5 meters high among all European fire furnaces. However in reality, these walls can be up to 20 meters high which means that an extension needs to be applied to the experimental results. Therefore the question arises about how to apply the extension on the basis of testing and what is the available procedure to use. Apparently, the only way to overcome all these difficulties is to provide a more practical and economical solution by developing design rules at elevated temperatures and incorporating them then into either the fire parts of Eurocodes or corresponding European standards.

1.2 OBJECTIVES

With reference to the considerations given in previous paragraph, the current RTD project is aimed at following objectives:

• to increase understanding of the fire behaviour and failure mechanisms of lightweight steel frame structures under fire exposure by performing fire resistance tests and/or numerical simulations on small and full scale specimens, including some heat transfer with natural fire developments;

• to obtain accurate data on the mechanical properties of cold formed steel at elevated

temperatures;

/250

• to check the ability of existing computer models to simulate the experimental behaviour of lightweight steel elements;

• to develop simple calculation models on the fire behaviour of lightweight steel frame structures for the fire design of load bearing structures and the extrapolation of test results on lightweight steel partitions.

The features to be studied to enable the development of above calculation methods are: • material behaviour of cold formed thin wall steel at elevated temperatures up to 1000 °C; • mechanical behaviour of lightweight steel sections in compression and compression-

bending at both room and elevated temperatures when they are, or not, connected to boards;

• temperature rise of steel sections for 30 and 60 min (possibly up to 2 hours), of fire duration within gypsum partitions (considering two kinds of boards);

• mechanical performance of load-bearing steel frames at elevated temperatures. From this amount of knowledge, it was possible to propose some additional design rules for part 1.2 of Eurocode 3 [2] as far as lightweight steel structures are concerned and to propose specific rules for the extension of fire test results of partition elements using steel structures for the new set of standards under development within CEN-TC 127 "fire safety in buildings".

1.3 SUMMARY OF TECHNICAL CONTENT AND ITS MANAGEMENT

The whole project covers the following technical features:

• Material properties of cold formed lightweight steels at elevated temperatures; • Mechanical behaviour of cold formed lightweight steel members as well as their

assemblies at room temperature; • Mechanical behaviour of lightweight steel members fully engulfed in fire; • Mechanical behaviour of lightweight steel members maintained by boards (as

gypsum/calcium silicate boards or glazed panels), at elevated temperatures; • Fire behaviour of load-bearing walls, floors and their assemblies; • Fire resistance assessment of high non load-bearing partition walls built with cold

formed lightweight steel members and plasterboards. For majority of above technical features, the work started firstly with an important experimental investigation followed then by a number of numerical analysis using validated computer models. On the basis of the results obtained, corresponding design rules were developed and the comparison was systematically performed to check their validity against both experimental and numerical results. A summary of the work performed within the scope of this project on above features is given below. Material properties of cold formed lightweight steels at elevated temperatures One important parameter in the development of design rules to assess the fire resistance of lightweight steel structures is how thin gauge steel, as a basic material, behaves mechanically at elevated temperatures. In order to get a good knowledge on this feature, this part of work has been concentrated on material elevated temperature tests with different types of steel as well as on establishment of corresponding mathematical models for describing mechanical material behaviour of these steels.

/250

Based on above objectives, three types of steel from three different sources as well as from both formed steel profiles and steel coil were investigated in detail by carrying out a series of fire tests for each of them. These test results have shown that steels can behave quite differently according to the origin and the steels studied in the project may be classified as two categories. It seems that the steel for non load-bearing use of lightweight structures could have a much worse material resistance compared to model recommended in fire part of EC3. As a consequence, the developed material model for lightweight steel in the project takes account of this aspect and two types of resistance reduction factors are therefore proposed. In addition, the above material model is intentionally kept in perfect agreement with Eurocode model in order that it cab be incorporated easily in future fire part of Eurocode 3. Mechanical behaviour of cold formed lightweight steel members as well as their assemblies at room temperature At the fire limit state, it is usual to take the existing ambient temperature design rules and modify them to reflect performance at elevated temperatures. Therefore it is important that the ambient design rules are fully understood as they form the basis of the fire limit design rules. For this purpose, the mechanical behaviour of light steel frames at room temperature was studied in this project for comparison with mechanical behaviour at the fire limit state investigated in both experimental and numerical ways, in which performance of light steel frame arrangements was investigated by a combination of a static testing, numerical modelling and direct comparison with existing design procedures. Mechanical behaviour of lightweight steel members fully engulfed in fire In real buildings using lightweight steel structures, situations can be encountered when structure members are without any fire protection so that under fire situation, they will be engulfed fully in fire. In order to provide basic information on fire behaviour of this situation, a series of fire tests have been carried out on both short stub columns, dominated mainly by local buckling behaviour, and tall studs, where both global buckling and local buckling in general govern the whole resistance. Additionally, the fire performance of lightweight steel members was studied in numerical investigations, in particular through a parametric study, which allowed the validation of simple design rules developed especially for assessing the mechanical resistance of this type of lightweight steel members in case of fire. Mechanical behaviour of lightweight steel members maintained by boards at elevated temperatures An important part of work of this project was focused on both experimental investigation and numerical analysis of the mechanical behaviour of lightweight steel members (studs) maintained by plasterboards. Regarding the experimental investigation shared by VTT and CTICM, a number of fire tests have been carried out under various conditions. On the basis of these fire tests, corresponding numerical analysis has been made using several advanced calculation models to check, on the one hand, the validity of these models, and on the other hand, to perform a parametric study with the purpose of developing a simple calculation model, thus, providing a practical rule for daily design of lightweight steel studs maintained laterally which is a common design case for either load-bearing or non load-bearing partition walls. Fire behaviour of load-bearing walls, floors and their assemblies In general, the fire behaviour (thermal and mechanical) of cold formed lightweight steel members were investigated mainly on the basis of isolated elements, such as floors, walls, etc. However in real buildings, these elements are assembled together to provide whole

/250

structure of the building. As a consequence, this part of work is focused on the fire behaviour of assembled cold formed lightweight structures. Different types of fire tests were carried out on two European construction systems, which include not only individual load-bearing floors and walls, but also the assembled structures of floor and wall. These tests have shown that in general the fire rating of assembled structures is dominated largely by floor element due to the fall of plasterboards fixed to the lower flange of corresponding steel joists. Nevertheless, attention must be paid to local squash resistance of floor to wall joints under fire situation if descending load from above parts of building becomes important. In addition to above experimental investigation, a numerical study has been carried out exclusively on steel joists and the corresponding results lead to confirmation of the test observation that the fixing system of plasterboards is the determinant parameter for fire resistance of floor composed of lightweight steel members. Fire resistance assessment of high non load-bearing partition walls built with cold formed lightweight steel members and plasterboards Nowadays, with the existing testing capabilities, the non load-bearing partition walls composed of lightweight steel members and fire boards can be tested up to only five meters high. However, in reality, they can be applied to the height up to fifteen or even twenty meters. Therefore, the question arises about how to extend the test results obtained on small size partition walls to very high partition walls. Some assessment methods exist already. However, either they are based on the mechanical resistance of lightweight steel members alone or they require a quite complicated analysis procedure based on advanced numerical models. As a consequence, within the project, a simple extrapolation method based only on hand calculations is proposed which tries to combine deformation compatibility criteria of plasterboards and the mechanical resistance of lightweight steel members. A full explanation of this method is then given together with some validation cases against test results. In order to give a good overview of the work carried out during this project, a full description covering all above technical features is presented in the following six chapters. In addition, more detailed results are given in technical reports of the project as well as corresponding excel files, which are all copied to CD-Rom support delivered together with actual report. Within the scope of the project, all above technical features are managed in such a way that they were divided into 8 technical work packages and shared between seven partners as indicated in Table 1-1.

/250

Work package

Principal tasks

WP leader

WP 1 Stress-strain relationships of cold formed steel at elevated temperatures

CSM

WP 2 Mechanical behaviour of lightweight steel sections maintained by boards, at room temperature (tests);

verification and improvement of design rules CORUS

WP 3 Mechanical behaviour of lightweight steel sections, at elevated temperatures (tests) VTT

WP 4 Development of design rules for lightweight steel elements, at elevated temperatures SBI

WP 5 Mechanical behaviour of lightweight steel sections

maintained by boards (as gypsum/calcium silicate boards or glazed panels), at elevated temperatures (tests)

CTICM

WP 6 Development of design rules for lightweight steel elements

maintained by boards or glazed panels, at elevated temperatures

LABEIN

WP 7 Global fire behaviour of partitions (with boards or glazed elements), suspended ceilings and frames (tests) CTICM

WP 8 Development of extrapolation rules for partitions, suspended ceilings and frames, at elevated temperatures PROFILARBED

Table 1-1 : Technical management of the project

In addition to above technical work packages, one special work package is dedicated to the global management of the project whose leader is CTICM. During the whole period of the project, 11 coordination meetings were held and more than 70 new technical reports have been produced.

/250

2. MATERIAL MECHANICAL PROPERTIES OF COLD FORMED STEEL AT ELEVATED TEMPERATURES

2.1 GENERAL

The main aim of the activity reported in actual chapter is to get, by means of mechanical testing on small scale specimens, knowledge on the mechanical properties of cold formed steels at elevated temperatures in order to establish an analytical equation to define the relationship between stress and strain for cold formed steels. In order to achieve this goal, an experimental activity consisting of tensile tests at room temperature, tensile steady state tests at high temperatures, and tensile anisothermal transient tests at elevated temperatures were carried out. This testing procedure has been largely applied previously in other research projects [3, 4] not only for carbon but also for stainless steels. Based on experimental results obtained previously, an analytical study was made in which different parameters used for describing stress-strain relationships of lightweight steels at elevated temperatures have been proposed in fully agreement with the mathematical model of fire part of EC3 [2] so that they could be incorporated directly into future version of this Eurocode.

2.2 TESTING METHODOLOGY

2.2.1 Tensile tests – Room temperature

In order to provide full information about the stress-strain relationship of cold formed steels, tensile tests at room temperature were performed. These tests were performed according to the Standard EN10002-1 on specimens machined in the rolling direction and the specimen sketch is shown in Figure 2-1: Tensile tests – Specimen sketch

Figure 2-1: Tensile tests – Specimen sketch

2.2.2 Tensile steady state tests - high temperature

In these tests each specimen was firstly heated to the fixed temperature value, kept constant afterwards during the whole test, and then loaded gradually until its collapse occurs.

/250

The test procedure is briefly illustrated in Figure 2-2: Temperature and applied load versus time in steady state tests In particular the selected temperature levels were T=400°C, T=600°C and T=800°C. The tests were performed according to the EN10002-5 on the same specimen typology used in tensile tests at room temperature (see Figure 2-1).

Timet0

θ0

Temperature

Timet0

σu

Load

Figure 2-2: Temperature and applied load versus time in steady state tests

2.2.3 Tensile anisothermal transient tests

Nowadays it is more and more common to perform anisothermal tests in which specimens are firstly loaded to a selected stress level and then heated progressively up to their collapse. The test procedure is presented in Figure 2-3.

Timet0

θu

Temperature

Timet0

σ0

Load

Figure 2-3:Temperature and applied load versus time in anisothermal tests

This test typology is particularly representative of fire event in which buildings are subjected to both a near steady applied load and a transient temperature field increasing with time. However, because most test apparatus is not designed for doing such tests, the strain measurement of this type of test induces some “parasite strain” related directly to the measurement apparatus (see figure 2-5a). In order to overcome this difficulty, an additional test with a very weak load level was carried out to investigate specially the behaviour of this “parasite strain”. The testing equipment used was a Mayes machine, shown in Figure 2-4, typically used for “creep” tests. During high temperature tests, the specimens heating was carried out by means of a resistor oven that allows to reach test temperature values up to 1100°C. As visible in Figure 2-5, where the testing machine frame is shown, the oven lifting is allowed in

/250

order to correctly set the specimens in the clamps. The load was applied by means of a dead weight at room temperature more exactly before heating of specimens. The specimen elongation was measured with a recording system made of two concentric alumina rods with two knives connected to the specimen clamps as shown in Figure 2-6. In addition, a LVDT allows the acquisition of measured elongation. The temperature values during the tests were measured both in the oven and directly on the specimens by means of two thermocouples as shown in Figure 2-6. The heating rate was 10°C/min and in Figure 2-7, the trend of the temperature increase is illustrated. In general, the specimens were heated until the temperature was 800°C or until the fracture occurred. The tensile test specimens were machined in longitudinal direction according to the sketch given in Figure 2-8.

Figure 2-4: Testing equipment – MAYES

A: Strain measurement with vertical rods (CSM) B: Strain measurement with horizontal rods (Helsinki

university)

Figure 2-5: Testing equipment – Frame

/250

Figure 2-6: Thermocouples location

Figure 2-7: Temperature vs Time curve

Figure 2-8: Tensile test specimen

Ramp v=10°C / min - Isothermal T = 800°C

0

100

200

300

400

500

600

700

800

900

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 Time (minutes)

Tem

pera

ture

(°C

)

/250

In Figure 2-9, the trend of strain rate versus temperature is shown in order to give an idea about the method used to define the strain per cent value at collapse: the discontinuity detectable in the graph highlights the temperature value at which the specimen collapsed and therefore the strain per cent value at failure moment. The strain rate has been evaluated using following formula:

01

01.

tttt

−−

=εεε

Figure 2-9: Example of the evaluation of the collapse temperature

2.3 CHARACTERISTICS OF INVESTIGATED COLD FORMED STEELS

In this research programme, two steel grades, S350 and S280, supplied by different partners were experimentally investigated. The following Table (Table 2-1) gives details of the investigated materials.

Steel Grade Label Section size (mm) Supplier

S280 Small C1 100 x 50 x 0.6 LAFARGE

S350 Medium C2 150 x 57 x 1.2 CORUS

S350 Large C3 250 x 80 x 2.5 RAUTARUUKKI

S350 AWS 150 x 1.2 RAUTARUUKKI

Table 2-1 : Investigated materials The test results will be presented in the following sections.

0

1

2

3

0 100 200 300 400 500 600 700 800 Temperature [°C]

ε %

/250

2.4 DETAILED EXAMPLES OF TESTS RESULTS

In this section, detailed examples of the results obtained from the testing activity in this project are reported. For all other detailed experimental results, they are already given in [5, 6].

2.4.1 Tensile tests at room temperature

For each investigated steel three tensile tests at room temperature were carried out. An example of the test results for steel grade S350 Large is shown in Figure 2-10.

Figure 2-10: Large C3 steel grade S350 - Stress – Strain curve


For each investigated steel steady state tensile tests at three different temperature levels, were carried out. In particular the selected temperature values were T = 400°C, T = 600°C and T = 800°C. The majority of above tests were performed under load control condition. As a consequence, the curves are not available in electronic format at the moment that the specimen failure occurs, because before failure arrival the extensometer was taken off. Only the last tests performed on AWS steel were performed under strain control condition. In particular for the Small C1 steel at high temperature level T=800°C it was not possible to apply the extensometer due to too soft behaviour of this steel at this temperature, so only the tensile strength was evaluated. In Figure 2-11, the tests on steel grade S350 Large C3 at the selected temperature values are reported as an example. As expected the strength of the investigated steels decreases when temperature increases.

Strain 0.00 0.05 0.15 0.20 0.250.10

0

Stre

ss [M

Pa]

400

500

300

200

100

/250

0

100

200

300

400

500

600

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Strain

Stre

ss [M

Pa] T=400°C

T=600°C

T=800°C

Figure 2-11: Large C3 steel grade S350 - Stress – Strain curves


During this kind of tests the applied stress varied in the range of 10%-90% of the 0.2% proof yield stress measured at room temperature. As previously mentioned, the strain measurement of this type of test induces some “parasite strain” related directly to the measurement apparatus (see figure 2-5a). In order to quantify this “parasite strain” an additional test with an applied stress of 1% of the 0.2% proof yield stress measured at room temperature was performed. This “parasite strain” was then subtracted from the strain recorded during the anisothermal transient tests. A typical example of such test results is given in Figure 2-12. In the same figure, the results obtained from another strain measurement methodology shown in figure 2-5b [3] as well as Eurocode recommendation are included. It can be found easily that the so called “parasite strain” is much smaller because that the thermal elongation of two vertical rods used to measure the strain would also have an influence on real strain of the specimen. In Figure 2-13, the results of the tests performed on steel grade S350 Large C3 are shown. As expected the collapse temperature decreases as the applied stress increases.

/250

Figure 2-12: Parasite strain recorded - Steel grade S350 Large C3

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 200 400 600 800 1000

Temperature (°C)

Stra

in

90%

80%

70%

60%

50%

40%

30%

20%

10%

Figure 2-13: Tensile anisothermal transient tests results – Steel grade S350 Large C3

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 200 400 600 800 1000 1200Temperature (°C)

Stra

in (%

) Eurocode

Helsinki university

S350 Large C3

S350 Medium C2S280 Small C1

/250

2.5 SUMMARY OF TESTS RESULTS

2.5.1 Tensile tests at room temperature

In the following tables, the average results of tensile tests at room temperature performed by different partners for all investigated steels are indicated.

Steel Thickness

(mm) 0.2% Proof Strength

(MPa) Tensile Strength

(MPa) E

(MPa) A

(%)

Small C1 0.6 312 383 212000 21

Medium C2 1.2 Yp =419* 486 205500 27

Large C3 2.5 327 461 190500 36

AWS 1.2 370 495 174000 31

* Yp = Yield point: Not continuous yielding

Table 2-2: CSM tensile tests results – Room temperature

Steel Thickness

(mm) Yield stress

0.2% proof stress (MPa)

Ultimate tensile stress (MPa)

Elongation (%)

Small C1 0.6 285.8 363.6 33

Medium C2 1.2 399.8 492.3 29

Large C3 2.5 333.8 454.5 36

AWS 1.2 359.3 485.4 33

Table 2-3: CORUS Measured yield stress of test sections

Steel Thickness

(mm) Yield stress

0.2% proof stress (MPa)

Ultimate tensile stress (MPa)

Elongation (%)

Small C1 0.6 309 387 29

Medium C2 1.2 450 485 25

Large C3 2.5 341 462 31

AWS 1.2 372 498 27

Table 2-4: VTT Measured yield stress of test sections

Certain difference is observed between these test values, which comes from the fact that, on the one hand, in some test results (for example CORUS tests), the zinc thickness is taken into account so that in general lower strength values are obtained, and on the other hand, the testing method used to define the yield stress is also more or less different between different partners.

/250


In the following table, a summary of the results of the tensile steady state tests performed at high temperature values are reported.

Material

Thickness (mm)

Temperature (°C)

0.2% Proof Strength

(MPa)

Tensile Strength

(MPa)

E (MPa)

A (%)

400 140 274 85000 33

600 72 111 40000 40 Small C1 0.6

800 * 45 - 43

400 252 432 140000 36

600 112 182 86500 49 Medium C2 1.2

800 51 58 13000 65

400 266 419 157000 41

600 123 179 89000 52 Large C3 2.5

800 44 83 39500 58

400 300 405 135000 46

600 147 161 73200 48 AWS 1.2

800 48 53 43000 63 * Not recorded

Table 2-5: Tensile steady state tests results – High temperature


Tensile anisothermal transient tests were performed on steel grade S350 Large C3 and Medium C2 and on steel grade S280 Small C1. In following figures, the strain versus temperature is illustrated for each investigated steel typology.

/250

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 100 200 300 400 500 600 700 800Temperature (°C)

Stra

in90%

80%

70%

60%

50%

40%

30%

20%

10%

Figure 2-14: Tensile anisothermal transient tests results – Steel grade S280 Small C1

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 200 400 600 800 1000

Temperature (°C)

Stra

in

90%

80%

70%

60%

50%

40%

30%

20%

10%

Figure 2-15: Tensile anisothermal transient tests results – Steel grade S350 Medium C2

/250

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0 200 400 600 800 1000

Temperature (°C)

Stra

in90%

80%

70%

60%

50%

40%

30%

20%

10%

Figure 2-16: Tensile anisothermal transient tests results – Steel grade S350 Large C3

As expected, for all investigated steel grades, the behaviour that the collapse temperature decreases as the applied stress increases is generally confirmed.

2.6 PROPOSAL FOR STRESS–STRAIN RELATIONSHIPS AT ELEVATED TEMPERATURES

On the basis of the experimental activity carried out on the selected steels, numerical investigations were made in parallel in order to obtain a mathematical model representing the stress–strain relationships for cold formed steels at elevated temperatures. In order to achieve this goal the following steps were followed:

• analysis and post processing of the tensile anisothermal transient tests, • selection of the mathematical model, • derive of suitable parameters to be used in the mathematical model, • comparison between the experimental results and the mathematical model.

These steps will be described in detail in following paragraphs.

2.6.1 Analysis of tensile anisothermal transient tests

The strain versus temperature curves obtained by means of tensile anisothermal transient tests, from which the “parasite strain” was subtracted, were analysed in order to get stress-strain curves in conditions as close as possible to real building heating conditions in event of fire. The results of this type of analysis are shown in figures from 17 to 19.

/250

0

100

200

300

400

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08Strain

Stre

ss (M

Pa)

T=200°C

T=300°C

T=400°C

T=500°C

T=600°C

Figure 2-17: Stress – Strain curve derived from anisothermal transient tests - Steel grade

S280 Small C1

0

100

200

300

400

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12Strain

Stre

ss (M

Pa)

T=200°C

T=300°C

T=400°C

T=500°C

T=600°C

T=700°C

T=800°C

Figure 2-18: Stress – Strain curve derived from anisothermal transient tests - Steel grade S350 Medium C2

/250

0

100

200

300

400

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20Strain

Stre

ss (M

Pa)

T=200°C

T=300°C

T=400°C

T=500°C

T=600°C

T=700°C

T=800°C

Figure 2-19: Stress – Strain curve derived from anisothermal transient tests - Steel grade S350 Large C3

These results together with the ones from tensile isothermal tests at high temperature values, constituted a basic database to develop the mathematical model describing the stress-strain relationship for cold formed steels at elevated temperatures.

2.6.2 Mathematical model for stress-strain relationship of cold formed steels at elevated temperatures

The mathematical model hereby proposed to define the stress–strain relationships for cold formed steels at elevated temperatures is based on Part 1.2 of Eurocode 3 [2]. The stress-strain relationship proposed in Part 1.2 of Eurocode 3 [2] is reported in detail in Table 2-6. In particular, as it can be found in Figure 2-20 where the shape of the corresponding curve for a defined temperature values θ is represented, the stress-strain curve is divided into four different regions depending on the strain range. The mechanical properties such as, yield strength, proportional limit and Young modulus, at different temperature levels can be evaluated by means of appropriate reduction factors recommended by the Eurocode 3 Part 1.2 [2] and reported in Table 2-7.

/250

Table 2-6: Stress – strain relationship recommended in Eurocode3 Part 1.2

Figure 2-20: Stress – strain relationship proposed in Eurocode 3 Part 1.2

Steel

Temperature θa (°C)

Reduction factor for effective yield strength

kyθ = fyθ/fy

Reduction factor for proportional limit

kpθ = fpθ/fy

Reduction factor for the slope of the linear elastic range

kEθ = Eaθ/Ea

20 1.000 1.000 1.000

200 1.000 0.807 0.900

300 1.000 0.613 0.800

400 1.000 0.420 0.700

500 0.780 0.360 0.600

600 0.470 0.180 0.310

700 0.230 0.075 0.130

800 0.110 0.050 0.090

900 0.060 0.0375 0.0675

1000 0.040 0.025 0.045

1100 0.020 0.0125 0.0225

1200 0.000 0.000 0.000

Table 2-7: Reduction factors recommended in part 1.2 of Eurocode 3

/250

2.6.3 Reduction factors of cold formed lightweight steels used for mathematical model

The reduction factors to be used in the mathematical model described previously were drawn from the testing activity performed on the selected steels and in particular from both tensile steady state tests and tensile anisothermal transient tests at high temperatures. In addition, other available data from literature studies carried out at Helsinki University [3], in particular in this respect the structural steel S350GD+Z was considered, is also taken into account. In the scope of this project it was predicted initially to give some common reduction factors for different tested steels in two steel grades. However, when further investigation is made, enormous difference has been discovered concerning the behaviour of examined steels at high temperatures, which led us to classify these steels into two categories as indicated in Table 2-8.

Category of steel Tested steels

Type A Grade S280 – Small C1

Type B Grade S350 – Medium C2, Large C3 and S350GD+Z

Table 2-8: Classification of tested cold formed steels In following paragraphs, the reduction factors are reported separately for all tested steels, that is Grade S280–Small C1 and Grade S350 including Medium C2, Large C3 and S350GD+Z. For each type of steel, in addition to reduction factors used in part 1.2 of Eurocode 3 model, a new reduction factor related to the 0.2 proof strength is included due to the fact that lightweight steel is always used to form thin wall elements whose resistance is largely dominated by local panel instability. In this case, it is necessary to take a relevant strength parameter in simple design rules which has been proved to be 0.2 proof strength rather than the commonly used 2% effective strength for hot-rolled steel structure members.

2.6.3.1 Steel of Type A: Grade S280-Small C1

This paragraph gives the reduction factors obtained for Type A steel on the basis of the experimental results. In order to show the validity of analytical results, in Figure 2-21, the reduction factors proposed for effective strength (kyθ = fyθ/fy) drawn from the anisothermal tensile tests are shown together with the recommendations Part 1.2 of Eurocode 3 [2].

/250

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 200 400 600 800 1000 1200

Temperature (°C)

Stre

ngth

redu

ctio

n fa

ctor

Test results - ultimate strength

Test results - 2% strength

Part 1.2 of EC3

Proposal for Type A steel

Figure 2-21: Reduction factors proposed for 2% effective strength ky,θ of Type A steel

This steel, used generally for non load-bearing members, such as in non load-bearing partition walls, showed a quite poor fire resistance. It should be noted that the recommendations in part 1.2 of Eurocode 3 [2] greatly over estimate the steel resistance. On the contrary, the reduction factors proposed seem in good agreement with the experimental results. In Figure 2-22, the reduction factors proposed for the slope of the linear elastic part of the stress–strain curve are compared with the values suggested in part 1.2 of Eurocode 3 [2]. These values were established by integrating the recommendations from Eurocode 3 with the results from the steady state tensile tests. In fact, it is very difficult to measure this parameter using anisothermal tests and generally, isothermal tests give more consistent results. For this reason, this parameter is defined on the basis of isothermal test results.

/250

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Red

uctio

n fa

ctor

s fo

r E -

KE

θ

EC3-1-2:10/2001

Proposed reduction factors

Figure 2-22: Reduction factors proposed for E

Finally in Figure 2-23, the reduction factors proposed for proportional limit kpθ are shown.

These values were obtained using the same ratio θ

θ

y

p

kk

given in Eurocode 3, compared with

the proposed reduction factors for effective yield strength.

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Red

uctio

n fa

ctor

for p

ropo

rtio

nal l

imit

Kp θ

EC3-1-2:10/2001


Figure 2-23: Reduction factors proposed for proportional limit

In conclusion all above reduction factors proposed for Type A steel are reported in Table 2-9.

/250

Steel Temperature

θa

Reduction factor for effective yield

strength

kyθ = fyθ/fy

Reduction factor for proportional

limit

kpθ = fpθ/fy

Reduction factor for 0.2 proof

strength

k0.2p,θ = f0.2p,θ/fy

Reduction factor for the slope of the

linear elastic range

kEθ = Eaθ/Ea

20°C 1.000 1.000 1.000 1.000

100°C 1.000 1.000 1.000 1.000

200°C 1.000 0.807 0.849 0.900

300°C 1.000 0.613 0.630 0.650

400°C 0.560 0.235 0.310 0.400

500°C 0.320 0.148 0.203 0.270

600°C 0.200 0.077 0.110 0.150

700°C 0.100 0.033 0.064 0.100

800°C 0.060 0.027 0.042 0.060

900°C 0.040 0.025 0.034 0.045

1000°C 0.027 0.017 0.023 0.030

1100°C 0.013 0.008 0.011 0.015

1200°C 0.000 0.000 0.000 0.000

Table 2-9: Proposed reduction factors for Type A steel

2.6.3.2 Steel of Type B

This paragraph deals with the reduction factors to be used in the mathematical model for Type B steel which were also determined on the basis of the experimental results. In the analytical results were taken into account the S350 steels tested within this project, such as Medium C2 and Large C3, and the S350GD+Z tested at the Helsinki University [3]. In a similar way in Figure 2-24 are illustrated the anisothermal tensile test results for steel from medium sections together with the recommendations of part 1-2 of Eurocode 3 [2] and the proposed corresponding reduction factors. In addition, the results from Helsinki University for 2% effective strength are also included in the same figure. This steel is characterised by a nominal thickness of 2.0 mm and provided by the same steel manufacturer for steel used for large section.

/250

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 100 200 300 400 500 600 700 800Temperature (°C)

Stre

ngth

Red

uctio

n fa

ctor

s K

y θ

Test results-ultimate strength-Medium section

Test results-2% strength-Medium section

VTT-Helsinki University-ultimate strength-S350GD+Z

VTT-Helsinki University-2% strength-S350GD+Z

EC3-1-2:10/2001


Figure 2-24: Reduction factors proposed for effective yield strength – Medium section

It can be found that for these steels, the 2% effective strength is slightly lower than ultimate strength and the proposed reduction factors follow quite well the ultimate strength results. Similarly in Figure 2-25, the anisothermal tensile test results for steel from large sections (Large C3), are presented in terms of ultimate as well as 2% effective strength.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 100 200 300 400 500 600 700 800Temperature (°C)

Red

uctio

n fa

ctor

s K

y θ

Test results-ultimate strength-Large section

Test results-2% strength-Large section

VTT-Helsinki University-ultimate strength-S350GD+Z

VTT-Helsinki University- 2% strength-S350GD+Z

EC3-1-2:10/2001


Figure 2-25: Reduction factors proposed for effective yield strength – Large section

/250

For this steel, it can be found that the proposed reduction factors are very slightly lower than the 2% effective yield strength while on the contrary recommendations of part 1.2 of Eurocode 3 [2] seem to over estimate the steel resistance. In Figure 2-26, the comparison between the proposal and all the test results in terms of 2% effective strength for Type B steel is reported. One can find easily that the proposed reduction factors are representative of an average value, which for this reason is considered to be the best compromise of the whole results.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 100 200 300 400 500 600 700 800Temperature (°C)

Stre

ngth

redu

ctio

n fa

ctor

s K

Y θ

Tests results-2% strength-Large section

Tests results-2% strength-Medium section

VTT Helsinki University results-2% strength-S350GD+Z

EC3-1-2:10/2001


Figure 2-26: Reduction factors proposed for effective yield strength-Medium and Large

section As the dominant failure mode of thin wall members is local buckling, it is impossible for them to reach the 2% effective strength before failure. Therefore it is important to give the adequate parameters in order to facilitate the development of simple calculations rules for this type of elements. As a consequence the conventional yield strength for non linear steel material behaviour is adopted, that is the 0.2% proof strength which can be directly derived from the material model. In Figure 2-27and Figure 2-28 the reduction factors drawn for E and the proportional limit are shown. All corresponding reduction parameters are reported in Table 2-10.

/250

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 200 400 600 800 1000 1200 1400Temperature (°C)

Red

uctio

n fa

ctor

s K

E θ Large section

Medium section

VTT-Helsinki University-S350GD+Z

EC3-1-2:10/2001


Figure 2-27: Reduction factors proposed for E

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 200 400 600 800 1000 1200 1400

Temperature (°C)

Red

uctio

n fa

ctor

for p

ropo

rtio

nal l

imit

Kp θ

EC3-1-2:10/2001


Figure 2-28: Reduction factors proposed for proportional limit

/250

Steel Temperature

θa


strength

kyθ = fyθ/fy


limit

kpθ = fpθ/fy

Reduction factor for 0.2 proof

strength


Reduction factor for the slope of the

linear elastic range

kEθ = Eaθ/Ea

20°C 1.000 1.000 1.000 1.000

100°C 1.000 1.000 1.000 1.000

200°C 1.000 0.807 0.896 0.900

300°C 1.000 0.613 0.793 0.800

400°C 0.890 0.374 0.616 0.680

500°C 0.570 0.263 0.407 0.450

600°C 0.340 0.130 0.229 0.250

700°C 0.180 0.059 0.117 0.110

800°C 0.070 0.032 0.049 0.080

900°C 0.053 0.024 0.037 0.060

1000°C 0.035 0.016 0.025 0.040

1100°C 0.018 0.008 0.013 0.020

1200°C 0.000 0.000 0.000 0.000

Table 2-10: Proposed reduction factors for Type B steel

2.6.4 Comparison between mathematical model and test results

In this paragraph, the comparison between the test results and the mathematical model is shown separately for both Type A steel and Type B steel.

2.6.4.1 Type A steel

In Figure 2-29, a general comparison between the stress-strain curves drawn from the model and the experimental results from transient tests at different temperature values is reported. In this case, the stress is normalised with respect to the yield strength measured at room temperature. As it can be seen, the agreement is also generally good.

/250

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain ε

σ / f

y

Model

T = 200°C

T = 300°C

T = 400°C

T = 500°C

T = 600°C

200°C300°C

400°C

500°C

600°C

700°C 800°C 900°C 1000°C 1100°C

Figure 2-29: Comparison between test and mathematical model

2.6.4.2 Type B steel

In figures from 30 to 36 the comparison for each temperature value between the experimental stress-strain curves and analytical curves drawn from the proposed mathematical model is reported. In each figure are included the experimental results from Large section, Medium section and S350GD+Z steels. In particular the stress is normalised with respect to the yield strength at room temperature of each considered steel which means that the curve from the model is representative of all three steels, since the proposed reduction factors are the same. A general good agreement can be observed.

/250

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain ε

σ / f

y

Model

Large section

Medium section

S350GD+Z

Figure 2-30: Comparison between test and mathematical model – T=200°C

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain ε

σ /

f y

Model

Large section

Medium Section

S350GD+Z


/250

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0.15 0.2

Strain ε

σ /

f y

Model

Large section

Medium section

S350GD+Z


0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain e

σ / f

y

Model

Large section

Medium section

S350 GD+Z


/250

0

0.2

0.4

0.6

0.8

1

1.2

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain ε

σ / f

y

Model

Large section

Medium section

S350GD+Z


0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain ε

σ / f

y Model

Large section

Medium section


/250

0

0.2

0.4

0.6

0.8

1

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

Strain ε

σ / f

y

Medium section

Large section


2-7 Comparison between two types of steel

In Figure 2-37 the comparison between the stress-strain curves obtained from the model for two different types of steel is reported. It is observed that, as highlighted before, starting from T = 400°C Type A steel shows a lower fire resistance with respect to Type B steel.

Figure 2-37: Comparison between the model for load and non load bearing sections steels

0

0.2

0.4

0.6

0.8

1

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02

Strain ε

σ / f

y

Steel forload bearinelements

Steel fornon loadbearingelements

200°C

300°C

400°C

500°C

600°C

700°C

800°C 900°C 1000°C 1100°C

Type B steel

Type A steel

/250

2-8 Conclusions

The mathematical model hereby proposed to define the stress–strain relationship for cold formed steels at elevated temperatures is based on the recommendations of part 1-2 of Eurocode 3 [2]. In such model for each strain range the suitable equation to evaluate the stress is suggested, as previously reported in Table 2-6. To apply such model the following parameters are necessary:

• Reduction factor for effective yield strength ( )C20ff

ky

yy °

= θθ

• Reduction factor for proportional limit ( )C20ff

ky

pp °

= θθ

• Reduction factor for the slope of the linear elastic range ( )C20EEk

a

aE °

= θθ

The outcome of this part of research work is that different reduction factors are established for two types of steel which apparently need to be differentiated in consideration of the important scatter in respect with resistance.

/250

Therefore, for Type A steel the values given in Table 2-11 may be applied.

Steel Temperature

θa


strength

kyθ = fyθ/fy


limit

kpθ = fpθ/fy

Reduction factor for 0.2

proof strength


Reduction factor for the slope of

the linear elastic range

kEθ = Eaθ/Ea

20°C 1.000 1.000 1.000 1.000

100°C 1.000 1.000 1.000 1.000

200°C 1.000 0.807 0.849 0.900

300°C 1.000 0.613 0.630 0.650

400°C 0.560 0.235 0.310 0.400

500°C 0.320 0.148 0.203 0.270

600°C 0.200 0.077 0.110 0.150

700°C 0.100 0.033 0.064 0.100

800°C 0.060 0.027 0.042 0.060

900°C 0.040 0.025 0.034 0.045

1000°C 0.027 0.017 0.023 0.030

1100°C 0.013 0.008 0.011 0.015

1200°C 0.000 0.000 0.000 0.000

Table 2-11: Reduction factors for steel non load bearing elements at high temperatures

/250

And for Type B steel the values given in Table 2-12 can be applied.

Steel Temperature

θa


strength

kyθ = fyθ/fy


limit

kpθ = fpθ/fy

Reduction factor for 0.2

proof strength


Reduction factor for the slope of

the linear elastic range

kEθ = Eaθ/Ea

20°C 1.000 1.000 1.000 1.000

100°C 1.000 1.000 1.000 1.000

200°C 1.000 0.807 0.896 0.900

300°C 1.000 0.613 0.793 0.800

400°C 0.890 0.374 0.616 0.680

500°C 0.570 0.263 0.407 0.450

600°C 0.340 0.130 0.229 0.250

700°C 0.180 0.059 0.117 0.110

800°C 0.070 0.032 0.049 0.080

900°C 0.053 0.024 0.037 0.060

1000°C 0.035 0.016 0.025 0.040

1100°C 0.018 0.008 0.013 0.020

1200°C 0.000 0.000 0.000 0.000

Table 2-12: Reduction factors for steel load bearing elements at high temperatures

/250

3. MECHANICAL BEHAVIOUR OF LIGHTWEIGHT STEEL MEMBERS AND ASSEMBLIES AT ROOM TEMPERATURE

3.1 GENERAL

The mechanical behaviour of light steel frames at room temperature was studied for comparison with mechanical behaviour at the fire limit state. At the fire limit state, it is usual to take the existing ambient temperature design rules and modify them to reflect performance at high temperature. Therefore it is important that the ambient design rules are fully understood as they form the basis of the fire limit design rules. Performance of light steel frame arrangements was investigated by a combination of a static testing, numerical modelling and direct comparison with existing design procedures.

3.2 STATIC TEST PROGRAMME

The static testing programme was split into three parts and was closely co-ordinated with the fire testing programme. The first part consisted of a series of stub column tests carried out at VTT on each of the section sizes to obtain the effective area of the section. The second part consisted of a series of control tests carried out at Corus on double studs supported by different plasterboard arrangements under differing loading conditions. The third part also consisted of control tests carried out at Corus and consisted of tests on two floor/ wall panel arrangements to examine the effect of practical load transfer in a more realistic construction arrangement. The section sizes tested in the programme are outlined in Table 3-1. The small section was provided with service holes with a diameter of 32 mm at a spacing of 500 mm. Section AWS had an offset web which increased section breadth to 90 mm for part of the web and was perforated. Section TC150 was a C-section with a perforated web.

Section Steel Grade Supplier Nominal Dimensions Small 280 MPa Lafarge (Fr) 100 x 50 x 0.6

Medium 350 MPa Metsec (UK) 150 x 57 x 1.2

Large 350 MPa Rautaruukki Oy (Fin) 250 x 80 x 2.5

AWS 350 MPa Rautaruukki Oy (Fin) 150 x 50/90 x 1.2

TC150 350 MPa Rautaruukki Oy (Fin) 150 x 50 x 1.2

Table 3-1: Section sizes used in Test Programme

3.2.1 Stub Column Tests

In the first part of the programme, 6 tests on the section sizes used in the testing programme. Full details of the specimens tested are given table 3-2 in the results section and are not repeated here.

3.2.2 Double Stud Tests

In the second part of the test programme, 22 tests were carried out. All specimens tested were 2.85 m long and consisted of double studs at 600 mm centres supported by different plasterboard arrangements.

/250

The test programme was split into a number of different areas. These consisted of:

a) Tall stud tests on unsupported specimens b) Boundary condition tests to examine effect of realistic support scenarios c) Load eccentricity tests to examine the effect of centric and eccentric loading d) Sections supported by plasterboard on one face only e) Sections supported with plasterboard and steel sheets.

Full details of the specimens tested within each area are given tables 3-3 to 3-7 in the results section and are not repeated here.

3.2.3 Floor & Wall Assembly Tests

The third part of the test programme consisted of tests to study the effect of load introduction to the wall through a realistic floor/wall detail and to provide control tests at room temperature for comparison with fire tests on the same assembly. A schematic of the assembly studied is given in Figure 3-1. Wall and floor sections were 3.0 m wide and each was constructed using six sections at ~600 mm centres.

P2P1

~5.2m

3.0m

P2P1

~5.2m

3.0m

Figure 3-1: Floor/wall assembly test setup

The dead load applied to the structure (P2) was up to the serviceability load of the floor structure. This was applied by means of dead weight suspended below the floor for health and safety reasons. The wall studs were then tested to failure by application of load (P1) via four jacks.

3.3 TESTING METHODOLOGY


The stub column tests were carried out according to instructions given in Eurocode 3: Design of steel structures - Part 1-3: General rules - Supplementary rules for cold formed thin gauge

/250

members and sheeting [1] and AISI Load and Resistance Factor Design Specification for Cold-Formed Steel Structural Members (1996). The test specimen for each test was short enough so that global buckling modes should not reduce the resistance but long enough to detect distortional buckling failure. The height of the small and medium sections was 600 mm and that of the large and AWS sections was 1000 mm. The ends of the specimens were machined. Both ends of the specimen were reinforced with a timber block to avoid local crushing before the cross-sectional resistance was reached at the desired failure mode (see Figure 3-2 below).

Figure 3-2: Stub Column Test Setup


Each specimen was constructed in the test rig as outlined in Figure 3-3. Each strut was placed in the rig and adjusted until vertical in both directions. Plasterboard, if used, was then attached to the relevant specimens at the required screw spacing.

/250

Figure 3-3: Building specimen in test rig A view of the test setup is given in Figure 3-4. Lateral displacements were measured at the mid and quarter points of each strut (Figure 3-5). Load was applied via two jacks located at the head of the test rig. Tests were continued until the specimen could not sustain any more load.

Figure 3-4: View of test setup

/250

Figure 3-5: View of lateral measurement devices


The dead load to be applied to the structure (P2) was up to the serviceability load of the structure. This was applied by means of dead weight suspended below the floor for health and safety reasons. A total load of 60.0 kN was applied at six points evenly spaced along the central four beams of the floor system. This gave a total load of 15 kN per beam. The four central wall studs were then tested to failure by application of load via the jacking system. Central lateral deflections of the four central wall studs were monitored during the test. A view of the test frame constructed to test the floor/wall assembly is given in Figure 3-6. Figure 3-7 gives a more detailed view of the load introduction system used to apply the dead weight to the floor system.

/250

Figure 3-6: View of test rig for floor/wall assembly

Figure 3-7: View of load introduction on floor system

3.4 TEST RESULTS


The test results for the series are outlined in Table 3-2. The medium section, 150x57x12/1.2, was also tested with a service hole in the centre and with pinned boundary conditions.

/250

Length NTest Test

Stud (mm) (kN)

Remarks

1 C100x50x6/0.6 600 8.6

2 600 59.6

3 600 67.4 With service hole in centre

4

C150x57x12/1.2

600 60.9 With pinned boundary conditions

5 C250x80x22/2.5 1000 195.5

6 AWS 150/1.2 1000 74.1

Table 3-2: Summary of stub column test results All C-shaped specimens failed through distortional buckling which was preceded by local buckling. The used of flat ended boundary conditions compared to pin-ended in fire tests does not have any effect on the behaviour nor the failure load. The results obtained for the medium stud with a service hole shows an interesting phenomena in that the hole in the web seems to reinforce the section. The interaction of local and distortional buckling modes does not coincide at the same wave length due to the hole. It transfers maximum plate buckling deformation above and below the mid-height. Therefore rotational support of the web to the stiffened flange is not decreased after local buckling deformations as in the case where no hole exists. Also the AWS stud profile failed through distortional buckling. Due to the shape of the AWS stud, distortional buckling is also a critical failure mode for longer specimen length. A view of the final buckled shapes is given in Figure 3-8.

Figure 3-8: Stub Column failure models


In the second part of the testing programme, each series of tests were designed to look at a particular aspect of the behaviour of cold formed sections and the manner in which they are supported by non-structural items. Within each of the tests a number of basic failure modes

/250

are possible. These failure modes can be split into local and global failure modes. Local failure modes for the common lipped C cold formed sections tested in this study are illustrated in Figure 3-9 and overall global failure modes are illustrated in Figure 3-10. The type of failure mode will be identified for each test. It should be noted that interactive global/local failure modes are also possible.

Basic section

Distortional BucklingWeb Buckling

Flange BucklingBasic section

Distortional BucklingWeb Buckling

Flange Buckling

Figure 3-9: Basic failure modes – local

Major axis

Minor axis

Torsional

Lateral Torsional

Distortional Lateral

P

P

P

P P

Pe

e

Major axisMajor axis

Minor axisMinor axis

TorsionalTorsional

Lateral TorsionalLateral Torsional

Distortional LateralDistortional Lateral

P

P

P

P

P

P

P

P P

Pe

eP

Pe

e

Pe

e

Figure 3-10: Basic failure modes - global

3.4.2.1 Tall stud tests

The tall stud tests were designed to test single unsupported elements under similar boundary conditions to those used in the main plasterboard tests. In this case it was decided to use exactly the same test rig and end supports as used in the main test series. This meant that two specimens were tested at the same time. The test results for the test series are outlined in Table 3-3. The number in brackets is the test number. It can be generally noted that results are correlated by section dimensions and thickness. These results need to be compared to later tests to be put into perspective and will be discussed later.

/250

Size and grade of sections Testing conditions

Loading Section type Small (100x50x0.6)

Medium (150x57x1.2)

Large (250x80x2.5)

AWS (150x 1.2)

280 MPa 350 MPa 350 MPa 350 MPa Centric Eccentric

(0.25 h) No perf. Perf.

6.1 kN(18) 50.8 kN(19) 177.0 kN(22) - √ √ - - - 46.5 kN(20) √ √ - - - 48.6 kN(21) √ √

Table 3-3: Summary of tall stud test results

Comparison of the failure modes of the medium and large section are given in Figure 3-11 and of the AWS section under centric and eccentric loading in Figure 3-12. It can be seen that the overall failure mode in each test was global lateral torsional buckling. This was initiated by local buckling of the web of the specimen near to the centre of the lipped C sections and by some kind of distortional local buckling mode in the AWS sections. It would be expected that the AWS section under eccentric loading would give a lower failure load than the centric case but, as can be seen in Figure 3-12, the global modes are very similar suggesting that overall buckling dominates before the bending moment due to eccentricity has any effect.

Medium – failure = 50.8 kN Large – failure = 177 kN

Figure 3-11: Comparison of medium and large specimen failures in tall stud tests

/250

Centric – failure = 46.5 kN Eccentric – failure = 48.6 kN

Figure 3-12: Comparison of AWS specimen tall stud tests under centric and eccentric loading

3.4.2.2 Boundary condition tests

It was recognised early in the project that the normal method of supporting loadbearing studs in channel tracks may be a source of variability between different tests. It was decided to test most of the specimens with idealised support conditions to the studs to ensure consistent behaviour between tests. These support conditions consisted of heavy plates and channels which were fixed to the jacks at the top of the specimens and pinned off the test frame at the bottom of the specimen (Figures 3-3 and 3-4). This test programme was formulated to investigate the exact effect of actual support conditions on section behaviour. In the first test the studs were simply inserted in the channel tracks, the specimen was built within the test rig with double boards on each side of the studs and then the specimen was tested. The second test was a repeat of the first with the studs fixed with a single screw to the channel track. The third test was carried out with no track under idealised end conditions. The maximum loads obtained in each of the tests are given in Table 3-4. The load deflection plots are compared in Figure 3-13. It is clear that the presence of the tracks has some effect on the load-deflection behaviour. The presence of the tracks also appears to have an effect on the maximum failure load with both tests failing at a lower load than the idealised end condition specimen. The reason for this can be clearly seen in Figure 3-14. Both tracked specimens fail by very localised buckling of the section at the very end of the specimen whereas the ideally supported specimen fails by a local buckling failure near to the end but mobilising the full section capacity due to greater support to the end of the specimen by the heavy plate and channels. The local buckle is towards one flange in this case due to the eccentric loading that was applied in these tests. It can be concluded that the idealised end conditions are better as the main area of interest is overall sectional failure rather than the very localised end failures that occurred in the tests with the channel tracks.

/250



Medium (150x57x1.2)

Large (250x80x2.5)

AWS (150x 1.2)

280 MPa 350 MPa 350MPa 350 MPaEccentric(0.25 h) Boundary conditions

- 36.6 kN(1) - - √ Studs simply inserted in channel tracks

- 49.6 kN(2) - - √ Studs in channel tracks fixed by screws

- 54.9 kN(3) - - √ One end fixed/one end pinned

Table 3-4: Summary of boundary condition test results

Figure 3-13: Comparison of load-deflection curves of specimens with different boundary

conditions

Inserted in tracks – failure = 36.6 kN

0

10

20

30

40

50

60

0 5 10 15 20 25 30 Axial Displacement (mm)

Load

(kN

)

Tracks - Inserted Tracks - Fixed Fixed-Pinned

/250

Fixed in tracks – failure = 49.6 kN

Fixed at jack/pinned at bottom – failure = 54.9 kN

Figure 3-14: Comparison of failure modes of specimens with different boundary conditions

3.4.2.3 Load eccentricity tests

This tests series was designed to quantify the effect of eccentric load application on all of the sections. These tests were supported by double boards screwed at approximately 300 mm centres using self tapping screws. Each section size was tested in this test series. The maximum loads obtained in each of the tests are given in Table 3-5. In each test, local buckles of the web were clearly discernable whilst the specimen was still elastic (Figure 3-15). Once the local buckling capacity of the section was reached the specimen could no longer sustain a load and the specimen was deemed to have failed. The effect of the eccentricity was to reduce the failure load of all the specimens due to the extra bending moment induced as expected. Also included is test 24 (*) which was an extra test carried out on a TC150 section.

/250



Medium (150x57x1.2)

Large (250x80x2.5)

AWS (150x 1.2)

280 MPa 350 MPa 350 MPa 350 MPa Centric Eccentric

(0.25 h) No perf. Perf.

9.9 kN(8) 74.4 kN(4) 223.0 kN(15) - √ √ - - - 95.1 kN(11) √ √

7.2 kN(9) 54.9 kN(5) 168.5 kN(16) - √ √ - - - 57.5 kN(12) √ √ - - - 45.6 kN (24)* √ √

Table 3-5: Summary of load eccentricity test results

Figure 3-15: Typical elastic local buckles in web of specimen The difference in local buckling behaviour between the centric and eccentrically loaded lipped C section specimens is clearly illustrated in Figures 3-16 and 3-17. Centrically loaded specimens exhibit local buckles involving the whole of the section whereas eccentrically load specimens exhibit local buckles involving the flange which is nearest to the point of application of the eccentric load. In each case the local buckle occurs between the last set of screws nearest to either the point of loading or, more usually, the point of support. The failure modes obtained in the AWS section tests (Figure 3-18) are slightly different in that they tend to extend along a greater portion of the specimen. This means that the buckled portion tends to extend across the points of screw support and involves the studs pulling the screws through the plasterboard. Testing of AWS sections generally was more difficult due to differences in the bearing of the studs at the support due to the differences where the perforations in the web were cut at the end. The perforations are also thought to contribute to

/250

section instability near to the local buckling point giving rise to highly localised effects that contribute to screws being pulled through the plasterboard. These problems are illustrated in Figure 3-19.

Centric – failure = 74.4 kN Eccentric - failure = 54.9 kN

Figure 3-16: Comparison of failure modes of centric and eccentric loaded medium specimens supported on both sides

Centric – failure = 223 kN Eccentric – failure = 168.5 Kn

Figure 3-17: Comparison of failure modes of centric and eccentric loaded large specimens supported on both sides

/250

Centric – failure = 95.1 kN Eccentric – failure = 57.5 kN

Figure 3-18: Comparison of failure modes of centric and eccentric loaded AWS specimens supported on both sides

Inconsistent support conditions Section instability due to weakened web

- gives rise to localised effects

Figure 3-19: Problems with AWS testing

/250

3.4.2.4 Specimens supported with plasterboard on one side only

This test series was designed to examine the effect of having an unsupported stud flange. This arrangement is common in partition walls where there are staggered studs to increase acoustic performance of the wall. Each specimen was tested with the eccentricity point nearest to the unsupported stud flange. This is the worst case in both the fire test where the deflection due to thermal bowing is enhanced by that due to the extra bending moment and in the static test due to the increased compression force in the unsupported flange. The maximum loads obtained in each of the tests are given in Table 3-6. Loads obtained are lower than those of the studs supported by plasterboard on both sides as expected. An additional test was performed for the medium section with the eccentricity at the plasterboard supported side. The actual eccentricity in a real wall will be dependent upon the nature of the connection between the wall and any supported floor or wall above the wall of interest. This test gave a higher failure load of 57.4 kN which is approximately the same as that obtained in the equivalent test (54.9 kN) with the stud supported on two sides with plasterboard.

Size and grade of sections Testing conditions Loading Section type Small

(100x50x0.6) Medium

(150x57x1.2) Large

(250x80x2.5)AWS

(150x 1.2) 280 MPa 350 MPa 350 MPa 350 MPa

Centric Eccentric (0.25 h) No perf. Perf.

7.3 kN(10) 44.9 kN(6) 153.5 kN(17) - √ √ - - - 43.2 kN(13) √ √

Table 3-6: Summary of test results of specimens supported on one side only

The buckling modes obtained for the medium and large specimen tests are illustrated in Figure 3-20. The buckling modes for the medium and large specimens tested with eccentricity to the unsupported side are clearly pure flange buckling rather than the local web/ whole section buckling modes observed in the other tests. This is expected due to the increased compression force in the unsupported flange and illustrates the role the screws play in suppressing lower flange buckling modes in the other tests. The similarity of the buckling mode obtained for the specimen with load to the supported side to the previous tests (compare Figures 3-16 and 3-20) also clearly illustrates this. The buckling modes for the AWS test are illustrated in Figure 3-21. Similar behaviour to that observed the lipped C section tests i.e. compression flange buckling are observed.

/250

Medium Failure=44.9 kN

Medium Failure=57.4 kN

Large Failure=154 kN

Figure 3-20: Comparison of large and medium section failure modes for specimens supported on one side only

AWS – Failure=43.2 kN

Figure 3-21: AWS section failure modes for specimens supported on one side only

3.4.2.5 Effect of including steel sheet

The time to failure in a fire test is strongly related to the mechanical performance of the plasterboard. When a wall is exposed to a significant heat source the plasterboard’s main

/250

role is to protect the structural elements of the wall by reducing the rate of temperature rise. However in standard fire tests, single plasterboard walls soon suffer shrinkage cracking. Once cracked, hot gases can penetrate the cavity of the wall, the steel rapidly heats up and structural failure soon follows. Although the plasterboard suffers an integrity failure, the majority of the board still continues to perform its fire protection role. This gives rise to double plasterboards being the used, the first plasterboard layer cracks but protects the second plasterboard layer greatly increasing the time to cracking of this layer and hence time to failure of the wall as a whole. Fire tests on steel protected plasterboard were carried out to examine if the greater structural integrity provided by the steel sheet would increase fire resistance periods. Tests were carried out at room temperature to provide control tests to performance of such a system in fire. Maximum loads for two tests on the medium and AWS sections are given in Table 3-7. It can be seen that the steel sheet has very little effect on the maximum load obtained for the medium section – 57.9 kN compared to 54.9 kN. This is because the failure mode is still local buckling of the section close to the end of the specimen. This is illustrated in Figure 3-22 in which identical failure modes for both tests can be seen. However, there is a significant increase in the maximum load for the AWS section – 70 kN compared to 57.5 kN. This is because the steel sheet reduces the tendency of the AWS section to pull the screws through the plasterboard. This shortens the buckling length of the flange leading to an enhanced load carrying capacity for the section. This is clearly illustrated in Figure 3-23.


(100x50x0.6) Medium

(150x57x1.2) Large

(250x80x2.5)AWS

(150x 1.2)280 Mpa 350 MPa 350 MPa 350 MPa

Centric Eccentric (0.25 h) No perf. Perf.

- 57.9 kN(7) - - √ √

- - - 70.0 kN(14) √ √

Table 3-7: Summary of test results of specimens with additional steel sheet

Without- Failure = 54.9 kN With- Failure = 57.9 kN Figure 3-22: Effect of including steel sheet on medium section failure modes

/250

Without – Failure=57.5 kN With – Failure=70 kN

Figure 3-23: Effect of including steel sheet on AWS section failure modes

3.4.2.6 Comparison of test results across test series

The load deflection curves for each section size are compared in Figures 3-24, 3-25, 3-26, and 3-27 for the small, medium, large and AWS sections respectively.

Figure 3-24: Comparison of load-deflection curves of small specimens

0

2

4

6

8

10

12

0 2 4 6 8 10 12 14 16 18 20

Axial Displacement (mm)

Load

(kN

)

Tall stud

Both Flanges - Centric

Both Flanges - Eccentric

One Flange - Eccentric

/250

Figure 3-25: Comparison of load-deflection curves of medium specimens

Figure 3-26: Comparison of load-deflection curves of large specimens

0

50

100

150

200

250

0 5 10 15 20 25

Axial Displacement (mm)

Load

(kN

)

Tall stud




0

10

20

30

40

50

60

70

80

0 2 4 6 8 10 12 14 16 18Axial Displacement (mm)

Load

(kN

) Tall stud




Both Flanges + steel - Eccentric

/250

Figure 3-27: Comparison of load-deflection curves of AWS specimens

In the previous discussion, the medium, large and AWS sections have mainly been concentrated on. This is because the small section is not really a ‘structural’ section being formed from 0.6 mm steel. It was included in this study to provide a lower bound to the sections considered in the study whilst having a width to thickness ratio which would be onerous for the sections considered. However, the results obtained (Figure 3-24) do follow the same trend as the other sections and the initial stiffness of each test is very similar once bedded down. There is ~25% difference in maximum load obtained between centric and eccentric loading. A maximum load of 6.1 kN was obtained from the tall stud test reflecting the lower global lateral torsional buckling mode when unsupported by plasterboard. However, approximately the same load was obtained when the section was supported by boards both on two sides and one side only. The medium, large and AWS section results (Figures 3-25, 3-26 and 3-27) exhibit the expected trends. Initial stiffnesses of all tests are consistent up to failure when sudden buckling takes place in the relevant mode. In terms of failure loads, all trends are as expected reflecting the dominance of the local buckling failure modes.


3.4.3.1 Test on Rannila Floor and Wall assembly (Finnish system)

The Rannila floor and wall assembly was firstly tested with the wall loads applied through a small dado wall - 150mm high – to study the effect of load introduction through the bottom of a stud wall above. This test failed prematurely by local buckling of the dado wall at a load of 62 kN per stud. This is very close to the squash load of the section. The wall appeared to be undamaged at this load. It was decided to re-test the wall/floor assembly, removing the dado wall and applying the load directly to the end channel of the floor system. The wall failed at an average stud load of 67.3 kN per stud. Note that this load is in addition to the floor load of ~7.5kN per stud. The

0

10

20

30

40

50

60

70

80

90

100

0 2 4 6 8 10 12 14 16 18 20Axial Displacement (mm)

Load

- kN

Tall stud - Centric Tall stud - Eccentric Both Flanges - Centric Both Flanges - Eccentric One Flange - Eccentric Both Flanges + steel -Eccentric

/250

load-deflection plot is given in Figure 3-28. A view of the final buckled shape of the wall assembly is given in Figure 3-29.

Figure 3-28: Load –Displacement of Rannila Wall Assembly

Figure 3-29: Final buckled shape of Rannila Wall Assembly

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40Axial Displacement - mm

Ave

rage

Stu

d Lo

ad (

kN)

/250

The final failure load per stud of ~74.8kN (including contribution from floor) needs to be compared with the result from the double stud load test on the TC150 specimen with idealised end conditions (test 24). This test included the effect of eccentric load and failed at a stud load of 45.6kN. As the failure load is greatly in excess of this load it would suggest that not much eccentricity is being induced in the section in the practical situation. It would also suggest that much greater support is given to the studs in practical walls with enclosed ends than in the double stud tests.

3.4.3.2 Test on the Metsec Floor and Wall assembly (UK system)

It was decided to test this wall/floor assembly with no dado wall and applying the load directly to the end channel of the floor system. The wall failed at an average stud load of 76.9kN per stud. Note that this load is in addition to the floor load of ~7.5kN per stud. The load-deflection plot is given in Figure 3-30. A view of the final buckled shape of the wall assembly is given in Figure 3-31.

Figure 3-30: Load –Displacement of Metsec Wall Assembly

0

10

20

30

40

50

60

70

80

90

0 10 20 30 40 50 60Axial Displacement (mm)

Ave

rage

Stu

d Lo

ad (k

N)

/250

Figure 3-31: Final buckled shape of Metsec Wall Assembly The final failure load per stud of ~84.4kN (including contribution from floor) needs to be compared with the result from the double stud load test on the medium section with idealised end conditions (tests 4 and 5). The test with eccentric load failed at a stud load of 54.9kN and the test with centric load failed at 74.4 kN. As the failure load is in excess of both these loads it would suggest that not much eccentricity is being induced in the section in the practical situation. It would also suggest that much greater support is given to the studs in practical walls with enclosed ends than in the double stud tests and that the overall failure is governed by the local buckling capacity of the section.

3.5 NUMERICAL MODELING OF TESTS

3.5.1 Numerical simulation of stub column tests

The commercially available computer code ABAQUS was used to model the tested steel stub columns. The numerical model was created as close as possible to real test conditions as illustrated in Figure 3-32. The main modelling features are listed below:

• The steel stud itself was modelled with a 4-node shell element (Figure 3-32a). • The end plates were modelled with rigid elements corresponding to a reference point

where the load and boundary conditions was applied (see Figure 3-32b). • For the room temperature simulations, the steel studs were analysed using two

different types of interactions between the endplate and the steel section in order to analyse the influence of different end boundary conditions and also because the testing in room temperatures and fire was made with different end connections. The different types of interactions are shown in figure 3-32c which is respectively a

/250

surface-to-surface contact between stud section and end plates and a tie constraint with active degrees of freedom equal for the section and end plates.

• Furthermore the steel studs in the room temperature tests had a small piece of timber between the flanges at the end of the steel section, which was clamped between the flanges. The end portion of the stud was modelled taking into account a stiffness of the timber piece by restraining the displacement of the flanges in perpendicular direction (see Figure 3-32d).

• To evaluate the influence of local buckling, different magnitudes of a sine-shaped deformation mode of the stud were considered. The imperfection is implemented by making an Eigenvalue analysis. Figure 3-32e shows the deformation mode made by an Eigenvalue analysis for the large section.

• Global imperfection in strong direction was introduced by load eccentricity, which gives a intended bow corresponding to a magnitude of L/1000. This approach is slightly conservative compared to a bow.

• Global imperfection in weak direction was introduced by applying a lateral displacement (which gives the intended bow imperfection) since the end boundary conditions used in the simulation does not allow the use of load eccentricity.

b) Boundary condition applied to a reference point at the end plate

c) Two types of connection condition between stud and plate

a) View of modelled steel stud

d) Modelling of timber piece and clamp in room temperature tests

e) Geometric imperfection – local buckling

Figure 3-32: Modelling principles of C-type cross-sections - stub column

It is realistic to assume that geometrical imperfections are a combination of different initial imperfections. In order to give an idea about the influence of different imperfections on compression resistance of stub columns, a parametric study has been carried out, using medium section, with different amplitudes of local and global buckling for the stub column. The corresponding results are presented in the table below (Table 3-8).

/250

Global imperfection in weak direction (about strong axis) Local imperfection

L/1000 (-) L/1000* None b/100 61.2 kN 65.0 kN - b/200 63.4 kN 66.8 kN 66.5 kN

(-) b/200* 65.3 kN - - None - - 70.5 kN

* (-) sign indicate negative buckling mode from buckling analysis or static analysis, which is meaning that an imperfection in the opposite direction is used.

Table 3-8: Compression resistance of the steel stud for different magnitudes of global and

local imperfections (b is the height of the web) It can be found that the difference is rather small in compression resistance for the different magnitudes of initial imperfections. As a consequence, in our numerical simulations a magnitude of the local buckling imperfection is chosen as b/200, where b is the height of the web. Another parameter, which has been studied, is the influence of sharp or rounded corners on compression resistance of stub columns. The numerical simulations were made once again with medium section with two different cases of loading condition, one case with imposed load simulation and another case with imposed displacement simulation. The results from above calculations are presented in Table 3-9.

Critical stress Sharp corners Agr = 332 mm2

Rounded corners Agr = 327 mm2

Concentrated load 66.7 MPa 66.9 MPa

Displacement 68.0 MPa 67.9 MPa

Table 3-9: Critical stresses from numerical calculations The results are showing that there are not any big differences between sharp or rounded corners. Although for the purpose of correct modelling, rounded corners are used in our numerical modelling. The numerical simulation was made with two of three different boundary conditions as described earlier. The results from numerical calculations are presented in Table 3-10. Two different models that is FEA(1) and FEA(2) were used. In fact, the model FEA(1) is considered to be close to room temperature test conditions and FEA(2) to be close to fire test conditions.

/250

Small section Medium section Large section

fy 309 MPa 450 MPa 341 MPa

Nu = Aeff x fyb 10.9 kN 59.0 kN 215.2 kN

Nu.tests 8.6 kN 59.6 kN 195.5 kN

FEA (1) 10.9 kN 63.2 kN 182.7 kN

FEA (2) 11.5 kN 67.3 kN 204.9 kN

Table 3-10: Ultimate compression resistance Nu considering local buckling according to part 1-3 of Eurocode 3 [1], comparison with tests results and numerical calculations – room

temperature calculations The results presented in Table 3-10 shows a quite good agreement between test results, numerical modelling and simple calculation model in part 1-3 of Eurocode 3 [1]. Notice that the numerical simulation named FEA (1) is the numerical model similar to the test conditions at room temperature. The numerical model similar to the fire tests FEA (2) gives slightly higher values of the ultimate resistance. This is due to the fact that the restrained and tied nodes at the end of the section with end plates. The results in Table 3-10 are also presented graphically in Figure 3-33 in which the relationships between FE calculations and the test results and simple calculation rules in part 1-3 of Eurocode 3 [1] are illustrated.

Numerical simulations compared to tests and EC3

0.00.20.40.60.81.01.21.41.6

C-100 C-150 C-250

FEA/Test FEA (1)FEA (2)FEA (3)EC3

Figure 3-33: Comparison between test results, numerical calculations and EC3 (FEA (3) is similar to FEA (2))

3.5.2 Numerical simulation of tall stud tests

The experimental programme was supplemented with numerical models of the tests carried out. The models aimed at capturing the observed structural failure modes and confirming the validity of the numerical models. Modelling was carried out at Corus using ABAQUS and at CTICM using ANSYS.

/250

3.5.2.1 Assumption for numerical simulations

The numerical simulations with the computer codes ABAQUS and ANSYS (illustrated here) of the mechanical behaviour of steel studs maintained by plasterboards have been performed using the following assumptions:

• The whole steel stud is modelled with shell elements as shown in Figure 3-34.

Figure 3-34: Modelling of steel studs with shell element

• The connection with plasterboard is represented by a boundary condition restraining the lateral displacement of steel stud at position of screws reported in Figure 3-35. These restrained displacement conditions are located at the centre of both flanges for studs maintained by plasterboards on two sides and only at the centre of one flange (corresponding to supported side) for studs fixed with one plasterboard only.

/250

Y=165 Y=130

Y=473.75 Y=638

Y=782.5

Y=1400

Y=1146 Y=1091.25

Y=1708.Y=1654

Y=2017.5 Y=2162

Y=2326.25

Y=2670 Y=2635

Figure 3-35: Position of screws along the steel stud

• In accordance with tests, the behaviour of steel studs is simulated with two different end conditions, namely:

o Fixed at both ends (restraining UX, UY, UZ, ROTX, ROTY and ROTZ), or o Fixed at one end (restraining all degrees of freedom) and hinged at the other

end (restraining UX, UY, ROTY and ROTZ).

• Moreover, in ANSYS both ends of steel stud are modelled using a stiffer material (corresponding to blue colour element) with the value of modulus of elasticity taken as 210×105 MPa. As an example, Figure 3-36 shows the boundary conditions which have been adopted in the numerical simulations of some tests, when the steel stud is assumed as hinged at one end and fixed at the other end. In ABAQUS, each end of the C-section is connected to the load/support point by a series of rigid links.

/250

Lateral restrain condition for screws

Free end

Fixed end

Restrained UX, UY, UZ, ROTX, ROTY and ROTZ

Restrained UX, UY, ROTY and ROTZ

Steel stud

Rigid part

Steel stud

Rigid part

Figure 3-36: Example of boundary conditions adopted for steel suds

o In ANSYS, the load is applied as a surface load as shown in Figure 3-37 and is applied by increment up to the failure. The load application direction (parallel to Z axis) is constant during calculations. For specimens under centric load, an eccentricity of 5 mm is used in numerical simulations. In ABAQUS, the load is applied as a prescribed displacement.

Exposed flange

Unexposed flange

Web

p

Figure 3-37: Applied load conditions (pressure on free end surface parallel to Z axis)

/250

o Initial imperfection obtained from eigenvalue buckling analysis is used in numerical simulations. It consists of sinusoidal waves in the web with maximum amplitude of 1mm.

o At room temperature the mechanical properties of steel stud are those given by part 1.1 of Eurocode 3 [7].

3.5.2.2 Example Analysis

As a detailed example of the numerical analysis carried out, the numerical results obtained with the computer code ANSYS for the specimen with medium section: tests number 3 and 7 are given below. The tests were performed with the studs connected to plasterboard on two sides. The steel studs were submitted to an eccentric axial load. At ordinary temperature steel studs are designed as hinged at one end and fixed at the other end. Assuming the same support conditions, the calculated failure load is 48.5 KN. When the steel stud is assumed as fixed at both ends, the calculated failure load becomes 52 KN which is comparable to the experimental loads, namely 54.9 KN for test number 3 and 57.9 KN for test number 7. The evolution of the lateral displacement calculated at several points along the steel stud of test number 3 (at level of sections N1, N2 and N3) are shown in Figure 3-38 and Figure 3-39. These displacements are compared to the measured ones. Figure 3-40 and Figure 3-41 give similar results for test number 7. It should be noted that in the case of hinged support conditions at both ends, the stud displacements are somewhat sub-estimated in comparison to experimental displacements. Moreover, when the specimen is assumed as fixed at both ends, calculations results agree very well with test results. As example, Figure 3-42 shows the deformed shape of the specimen at the last load step when the steel stud is fixed at one end. Figure 3-43 gives similar results when the steel stud is fixed at both ends. Photograph of the specimen the test number 7 is given in Figure 3-44.

/250

0

10

20

30

40

50

60

0 2 4 6 8 10Displacement (mm)

test DEF1test DEF2test DEF3test DEF4test DEF5test DEF6Calculation N2 (one fixed end)Calculation N1 (one fixed end)Calculation N3 (one fixed end)

Axial load (KN)

Figure 3-38: Lateral displacement of specimen of test n°3 assuming

the steel stud as fixed at one end

0

10

20

30

40

50

60


test DEF1test DEF2test DEF3test DEF4test DEF5test DEF6Calculation N2 (two fixed end)Calculation N1 (two fixed end)Calculation N3 (two fixed end)

Axial load (KN)


the steel stud as fixed at both ends

/250

0

10

20

30

40

50

60


DEF1DEF2DEF3DEF4DEF5DEF6Calculation N1 (onr fixed end)Calculation N2 (onr fixed end)Calculation N3 (onr fixed end)

Axial load (KN)


the steel stud as fixed at one end

0

10

20

30

40

50

60


DEF1DEF2DEF3DEF4DEF5DEF6Calculation N1 (two fixed ends)Calcuationl N2 (two fixed ends)Calculation N3 (two fixed ends)

Axial load (KN)


the steel stud as fixed at both ends

/250

Figure 3-42: Deformed shape of the specimen assumed as fixed at one end

Figure 3-43: Deformed shape of the specimen assumed as fixed at both ends

/250

Figure 3-44: View of specimen after test number 7

3.5.2.3 Parametric study with end restrain and imperfection conditions

One special parametric study was carried out with the computer code ABAQUS to investigate the influence of different end restrain and imperfection condition on tall stud resistance at room temperature. One example is given here in which numerical modelling was compared to one of the tests performed by CORUS with medium section. In the numerical modelling, end steel plates are modelled and connected rigidly with steel stud and end boundary conditions are applied directly to modelled end plates as shown in Figure 3-45. Two different types of boundary conditions were simulated. One fully restrained (FEA_1) and one with restrained rotation about weak axis (FEA_2). In addition to local imperfection obtained from eigenvalue analysis, a global imperfection was taken into account by applying the load eccentric to the structure (see Figure 3-45). The magnitude of the eccentricity was L/1000 corresponding to bending about strong axis. One simulation was made including global imperfection about minor axis (FEA_3) with the same boundary conditions as in FEA_1(see Figure 3-45). As seen from the results, global imperfection about minor axis gives conservative prediction of the stud resistance. By neglecting this, the resistance and the behaviour of the steel stud act more closely to the test result.

/250

End boundary condition Local and global imperfections

Figure 3-45: Modelling features of high studs at room temperature

According to numerical simulation, the failure of the steel stud is dominated by global failure. Compared to the test results the failure mode and compression resistance of numerical simulation FEA_2 corresponds very well (see Figure 3-46). If global imperfection is given about the weak axis (z-axis), the simulated compression resistance of the stud is largely lower than test result. Therefore, the stud buckling occurs more likely about strong axis, which is clearly shown in Figure 3-11. As seen from the test results, and also explained in paragraph 3.4.2.2, the failure load of the section with studs inserted in channel tracks fixed by screws gives a similar compression resistance as the one with idealised end conditions. It is difficult to tell in which way a section is going to fail in reality, however the main area of interest is overall sectional failure rather than the very localised end failures that occurred in the test with channel tracks. Therefore the numerical result gives a good idea about the validity of adopted numerical model.

/250

Compression resistance

Test result (Test number 19 – Chapter 3 with idealised end conditions) 50.9 kN

Test result (Test number 19 – Chapter 3 with studs in channel tracks fixed by screws) 49.6 kN

FE simulation without global imperfection about strong axis (FEA_1) 53.9 kN

FE simulation without global imperfection about strong axis (FEA_2) 47.8 kN

FE simulation with global imperfection about strong axis (FEA_3) 41.0 kN

Table 3-11: Comparison of numerical simulation with tests. The characteristic resistance according to part 1-3 of Eurocode 3 [1] is 46.5 kN with end boundary conditions similar to

FEA_2

Failure mode of the tested steel studs The failure mode of the simulated steel stud (FEA_2)

Figure 3-46: Numerical failure mode governed by distortional buckling of flange but also by

torsional-flexural buckling.

3.5.2.4 Comparison with numerical modelling results

Calculations have been performed dealing with 18 tests performed at room temperature on lightweight steel sections. The results of calculations are summarised in Table 3-12. In this

/250

table, failure load calculated for each specimen is given as function of end restraint conditions (namely two fixed ends or one fixed end other end hinged) and compared to the experimental failure load. The comparison results are also plotted in figure 3-47. Except some tests related to steel studs without plasterboards and steel studs maintained on one side only, the difference between failure loads ascertained numerically and experimentally does not exceed 10% which is fully acceptable considering the various uncertainties inherent to test data such as the actual degree of rotational restrained at the ends of specimens, the real eccentricity of loading or the value of the actual material properties of steel studs. In most tests, difference between calculations and experimental results may be explained on the one hand by some additional eccentricity of loading which appears during the test with the deformations of the specimen and on the other hand by possible additional restraint conditions (against rotation) at both ends (despite bearings or end plates at one end of specimens is assumed to provide hinged supports condition). For steel studs maintained on one side, difference between calculations and test results may be also explained by other restrained displacements with the plasterboard than those used in the model (restraining only the lateral displacement of the steel stud at position of screws). However, results can nevertheless be regarded as satisfactory. So, these comparisons show that the model can simulate appropriately the structural behaviour of lightweight steel sections maintained by plasterboards and provide a good estimation of failure load.

Figure 3-47: Comparison of failure loads between numerical modelling and tests

0

50

100

150

200

250

0 50 100 150 200 250 Test Failure Load kN

Small-CTICM Medium-CTICM Medium-Corus Large-CTICM Large-Corus AWS-Corus

Safe

Unsafe

-10%

+10%

Calculation Failure Load kN

/250

CTICM Calculated failure load

(KN)

Corus Calculated failure load

(KN) Stud N° of test Boards Eccentricity

Measured failure Loads (KN) Hinged

-fixed Fixed-fixed

Hinged-fixed

18 None No 6.1 (*) 8.0 (*)

8 Both sides No 9.9 10.3 10.5 (*)

9 Both sides Yes 7.2 6.7 7.5 (*)

100x50x0.6

10 One side Yes 7.3 6.5 7.0 (*)

19 None No 50.8 (*) 36.6 42.6

3,5 Both sides Yes 54.9 48.5 52.0 58.6

4 Both sides No 74.4 68.8 69.5 78.9

6 One side Yes 44.9 34.0 36.0 50.9

150x57x1.2

7 Both sides Yes 57.9 48.5 52.0 58.6

22 None No 177.0 (*) 160.2 (*)

15 Both sides No 223.0 230.0 (*) 231.0

16 Both sides Yes 168.5 160.8 168.9 179.0

250x80x2.5

17 One side Yes 153.5 136.4 143.7 176.0

20 None No 46.5 (*) (*) 57.9

11 Both sides No 95.1 (*) (*) 96.6

12 Both sides Yes 57.5 (*) (*) 64.7

AWS 150 x 1.2

13 One side Yes 43.2 (*) (*) 50.1

Table 3-12: Comparison of failure loads of test specimens

3.5.2.5 Additional numerical modelling on floor and wall assemblies

Numerical modelling of the Ranilla stud and joint detail was carried out to determine failure loads. The wall system consists of perforated studs and the effect of these perforations on overall load transfer was not known. Two different models were developed – one to determine the stub resistance of a short length of stud and one to model in detail the effect of load introduction through the wall/floor joint detail.

/250

A view of the finite element model for the stub column is given in Figure 3-48. This model consists of a shell element representation of the stud with the effect of perforations explicitly included. The buckling load obtained was 65 kN. A view of the displaced shape and stress state at failure is given in Figure 3-49. The buckling load is consistent with the obtained load in the wall panel test which was 74.8kN. The model developed to study the effect of load introduction through a realistic floor/wall joint is given in Figure 3-50 and a close up of the joint detail is given in Figure 3-51. The final deformed shape and stress state at failure is given in Figure 3-52. The ultimate failure load obtained was 45 kN. This was the load in excess of the applied floor load contribution of 3.8 kN. The total stud load of 48.8kN is far less than the 74.8 kN obtained in the test. This is probably due to the conservative modelling assumptions made about points of contact along the stiffener detail and from the end channel and the end of the stud.

Figure 3-48: Finite element model of stub column test

/250

Figure 3-49: Final deformed shape and stress state of column stub model

Figure 3-50: Finite element model of stud/floor assembly

/250

Figure 3-51: Detail of finite element model – joint area

Figure 3-52: Deformed shape and stress state at failure

3.6 COMPARISON OF TEST RESULTS WITH SIMPLE CALCULATION RULES

Design of cold formed steel sections is carried out in part 1-3 of Eurocode 3 [1]. The general procedure to calculate the resistance, according to Eurocode, of a cold formed lipped C-

/250

section steel strut which is restrained by plasterboard on both sides about its minor axis in axial compression and combined axial compression and bending moment at the ultimate limit state is as follows (Table and section references refer to final draft of Eurocode 3 [1]): 1. Choose basic yield strength and ultimate tensile strength from Table 3-1 depending on

type of steel 2. Check that sections conform with thickness limitations for code (section 3.1.3) 3. Calculate net area of section by deducting area of holes, etc (section 3.3.3) 4. Calculate dimensions of section by allowing for the effect of rounded corners (section

3.3.4) 5. Check geometrical proportions to check for validity of design calculations (section 3.4) 6. Choose modelling strategy for individual elements of section from Table 3-3 under pure

compression and pure bending. 7. Calculate effective area of section taking into account the effects of local buckling on

each element of section (section 4) 8. Calculate resistance of cross-section under relevant sectional forces (section 5)

a. Axial compression (section 5.3) b. Bending moment (section 5.4) c. Calculate buckling resistance of member under axial compression (section 6.2)

including checks on: d. Flexural buckling e. Torsional buckling and torsional flexural buckling

9. Calculate combined resistance of section under combined axial compression and bending moment (section 6.5) noting that bending moment is equal to eccentricity applied axial load.

It should be noted that perforated sections, such as the AWS and TC150 section, are not within the scope of either code. In these cases, designers must refer to the relevant manufacturer to obtain design information on the section concerned. Therefore, comparisons have only been made for lipped C sections. The results of the stub column tests can be compared with the calculated value of effective area of the cross-section (step 7). The results of the test and calculated values to the Eurocode are given in Table 3-13. The comparisons of the test results for the double stud tests with the calculated values from the design codes are given in Tables 3-14 to 3-17. The AWS section results are also included for completeness. In terms of performance, the AWS section is closest to the medium lipped C section having flange widths and thicknesses closest to this section.

/250


(100x50x0.6) Medium

(150x57x1.2) Large

(250x80x2.5)AWS

(150x1.2)280 Mpa 350 MPa 350 MPa 350 MPa Centric Eccentric

(0.25h) No perf. Perf.

8.6 kN 7.5 kN

59.6kN 54.9 kN

195.5 kN 216.3 kN - √ √

- - - 74.1 kN √ √ Key: 6.1 kN = Test Result 4.0 kN = EN 1993-1-3 Design Value

Table 3-13: Comparison with design rules for stub column test results


(100x50x0.6) Medium

(150x57x1.2) Large

(250x80x2.5)AWS

(150x1.2) 280 Mpa 350 MPa 350 MPa 350 MPa Centric Eccentric

(0.25h) No perf. Perf.

6.1 kN 3.6 kN

50.8 kN 28.3 kN

177.0 kN 196.3 kN - √ √

- - - 46.5 kN √ √ - - - 48.6 kN √ √

Key: 6.1 kN = Test Result 4.0 kN = EN 1993-1-3 Design Value

Table 3-14: Comparison with design rules for tall stud test results

Size and grade of sections Testing conditions Loading Section type Medium

(150x57x1.2) EN1993-1-3

350 MPa Eccentric (0.25 h) Boundary conditions

36.6 kN 31.0 kN √ Studs simply inserted in channel tracks 49.6 kN 32.2 kN √ Studs in channel tracks fixed by screws54.9 kN 32.2 kN √ One end fixed/one end pinned

Table 3-15: Comparison with design rules for boundary condition test results


Loading Section typeSmall (100x50x0.6)

Medium (150x57x1.2)

Large (250x80x2.5)

AWS (150x 1.2)

280 Mpa 350 MPa 350MPa 350 Mpa

Centric Eccentric (0.25 h)

No perf. Perf.

9.9 kN 6.4 kN

74.4 kN 51.9 kN

223.0 kN 217.0 kN - √ √

- - - 95.1 kN √ √ 7.2 kN 4.1 kN

54.9 kN 32.2 kN

168.5 kN 134.5 kN - √ √

- - - 57.5 kN √ √ Key: 6.1kN = Test Result 4.0kN = EN1993-1-3 Design Value

Table 3-16: Comparison with design rules for load eccentricity test results

/250


Loading Section typeSmall (100x50x0.6)

Medium (150x57x1.2)

Large (250x80x2.5)

AWS (150x 1.2)

280 Mpa 350 MPa 350 MPa 350 Mpa Centric Eccentric

(0.25 h) No

perf. Perf.

- 57.9 kN 32.2 kN - - √ √

- - - 70.0 kN √ √ Key: 6.1kN = Test Result 4.0kN = EN1993-1-3 Design Value

Table 3-17: Comparison with design rules for test results with additional steel sheet

Figure 3-53: Comparison of test and design failure loads

Figure 3-51 plots the design values against the test values. Design values for the Eurocode are higher than the obtained loads for the larger 250 mm specimen for both the stub and tall stud tests but are acceptable for the more practical cases where the sections are supported by plasterboard. For all other sections design rules are acceptably conservative.

3.7 CONCLUSIONS

• Overall mechanical behaviour at room temperature can be said to be consistent with experimental results exhibiting the expected trends in terms of differences of load eccentricity and levels of support from the plasterboard on overall failure loads.

• The wall and floor assembly tests demonstrated that there is not much effect of load eccentricity through practical connection details with the local squash capacity of the section governing overall failure loads.

0

50

100

150

200

250

0 50 100 150 200 250 Test Failure Load kN

Design Failure Load kN

Small

Medium Safe

Unsafe

-10%

+10%

Large

/250

• Advanced calculation models have been shown to predict failure loads within acceptable limits for the most practical cases of studs supported by plasterboards and can therefore be safely used in parametric studies.

• Design values for most of the sections tested are conservative but acceptable under the Eurocode.

/250

4. MECHANICAL BEHAVIOUR OF INDEPENDENT LIGHTWEIGHT STEEL MEMBERS ENGULFED IN FIRE

4.1 GENERAL

The work reported in this chapter was focused on both experimental and numerical analysis of the mechanical behaviour of isolated lightweight steel members engulfed in fire. The experimental work was carried out by VTT and CTICM. In addition, the numerical simulations were performed by CTICM and SBI for the purpose of developing and validating a simple calculation model for this specific situation of lightweight steel members. The experimental work comprised fire tests on five different lightweight steel sections to study the axial resistance capacity against local buckling of the short stub columns at elevated temperatures. These tests on short stub columns (L = 600 mm or 1000 mm) were with centric loading kept constant during the test and with temperature increased nearly linearly as a function of time. For some sections fire tests were performed also on tall studs (L = 3500 mm) to study global buckling behaviour of isolated lightweight steel members. The steel sections were of two different steel grades, S 350 GD + Z and S 280 GD + Z. The tests on short stub columns were performed at VTT and the tests on tall studs at CTICM. Numerical analyses have been performed for both short stub column and tall stud tests with different computer codes. Once the numerical modelling validated against experimental results, the numerical parametric study has been made to check the validity of the simple calculation models and to develop design rules for isolated lightweight steel members under compression at elevated temperatures.

4.2 EXPERIMENTAL WORK

4.2.1 Tests on short stub columns

4.2.1.1 Testing methodology

Fire tests on the short stub columns were carried out in the model furnace (1.5x1.5x1.5 m3) of the fire-testing laboratory of VTT, Espoo, Finland. Altogether nine tests were performed [31, 32]. Test specimens were short stub columns of five types of lightweight steel sections supplied by Corus (UK), Rautaruukki Oy (Finland) and Lafarge (France). The steel sections were of two different steel grades and the specimens were of two different lengths. Basic characteristics of the specimens are given in Table 4-1.

Section Steel grade Supplier Length [mm] Small (C1); C 98-51/49-6/0.6 280 MPa Lafarge 600 Medium (C2); C 150-57-13/1.2 350 MPa Corus 600 Large (C3); C 250-80-21.5/2.5 350 MPa Rautaruukki Oy 1000 AWS 150/1.2 350 MPa Rautaruukki Oy 1000 TC 150/1.2 350 MPa Rautaruukki Oy 600

Table 4-1: Short stub column specimens

/250

Section C1 was provided with service holes with a diameter of 31.8 mm and a spacing of 500 mm. The thickness of the zinc coating was 20 µm, measured by VTT. Section C2 was manufactured from pre-hot dipped galvanised steel to BS EN 10147 grade S350 GD + Z coating G274. The thickness of the coating was 22.5 µm. The zinc coating in sections C3, AWS 150 and TC 150 is 275 g/m2, which corresponds to a thickness of 20 µm. The influence of the service holes was also studied with section C2 that was tested both without a hole and with a hole (Ø 35.2 mm) at mid-height of the specimen. Sections AWS 150 and TC 150 are perforated. The specimens were tested with external centric load (NTest,fi) applied about 30 minutes before the starting of fire test and kept constant during the test. The load in tests 0 and 5 was applied by weights and in the other tests by a hydraulic jack controlled manually during the test. The test load was determined on the basis of the cross-sectional resistance of the sections determined at normal temperature (NTest.ref). The applied load levels were 0.07, 0.2, 0.4 and 0.6 for the C2 sections (Medium) and 0.4 for the others. Both ends of the specimens were free to rotate about strong axis but restrained to rotate about weak axis (see Figure 4-2). At the beginning of the tests the furnace temperature reached 200°C in about 5 minutes and after that the heating rate was about 10°C/min. Perforated steel sheets surrounded the specimen to prevent the flames from the burners impinging the specimen and to ensure a uniform temperature distribution around the specimen. The diameter of the surrounding shield was about 500 mm. During the fire tests the temperatures of the specimen were measured at three heights of the specimens. The furnace temperature was measured at the same levels with twelve thermocouples (K-type Ø 3 mm stainless steel sheathed) on four sides of the specimen 100 mm from the surface of the specimen. The change of the length of the specimen was measured as vertical displacement of the top of the water-cooled steel unit above the specimen. The tests were conducted until the failure of the specimen. The test programme is presented in Table 4-2. The test arrangement is presented in Figure 4-1 and 4-2, a photograph of a specimen in the furnace before fire testing in Figure 4-6 and the location of the measuring points in the C-sections in Figure 4-3. Photographs of the test specimens after the fire tests are shown in Figures 4-7 to 4-9.

/250

Burners

1300

FA - A

1500 300300

2100

Steelstud

600 or1000

Water-cooled steelunit

1500

15001000

A A

Burners 1 and 2

Burners 3 and 4

Steel mesharound thestud

Steelmesh

Burners 1 and 4 were used in the tests.

Figure 4-1: Test arrangement in the furnace; horizontal and vertical sections.

Steel

30

30

Steel

6

Steel bar as a

Steel

Groov

Steel

Steel bar as a

Loading

GroovAA

A -

Figure 4-2: Support conditions of the steel stud.

/250

Figure 4-3: Position of the measuring points C-sections

x

xx

xx

x

16

140 or 340

140 or 340

B

AA

3 1 2

6 54

89 7

16 14

18 20

22 24

B B

B

16

x

xx

xx

x

16

140 or 340

140 or 340

B

AA

3 1 2

6 54

89 7

16 14

18 20

22 24

x

xx

xx

x

3,2

9,8

6,5

131

7

4

15

21

17

23

19

B B

B x

x

2,5,8 14,18,22 16,20,24

15,19,23

100

100

13,17,21

xx

3,6,9

A - A

1,4,7

16

x

xx

xx

x

16

140 or 340

140 or 340

B

AA

3 1 2

6 54

89 7

16 14

18 20

22 24

x

xx

xx

x

3,2

9,8

6,5

131

7

4

15

21

17

23

19

B - B

B

temperature measurement points 1-9 in the stud x temperature measurement points 13-24 in the furnace measurement point for axial contraction

/250

4.2.1.2 Test results

The test results are summarized in Table 4-2. Test time (min) given in the table is the failure time of the specimen. The criteria for the failure time are the ability of the section to carry the test load. In the table also the temperature of the specimen at the failure time is given. As an example, furnace and specimen temperatures measured at different levels in Test 3 are presented in Figures 4-4 and 4-5. Photographs of the specimens after the fire tests are in Figures 4-6 to 4-9.

Fire test Stud Length (mm)

NTest.ref.

(kN)

NTest,fi (load level)

(kN)

Max temperature

of failure (oC)

Test time(min)

Test 0 20.2.2002 C 150-57-13/1.2 600 59.6 3.9 (0.07) 1082 94.4

Test 1 25.2.2002 C 150-57-13/1.2 600 59.6 35.8 (0.6) 408 26.7

Test 2 27.2.2002 C 150-57-13/1.2 600 59.6 11.9 (0.2) 680 53.0

Test 3 1.3.2002 C 150-57-13/1.2 600 59.6 23.8 (0.4) 531 39.0

Test 4 5.3.2002

C 150-57-13/1.2 with service hole 600 67.4 23.8 (0.4) 534 37.8

Test 5 7.3.2002 C 100-50-6/0.6 600 8.6 3.3 (0.4) 491 32.8

Test 6 19.3.2002 AWS 150/1.2 1000 74.1 29.6 (0.4) 638 47.0

Test 7 22.3.2002 C 250-80-22/2.5 1000 195.5 78.2 (0.4) 618 43.7

Test 8 7.3.2003 TC 150-1.2 600 41.5 16.6 (0.4) 630 48.0

Table 4-2: The results of short stub column tests performed at room temperature and at elevated temperatures

050

100150200250300350400450500550600650700

0 10 20 30 40 50 60TIME (min)

TEM

PER

ATU

RE

( oC

)

Average 13-16Average 17-20Average 21-24

Figure 4-4: Average temperature of the furnace in Test 3

/250

050

100150200250300350400450500550600650700

0 10 20 30 40 50 60TIME (min)

TEM

PER

ATU

RE

( oC

)

Average 1-3Average 4-6

Average 7-9

Figure 4-5: Specimen temperatures at different levels in Test 3

Figure 4-6: Mounting of the specimen (AWS–section)

/250

Figure 4-7: Test specimens 1–4 after the fire tests

Figure 4-8: Test specimens 4–7 after the fire tests

/250

Figure 4-9: Test specimen 8 after fire test

4.2.1.3 Summary of test results

The axial resistance of five cold-formed lightweight steel sections (C 100, C2 150, C3 250, AWS 150 and TC 150) was determined with tests on short stub columns (L = 600 mm or 1000 mm) both at room and at elevated temperatures. The fire tests were performed with different load levels. The load level for section C 150 were 0.07, 0.2, 0.4 and 0.6 and for the others 0.4. The cross sectional resistance NTest,ref determined at room temperature was used to set the test loads in fire tests. The dependence of the failure temperature on the load level (NTest,fi/NTest,ref) is shown in Figure 4-10. Load level 1 corresponds the axial resistance at ambient temperature (NTest,ref). Load level being 0.4 the failure temperatures were 491 oC for section C 100, 534 oC and 531 oC for sections C2 150 (one without a hole and one with a hole), 618 oC for section C3 250 and 638 oC for AWS 150 section and 630 oC for TC 150 section. The dependence of the strain on the steel temperature is shown in Figure 4-11.

/250

0.0

0.2

0.4

0.6

0.8

1.0

0 200 400 600 800 1000 1200TEMPERATURE ( oC)

LOAD

LEV

EL

C150 C100 AWS C250 TC150

Figure 4-10: Failure load level (NTest.fi / NTest.ref) as a function of the temperature for different steel sections (Load level 1.0 corresponds to reference load Ntest.ref)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

0 200 400 600 800 1000 1200TEMPERATURE ( oC)

STR

AIN

C150/4 C150/0 C150/2 C150/6 C150h/4C100/4 AWS150/4 C250/4 TC150/4

Figure 4-11: Strain (∆L/L) as a function of temperature for different steel sections and load levels

* No failure at load level 0.07

*

/250

4.2.2 Test on tall studs

4.2.2.1 Testing methodology

Fire tests on tall studs fully engulfed in fire were performed at CTICM. Altogether six tests were performed. The specimens were 3500 mm tall steel studs of three different types of lightweight steel sections designated as Medium, Large and AWS. The basic characteristics of the steel sections are given in paragraph 4.2.1.1. In the fire tests, all specimens were subjected to an axial load, which were applied before the test and kept constant until failure. Some specimens were tested with eccentric load. At room temperature, the specimens were considered as hinged at one end and restrained against rotation at the other end about the strong axis. All rotations about weak axis at both ends of studs are assumed to be restrained. The boundary condition in AWS section stud test is presented in Figure 4-12. During all the tests, the furnace temperature was continuously recorded. In order to determine the temperature field in the steel studs, thermocouples were installed on the steel studs (both flanges and web) at four different levels N1, N2, N3 and N4 along the specimen length. The positions of thermocouples are shown in Figure 4-13 for the C-sections and in Figure 4-14 for the AWS section. Lateral and longitudinal displacements of the specimens were recorded during the tests. The location of the displacement measurements for the AWS section is presented in Figure 4-15.

180

3105

125

Jack

Applied load: 18 kN Axial load without eccentricity

Figure 4-12: Boundary condition of AWS section stud test

/250

N4

N2

N1

570

775

775

Thermocouple

A

B

C

775

605

N3

Figure 4-13: Location of the temperature measurement points in the C-sections

N4

N2

N1

570

775

775

Thermocouple

775

605

N3

A

B

C

D

E

Figure 4-14: Location of the temperature measurement points AWS section

/250

875

875

D4

875

875

D9

D3

D1

D2

D5

D6

D10

D8 D9

D1, D2, D3 D7

D10

D4, D5, D6

D7

Figure 4-15: Location of the displacement measurement points in AWS section The test program is presented in Table 4-3.

4.2.2.2 Test results

The failure time measured during the tests, which are reported in Table 4-3, corresponds to the condition when each specimen (steel stud) could not carry the applied load any more.

Loading condition Test Stud Length

(mm) Load (kN) Ecc.

(mm)

Maximum Temp. (°C)

Test time (min)

03-S-373 medium 3500 15 37.5 257.0 18.0

03-S-357 medium 3500 25 0 245.0 23.0

03-S-369 medium 3500 15 0 500.0 28.5

03-S-316 large 3500 60 0 565.0 57.0

03-S-348 large 3500 60 0 540.0 51.0

03-S-379 AWS 3500 18 0 529.0 35.0

Table 4-3: Summary of fire tests on tall studs As an example, temperatures measured at different levels in the test on the AWS section are presented in Figures 4-16 to 4-19, lateral displacements measured along strong axis and along weak axis of AWS section in Figures 4-20 and 4-21 and vertical displacement in Figure 4-22. The actual applied load during the test is presented in Figure 4-23.

/250

Some specimens after the tests are shown in Figures 4-24 to 4-26 in order to give an idea about the failure mode of these studs.

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30 35 40Time (min)

Tem

pera

ture

(°C

)

Point A Point BPoint C Point DPoint E

Figure 4-16: Temperatures measured on section N1 versus time in the test on AWS section

0

100

200

300

400

500

0 5 10 15 20 25 30 35 40Time (min)

Tem

pera

ture

(°C

)

Point A Point B

Point C Point E


/250

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40Time (min)

Tem

pera

ture

(°C

)

Point A Point B

Point C Point E


0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40Time (min)

Tem

pera

ture

(°C

)

Point A Point BPoint C Point DPoint E


/250

-50

-40

-30

-20

-10

0

10

20

0 5 10 15 20 25 30 35 40Time (min)

Dis

plac

emen

t (m

m)

D1

D2

D10

Figure 4-20: Lateral displacements measured along strong axis versus time

in the test on AWS section

-50

0

50

100

150

200

0 5 10 15 20 25 30 35 40Time (min)

Dis

plac

emen

t (m

m)

D4 D5 D6

D8 D9

Figure 4-21: Lateral displacements measured along weak axis versus time in the test on

AWS section

/250

-20

0

20

40

60

80

0 5 10 15 20 25 30 35 40Time (min)

Dis

plac

emen

t (m

m)

D7

Figure 4-22: Measured vertical displacement versus time in the test on AWS section

0

4

8

12

16

20

0 5 10 15 20 25 30 35 40Time (min)

Dis

plac

emen

t (m

m)

Applied axial force

Figure 4-23: Measured applied force versus time in the test on AWS section

/250

Figure 4-24: C-sections specimens after the fire tests (C 250)

Figure 4-25: C-sections specimens after the fire tests (C 250)

/250

Figure 4-26: AWS-section specimen after the fire test

4.2.2.3 Comparison between the results of tests on short and tall columns

The failure temperatures of the steel sections C 150, C 250 and AWS 150 in funcion of the load level in the tests on short (600 mm and 1000 mm) and tall (3500 mm) columns are presented in Figure 4.27. For C 150 section the failure temperature of the tall columns is

/250

100-200 oC lower than that of the short columns with load levels 0.2 - 0.6. For C250 and AWS 150 sections the corresponding difference is about 100 oC with a load level of about 0.4,

0

100

200

300

400

500

600

700

800

0.0 0.2 0.4 0.6 0.8 1.0

LOAD LEVEL

C150s C150t AWSs AWSt C250s C250t Figure 4-27: Failure temperatures of different steel sections in function of load level in fire

tests on short short and tall columns

4.3 NUMERICAL SIMULATIONS OF FIRE TESTS

4.3.1 General

Numerical studies of the mechanical behaviour of isolateted lightweight steel sections engulfed in fire were performed by both SBI and CTICM. The numerical simulations have been made based on the fire tests carried out at CTICM and VTT to validate the calculation model. Tests were performed on short (600 or 1000 mm) stub columns and tall (3500 mm) studs under constant load during the fire test. Also numerical simulations at room temperatures were made in order to validate numerical model. One of the purposes of the simulations was to validate the proposed reduction factors for steel at elevated temperatures agreed in Chapter 2. The tests made on stub columns (600 or 1000 mm) at VTT at both room and elevated temperatures were used to verify the validity of these reduction factors through numerical simulations. This paragraph also gives a proposal of a simple calculation method based on parametric studies of isolated steel studs engulfed in fire with and without temperature gradient.

s = short column, t = tall

/250

4.3.2 Numerical modelling of stub column tests

4.3.2.1 Description of numerical modelling

Four different types of steel sections have been evaluated which are referred here as small, medium, large and AWS sections. The types as well as the dimensions of these sections have already been illustrated in detail in previous paragraphs. The geometric data used in the numerical modelling of elevated temperature tests is from both measured values on test specimens and also nominal values. The web-heights, flange-widths and the edge stiffeners length are taken as nominal values. The thickness of the profiles and the radius of the rounded corners are taken as the measured values. All these values are indicated respectively in Tables 4-4 and 4-5. In all stub column tests the load was applied centric to the steel section as shown in Figure 4-3.

Element Small section Medium section Large section AWS section

Length (l) 600 600 1000 1000

Web height (h) 100 150 250 20 + 110 + 20

Flange width (b) 50 57 80 40 + 50

Edge stiffener length (c) 6 13 21.5 15.5

Inner radius (r) 1.8 1.2 4.5 3.2

Thickness (t) 0.6 1.2 2.5 1.2

Table 4-4: Geometric data for the tested stub columns - nominal values (mm)

Element Small section Medium section Large section AWS section

Inner radius (r) 2.25 6 4.5 3.5

Core thickness (tcore) 0.56 1.155 2.41 1.145

Table 4-5: Measured geometric data for core thickness and corner radius used in the numerical calculations (mm)

The details of numerical modelling have been fully explained in paragraph 3.5.1. The material model used at elevated temperatures in the numerical calculations are based on the material model given in part 1-2 of Eurocode 3 [2], also explained in paragraph 2.6.2, with the yield strength and ultimate tensile strength presented in Table 2-2c, based on tensile tests performed by VTT for the tested specimens. The reduction factors used in the material model were taken as the proposed values from paragraph 2.6.3 (see Table 2-9 for Type A steel from small section and Table 2-10 for Type B steel from medium, large as well as AWS section). Conversely, in order to fully characterise the material model at room temperature, the stress-strain relationship for each investigated steels was taken as the tensile test results at room temperature explained in paragraph 2.4.1.

/250

In order to investigate the validity of the reduction factors derived from tests, they are directly included into the material model to simulate the material behaviour at elevated temperatures of the specimens. The thermal elongation was taken as the temperature dependent coefficient given in part 1-2 of Eurocode 3 [2] (see also Figure 2-12).

4.3.2.2 Numerical results

The stub column tests of C-type cross section at elevated temperatures made by VTT was analysed with computer code ABAQUS. The temperature evolution in the steel stud was measured during the tests at several points as shown in Figure 4-28. The temperatures used in the numerical modelling were taken as the average value along and also across the section. One example is shown in Figure 4-28 for the medium section. Since the thermocouples in the tests stop recording the temperature evolution in the steel stud when the experiment stops the temperature evolution must be extended in order to simulate the extension of the temperature curve. This was done in the numerical modelling by extrapolation of the temperature curve from the tests.

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120

Time [min]

Temperature [°C]

Load level 0.2Load level 0.4Load level 0.6Load level 0.07

Figure 4-28: Temperature evolution in numerical modelling for medium section with load

levels 0.07, 0.02, 0.4 and 0.6 The results are shown in Figure 4-29. As seen from the comparison between numerical calculations and test results, the agreement is fully satisfactory since the relative difference of critical temperature is within 10% for all sections.

/250

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700 800

Temperature FEA (°C)

Temperature tests (°C)

SmallReference(+)10%(-)10%MediumLarge

Figure 4-29: Comparison of failure temperatures for the different tested steel studs with

numerical calculations

4.3.2.3 Evaluation of proposed reduction factors

A parametric study was performed to investigate the proposed reduction factors for Type A steel and Type B steel, also explained in Chapter 2. In fact, this study can give an idea about the value to be used to calculate the design buckling resistance at elevated temperatures for lightweight steel members. A comparison was made between different reduction factors given in part 1-2 of Eurocode 3 [2] and within this report. The numerical calculations were made with the proposed material model explained in Chapter 2. The ultimate resistance equivalent to corresponding temperature is normalised to room temperature resistance. In this way the appropriate reduction factor for simple calculation was evaluated. The failure of the steel stud depends on local buckling, which means that Nu = Aeff fy. The results (see Tables 4-6 and 4-7) show that there is a good agreement by using the 0.2% proof strength for Type A steel and Type B steel respectively to calculate compression resistance considering local buckling. However, it can be seen that the reduction factor for 0.2% proof strength given in part 1-2 of Eurocode 3 is systematically higher, in particular for small section (Type A steel). Considering the good agreement between proposed reduction factors in this project and test results, it is therefore necessary to modify actual values of Eurocode for this parameter.

/250

Temperature 2.0 % - Chapter 2

0.2 % - Chapter 2

2.0 % - EC3

0.2 % - EC3

Numerical calculation (Small section)

20 1.000 1.000 1.000 1.00 1.00

200 1.000 0.849 1.000 0.89 0.88

400 0.560 0.310 1.000 0.65 0.35

600 0.200 0.110 0.470 0.30 0.13

800 0.060 0.042 0.110 0.07 0.05

1000 0.027 0.023 0.040 0.03 0.03

Table 4-6: Comparison between different reduction factors and numerical calculations on small section (Type A steel)

Temperature

2.0 % - Chapter 2

0.2 % - Chapter 2

2.0 % - EC3

0.2 % - EC3

Numerical calculation (Medium section)

Numerical calculation

(Large section)

20 1.000 1.000 1.000 1.00 1.00 1.00

200 1.000 0.896 1.000 0.89 0.88 0.85

400 0.890 0.616 1.000 0.65 0.57 0.54

600 0.340 0.229 0.470 0.30 0.21 0.20

800 0.070 0.049 0.110 0.07 0.05 0.05

1000 0.0035 0.025 0.040 0.03 0.03 0.02

Table 4-7: Comparison between different reduction factors and numerical calculations on medium and large sections (Type B steel)

4.3.3 Numerical modelling of high studs engulfed in fire

4.3.3.1 Elevated temperature simulations with C-type section tall studs

The numerical simulations of the mechanical behaviour of unbraced steel studs engulfed in fire were made with the computer code ANSYS. The following assumptions were used:

• The whole steel stud is modelled with shell element (see Figure 4-30)

• Steel studs are hinged at both ends about strong axis of the stud and subjected to a constant load during the fire (figure 4-30). Moreover, both ends of steel stud are modelled using a stiffer material (corresponding to blue colour element) with the value of modulus of elasticity taken as 210×105 MPa

/250

Free end

Free end



Steel stud

Rigid part

Steel stud

Rigid part


• Initial imperfection obtained from eigenvalue buckling analysis is used in numerical simulations. It consists of sinusoidal waves in the web with maximum amplitude of 1 mm.

• The mechanical materials properties have been taken to be in accordance with the proposed reduction factor for steel of both non load and load bearing members (see Chapter 2), with the mechanical properties at room temperature given in Table 2-2b

• The axial load is applied as a surface load as shown in figure 3-37. The load application direction (parallel to length of the stud) is kept constant whatever the stud end rotation is

• A temperature gradient along the length of the steel studs shown in Figure 5-31 is taken into account, which is based on temperature measurement from 4 sections N1, N2, N3 and N4 with a linear variation of temperatures between two successive sections and a uniform temperature distribution between N1, N2 and their corresponding stud ends

• Concerning the temperature distribution on cross section, the temperature is constant in each of two flanges, and varies linearly from one flange to the centre of the web, then linearly again from the centre of the web to the other flange (see figure 5-32).

The numerical simulations have been performed on 5 fire tests carried out at CTICM. One example of these calculations is given in figure 4-31 and the results of all calculations are summarised in Table 4-8, in which the critical temperature calculated for each specimen is compared with the experimental maximum temperature at failure time. It can be found that the agreement between calculation and test is generally very satisfactory except one test which can be explained by the fact that the real temperature gradient could be different from that used in numerical modelling.

/250

-10

0

10

20

30

40

50

60

70

0 5 10 15 20 25

test D4test D5test D6test D8test D9Simulation (two free ends)

Time (min)

Lateral displacement (mm)

Dx

Figure 4-31: Comparison of lateral displacement of steel stud about weak axis between

numerical simulation and fire test

Loading condition Test Stud Length

(mm) Load (kN)

Eccentricity(mm)

Maximum test

temperature (°C)

Calculated critical

temperature(min)

Stud 1 medium 3500 15 37.5 257.0 467.0

Stud 2 medium 3500 25 0 245.0 230.0

Stud 3 medium 3500 15 0 500.0 541.0

Stud 4 large 3500 60 0 565.0 550.0

Stud 5 large 3500 60 0 540.0 550.0

Table 4-8: Comparison of failure temperature of studs engulfed in fire between numerical calculation and fire test

As a whole, the agreement between numerical modelling and tests can be considered as fully satisfactory and it is convenient to develop simple calculation model based on results obtained by means of numerical modelling.

4.3.3.2 Numerical modelling of AWS-type cross section tall studs

The AWS section is a special section stud, so it is exclusively dealt within this paragraph. The basic geometry of the simulated AWS section is based on the nominal dimensions of the specimen tested at CTICM and is shown in Table 4-9 and Figure 4-32. Figure 4-33 shows two pictures of the modelled stud.

/250

Length of the stud 3500 mm

Web height 20 + 110 + 20 mm

Flange width 40 + 50 mm

Edge fold 15.5 mm

Thickness used in numerical modelling (without zinc) 1.145 mm

Thickness (nominal) 1.2 mm

Table 4-9: Basic nominal geometry for the AWS section

Figure 4-32: Basic nominal geometry of the tested AWS section

In direction of the tested specimen the right end in the figure corresponds to the top and is named End_1. The left end corresponds to the bottom and is named End_2

Figure 4-33: Modelled AWS steel stud

Numerical modelling of AWS-type section tall stud The model for AWS-type section tall stud consists of three different parts joined together to function as a whole structure. The different parts modelled are two endplates attached to the

/250

ends of one section. The section was structurally modelled as one part and the endplates was structurally modelled as one part. The steel stud was analysed with two different end boundary conditions. The displacement constraints and the rotational constraints used for the two different models are described in Table 4-10 and shown in Figure 4-34. Figure 4-36 shows the axis convention. Table 4-10 shows the degrees of freedom as they are referred to in Table 4-11. Convention Degrees of freedom Comment U1 x-displacement Displacement in direction 1 U2 y-displacement Displacement in direction 2 U3 z-displacement Displacement in direction 3 UR1 Rotation about the x-axis Rotation about axis 1 UR2 Rotation about the y-axis Rotation about axis 2 UR3 Rotation about the z-axis Rotation about axis 3

Table 4-10: Symbols used for applying boundary conditions Numerical

model Boundary condition at support – End_1 Boundary condition where the load is

applied – End_2

FEA_1 U1=0, U2=0, U3=0 UR1=0, UR2=0, UR3=0

U1=0, U2=0 UR2=0, UR3=0

FEA_2 U1=0, U2=0, U3=0 UR2=0, UR3=0

U1=0, U2=0 UR2=0, UR3=0

Table 4-11: End boundary conditions for the different numerical models

The load was applied at the reference point at End_2 (Figure 4-35). The load applied was similar to the load in the test (18 kN).

Figure 4-34: The endplate and the section was connected with the keyword TIE

Figure 4-35: The load and the end boundary conditions were applied at the reference point at each end of the stud

The steel section part was modelled with a 4-node shell element - S4R. The average element size was 6 mm. The end plates were modelled with rigid elements corresponding to a reference point where the load and boundary conditions was applied. The modelled steel stud was connected to the endplate using the keyword TIE in ABAQUS/Standard. This is suitable when joining parts together that may have different element types, mesh densities, etc. but the corresponding degrees of freedom at the boundary of each part can be equal.

/250

To resemble the test conditions for the end of the steel stud and to apply the load into the steel stud correctly a 87 mm long part of the stud’s ends where modelled using a thickness of 10 mm. The material properties for this part were taken with room temperature properties, but with a thermal expansion according to part 1.2 of Eurocode 3 [2]. Local imperfections were introduced by a perturbation in the geometry. In the numerical simulations the buckling mode shape was multiplied with a magnitude of b/200, where b is the width of the widest plate in the section. Global imperfection was introduced to the model by assuming an eccentric loading to the structure. The magnitude of the eccentricity was taken as L/1000 (see Figure 4-36). The yield strength and Young’s modulus used in the numerical simulation were based on the data given in Chapter 2 (see Table 2-4). The material properties at elevated temperatures were calculated with the material model presented in part 1.2 of Eurocode 3 [2] with theyield strength and Young’s modulus reduced at elevated temperatures with the proposed reduction factors proposed in Chapter 2 for Type B steel. The value of Young’s modulus was taken as 210000 MPa. The coefficient of thermal expansion was taken according to 1.2 of Eurocode 3 [2] for all the elements except the rigid endplates. The temperature evolution in the numerical model was applied at four different levels on the stud. The temperatures were taken as the mean value from different levels recorded in the test. The four different levels are illustrated in Figure 4-14. The mean value of the temperature was calculated from the five points A - E, at the layers N1, N2, N3 and N4, see Figure 4-38. The temperature curve used in the numerical simulations was also extended to a time beyond the failure time for the test. This has to be done because the temperature record from the test stops when failure of the steel stud occurs, in this case approximately after 29 minutes. From that point the temperature evolution was extended linearly to 55 minutes. The temperature variation across the section in the numerical simulation was neglected.

Figure 4-36: Basic geometry showing mesh

and axis convention Figure 4-37: Local buckling mode shape

used for local initial imperfections

/250

Average temperature evolution in AWS section at different levelsCTICM tall column test

0100

200300400

500600700

800900

0 10 20 30 40 50 60

Time [min]

Temperature [°C]

N1N2N3N4

Figure 4-38: Temperature evolution at different levels used in the numerical simulation

Experimental results versus numerical simulations The result from the numerical simulations shows a good agreement with the test particularly the numerical model FEA_1. The failure temperature recorded in the test is compared with the two simulations with different end boundary conditions in Table 4-12.

Maximum failure temperature (°C)1

Numerical modelling/(CTICM test)

CTICM test 529

FEA_1 501 0.95

FEA_2 479 0.91

Table 4-12: Summary of failure temperatures from test and numerical simulations The displacements recorded in the numerical simulations are compared to the test and one example is shown in Figures 4-39 and 4-40. In some cases it can be difficult to compare the results because the very small displacements. But it seems to correspond well with the test if the difference in the failure time is taken into account.

/250

Figure 4-39: Lateral displacement along strong axis versus time for numerical model FEA_1

compared to test results

Figure 4-40: Lateral displacement along strong axis versus time for numerical model FEA_2

compared to test results

Lateral displacement - strong axis

-120

-100

-80

-60

-40

-20

0

20

40

0 10 20 30 40 50 Time [min]

Displacement [mm]

Test - D1Test - D2Test - D3D1 D2 D3

Lateral displacement - strong axis

-120

-100

-80

-60

-40

-20

0

20

40

0 5 10 15 20 25 30 35 40 Time [min]

Displacement [mm]

Test - D1Test - D2Test - D3D1 D2 D3

/250

4.4 DEVELOPMENT OF SIMPLE CALCULATION MODEL

4.4.1 General

The simple calculation model presented in this section gives a design proposal for isolated lightweight steel members and is proposed for two design situations:

• Uniform temperature distribution over the section, • Non-uniform temperature distribution over the section with a thermal gradient taken

into account by considering a thermal bow. The temperature distribution along the stud is assumed to be uniform in both situations. The design model is based on expressions taking flexural buckling and lateral-torsional buckling into account in a way similar to that in part 1.3 of Eurocode 3 [1]. The load applied is an axial force that acts along the x-axis (length direction). The stud is assumed to rotate about the y-axis (strong axis) at supports. Different boundary conditions for rotation about the z-axis (weak axis) are considered. In order to develop simple calculation rules, a parametric study was performed in which several parameters were studied. Based on the results of this parametric study the simple calculation model was evaluated. To avoid time-consuming calculations a simplified approach was taken as a starting point for the design method. First simplification is that all slenderness parameters λ for local and global buckling are calculated at 20°C. This simplification is based on the fact that fy,0.2.θ / Eθ varies only slightly with temperature. It means that the reduction of the strength due to heating is solely taken into account by the use of fy,0.2,θ in the resistance formulae. Second simplification is that the bending due to the thermal gradient is considered equivalent to a constant bending moment. The reduction of the yield strength should be based on the temperature in the cross section as described below. In the parametric calculations the steel stud was modelled with restrained rotation about weak axis at support, consequently no external bending moments about z-axis (weak axis) are applied. On the other hand, since the c-shaped section is mono symmetric about y-axis (strong axis) the possible shift of the centroid of the effective area Aeff relative to the gravity of the gross cross section gives an additional moment about z-axis (weak axis), which should be taken into account. It is necessary to point out that the simple calculation model presented here is considered only to be valid for normal type c-section members.

4.4.2 Numerical parametric study with high studs engulfed in fire

For the purpose of developing simple calculation model for studs fully engulfed in fire, a parametric study was performed, in which following parameters have been studied:

• Length of steel stud: 600 mm, 3000 mm and 5100 mm • Stud sections: 100x0.6, 150x1.2, 250x2.5 • Steel grade: S350 with fy = 350 MPa • Temperature fields according to Figures 5-59 and 5-60: Uniform heating and heating

with three different temperature gradients • Boundary conditions: hinged about strong axis and restrained about weak axis • Loading conditions: centric loading and eccentric loading 0.5xh (h = web height of

steel stud)

/250

• Load levels: 0.3xNu and 0.5xNu (Nu according to numerical analysis at room temperature, refer to Table 4-13)

Axial compression resistance Nu (kN) Loading

condition Length (mm) 100x0.6 150x1.2 250x2.5

600 13.8 65.3 238.7

3000 8.7 53.3 224.2 Centric loading

5100 4.6 22.8 164.3

600 9.3 47.0 164.4

3000 6.0 34.4 150.8 Eccentric loading

5100 3.5 16.1 107.7

Table 4-13: Numerical compression resistance of steel studs at room temperature A full parametric study was made at elevated temperatures according to the parameters explained. One example of the corresponding results is given respectively in figures 4-41 and 4-42 as well as in table 4-14 (for full results of this parametric study, refer to [30]).

C-250x2.5Centric - load level 0.3

0

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000

Length (mm)

Temperature (°C)

T1 - uniform heating T2 - uniform heatingT1 - gradient heating 0.6 T2 - gradient heating 0.6T1 - gradient heating 0.3 T2 - gradient heating 0.3T1 - gradient heating 0.0 T2 - gradient heating 0.0

C-250x2.5Eccentric - load level 0.3

0

100

200

300

400

500

600

700

800

900

0 1000 2000 3000 4000 5000 6000

Length (mm)

Temperature (°C)

T1 - uniform heating T2 - uniform heatingT1 - gradient heating 0.6 T2 - gradient heating 0.6T1 - gradient heating 0.3 T2 - gradient heating 0.3T1 - gradient heating 0.0 T2 - gradient heating 0.0

Figure 4-41: Critical temperature results of the numerical calculations (large section,

centric load and load level of 0.3)

Figure 4-42: Critical temperature results of the numerical calculations (large section,

eccentric load and load level of 0.3)

/250

T1 = T2 T2 = 100+0.6x(T1-100)

T2 = 100+0.3x(T1-100) T2 = 100

Load condition

Length (mm) T1

(°C) T2

(°C) T1

(°C) T2

(°C) T1

(°C) T2

(°C) T1

(°C) T2

(°C)

600 505 505 535 361 535 231 535 100

3000 520 520 550 370 565 240 580 100 Centric load

5100 546 546 578 387 584 245 565 100

600 520 520 520 352 520 226 535 100

3000 520 520 535 361 550 235 565 100

Eccentric load on exposed

side (0.5xh)(*) 5100 543 543 577 386 595 249 625 100

(*) h is the total depth of the cross section Table 4-14: Critical temperatures for the C-250x2.5 section – load level of 0.3

It can be found from these results that:

• The critical temperature of steel studs, without any lateral supports, could have a critical temperature higher than 350°C which corresponds to the value of fixed critical temperature given in part 1.2 of Eurocode 3 [2] for all class 4 section steel elements.

• Temperature gradients do not lead to decreased critical temperatures of the studied elements (maximum temperature) even though the additional bowing effect could be very important. On the contrary, in some cases, the critical temperatures (maximum temperature) increase very slightly as temperature gradient increases

These results have been used in the development of simple calculation model presented hereafter.

4.4.3 General principles of simple calculation model

The design includes a check of global buckling according to the applicable cases given in paragraphs 4.4.3.1 to 4.4.3.3 and a check of cross sectional resistance according to paragraph 4.4.3.4. Axis convention according to part 1.1 of Eurocode 3 was adopted.

4.4.3.1 Buckling with uniform temperature distribution and centric load

The model of flexural buckling with centric load and uniform temperature distribution for an axially compressed steel stud is based on the equation given in part 1.3 of Eurocode 3 [1]. The equation is:

. .

. .min .

. .

1fi Ed fi Ed N

y yeff eff z

M fi M fi

N N ef f

A Wθ θχγ γ

⋅+ ≤

⋅ ⋅ ⋅ (4-1)

fy.θ is the 0,2 % proof strength at temperature θ for the section according to

relevant material model Aeff is the effective area of a cross section when subject to stresses due to uniform

axial compression

/250

Weff is the effective section modulus when subject only to bending stresses about relevant principal axis

The effective area Aeff and the effective section modulus Weff should be determined in accordance to part 1.3 and 1.5 of Eurocode 3, i.e based on material properties at 20°C. Nfi.Ed is the design axial force in the fire design situation γM.fi is a partial safety factor for the fire design situation with recommended value 1.0 eN is the shift of the centroidal axis when the cross-section is subjected to uniform

compression only χmin is the minimum of χy and χz and χT (for normal C-sections χz is smallest) χT is the reduction factor due to torsional flexural buckling χy , χx is the reduction factor due to flexural buckling about relevant principal axis

2 2

1 1.0χφ φ λ

= ≤+ −

(4-2)

yb eff

cr

f AN

λ = (4-3)

( )[ ]22.015.0 λλαφ +−+= (4-4)

with α = 0.34 (buckling curve b) Ncr is the elastic critical force for the relevant buckling mode based on gross cross

sectional properties at 20°C. Flexural buckling about relevant principal axis:

2

2crc

EINl

π= (4-5)

Torsional-flexural buckling:

2 2

. . . 0 ..

. . 0 .

1 1 42

cr y cr T cr T cr Tcr TF

cr y cr y cr y

N N N y NNN N i Nβ

= + − − +

(4-6)

2

. 2 20

1cr T w v

c

N EK GKi l

π = +

(4-7)

2

0

0

1 yi

β

= −

(4-8)

lc is the relevant buckling length fyb is the yield strength at 20°C of the base material y0 is the distance between shear centre and gravity centre along y-axis Kw is the warping constant of the gross cross section

/250

Kv is the torsion constant of the gross cross section E is Young’s modulus at 20°C I is the second moment of area of the gross cross section about relevant principal

axis

2 20 0

y z

gr gr

I Ii yA A

= + + (4-9)

Agr is the gross cross sectional area

4.4.3.2 Buckling with uniform temperature distribution and eccentric load

For members with mono-symmetric open cross sections (i.e. c-sections), account must be taken of the possibility that the resistance of the member to torsional-flexural buckling might be less than its resistance to flexural buckling. In case of eccentric loading and when the stud is laterally unrestrained the design check for torsional-flexural buckling is given by (4-10). In addition, Erreur ! Source du renvoi introuvable. should be checked, which may govern for small moments My.

0.8 0.8. . .

. .min .

. .

1fi Ed y fi Ed

y yeff LT eff y

M fi M fi

N Mf f

A Wθ θχ χγ γ

+ ≤ ⋅ ⋅ ⋅ ⋅

(4-10)

fy.θ is the 0,2 % proof strength at temperature θ according to relevant material

model. My.fi.Ed is the bending moment about the y-axis (strong axis) in the fire design situation.

If the load is applied eccentrically, then: . . .y fi Ed fi Ed zM N e= ⋅ (4-11) ez is the eccentricity of the axial load

2 2

1 1.0LT

LT LT LT

χφ φ λ

= ≤+ −

(4-12)

( ) 20.5 1 0.2LT LT LTφ α λ λ = + − + (4-13)

with α = 0.21 The non-dimensional slenderness due to torsional-flexural buckling can be written:

cr

elybLT M

Wf ⋅=λ (4-14)

Wel is the elastic section modulus of the gross cross section at 20°C Mcr is the elastic critical moment, which can be calculated according to:

/250

2 2

2w

cr z vEKM EI GK

L Lκ πκπ

= +

(4-15)

κ is a coefficient taken different end boundary conditions into account according

to Figure 4-43, assuming same conditions for lateral bending and for warping. L is the length of the member

With Kv = 0 equation (4-15) can be simplified to:

2 22

z wcr

E I KM

Lκ π

⋅= (4-16)

Figure 4-43: Coefficient of κ for different end restraint conditions

4.4.3.3 Flexural or torsional flexural buckling with temperature gradient

A thermal gradient causes a bow of the steel stud due to dissimilar thermal expansion of the flanges. The magnitude of the thermal deflection at midspan can be calculated from:

h

TLe TT 8

2 ∆⋅⋅=

α (4-17)

αT is the coefficient of thermal expansion, 614 10Tα −= ⋅ . L is the length of the member ∆T is the temperature difference between the colder flange and the warmer flange h is the web height

/250

The bow causes an eccentricity in the z-direction (weak axis), which has to be added to the bending moment caused by eccentric axial load. The two cases considered is first when the bending moment due to eccentric load on the warm side decreases the thermal bowing, and second when the eccentric load is applied on the cold side which increases the thermal bowing. Note that the thermal eccentricity can be larger than the eccentricity of the load. Thus the design check for the first case can be written:

( )

0.80.8..

. .max . .maxmin .

. .

1fi Ed z Tfi Ed

y yeff LT eff y

M fi M fi

N e eNf f

A Wθ θχ χγ γ

⋅ − + ≤ ⋅ ⋅ ⋅ ⋅

(4-18)

fy.θ,max is the 0,2 % proof strength at temperature θ for the hot flange according to

relevant material model. Similarly for the second case:

( ) 0.80.8

. .

. . . .min .

. .

1fi Ed fi Ed z T

y av y aveff LT eff y

M fi M fi

N N e ef f

A Wθ θχ χγ γ

⋅ + + ≤

⋅ ⋅ ⋅ ⋅

(4-19)

fy.θ,av is the 0,2 % proof strength at temperature θ for the average temperature over

the section according to relevant material model.

4.4.3.4 Cross sectional resistance

In addition to the check for global buckling, a check of the cross sectional resistance should be done. This may govern for short studs. Centric load with uniform temperature distribution:

. .

. ..

. .

1fi Ed fi Ed N

y yeff eff z

M fi M fi

N N ef f

A Wθ θ

γ γ

⋅+ ≤

⋅ ⋅ (4-20)

Eccentric load with uniform temperature distribution:

. . . .

. . .. .

. . .

1fi Ed y fi Ed fi Ed N

y y yeff eff y eff z

M fi M fi M fi

N M N ef f f

A W Wθ θ θ

γ γ γ

⋅+ + ≤

⋅ ⋅ ⋅ (4-21)

Centric load with temperature gradient:

. . .

. .max . .max . .max. .

. . .

1fi Ed fi Ed T fi Ed N


M fi M fi M fi

N N e N ef f f

A W Wθ θ θ

γ γ γ

⋅ ⋅+ + ≤

⋅ ⋅ ⋅ (4-22)

/250

Eccentric load on the warm side with temperature gradient:

( ).. .

. .max . .max . .max. .

. . .

1fi Ed z Tfi Ed fi Ed N


M fi M fi M fi

N e eN N ef f f

A W Wθ θ θ

γ γ γ

⋅ − ⋅+ + ≤

⋅ ⋅ ⋅ (4-23)

Eccentric load on the cold side with temperature gradient:

( ). . .

. . . . . .. .

. . .

1fi Ed fi Ed z T fi Ed N

y av y av y aveff eff y eff z

M fi M fi M fi

N N e e N ef f f

A W Wθ θ θ

γ γ γ

⋅ + ⋅+ + ≤

⋅ ⋅ ⋅ (4-24)

4.4.4 Comparison of mechanical performance of studs engulfed in fire between simple calculation model and advanced numerical model

In order to show the validity of proposed simple calculation model described in previous paragraph, results of numerical calculations are compared to simple calculation method (see example for the medium section in Tables 4-15 and 4-16). It can be found that the agreement is quite well. It is worth mentioning that ratio b/t for the small section is 83, which is larger than 60. It means that this cross section is outside the range of validity of procedure given in part 1.3 of Eurocode 3.

Tcr NFEA Nu.code Tcr NFEA Nu.code Tcr NFEA Nu.code

520 14.1 11.4 535 10.3 8.1 579 4.8 3.6

400 23.5 18.8 416 17.2 13.6 482 8.0 5.9

Table 4-15: Comparison between simple calculation method and numerical calculations for medium section (Uniform temperature, eccentric loading)

Tcr NFEA Nu.code Tcr NFEA Nu.code Tcr NFEA Nu.code

520 19.6 18.4 535 16 14.5 579 6.9 7.9

400 32.7 30.6 416 26.6 25.5 482 11.4 13.2

Table 4-16: Comparison between simple calculation method and numerical calculations for medium section (Uniform temperature, centric loading)

In addition, in Figures 4-44 to 4-45 is given the comparison between results of the numerical calculations and the simplified calculation method for studs submitted to centric and eccentric axial load, with uniform temperature over the section for the small, medium and large section respectively. From these figures, it can be found that: • For centric and eccentric loading with uniform temperature over the section, the simplified

method can predict the buckling resistance very well compared to the numerical calculations. As seen from Figure 4-44 and 4-45 all points can be found on the safe side.

/250

Comparison between FEA and simple calculation

Centric load with uniform temperature

0.00.20.40.60.81.01.21.41.61.82.0

0 100 200 300 400 500 600 700Temperature

FEA/

Sim

ple

calc

ulat

ion Small L=600

Medium L=600Large L=600Small L=3000Medium L=3000Large L=3000Small L=5100Medium L=5100Large L=5100

Comparison between FEA and simple calculationEccentric load with uniform temperature

0.00.20.40.60.81.01.21.41.61.82.0

0 100 200 300 400 500 600 700Temperature

FEA/

Sim

ple

calc

ulat

ion Small L=600


Figure 4-44: Comparison of buckling resistance between numerical results and simplified calculation method for the small, medium and large section. Relationship between numerical results (FEA) and simplified method. Centric load with uniform temperature over the section.

Figure 4-45: Comparison of buckling resistance between numerical results and simplified calculation method for the small, medium and large section. Relationship between numerical results (FEA) and simplified method. Eccentric load with uniform temperature over the section.

Figure 4-46 to 4-48 shows the comparison between results of the numerical calculations and the simplified calculation method for studs submitted to centric and eccentric load, with temperature gradient over the section for the small, medium and large section respectively. A temperature gradient over the section is not in reality reasonable when the stud is fully engulfed in fire, but it is necessary to be able to predict the mechanical behaviour when subjected to temperature differences to increase the understanding of failure mechanisms of lightweight steel section in fire. From these figures, it can be found that: • The results show rather big scattering when a temperature gradient over the section is

considered. However, the results are always on the safe side except when considering large temperature gradients and eccentric loading on the cold side.

• As seen from Figure 4-47, when the load is applied eccentrically on the fire side, the scattering decreases slightly. This could be explained by the fact that the reduction factor is used for the hot flange where the load is applied.

/250

Comparison between FEA and simple calculationCentric load and T2=0.6(T1-100)+100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Comparison between FEA and simple calculationCentric load and T2=0.3(T1-100)+100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Comparison between FEA and simple calculationCentric load and T2=100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Figure 4-46: Comparison between numerical results and simplified calculation method for the small, medium and large section. Centric load with temperature gradient.

Comparison between FEA and simple calculationEccentric load fire side and T2=0.6(T1-100)+100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Comparison between FEA and simple calculationEccentric load fire side and T2=0.3(T1-100)+100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Comparison between FEA and simple calculationEccentric load fire side and T2=100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Figure 4-47: Comparison between numerical results and simplified calculation method for the small, medium and large section. Eccentric load on fire side with temperature gradient.

/250

Comparison between FEA and simple calculationEccentric load cold side and T2=0.6(T1-100)+100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700 800Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Comparison between FEA and simple calculationEccentric load cold side and T2=0.3(T1-100)+100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700 800Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Comparison between FEA and simple calculationEccentric load cold side and T2=100

0.0

0.5

1.0

1.5

2.0

2.5

0 100 200 300 400 500 600 700 800Tmax = T1

FEA/

Sim

ple

calc

ulat

ion Small L=600


Figure 4-48: Comparison between numerical results and simplified calculation method for the small, medium and large section. Eccentric load on cold side with temperature gradient.

4.5 CONCLUSIONS

Lightweight steel members are often class 4 section elements, so they are very sensitive to local buckling behaviour. For that reason it is important to know what the appropriate characteristic values should be to be used in design in order to assess the mechanical resistance in right the way. As a consequence, one part of the work presented in this chapter was focused on this aspect. First of all, the stub column tests have been carried out on three different C-type sections and one special section called as AWS, which has helped to get an experimental basis for validating the numerical modelling. Secondly, the application of numerical modelling to different stub columns show that under fire situation, the 0.2 % proof characteristic strength should be used to predict the local buckling resistance of lightweight steel members since the reduction strength of stub columns follows closely the reduction factor in respect to this characteristic strength. Also in some cases, load-bearing lightweight steel members could be fully engulfed in fire. Their mechanical performance needs to be predicted. Nevertheless, there is no design rule for fire situation regarding this feature. Consequently, another part of the work within the scope of this chapter is related exclusively to the behaviour of high studs in lightweight steel surrounded entirely by fire. Several tests have been performed on high studs with different cross sections. The numerical modelling is also validated against these tests and then applied in a parametric study. Based on the results of above study, a simple calculation model available for C-type section members is proposed. The comparison of this simple design rule with parametric study show a good agreement for uniformly heated members, which in fact correspond the most common situation of lightweight steel studs engulfed in fire. Nevertheless, if temperature gradient exists on cross section of isolated lightweight steel studs, the simple calculation model predicts quite different results from numerical analysis. This phenomenon is very possibly due to the fact that the section is no longer a

/250

homogeneous section in stiffness and strength leading to a very different torsional behaviour and as a consequence an important scatter between numerical analysis and simple calculation model based on homogeneous sectional properties.

/250

5 MECHANICAL BEHAVIOUR OF LIGHTWEIGHT STEEL MEMBERS MAINTAINED BY BOARDS AT ELEVATED TEMPERATURES

5.1 GENERAL

One of the most important applications of cold formed lightweight steel structures is the case of plasterboard partition walls in which lightweight steel studs are used as supporting frame of this type of walls and in general they are maintained by corresponding boards. As a consequence, the work of this chapter was focused on both experimental and numerical investigation of the mechanical behaviour of lightweight steel studs maintained by plasterboards. Within the experimental investigation shared by VTT and CTICM, a number of fire tests have been carried out under different conditions. Based on these fire tests, corresponding numerical analysis has been made using several advanced calculation models to check, on the one hand, the validity of these models, and on the other hand, to perform, once the numerical modelling is available, parametric studies with the purpose of developing a simple calculation model providing a practical rule for daily design of lightweight steel studs maintained laterally which are, as explained earlier, widely encountered in case of either load-bearing or non load-bearing partition walls.

5.2 EXPERIMENTAL INVESTIGATION

5.2.1 Testing Methodology

In order to achieve the predicted objectives, a number of fire tests have been programmed and shared between VTT and CTICM in which various sensitive parameters capable of affecting the fire resistance of lightweight steel studs, such as cross-section size, load condition, eccentricity of loading, internal insulation, heating condition, type of plasterboard and connection condition between steel studs and plasterboards have been taken into account. In total, twenty nine fire tests were carried out among which fifteen at VTT Building and Transport and fourteen at CTICM [13, 14, 15]. As shown in Figure 5-1, test specimens considered correspond to a small part of partition walls which occupies a surface of 1200×2800 mm² with steel framework and plasterboard facings. The steel framework of specimens is made of two vertical studs (simple or double) of different types of lightweight steel sections (C-section, AWS-section and TC section) which may be perforated. Each facing is made of two layers of fire resistant or standard plasterboards, screwed on the flanges of two steel studs. In some tests, double layers of plasterboards are fixed on both flanges of two studs. For others specimens, only the two layers of plasterboards exposed to fire is fixed on the flange of the two steel studs and the plasterboards on the unexposed side is connected to two lateral walls made of cellular concrete blocks with a certain spacing to the unexposed flanges of studs (see figure 5-3 for more details). Internal thermal insulation (rock-wool panels) may be installed to fill the void between the exposed and unexposed plasterboard facings. In one specimen, a 1 mm thick steel sheet is added between exposed plasterboards and the steel studs of the specimen. Three of above tests were performed at CTICM with different end conditions in order to check the difference between so-called idealized end conditions (one end fixed and other end hinged) and real end conditions (studs simply inserted in channel tracks and studs in channel tracks fixed by screws).

/250

The details of these specimens are given in tables 5-1 to 5-4. A summary of all corresponding test results is given in paragraph 5.2.

plasterboard

Eccentricity

Φ80 roll

N

N

Steel stud

Figure 5-1: Schematic view of lightweight steel sections maintained by plasterboards Figure 5-2 shows a schematic view of the basic test arrangement used for these fire tests.

Plasterboards Loading Test

Type Maintain condition

Internal insulation

(rock wool) Level (1) Load Section type (perforated)

Testing organisation (test number)

S1 Fire board Two sides No 0.4 Centric No CTICM (8)

S2 Fire board Two sides Yes 0.4 Centric No CTICM (9)

(1) Initially predicted applied load level

Table 5-1: Summary of fire tests performed on small steel stud (100x50x0.6)

/250

Plasterboards Loading

Test Type Maintain

condition

Internal insulation

(Rock wool) Level Load Section type (perforated)


M1 Fire board Two sides No 0 Eccentric No CTICM (1)

M2 (1) Fire board Two sides No 0.4 Eccentric No CTICM (6)


M4 Fire board Two sides No 0.2 Centric No VTT


M6 Fire board Two sides No 0.4 Eccentric No CTICM (2)


M8 Fire board One side No 0.4 Eccentric No CTICM (4)

M9 (3) Standard board Two sides Yes 0.4 Eccentric No CTICM (3)

M10 Fire board Two sides Yes 0.6 Centric No VTT

M11 Fire board Two sides Yes 0.6 Eccentric No VTT

M12 Fire board One side Yes 0.4 Eccentric No CTICM (5)

M13 (7) Fire board Two sides Yes 0.4 Eccentric No VTT

M14 Standard board Two sides No 0.4 Eccentric No VTT

M15 (3) Standard board Two sides Yes 0.4 Eccentric No VTT


M17 (4) Fire board Two sides Yes 0.4 Eccentric No CTICM (11)



M20 (6) Standard board Two sides No 0.4 Eccentric No CTICM (14)

(1) Studs simply inserted in channel tracks, (2) Studs in channel tracks fixed by screws (3) French standard boards (4) Double studs

(5) Eccentric load located at exposed side (6) Specimen exposed to natural fire (7) Steel sheet between the steel stud and the plasterboard on the exposed side

Table 5-2: Summary of fire tests performed on medium section (150x57x1.2)



Internal insulation



T1 Fire board Two sides yes 0.4 Centric yes VTT

(1) Initially predicted applied load level

Table 5-3: Summary of fire tests performed on TC-section (150x1.2)

/250

Plaster boards Loading

Test Type Maintain

condition

Internal insulation



L1 Fire board Two sides No 0.4 Centric No VTT

L2 (1) Fire board Two sides Yes 0.4 Centric No VTT

L3 Fire board Two sides Yes 0.6 Centric No VTT

(1) Steel sheet between the steel stud and the plasterboard on the exposed side (2) Initially predicted applied load level

Table 5-4: Summary of fire tests performed on large steel stud (250x80x2.5)



Internal insulation


Testing organisation

A1 Fire board Two sides Yes 0.4 Centric yes VTT

A2 Fire board Two sides Yes 0.4 Eccentric yes VTT

A3 (1) Fire board Two sides Yes 0.6 Eccentric yes VTT

A4 Fire board Two sides Yes 0.6 Eccentric yes VTT

(1) Steel sheet between the steel stud and the plasterboard on the exposed side (2) Initially predicted applied load level

Table 5-5: Summary of fire tests performed on AWS steel stud (150x1.2) In all fire tests, specimens were placed in front of the furnace and subjected to a vertical load applied before fire and kept constant during the test up to the failure. The load was applied at the bottom of the specimen via hydraulic jacks controlled manually during the test. Three types of eccentricity, that is centric, eccentric on unexposed side and eccentric on exposed side, were used. In order to create an idealized restrained condition, specimens were placed between two supporting systems. Each of them was composed of two UAP steel profiles fixed together to a steel plate in which steel studs are inserted (see figure 5-2). In CTICM tests, the upper steel end plate was simply supported by a roll and the lower steel end plate was rigidly supported on two hydraulic jacks. On the contrary, in VTT tests, the upper steel end plate was rigidly supported by a steel frame and the lower steel end plate was simply supported through a roll on a mobile steel box beam pushed up with help of hydraulic jacks (see figure 5-2). The supporting end plates allow specimen rotate out of plane but preventing the in-plane rotation of the specimen. As a consequence, studs can be then considered as hinged at one end and restrained against rotation at the other end. The majority of specimens were exposed to a heating regime controlled in such a way that the average temperature in the furnace follows the “standard time-temperature curve” (EN1363-1). Some specimens were exposed to natural fire condition in order to study the behaviour of studs with plasterboards under this special heating condition.

/250

a) CTICM test set up b) VTT test set up

Figure 5-2: Test arrangement of lightweight steel studs During all these tests, the furnace temperature was continuously recorded with plate thermometers. In order to know the heating of specimens, thermocouples were installed on the steel studs (exposed flange, web and unexposed flange), on the cavity between plaster boards as well as in the plaster boards (interface between the two exposed plaster boards, interface between the two unexposed plaster boards and outside chamber). The position of thermocouples is shown in figure 5-3. In fact, three cross-sections (N1, N2 and N3) were used along the specimen length to measure the heating regime of specimens.

80

FIRE 30

0 For 93 For 94

h =

2800

mm

steel frame

Loading beam

h =

2800

mm

FIRE

/250

a) Steel studs maintained by plasterboards on both sides without internal insulation

b) Steel studs maintained by plasterboards on only one side with internal insulation

Figure 5-3: Example of measuring points of temperature in some specimens

Both lateral and longitudinal displacements of the specimens were systematically recorded during the tests (Figure 5-4). The displacements of the specimens were measured in the direction perpendicular to their plane (lateral displacement) at three levels located respectively at h/4, h/2 and 3h/4 on both studs with help of displacements transducers placed on the unexposed side. In addition, the vertical displacement corresponding to axial contraction of the test specimens was measured on the lower supporting end plate. The rotations of the lower supporting end plate along two axes were also measured during the test by two inclination sensors.

/250

Figure 5-4: Location of the measurement sections along all specimens

5.2.2 Summary of all test results

The first series of tests performed at CTICM consists of nine fire tests with following configurations: a) M1: simple studs (medium section) connected to fire plasterboards on two sides and

subjected to restraint conditions against axial elongation, b) M6: simple studs (medium section) connected to fire plasterboards on two sides and

subjected to eccentric axial load, c) M9: simple studs (medium section) under eccentric load connected to standard

plasterboards on two sides, d) M8: simple studs (medium section) connected to fire plasterboards on only one side and

subjected to eccentric axial load, e) S1: simple studs (medium section) under eccentric axial load connected to fire

plasterboards on only one side with internal insulation between studs, f) S2: simple studs (small section) connected to fire plasterboards on two sides and

subjected to axial load, g) M3: simple studs (small section) under axial load connected to fire plasterboards on two

sides with internal insulation between studs, h) M2 and M3: simple studs (medium section) under eccentric axial load connected to fire

plasterboards on two sides and inserted in channel tracks (2 tests). Moreover, in order to investigate other configurations of steel studs maintained by plasterboards, five additional fire tests have been carried out at CTICM with following conditions: i) M16: double studs (medium section) connected to fire plasterboards on two sides and

subjected to eccentric axial load,

600

h/4

DH1 DH4

DH5

DH6

F 93 F 94

N3

300 300

h/4

h/4

h/4

N2

N1

h DH2

DH3

80

FIRE

300

h/4

DH1 DH4

DH2 DH5

DH3 DH6

For 93 For 94

DV1 DV2

DETAIL 1

DETAIL 1

Inc 1

Inc 2

DV1DV2

h

h/4

h/4

h/4

DH2

/250

j) M17: double studs (medium section) connected to fire plasterboards on only one side with internal insulation between studs and subjected to eccentric axial load,

k) M18: simple studs (medium section) connected to fire plasterboards on two sides and subjected to eccentric axial load located at exposed side,

l) M19: simple studs (medium section) under eccentric load connected to fire board on two sides and exposed to natural fire condition,

m) M20: simple studs (medium section) under eccentric load connected to standard plasterboard on two sides and exposed to natural fire.

In parallel, fifteen other fire tests have been carried out at VTT with following configurations: n) M4, M5 and M7: simple studs (medium section) connected to fire plasterboards on both

sides without internal insulation and subjected to a centric load (3 tests), o) M10 and M21: simple studs (medium section) connected to fire plasterboards on both

sides with internal insulation between studs and subjected to a centric load (2 tests), p) M11 and M14: simple studs (medium section) connected to fire plasterboards on both

sides with internal insulation between studs and subjected to an eccentric load, q) M13: simple studs (medium section) subjected to an eccentric load and connected to fire

plasterboards on both sides with internal insulation and steel sheet between the steel stud and the plasterboard on the exposed side,

r) M15: simple studs (medium section) connected to standard plasterboards on both sides with internal insulation under eccentric load,

s) A1 to A4: simple studs (AWS section) connected to fire plasterboards on both sides and with internal insulation between studs (4 tests),

t) L1: simple studs (Large section) connected to fire plasterboards on both sides without internal insulation under centric load,

u) L2 and L3: simple studs (Large section) connected to fire plasterboards on both sides with internal insulation between studs (2 tests) under centric load,

v) T1: simple studs (perforated C section) connected to fire plasterboards on both sides with internal insulation between studs under centric load.

The main structural characteristics of tested steel studs maintained by plasterboards and their experimental failure times are summarised in Tables 5-6, 5-7 (CTICM tests), and Table 5-8 (VTT tests). In these tables is given also the maximum temperature of exposed flange of the steel stud measured at the failure time. Failure time measured during the tests and reported in these tables corresponds to the condition when each specimen (steel studs) could not carry the applied load any more. Test loads were determined on the basis of tested resistance of similar specimens at normal temperature (see chapter 3). Only one applied load level was used in tests performed at CTICM which correspond to 0.4 while in VTT tests, load levels varied from 0.2 to 0.6.

/250

Plasterboards Loading Test Studs


Internal insulation Load

(kN) / level (3)Eccentricity

(mm)

Fire condition

Failure time (min)

Max steel temp. (°C)

Failing of the

boards

N°1 (M1) medium Fire board Two sides No 0

37.5 unexposed

side ENV1363-1 58.5 331 yes

N°2 (M6) medium Fire board Two sides No 25 / 0.46

37.5 unexposed

side ENV1363-1 72 511 yes

N°3 (M9) medium standard Two sides No 25 / 0.46

37.5 unexposed

side ENV1363-1 52 550 yes

N°4 (M8) medium Fire board One side No 25 / 0.46

37.5 unexposed

side ENV1363-1 63 408 No

N°5 (M12) medium Fire board One side Yes

rock wool 25 / 0.46 37.5

unexposed side

ENV1363-1 60 365 Yes

N°6 (1) (M2) medium Fire board Two sides No 25 / 0.46

37.5 unexposed

side ENV1363-1 87 482 No

N°7 (2) (M3) medium Fire board two sides No 25/ 0.46

37.5 unexposed

side ENV1363-1 75 419 No

N°8 (S1) small Fire board Two sides No 3 / 0.3 0 ENV1363-1 53 378 Yes

N°9 (S2) small Fire board Two sides Yes

rock wool 3 / 0.3 0 ENV1363-1 53 609 no

(1) Studs simply inserted in channel tracks (2) Studs in channel tracks fixed by screws (3) Actual applied load level

Table 5-6: Summary of first series of fire tests carried out at CTIM

Studs Plasterboards Loading

Test Section Type Maintain

condition

Internal insulation Load (KN) /

Level (1) Eccentricity

(mm)

Fire condition


Failure time (min

N°10 (M16)

Medium (double)

Fire board Two sides No 50 / 0.46

37.5 unexposed

side ENV1363-1 483 84

N°11 (M17)

Medium (Double) Fire board One side Yes

rock wool 50 / 0.46 37.5

unexposed side

ENV1363-1 656 88

N°12 (M18)

Medium Fire board Two sides No 25/ 0.46

37.5 exposed

side ENV1363-1 420 65

N°13 (M19)

Medium Fire board Two sides No 25/ 0.46

37.5 unexposed

side Natural fire 500 64

N°14 (M20)

Medium

standard board Two sides No 25/ 0.46

37.5 unexposed

side Natural fire 515 40

(1) Actual applied load level

Table 5-7: Summary of additional fire tests carried out at CTIM

/250

Fire test Studs Insulation Loading NTest,fi /load level (1)

(NTest) (kN)


Failure time (test time)

(min) Falling of

the boards

N°1 (M4) Medium No Centric 12.0 / 0.16 (74.4) 643 75 (76,3) Yes

N°2 (M5) Medium No Centric 36.0 / 0.48 (74.4) 429 69 (71,7) No

N°3 (M7) Medium No Centric 25.0 / 0.34 (74.4) 541 82 (82,2) Yes

N°4 (M10) Medium Yes Centric 36.0 / 0.48 (74.4) 316 53 (53,3) No

N°5 (M21) Medium Yes Centric 25.0 / 0.34 (74.4) 406 56 (58,2) No

N°6 (M11) Medium Yes Eccentric 25.0 / 0.46 (54.9) 122 34 (38,2) No

N°7 (M13) Medium + steel sheet Yes Eccentric 25.0 / 0.46 (54.9) 294 56 (58,6) No

N°8 (M15) Medium boards type A Yes Eccentric 25.0 / 0.46 (54.9) 248 48 (50,5) No

N°17 (M14) Medium Yes Eccentric 25.0 / 0.46 (54.9) 222 48 (49,1) No

N°18 (T1) TC 150 Yes Centric 17 / 0.26 672 74 (75) No

N°9 (A1) AWS Yes Eccentric 44.0 / 0.77 (57.5) 85 11,8 (14,2) No

N°10 (A2) AWS Yes Eccentric 15.0 / 0.26 (57.5) 770 74.5 (75.4) No

N°11 (A3) AWS Yes Eccentric 30.0 / 0.52 (57.5) 246 48.3 (49.2) No

N°12 (A4) AWS Yes Centric 30.0 / 0.32 (95.1) 430 56.2 (56.7) No

N°13 (L1) Large No Centric 78.0 / 0.35 (223.0) 628 105.3 (106.6) Yes

N°14 (L2) Large Yes Centric 117.0 / 0.52 (223.0) 667 83.0 (83.8) Yes

N°15 (L3) Large Yes Centric 78.0 / 0.35 (223.0) 676 84.0(85.5) Yes

(1) Actual applied load level

Table 5-8: Summary of tests carried out at VTT The following comments on the behaviour of steel studs with plasterboards have been established on the basis of both experimental observations and measured data: - Compared to CTICM tests, VTT tests seem to give lower critical temperatures of

maintained steel studs. This difference can be explained by the fact that in VTT tests, the fixed end of studs is located on the top end which has a more severe heating condition than the bottom end of stud modifying therefore the failure mode of steel studs;

- Three of above tests were performed at CTICM with different end conditions in order to check the difference between adopted end conditions and real end conditions. Comparison of test CTICM 2 and test CTICM 6 indicates that the predicted test end conditions (test CTCIM 2) are similar to end conditions with studs simply inserted in channel tracks. Regarding the collapse temperature of steel studs, it can be found that both tests (CTICM 2 and CTICM 6) gave about the same results;

/250

- The influence of the steel perforation on the heating regime (temperature difference between the flanges) is very small.

- The steel sheet seems to increase significantly the maximum collapse temperature of steel studs (see tests VTT 6 and VTT 7);

- The type of plasterboards (fire or standard) influence the collapse time but the same maximum temperature seems to be obtained at the moment of collapse (see tests CTICM 2 and CTICM 3);

- The type of connection between steel stud and plasterboard (fixed at both sides and only one side) has an important effect on both the collapse time and failure temperature (see tests CTICM 2 and CTICM 4). Maximum temperatures of steel studs with unsupported flange are, as expected, lower than those of studs supported by plasterboard on both sides because the failure mode of specimens is different (see figure 5-5). It can be seen that steel studs maintained on only the exposed side flange failed by combination of torsional buckling (of the colder flange) near mid-height of the specimen and flexural buckling about the major axis while steel studs fixed at both sides failed by global flexural buckling with local buckling on the unexposed flange;

- The presence of internal insulation (rock wool) inside the void between plasterboards has an important influence on both collapse time and failure temperatures (see tests CTICM 4 and CTICM 5 as well as tests CTICM 6 and CTICM 7). This effect appears to vary as function of stud section. With small section (tests CTICM 8 and CTICM 9) and large section (tests VTT 13 and VTT 15) the failure temperature of the exposed side flange is higher in the specimen with insulation than the specimen without insulation. For medium section the failure temperature is higher in specimens without insulation (see tests VTT 2 and VTT 4, VTT 3 and VTT 5, VTT 13 and VTT 15. This may be a consequence of the different failure modes of steel studs between non-insulated specimens. Medium sections failed towards cold side while small and large section failed towards the hot side. As shown in figure 5-7, It can be also noted that the failure mode observed in specimen with internal insulation is approximately the same as that obtained in non insulated specimens (see figure 5-7), i.e. overall buckling towards the furnace;

- In all cases, the failure of specimens was initiated by structural collapse of the studs; - Eccentricity of the applied load reduces the failure temperature of steel studs. Difference

of failure mode between the axially and eccentrically loaded specimens is illustrated in figure 5-8. With regard to specimen under eccentric load applied on the exposed side, the failure mode was flexural buckling about the major axis. This was initiated by local buckling (compressive failure) of the cold flange near mid-height due to the deflection of the specimen towards the furnace. Concerning specimens under centric load, different failure modes have been observed: In some tests a similar overall buckling mode as that obtained with eccentric loaded specimens was obtained, i.e local compression flange buckling at unexposed side. In other tests, failure resulted in overall buckling towards the unexposed side due to the compressive failure of the hot flange. In this case, it has been observed a reversal in the transversal movement near the end of the test, indicating failure of the studs away from the furnace. As shown in figure 5-8, differences of the observed structural behaviour of centrically loaded steel studs can be attributed to the location of the failure along the studs: close to the stud ends or near the mid-height of the specimen.

- The buckling modes for the AWS tests are illustrated in figure 5-8. Similar behaviour to that observed in lipped C-section tests, i.e. compression flange buckling, is observed.

/250

a) Steel studs connected to plasterboards on only one side (tests CTICM 4 and CTICM 5)

b) Steel studs connected to plasterboards on both sides(tests CTICM 3 and VTT 17)

Figure 5-5: Effect of the connection condition between steel stud and plasterboard on failure modes of studs

a) Steel studs under centric load (tests VTT 2 and CTICM 8) – failure towards the

cold side

b) Steel studs under centric load (test VTT 4) – failure towards

the furnace

c) Steel studs under eccentric load (test CTICM 3) - failure

towards the cold side Figure 5-6: Effect of eccentricity of the applied load on failure modes of studs

/250

a) Specimen with insulation (tests CTICM 9 and VTT 15).

b) Specimen without insulation (tests CTICM 8 and VTT 13).

Figure 5-7: Effect of internal insulation on the test failure modes

a) Specimen of test VTT 11 b) Specimen of test VTT 12 c) Specimen of test VTT 9

Figure 5-8: Failure mode of AWS steel stud section

5.2.3 Examples of detailed test results

In this paragraph, the results of four fire tests on lightweight steel studs maintained by plasterboards carried out at VTT Building and Transport and at CTICM are presented in detail. These results are from two VTT tests (will be called in the following VTT 3 and VTT 5) and two CTICM tests (called CTICM 2 and CTICM 5) on medium C-section.

/250

The main characteristics of these fire tests are summarised in Table 5-9. Test specimens consisted of two simple vertical steel studs with medium C-section (13×57×150×57×13 mm – e=12/10 mm). Two layers of 12.5 mm thick plasterboards were connected to the flange of the steel studs on both sides, except for test CTICM 5, where plasterboards were attached to one side only. The screw spacing for the two plasterboard layers was 510 mm and 310 mm, respectively. Specimens of CTICM tests were subjected to an eccentric load on the unexposed side while specimens of VTT were tested under a centric load. All test specimens were exposed to EN 1363-1 fire condition.



Internal insulation (rock wool)

Load (kN)

Eccentricity (mm)

CTICM 2 Fire board Two sides No 25 37.5 unexposed side

CTICM 5 Fire board One side Yes 25 37.5 unexposed side

VTT 3 Fire board Two sides No 25 0

VTT 5 Fire board Two sides Yes 25 0

Table 5-9: Summary of four of fire tests on lightweight steel studs maintained

by plasterboards with or without internal insulation Temperature distributions in the cross-section of steel studs recorded during the tests at different levels of the specimen are given in Figures 5-9 to 5-12.

0

100

200

300

400

500

600

0 10 20 30 40 50 60 70 80 90Time (min)

Tem

pera

ture

(°C

)

TC_10 TC_30 TC_47TC_11 TC_31 TC_48TC_12 TC_32 TC_49

exposed flange

web

unexposed flange

0

100

200

300

400

500

600

0 10 20 30 40 50 60Time (min)

Tem

pera

ture

(°C

)

TC_2 TC_17 TC_37

TC_3 TC_18 TC_38

TC_4 TC_19 TC_39

exposed flange

web

unexposed flange

Figure 5-9: Measured temperatures in test

VTT 3 Figure 5-10: Measured temperatures in test

VTT 5

/250

0

100

200

300

400

500

600

0 20 40 60 80Time (min)

Tem

pera

ture

(°C

)

TC 2 TC 3 TC 4 TC 19TC 20 TC 21 TC 28 TC 30TC 45 TC 46 TC 47 TC 54TC 55 TC 56 TC 71 TC 72TC 73

exposed flange

web

unexposed flange

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70Time (min)

Tem

epar

atur

e (°

C)

N3 exposed side flangeN3 webN3 unexposed side flangeN2 exposed side flangeN2 webN2 unexposed side flangeN1 exposed side flangeN1 webN1 unexposed side flange

63.5 min

Figure 5-11: Measured temperatures in test CTICM 2

Figure 5-12: Measured temperatures in test CTICM 5

From theses figures, it can be noted that: - The temperature rise of exposed flange consists of three phases: at first stage of test,

there is a rapid rise, then the heating rate decreases leading to a slower temperature increase which sometimes is even zero due to apparently the moisture content in the plasterboard and the duration of this temperature rise phase (water evaporation stage around 100°C) depends on the type as well as moisture content of the plasterboards, finally after evaporation of moisture, the temperature re-increase rapidly again until the collapse of the specimen.;

- The temperature rise of unexposed flange is analogous to that observed for exposed flange but with a certain time translation. In the test specimen with internal insulation, the translation between the temperature curves corresponds to the time necessary to evaporation of moisture contained in the mineral wool. In the test specimen without internal insulation, the presence of the gap interrupts direct heat conduction and leads to the delayed temperature rise in unexposed flanges of steel studs.

- Steel studs in specimens with internal insulation have higher temperature gradients along the depth of steel section;

- Temperatures measured at different height levels of the specimens with internal insulation are very similar (difference negligible). With regard to specimens without internal insulation, the temperatures measured on the unexposed flange as well as at mid-width of the steel stud are different along the specimen height;

These test results are summarised in Table 5-10. Test time given in this table is the failure time of the specimen. The criterion for the failure time is the loss of capability of the steel studs to carry the applied load. In this table the maximum steel stud temperature at the failure time is also given.

Test Max temperature at failure (°C) Failure time (min) Failing of the

boards CTICM 2 427 72 Yes CTICM 5 417 60 Yes

VTT 3 541 82 Yes VTT 5 406 56 No

Table 5-10: Results of fire tests CTICM 2, CTICM 5, VTT3 and VTT5

/250

Globally the failure of specimens was initiated in all cases by structural collapse of the studs. In CTICM tests, the failure mode was flexural buckling about the major axis initiated by a local buckling (compressive failure) of cold flanges. As shown in figure 5-13 (positive deflection indicates movement towards the furnace), the steel studs of the fire test CTICM 5 failed towards the furnace and two steel studs buckled at about mid-height. For test CTICM 2, the steel studs buckled near the top end of the specimen towards the furnace. The left stud buckled at 820 mm from the top end and the right stud buckled at 190 mm form the top end. In VTT tests, stud failure occurred in a overall buckling away from the furnace due to compressive local buckling failure of the hot flange (as shown in figure 5-14).

05

101520253035404550

0 5 10 15 20 25 30 35 40 45 50 55 60 65Time (min)

Late

ral d

ispl

acem

ent (

mm

) N2 left stud testN2 right stud test

-10

-5

0

5

10

0 10 20 30 40 50 60 70 80 90Time (min)

Late

ral d

ispl

acem

ent (

mm

)

test result D2test result D3test result D5test result D6

Figure 5-13: Lateral displacement measured at mid height of steel stud for test CTICM 5

Figure 5-14: Lateral displacement measured at mid height of steel stud for test VTT 3

5.3 ANALYSIS OF FIRE BEHAVIOUR OF STEEL STUDS MAINTAINED BY BOARDS WITH ADVANCED CALCULATION MODELS

In order to develop new design rules for lightweight steel elements maintained by boards, it is necessary to use not only experimental results presented previously but also validated advanced numerical models to extend to full range analysis. In this respect, a validation study has been carried out with different computer codes from different partners. The first part concerns the heat transfer analysis of steel studs with plasterboards and the second part deals with the mechanical analysis of lightweight steel studs.

5.3.1 Numerical modelling of heating regime of steel studs with plasterboards

To investigate the validity of different computer codes for heat transfer analysis in case of partition wall using steel studs with plasterboards, a comparison study have been performed between different computer codes used in this research, namely ABAQUS, ANSYS, FLUENT and SAFIR [16, 17, 18 and 19]. In total, four common cases were adopted for this study corresponding to different situations of steel studs and material properties (see figure 5-15). In numerical models, non linearities due to temperature dependency of material properties and boundary conditions are taken into account. It is assumed that conduction is the main heat transfer mechanism in the steel studs and plasterboards. Convection and radiation act essentially for heat transfer from fire to plasterboards. As simplification, radiation effects within the void between the gypsum boards are taken into account and convection effects within the plasterboards are neglected. Models don’t simulate mass transfer (moisture movement) in materials.

/250

Plaster board

Steel stud

Plaster board

Plaster board

Steel stud

Plaster board

Plaster board

Steel stud

Roc

kwoo

l

Linear and non-linear thermal

properties for plasterboard Non-linear thermal properties

for plasterboard Non-linear thermal properties for plasterboard and rock wool

Figure 5-15: Cases used for validation study of heat transfer As an example of the numerical analysis carried out, results of two cases are given below. The cases considered here are shown in figures 5-16. The corresponding mesh of the cross section for computer code is given in figures 5-17. Calculations have been performed until 90 minutes of fire and for every study cases, the results have been given on several points, namely two points on each plasterboards (surface and half depth at mid-width of steel stud) and three points on each stud (two flanges at mid-width and web at half depth).

600 mm

40 mm

70 mm 0.6 mm

25 mm

25 mm

Gypsum board Steel stud

εr = 0.5hconv = 25 W/m² Kγf = 1.0

Surrounding temperatureTf according to ISO 834

εr = 0.8hconv =0.0 W/m² Kγf = 1.00

Surrounding temperature Tf : 20 °C

Adia

batic

Adiabatic

Adia

batic

Adiabatic

εr = 0.5hconv = 16 W/m² Kγf = 1.0

a) Dimensions of the section for case 3a b) boundary conditions for case 3a 600 mm

40 mm

70 mm

0.6 mm

25 mm

25 mm

Gypsum board

Steel stud

Gypsum board

Mineral wool

εr = 0.5 hconv = 25 W/m² K γf = 1.0

Surrounding temperature Tf according to ISO 834

Surrounding temperature Tf : 20 °C

Adia

batic

Adiabatic

Adia

batic

Adiabatic

εr = 0.5 hconv = 16 W/m² K γf = 1.0

c) Dimensions of the section for case 4 d) boundary conditions for case 4

Figure 5-16: Details of studied specimens

/250

a) Finite element mesh of ANSYS for case 3a b) Finite element mesh of SAFIR for case 3a

a) Finite element mesh of ANSYS for case 4 b) Finite element mesh of ABAQUS for case 4

Figure 5-17: Section mesh of studied specimens

As shown in figures 5-.18 and 5-19, the results obtained from different computer codes show a good agreement between them. So it can be considered that all these computer codes are all available for heat transfer analysis if one of them is validated against tests.

0

100

200

300

400

500

600

700

800

900

1000

0 15 30 45 60 75 90Time (min)

Tem

pera

ture

(°C

)

Point APoint B

Point CPoint D

Point E

Point FPoint G

CTICM

ARBED0

100

200

300

400

500

600

700

800

900

1000

0 15 30 45 60 75 90Time (min)

Tem

pera

ture

(°C

)

Point A

Point B

Point CPoint D

Point E

Point FPoint G

CTCIMVTT

Figure 5-18: Comparison between ANSYS and SAFIR for case 3a

Figure 5-19: Comparison between ANSYS and ABAQUS for case 4

Some additional analyses have been made for heating up behaviour of steel studs with plasterboards based on CFD approach with computer code Fluent. In this study, after some numerical investigations, a new proposal of thermal properties (specific heat and conductivity) for used plasterboard have been given, which led to a good estimation of stud heating compared to test results. As shown in figure 5-20, the temperatures calculated in partition walls without internal insulation (at hot side and at cold side) are in good agreement with the measured ones. With regard to partition walls with internal insulation, the agreement is not so good, but can nevertheless be regarded as satisfactory (figure 5-21). Difference between theoretical and experimental curves is without consequences for analysis of mechanical performance: for low temperatures (at cold side), the steel mechanical properties

/250

are not affected, and for higher temperatures (hot side) the calculated curves are very close to experimental ones and in the safe side as well. Once validated with test results, using above thermal properties, the numerical model has been used to study the thermal regime of steel studs by varying different main parameters affecting the thermal behaviour of partition walls such as the height and the cross-section size. Calculations have been performed for partition walls (with 25 mm plasterboards thickness) with and without internal insulation as well as for 3, 6, 12 and 20 m heights and 150, 250 and 350 mm void thickness (corresponding to stud section).

0100200300400500600700800900

0 10 20 30 40 50 60 70Time (min)

Tem

pera

ture

(°C

)

T A EXP CTCIMT B EXP CTCIMT C EXP CTCIMT A SIMTB SIMT CE SIM

TA, test resultsTB, test resultsTC, test resultsTA, simulationTB, simulationTC i l ti

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70Time (min)

Tem

pera

ture

(°C

)

Test-exposed sideTest- centre of the chamberTest- unexposed sideSimulation- exposed sideSimulation- centre of the chamberSimulation - unexposed side

TA, test results TB, test results TC, test results TA, simulation TB, simulation TC, simulation

Figure 5-20: Temperature comparison of stud heating between calculation and test for non

insulated specimen

Figure 5-21: Temperature comparison of stud heating between calculation and test for

insulated specimen From numerical results, the following conclusions can be drawn:

- For non-insulated partition walls, the CFD heat transfer analysis shows that the hot gas movement inside the cavity leads to a higher gas temperature at the top end of studs and a lower temperature at the bottom end. The maximum temperature difference could be about 40°C. However, the effect of this hotter gas in top part of void seems to be of no significance considering the test results. In fact, during the tests, the temperature rise is usually more rapidly in the specimen parts nearest the mid-height than the top end. This difference between calculations and test results is explained on the one hand by the deflection of the steel stud (bending effect) which causes more cracking of plasterboard at this position leading to a more rapid heating of steel stud and on the other hand by the fact that the heating at ends of the specimen is affected in addition by edge effect. These effects are however not taken into account by the model;

- For partitions walls without internal insulation, the thermal regime of steel studs is very similar between all cases considered in this study, in spite of the very large variation of geometrical parameters (cross-section dimensions and stud height) as shown in figure 5-22;

- In the cases with internal insulation, the temperature distribution over the height of the specimen is uniform while there are very large temperature gradients within the cross-section. Temperature rises at the exposed side are analogous for all specimen widths and are fairly similar to those found at the same location for the non-insulated cases. On the other hand, temperatures increase less rapidly at mid-depth of the specimen when increasing the stud section (see figure 5-23) because of the longer evaporation stage of the water contained in the internal insulation;

- Globally, on the exposed side, the temperature increases quickly to 100°C (in 15 min). Then the temperature stay approximately constant until the moisture content in the plasterboard has been evaporated. At last, after 40 min, the temperature rise increases rapidly again. On the unexposed side, the temperature rise is later due to the void between plasterboards or internal insulation which restricts the passage of

/250

heat through the cavity causing an accelerated temperature rise in hot flange and a delayed temperature rise on the cold flange.

0

100

200

300

400

500

600

0 20 40 60 80 100 120Time (min)

Tem

pera

ture

(°C

)

Tmax, L=3mTmin, L=3mTmax, L=6mTmin, L=6mTmax, L=12mTmin, L=12mTmax, L=20mTmin, L=20m

0100200300400500600700800900

1000

0 20 40 60 80 100 120Time (min)

Tem

pera

ture

(°C

)

150mm, exposed side150mm, mid-width of chamber150mm, unexposed side250mm, exposed side250mm, mid-width of chamber250mm, unexposed side350mm, exposed side350mm, mid-width of chamber350mm, unexposed side

Figure 5-22: Temperatures calculated for chambers without internal insulation and 6m

height as function of chambers width

Figure 5-23: Temperatures calculated for chambers with internal insulation as function

of chambers width

5.3.2 Benchmark numerical study of mechanical behaviour of steel studs maintained by plasterboards using different computer codes

In order to study the validity of advanced numerical model to simulate the mechanical behaviour of lightweight steel studs maintained by boards, a benchmark study using the computer codes ABAQUS (VTT), SAFIR (ARBED)and ANSYS (CTICM) has been made. The validation cases considered in this study concerns a cold-formed lip-stiffened C-section stud which is laterally restrained at both flanges by plasterboards, as it would be in a normal partition wall structure. As shown in figure 5-24, three calculations have been performed:

- Calculation 1: room temperature resistance calculation. The first modelled case (case a) considers the buckling behaviour of the stud under normal temperature conditions subjected to an eccentric axial load,

- Calculation 2: reaction force calculation at elevated temperatures. The second case studied here (case b) involves the same stud as in Case 1, but both ends of the stud are also restrained axially. No external loads are applied and the stud is under heating condition assuming a uniform temperature distribution over the height of the stud. At any time the temperature is constant in each flange, and varies linearly from one flange to the other flange as shown figure 1,

- Calculation 3: high temperature resistance calculation. The third studied case involves the always same stud as in case 1 but without axial restraint. Constant vertical load of 25 kN is applied on the free end of the steel stud.

/250

Loade

20°C 20°C

150

57

1.2

13

Load e

150

57

1.2

13

a) stud column under normal temperature condition

b) Stud column restrained axially restrained at both ends

c) Stud column under fire condition

Figure 5-24: Cases used for validation study of mechanical behaviour

As example of results, the reaction force curves calculated by computer codes for case 2 are given in figure 5-25. It can be noted that the predicted maximum loads were practically the same in all three models. Figure 5-26 shows the axial displacement calculated at the top of the stud for case 3. All the numerical results show a very similar behaviour, the curves running almost parallel throughout the analyses.

0

10

20

30

40

50

0 10 20 30 40 50Time (min)

Rea

ctio

n Fo

rce

(kN

)

VTT ABAQUS Case2_04VTT ABAQUS Case2_05CTICM ANSYS resultsProfilARBED SAFIR results

-5

0

5

10

15

0 20 40 60 80Time (min)

Axi

al d

ispl

acem

ent (

mm

) CTICM ANSYS resultsProfilARBED SAFIR resultsVTT ABAQUS Case3_03

Figure 5-25: Reaction force curves for Case 2 between codes

Figure 5-26: Axial displacements calculated for Case 3 between codes

The most important results of the three simulation cases using ABAQUS (VTT), ANSYS (CTICM) and SAFIR (ProfilARBED) are summarized in table 5-11. It can be found that, the comparison between different computer codes shows a good agreement between themas it has been already explained previously.

/250

ABAQUS ANSYS SAFIR

Ultimate load Fu (kN) 68.4 51.9 51.293 Case 1 Axial displacement at

Fu (mm) 3.55 2.94

Ultimate reaction force Fu (kN) 46.43 50.62 50.77

Case 2 Time at Fu (min) 42.5 45.0 45.8

Elongation at 20°C (mm) -1.15 -1.15 -0.5

Maximum elongation emax (mm) 11.14 10.88 10.53 Case 3

Time at emax (min) 72.2 72 70

Table 5-11: Summary of main results of different codes

5.3.3 Numerical modelling of fire tests on steel studs maintained by plasterboards

The detailed results of the numerical analysis using ANSYS and ABAQUS performed with four fire tests of lightweight steel studs maintained by plasterboards presented in paragraph 5.2.3 (namely tests CTICM 2, CTICM 5, VTT 3 and VTT 5) as well as with one fire tests on Acoustic Walls Stud (AWS), namely test VTT 1, are given hereafter [20, 21, 22, 23 and 24].

5.3.3.1 Assumptions for numerical simulations

The numerical simulations of the mechanical behaviour of steel studs maintained by plasterboards and exposed to fire have been performed using the following assumptions:

• The whole steel stud is modelled with shell element as shown in figure 5-27;

a) Finite element of ANSYS for standard c-

section b) Finite element mesh of ABAQUS

for AWS section Figure 5-27: Modelling of steel studs with shell element

• The connection of steel stud with plasterboard is represented by a boundary condition

restraining the lateral displacement of it at position of screws. These restrained displacement conditions (restraining UX) are located only at the centre of the exposed flange for test CTICM 5, and at the centre of both exposed and unexposed

/250

flanges for others tests. As example, the position of screws is reported in figure 5-28 for standard c-section.

Y=165 Y=130

Y=473.75 Y=638

Y=782.5

Y=1400

Y=1146 Y=1091.25

Y=1708.75

Y=1654

Y=2017.5 Y=2162

Y=2326.25

Y=2670 Y=2635

Exposed flange

Unexposed flange

Web

p

Figure 5-28: Position of screws along the

steel stud

Figure 5-29: Applied load conditions (pressure on free end surface parallel to Z

axis) o The axial load is applied as a surface load as shown in figure 5-29. The load

application direction (parallel to Z axis) is kept unchanged. For specimens under centric load, an eccentricity of 5 mm was however used in numerical simulations.

Lateral restrain condition for screws

Free end

Free end



Steel stud

Rigid part

Steel stud

Rigid part


/250

• To illustrate the effects of end restraint conditions, the behaviour of steel studs is simulated with two different end conditions:

o hinged at both ends (restraining UX, UY, ROTY and ROTZ), or o Fixed at one end (restraining all degrees of freedom at the bottom of stud) and

hinged at the other end. Moreover, both ends of steel stud are modelled using a stiffer material (corresponding to blue colour element) with the value of modulus of elasticity taken as temperature–independent value of 210×105 MPa. As an example, figure 5-30 shows the boundary conditions which have been adopted in the numerical simulations of test CTICM 2, when the steel stud is assumed as hinged at both ends.

• With regard to CTICM test results, a temperature gradient has been assumed along the length of the steel studs as shown in figure 5-31. This gradient is defined from the 3 temperature fields related to the sections N1, N2 and N3, assuming a linear variation of temperatures between these sections and assuming a uniform temperature distribution beyond and to stud ends. The temperatures applied in VTT tests were based on the temperatures recorded at mid-height of the columns during the tests. The modelled temperatures were constant over column height and piecewise linear over section height.

• Temperatures along the edge stiffeners were taken as equal to those of the web at the corresponding height.

Exposed flange

Unexposed flange

WebTemperature field N2

Temperature field N2

Temperature field N1

Y=0

Y=1400

Y=740

Y=2060

Y=2800

150

57

1.2

13

Figure 5-31: Temperature gradient along the steel stud in numerical modelling

Figure 5-32: Section temperature distribution on steel stud in

numerical modelling

• The temperature measurement obtained at several points of the steel section has allowed introduce a temperature field of sufficient accuracy directly into the numerical simulations. At any time during the test, the temperature is constant in each flange, and varies linearly from one flange to the centre of the web, then linearly again from the centre of the web to the other flange, (see figure 5-32). The temperature field is then fully described by the evolution of 3 particular temperatures, the temperature in the exposed flange, the temperature in the centre of the web and the temperature in the unexposed flange.

/250

• Initial imperfection obtained from eigenvalue buckling analysis is used in numerical simulations. It consists of sinusoidal waves in the web with maximum amplitude of 1 mm.

• The mechanical material properties of steel stud as a function of temperature have been taken to be in accordance with the proposed reduction factor for steel of Type B (see Chapter 2), assuming the following mechanical properties at room temperature: yield strength equal to 402 MPa and modulus of elasticity equal to 210000 MPa. Poisson ratio was taken as a constant value of 0.3.

• The temperature dependent value of the coefficient of thermal expansion was taken as that given in prENV1993-1-2 and was applied to the whole structure (also the end parts having higher strength).

5.3.3.2 Results of numerical modelling

Some comments related to each analysis are given here while general conclusions and the summary of all results are presented in paragraph 5.5.3.

Fire test VTT 3 The temperature distribution on the steel stud assumed in the numerical simulations of test VTT3 is presented in figure 5-33. It should be noted that a uniform temperature has been assumed over the height of the stud.

0100200300400500600700800900

1000

0 10 20 30 40 50 60 70 80 90Time (min)

Tem

pera

ture

(°C

)

exposed side flangewebunexposed side flange

-10

-5

0

5

10

15

20

25

0 10 20 30 40 50 60 70 80 90Time (min)

Late

ral d

ispl

acem

ent (

mm

) Test result D2Test result D3test result D5Test result D6CTICM analysis (two free ends)VTT analysis (two free ends)CTICM analysis (one end fixed)VTT analysis (one fixed end)

Figure 5-33: Section temperature distribution assumed for test VTT 3

Figure 5-34: Lateral displacement of steel stud calculated at mid-height of test VTT 3

The evolution of the lateral displacement calculated at mid-height of the steel stud is given in figure 5-34. These displacements are compared to the measured ones. In all cases, the displacements obtained in the numerical analysis are larger than those obtained in the test. If more attention is paid to the failure mode, it can be found that experimental failure mode of the specimen is different from that ascertained numerically. In fact, the test specimen failed at the mid-height of the stud, but the numerical models failed near the unloaded end of the stud, as shown in figures 5-35 and 5-36. However, a slight dent can also be seen at the top end of the left stud in the test specimen. It is therefore not clear whether the failure originated at the end of stud or at its mid-height. In addition the specimen seems to buckle towards the unexposed side in the fire test while in calculations the steel stud buckles towards the furnace (compression on the unexposed side). A possible explanation of this difference may be the fact that when increasing temperature some unintentional eccentricity of loading appears on the exposed side due to differential thermal elongation of the specimen. The differential thermal elongations between exposed and unexposed flanges (as a result of the temperature gradient across steel stud) may lead to a full contact of exposed flange and at

/250

meantime a non contact of unexposed flange to end steel plates which creates then a shift of the applied load towards the exposed side. However, despite these differences of behaviour, the failure time corresponds well with that obtained in the test.

Figure 5-35: Failure modes obtained in test VTT 3

/250

a) VTT analysis: two free ends b) VTT analysis: one fixed end

c) CTICM analysis: two free ends b) CTICM analysis: one fixed end

Figure 5-36: Failure modes predicted in numerical analysis for test VTT 3

/250

Fire test VTT 5 The temperature distribution on the steel stud assumed in the numerical simulations of test VTT 5 is presented in figure 5-37. The displacements predicted in the numerical analysis are larger than those obtained in the test, as seen from figure 5-38. When the steel stud is assumed as hinged at both ends, the failure time is higher in the numerical calculations than in the test. On the other hand, there is a good agreement between measured and calculated failure time in the case of end restraint conditions at one end (the steel stud is fixed at one end).

0100200300400500600700800

0 10 20 30 40 50 60 70Time (min)

Tem

pera

ture

(°C

)

exposed side flangewebunexposed side flange

-10

0

10

20

30

40

50

60

0 10 20 30 40 50 60 70Time (min)

Late

ral d

ispa

lcem

ent (

mm

) Test result D2Test result D5CTICM ANSYS analysis (two free ends)VTT ABQ analysis (two free ends)CTICM ANSYS analysis (one fixed end)

Figure 5-37: Assumed section temperature distributions for test VTT5

Figure 5-38: Lateral displacement of steel stud calculated at mid-height of test VTT5

The failure mode of the stud is fairly well approximated by the numerical model, in particular when the steel stud is assumed as fixed at the top end, as seen in Figures 5-39 and 5-40. As observed in test (see figure 5-41), the failure occurs close to the top end of the stud column.

Figure 5-39: Failure modes obtained in VTT analysis for test VTT 5 assuming steel stud as hinged at both ends

/250

a) one fixed ends b) two free ends

Figure 5-40: Failure modes obtained in CTICM analysis for test VTT 5

Figure 5-41: Failure modes obtained in test VTT 5

Test CTICM 2 The temperature distribution (on the steel section and along the steel stud) assumed in the numerical simulations of test CTICM 2 is presented in figure 5-42.

/250

The evolution of lateral displacement calculated at mid-height of the steel stud is shown in figure 5-43. These displacements are compared to the measured ones. In the case of hinged conditions at both ends, there is a good agreement between measured and all calculated displacements. However, it should be noted that the stud displacements are somewhat over-estimated near the end of the test. A possible explanation of this difference may be the fact that studs are not really hinged at both ends and additional restraints may be provided by the loading jacks. Nevertheless, ccalculated failure time in numerical analysis as well as failure mode corresponds well with those obtained in the test. The longitudinal displacement of specimen hasn’t been directly the subject of measurement during the test (the value measured during the test including implicitly the rotation of the end steel plate). So, no comparison with the calculations has been made for this test. As example, figure 5-44, Figure 5-45 (numerical modeling) and figure 5-46 (Test) show the failure mode of specimen. There is a good agreement between test and calculations. The specimen failed towards the furnace in a combination of local buckling of the unexposed flange (located between the mid-height and the top end of the steel stud) and flexural bending about the major axis.

0100200300400500600700800900

0 20 40 60 80 100Time (min)

Tem

pera

ture

(°C

)

N3 exposed side flangeN3 webN3 unexposed side flangeN2 exposed side flangeN2 web corN2 unexposed side flangeN1 exposed side flangeN1 webN1 unexposed side flange

72 min

0

5

10

15

20

25

30

0 20 40 60 80Time (min)

Late

ral d

ispl

acem

ent (

mm

) N2 left stud testN2 right stud testN2 test averageCTICM ANSYS analysis (one fixed end)CTICM ANSYS analysis (two free ends)VTT ABQ analysis (two free ends)

Figure 5-42: Assumed section temperature distributions in numerical simulations of test

CTICM 2

Figure 5-43: Lateral displacement calculated at mid-height of steel stud for

test CTICM 2

a) ABAQUS analysis b) ANSYS analysis

Figure 5-44: Deformed shape predicted for steel stud of test CTICM 2 in VTT numerical

analysis

Figure 5-45: Deformed shape predicted for steel stud of test CTICM 2 in CTICM

numerical analysis

/250

Figure 5-46: Failure modes obtained in test CTICM 2

Test CTICM 5 The temperature distribution (on the steel section and along the steel stud) used in the numerical simulations of test CTICM 5 is presented in figure 5-47. The evolution of the lateral displacement calculated at mid-height of the steel stud is shown in figure 5-48. These displacements are compared to the measured ones. Again, the lateral displacements at mid-height predicted in numerical analysis are very close to those measured during the test. The longitudinal displacement of specimen hasn’t been directly the subject of measurement during the test (the value measured during the test including implicitly the rotation of the end steel plate). So, no comparison with the calculations has been made for this test. However, as example the measured longitudinal displacement is given in figure 5-49. It can be observed that at early stage of the test, the specimen bent towards the fire due to thermal bowing. Later, because of the decrease of temperature gradient between exposed and unexposed flanges, the bowing effect of the specimen reversed leading to a move away from fire. Finally, when temperature re-increased on the exposed side, the specimen bent again towards the furnace and failed by local compressive buckling on the cold flange near the mid-height of the specimen. Figures 5-50 to 5-52 show the failure mode of the specimen. The failure modes are similar in both numerical simulations and fire test with the failure occurring at mid-height of the stud.

/250

0

100

200

300

400

500

600

700

800

0 10 20 30 40 50 60 70Time (min)

Tem

epar

atur

e (°

C)

N3 exposed side flangeN3 webN3 unexposed side flangeN2 exposed side flangeN2 webN2 unexposed side flangeN1 exposed side flangeN1 webN1 unexposed side flange

63.5 min

05

1015202530354045

0 5 10 15 20 25 30 35 40 45 50 55 60 65Time (min)

Late

ral d

ispl

acem

ent (

mm

) N2 left stud testN2 right stud testN2 test averageCTICM ANSYS analysis (one fixed end)CTICM ANSYS analysis (two free ends)VTT ABQ analysis (two free ends)


CTICM 5

Figure 5-48: Lateral displacement calculated at mid height of steel stud for test CTICM 5

-2

0

2

4

6

8

10

0 10 20 30 40 50 60 70Time (min)

Axi

al d

ispl

acem

ent (

mm

) Test dep 91

Test dep 92

Figure 5-49:Vertical displacement measured at the bottom end of test specimen CTICM 5

Figure 5-50: Failure modes predicted in VTT analysis for test CTICM 5

a) One fixed end b) Two free ends

Figure 5-51: Deformed shape predicted for steel stud of test CTICM 5 in CTICM analysis

/250

Figure 5-52: Deformed state of studs in test CTICM 5

Test VTT 11 The temperature distribution on the steel section used in the numerical simulations of test VTT 11 is presented in figure 5-53. These temperatures correspond to the average measured temperatures at the mid-height of the two studs. The numerical model was capable of predicting the failure time of this test in a right way, as can be seen from figure 5.54 and 5.55. The lateral displacement curves obtained from the numerical analysis are a slightly higher than the test ones, but the axial displacement curves follow closely each other until prior to failure. The deformed shapes of both tested specimen and the numerical model are shown in figure 5-56 and figure 5-57, respectively. The agreement of the failure mode is rather good. However, it should be noted that the test failure occurred near the end of the stud, while in the numerical model, the large displacement took place near the mid-height of the stud. A possible explanation of this difference may be the fact that the stud is not uniformly heated over its whole length as assumed in calculations.

-20

-10

0

10

20

30

40

50

60

0 5 10 15 20 25 30 35 40 45 50 55Time (min)

Late

ral d

efle

ctio

n (m

m)

VTT analysisTest D2Test D5


VTT 11

Figure 5-54: Lateral displacement calculated at mid height of steel stud for test VTT 11

/250

-6-4-202468

1012

0 10 20 30 40 50 60Time (min)

Axi

al e

xpan

sion

(mm

)

VTT analysisTest C1Test C2

Figure 5-55: Axial displacement measured at the bottom end of test specimen VTT 11

Figure 5-56: Failure mode obtained in VTT analysis

Figure 5-57: Deformed state of studs in test VTT 11 Short summary The most important results of the numerical simulations using ABAQUS (VTT) and ANSYS (CTICM) are summarised in the following table. It can be seen from Table 5-12 that the failure times have, in general, a good agreement with the test results, except in the case of test VTT 5. Looking at Table 5-13, it appears that the agreement of the lateral deflection at mid-height between the numerical model and the test result is more difficult to predict when the stud is centrically supported and loaded (tests VTT 3 and VTT 5) in particular near the end of tests. However, the agreement is good for the eccentrically loaded tests (CTICM 2 and CTICM 5) for both VTT and CTICM analyses.

/250

As a whole, the results of the finite element analysis on the tested specimens can be considered to be good. The behaviour of cold-formed steel studs at high temperatures can be modelled in a satisfactory way using advanced numerical models.

Test Test failure time (min) VTT analysis CTICM analysis

CTICM 2 72 72.5 71

CTICM 5 60 59 56

VTT 3 82 82 82

VTT 5 56 63 63.5

VTT 11 48.2 49.5 -

Table 5-12: Comparison of failure times of steel studs between tests and numerical modelling

Test VTT analysis CTICM analysis

CTICM 2 Close to test Close to test

CTICM 5 Close to test Close to test

VTT 3 Larger than in test Larger than in test

VTT 5 Larger than in test Larger than in test

VTT 11 Slightly larger than test -

Table 5-13: Observation about deflection at mid-height between test and numerical simulation

5.3.4 Full comparison between tests and numerical modelling

In addition to above examples of numerical analysis, other numerical calculations have been made dealing with 21 fire tests carried out at CTICM and VTT on lightweight steel C-sections and AWS-sections maintained by plasterboards. The results of these numerical calculations are summarised in Table 5-14 for tests carried out at CTICM and VTT. In this table, the failure time predicted for each specimen is given for two end restraint conditions (namely two free ends or one fixed end) and compared to the experimental failure time. Except two tests, globally the difference about failure times between advanced numerical modelling and experimental investigation does not exceed 15% as illustrated in figure 5-58, which is fully acceptable considering the various uncertainties inherent to test data such as the degree of rotational restrained at the ends of steel studs, the real eccentricity of loading or the value of the actual material properties.

/250

CTICM analysis VTT analysis Test Number

Measured failure time

(min) Hinged-hinged

Hinged-fixed

Hinged-hinged

CTICM 1 58.5 56.5 (1) (2)

CTICM 2 72 75 71 72.5 CTICM 3 52 57 52.5 (2) CTICM 4 63 57 66 (2) CTIMC 5 60 62 56 59 CTICM 8 53 (1) 56 (2) CTICM 9 54 64 65 (2)

CTICM 10 84 86 (1) (2) CTICM 11 88 85 82 (2) CTICM 12 65 75 72 (2) CTICM 13 64 61 (1) (2) CTICM 14 40 40 40 (2)

VTT 3 82 82 82 82 VTT 5 56 58 63.5 63 VTT 10 75 (2) (2) 49.5 VTT 11 48.2 (2) (2) 49.5 VTT 12 56.5 (2) (2) 43 VTT 18 74.5 (2) (2) 70.5 VTT 13 105.3 (2) (2) 87.4 VTT 14 83.0 (2) (2) 73.4 VTT 15 83.3 (2) (2) 80.0

(1) No failure occurs during the fire exposure (2) No calculated

Table 5-14: Calculated failure times of fire test specimens

0102030405060708090

100

0 20 40 60 80 100

CTICM testsVTT tests

Test failure time (min)

Cal

cula

ted

failu

re ti

me

(min

)

+15%

-15%

Figure 5-58: Comparisons of failure times between numerical calculations and tests

/250

From all these numerical studies, it can be concluded that:

- It is particularly difficult to obtain a good agreement with test results in case of the centrically loaded steel stud. For these tests, the failure mode of specimens predicted numerically is often different from experimental failure modes. In calculations, some specimens buckle on the exposed side while in the fire test steel studs buckles towards the unexposed side. A possible explanation of this difference may be the fact that when increasing temperature certain supplementary eccentricity of loading appears on the exposed side because of different contact effects with end plates due to differential thermal elongations of steel stud.. In addition, other eccentricity due to loading imperfection may also exist.

- For some tests, the difference between calculations and experimental results may be

the fact that the end restraint conditions at the bottom of studs turn out to be more hinged support condition rather than fixed as planned, in particular in CTICM tests.

- Differences between tests and calculations may be also explained by the difficulties

to model accurately the boundaries conditions and partials restraints provided by the adjoining structures, namely the plasterboards. The secondary structure (mainly the contribution of the plaster boards to the structural entity) is ignored except for the in-plane boundary conditions applied at the screw locations in the flanges. It is clear that plasterboards provide some axial and out-of-plane restraint to the stud, although their main function (in addition to providing fire protection) is to provide restraint in lateral (in-plane) direction. Moreover, during exposure to fire, plasterboards gradually degrade and may reach a condition at which they are no longer capable of preventing lateral buckling. However, there is no accurate information available for the modeling of all restraining characteristics (and their temperatures dependencies) of the plasterboards which have been neglected in the calculations.

In spite of some discrepancies, globally these comparisons show that the numerical modelling can simulate in appropriate way the structural behaviour of lightweight steel studs maintained by plasterboards and provide a good estimation of their failure time under fire situation.

5.4 DEVELOPMENT OF SIMPLE CALCULATION METHOD FOR LIGHTWEIGHT STEEL STUDS MAINTAINED BY BOARDS

5.4.1 Parametric study

In order to obtain simple design rules to predict the mechanical resistance of steels studs maintained by plasterboards under fire situation, a parametric study have been performed by varying different main parameters susceptible to affect the fire resistance of steel studs, such as cross-section size, eccentricity of loading, load level, buckling length and heating condition [25, 26].

5.4.1.1 Calculation assumptions

The different assumptions adopted in this study are:

• Length of studs: 3000 mm, 5100 mm, 9900 mm and 15000 mm. • Stud sections: C-sections 100x0.6 (small section), 150x1.2 (medium section) and

250x2.5 (large section) and AWS section 150x1.2;

/250

• Steel grade: S280 (small c-section) and S350 (medium and large c-sections and AWS section);

• Temperature field based on four heating conditions as shown figures 5-59 and 5-60 with uniform temperature for two flanges and linear temperature distribution for web;

• Uniform temperature distribution over the height of the steel studs; • Boundary condition: steel studs are hinged at both ends; • Lateral maintenance condition of studs: two sides (studs maintained laterally 150 mm

from each end of stud and every 300 mm between then); • Loading condition: axial and eccentricity of 0.5H (H: height of section) located either at

unexposed or at exposed sides. The load is constant during the fire; • Load level: 0.1 and 0.3 for small section but 0.3 and 0.5 for medium and large sections

(load level is based on FEM calculation results).

20 °C

30 min 90 min

100 °C

900 °C

Time (min)

Temperature (°C) T1

T2

20 °C

30 min 90 min

100 °C

1000 °C

Time (min)

Temperature (°C) T1

T2=100 °C

T2=0.3(T1-100)+100

T2=0.6(T1-100)+100

T1

T2 T1=T2 T1>T2

Figure 5-59: Uniform heating condition of steel studs for parametric studies

Figure 5-60: Heating condition of steel studs with temperature gradient for parametric

studies

5.4.1.2 Results of parametric calculations

Results of this parametric study have been presented in form of critical temperature as function of stud sections, stud lengths, heating conditions and loading conditions. In order to avoid heavy presentation of the report, only four examples are given here in figure 5-61 to 5-64 (for more details, see [25, 26]). The results are divided according to type of loading (centric or eccentric) and its magnitude (0.1, 0.3 or 0.5 time of failure load).

0100200300400500600700800900

1000

3 6 9 12 15

T1, uniform heating T2, uniform heatingT1, gradient heating 1 T2, gradient heating 1T1, gradient heating 2 T2, gradient heating 2T1, gradient heating 3 T2, gradient heating 3

Length (m)

Tem

pera

ture

(°C

)

0

100

200

300

400

500

600

700

800

3 6 9 12 15


Length (m)

Tem

pera

ture

(°C

)

Figure 5-61: Temperatures calculated for the small section and a load level of 0.1 (as

function of heating conditions) assuming a centric loading

Figure 5-62: Temperatures calculated for the medium section and a load level of 0.3 (as function of heating conditions) assuming an

eccentric loading at unexposed side

/250

0

100

200

300

400

500

600

700

800

3 6 9 12 15


Length (m)

Tem

pera

ture

(°C

)

0100200300400500600700800900

3 5 7 9


Length

Tem

pera

ture

(°C

)

Figure 5-63: Temperatures calculated for the large section and a load level of 0.5 (as

function of heating conditions) assuming a eccentric loading at exposed side

Figure 5-64: Temperatures calculated for the AWS section and a load level of 0.3 (as

function of heating conditions) assuming an centric loading

From these results, following conclusions have been drawn:

• Under uniform heating, the critical temperature of studs increases slightly with the height if they are subjected to the same load level;

• In most cases, with temperature gradient, the failure of steel studs occurs with lower temperatures as their height increases due to a larger bowing effect;

• Steel studs failed in combination of local, distortional buckling and flexural bending about the strong axis;

• For shorter studs, it does appear that under uniform heating the failure mode is dominated by local buckling while with temperature gradient a combination of local buckling and distortional buckling globally is the governing failure mode;

• For tall studs under uniform heating, bending moment becomes significant in the stud cross section, so that failure is controlled by flexural buckling about the strong axis. With temperature gradient, the failure mode of stud is a combination of distortional buckling (exposed flange) and flexural buckling;

5.4.2 Proposal of a simple calculations rule for assessing fire resistance of lightweight steel studs maintained by boards

The method proposed for steel studs maintained by plasterboards consist in using the same type of calculation approach proposed for lightweight structures at room temperature in Part 1.3 of Eurocode 3 [1], with inclusion of modified material properties depending on temperature and taking into account thermal bowing effects. A full description of this simple calculation approach is given hereafter.

5.4.2.1 Simplified design method for studs under flexural buckling

Using the same type of approach as in Part 1.3 of Eurocode 3 [1] for cold formed steel members at room temperature, the buckling resistance of steel studs maintained by plasterboards under compression, Nfi,Rd, can be determined from an appropriate buckling curve which relates load capacity, Nfi,Rd, to the design resistance load, Nfi,c,Rd, and the elastic critical load, Nfi,r, as follows:

Nfi,Rd = χ(λ θ) Nfi,c,Rd (5-1)

/250

where χ is the reduction factor depending on the relative slenderness at elevated temperature λ θ , which may be defined as:

cr,fiR,pl,fi N/N=θλ (5-2) The reduction factor should be determined in the same way as at room temperature, but using an appropriate buckling curve. It should be reminded that part 1.1 of Eurocode 3 [7] considers three different column buckling curves for different types of column and Part1.3 of Eurocode 3 [1] recommends buckling curve “b” for C-section The design resistance load, Nfi,c,Rd, of the steel stud is calculated using the total effective cross-section of the stud. The resistance is assumed to be the summation of the strengths of alls individual plane elements i (flange, flange stiffeners and web) multiplying the corresponding effective element areas Aeff,i (depending of the effective width and obtained by assuming a uniform compressive stress) taking into account the effect of temperature on these elements, i.e

∑=i

i,,yi,effRd,c,fi fAN θ (5-3)

where i,,yf θ is the yield strength of steel at elevated temperature. Nfi,cr is the Euler buckling load calculated as a function of the effective flexural stiffness of the cross-section (EI)fi,eff and the buckling length Lθ of the stud in fire situation, i.e.:

Nfi,cr = π² (EI)fi,eff /Lθ² (5-4) The effective rigidity, (EI)fi,eff, is determined from the modulus of elasticity Ei,θ of each plate element at the appropriate elevated temperature θ multiplied by the second moment of area of each element Ii,θ:

θθ ,i,ii

eff,fi I.E.)EI( ∑= (5-5)

The reduction factor χ for buckling resistance is determined according to:

2θ

2φφ

1χλ−+

= but 1≤χ (5-6)

with

]0.2)-α([10.5 2θθ λλϕ ++= (5-7)

where α is an imperfection factor, depending on the appropiate buckling curve (as function of the buckling axis and geometrical characteristics). The effects of local buckling are taken into account on the basis of the effective widths of individual plate elements. The reduction factor ρ is determined from:

/250

1=ρ , when 673.0p ≤λ (5-8)

p

p/055.01λ

λρ

−= , when 673.0p >λ but 1≤χ

in which the plate slenderness pλ is defined by:

σπν

λEk

f)1(12t

b2

y2

pp

−= (5-9)

where t is the plate thickness, E is the elastic modulus of steel, ν is the Poisson’s ratio and

σk is the plate buckling factor which depends on the edge condition and stress distribution of the plate ( 4k =σ for elements under uniform compression).

5.4.2.2 Simplified design method for studs under bending and axial compression

The stability check of a lightweight steel member loaded by a combination of axial compression and combined bending requires the satisfaction of the following formula:

1M

)MM(kM

)MM(kNN

z,Rd,fi

sd,zsd,zz

y,Rd,fi

sd,ysd,yy

Rd,fi

sd ≤+

++

+∆∆

(5-10)

Where sdN is the applied axial load; sd,yM and the sd,zM are the applied bending moments

about the strong axis (y-y) and the weak (z-z) one, respectively; sd,yM∆ and the sd,zM∆ are the additional moment about the strong (y-y) and the weak (z-z) axis due to neutral axis shifts; Nfi,Rd, is the design buckling resistance of a compression member according to (1); Mfi,Rd,y and Mfi,Rd,z are the design bending moment resistance (based on the effective cross-section that is subjected to bending moment only) about the strong (y-y) and the weak (z-z) axis, respectively; yk and zk are modifications factors to take account of non uniform bending moment distributions in the column about the strong (y-y) and the weak (z-z) axis. To calculate the fire resistance of steel stud under eccentric load with temperature gradient, the following assumptions are made in this approach:

- The stress-strain relationships of cold formed steel at elevated temperature are perfectly linear elastic-plastic. The yield stress is taken as the 0.2% proof stress at any temperature level.

- Effects of local buckling and distortional buckling are taken into account according to Part 1.3 of EC3 [1] using the effective width for all plate elements;

- The flange stiffeners and the flanges on each side of the cross-section have the same temperature. Therefore, the method in Part 1.3 of Eurocode 3 [1] is directly used to evaluate their effective widths, but using the elevated temperature properties to replace those at ambient temperature;

- The temperature distribution along the web is linear. Due to the different steel properties at non uniform temperature distributions, the weighted average steel resistance (strength and stiffness) value is used to calculate the web effective width;

/250

- As the stud section is maintained by plasterboards at both flanges, the stud can deflect only about the strong axis. Therefore, Mz,sd=0. Flexural stiffness of the plasterboards and its influence to prevent displacement in the plane of the cross-section are taken into account;

- The bending moment about the weak axis (z-z) due only to the shift of the neutral axis is neglected: ∆Mz,sd=0 because its influence is very small;

- The modifications factors yk and zk to take account of non uniform bending moment distributions in the column are taken as 1.0;

- To simplify calculations, when compression is on the hot side of stud, the moment resistance Mfi,Rd of the cross-section is calculated with yielding occurring on the hot flange and a linear stress distribution in the web. When compression is on the cold side, the moment resistance is calculated with yielding occurring on both flange with bi-linear stress-distribution in the web on the hot side;

- At the mid-height of the column, the bending moment about the strong axis (y-y) is a result of the neutral axis and the thermal bowing. Near the stud ends, the bending moment about the strong axis is caused by a neutral axis shift only. Design calculations should check both cross-sections.

The bending moment at the end of stud about the strong axis is:

)ee(NMM Esdsd,ysd,y ∆∆ −=+ (5-11) At the mid-height, the bending moment about the major axis is:

)eee(NMM ETsdsd,ysd,y +−=+ ∆∆∆ (5-12) in which e is the effective eccentricity of the applied load; Ee∆ is the shift of neutral axis in the (z-z) direction (see figure 5-65), and Te∆ is the maximum mid-span horizontal deflection due to temperature gradient across the section defined as:

cr,fi

sd0T

NN1

1ee−

=∆ (5-13)

where 0e is the deflection related to thermal bowing, Nsd is the applied load and Nfi,cr is the Euler buckling load:

h8TLe

2T

0∆α

= (5-14)

in which ∆T is the temperature difference across the stud section in °C, h is the web depth, L is the column height and Tα is the thermal expansion coefficient of steel.

/250

y

z

h

b

c

y

z

y

z

e∆E

y

z

e∆T

a) cross-section at o at original position

b) temperature distribution on steel stud

c) Shift of neutral axis due to non uniform distribution

of rigidity

b) deflection of stud column at mid-height due

to thermal bowing

Figure 5-65: Shift of neutral axis due to temperature effects The movement of the neutral axis can be calculated from:

∑∑

=

ii,i

iii,i

E AE

AyEe

θ

θ

∆ (5-15)

where yi is the distance from the effective plate element i to the neutral axis at ambient temperature.

5.4.3 Comparison between numerical model and simplified method

For each cross-section, comparisons have been made between critical temperatures predicted analytically with the design method given above and results obtained numerically with ANSYS [27]. As an example, figures 5-66 and figure 5-67 show the comparison between ANSYS results (as function of buckling length and heating conditions) and simplified calculation method for studs under centric load, with small and medium c-section respectively. Figures 5-68 and 5-69 give similar results for studs with medium and large sections respectively, under eccentric load applied on cold or hot side. On the basis of the whole comparison, the following observations can be drawn:

- For medium and large sections the difference between the simplified method and the numerical model does not exceed 10%, except in the case of studs subjected to an eccentric load applied on the unexposed side, where some points are on the unsafe side;

- For small section, the majority of points situate on the unsafe side; - Under uniform temperature and with small temperature gradient, namely T2=0.6 (T1-

100)+100, all predicted critical temperatures using simplified method are close to the temperatures given by ANSYS. The simple method gives slightly higher resistance than numerical model;

/250

- With high temperature gradient, in some situation, (small section, large eccentricity on the unexposed side and lower load level), critical temperatures given by the simplified method may be 30% higher than the numerical temperatures (ANSYS).

0

100

200

300

400

500

600

700

800

0 100 200 300 400 500 600 700 800Temperature Ansys (°C)

T2=100T2=0.3(T1-100)+100T2=0.6(T1-100)+100T2=T1

Unsafe

safe

+10%

-10%

Tem

pera

ture

sim

plifi

ed m

etho

d (°

C)

0

100

200

300

400

500

600

700

0 100 200 300 400 500 600 700Temperature Ansys (°C)

T2=100T2=0.3(T1-100)+100T2=0.6(T1-100)+100T2=T1

Unsafe

safe

+10

-10%

Tem

pera

ture

sim

plifi

ed m

etho

d (°

C)

Figure 5-66: Comparison of temperatures calculated for the small section under centric

load and a load level of 0.1 (as function of heating conditions)

Figure 5-67: Comparison of critical temperatures calculated for the medium

section under centric load and a load level of 0.3 (as function of heating conditions)

0100200300400500600700800900

10001100

0 100 200 300 400 500 600 700 800 900 1000

1100Temperature Ansys (°C)

T2=100T2=0.3(T1-100)+100T2=0.6(T1-100)+100T2=T1

Unsafe

safe

+10%-10%

Tem

pera

ture

sim

plifi

ed m

etho

d (°

C)

0

100

200

300

400

500

600

0 100 200 300 400 500 600Temperature Ansys (°C)

T2=100T2=0.3(T1-100)+100T2=0.6(T1-100)+100T2=T1

Unsafe

safe

+10

-10%

Tem

pera

ture

sim

plifi

ed m

etho

d (°

C)

Figure 5-68: Comparison of critical temperatures calculated for the medium

section under eccentric load on the unexposed side and a load level of 0.3 (as

function of heating conditions)

Figure 5-69: Comparison of critical temperatures calculated for the large section

under eccentric load on the exposed side and a load level of 0.5 (as function of

heating conditions)

In order to have a better understanding of the discrepancy between both models, the failure mode of steel stud columns given by ANSYS has been analysed. From results of this investigation, it appears that:

- As illustrated in figures 5-70 and 5-71, different failure modes have been obtained, namely local buckling, flexural buckling about the strong axis or a combination of distortional and flexural buckling.

- Globally, there is a good agreement between simple calculation method and numerical model when failure is dominated by local buckling or a combination of local and flexural buckling about the major axis (see figure 5-70).

- , The dispersion of results is large when the distortional buckling becomes predominant. As seen in figure 5-71, in this case each component plate (flanges and web) distorts with lateral displacement (rotation of each flange around the flange-web junction inwards) leading to an excessive deformation of the stud section and decrease significantly its bending resistance.

/250

Apparently, differences between the numerical model and the simple calculation method appear to be mainly due to the different appreciation of the distortional buckling effects on the fire resistance of studs. In fire situation, numerical calculations show that the distortional buckling may lead to important deformations of the stud section which may have a significant effect on the strength (moment resistance) of the section. The proposed design method based on effective width calculations seems to be not capable of predicting this effect rightly especially when important temperature gradient is present.

Local buckling

fire

Distortional buckling

fire

a) Stud length L=3m b) Stud length L=9.9m

Figure 5-70: Failure mode of stud column with medium section subjected to a centric load (load level of 0.3) with higher temperature gradient (T2=100)

Distortional buckling

fire

distortional buckling

fire

a) Stud length L=3m b) Stud length L=9.9m

Figure 5-71: Failure mode of stud column with large section subjected to an eccentric load located at the unexposed side (load level of 0.3) with higher temperature gradient (T2=100)

5.5 CONCLUSIONS

In this chapter, the mechanical behaviour of lightweight steel studs maintained by plasterboards have been investigated both experimentally and numerically. From experimental observations and measured results, some precious data have been established on effects of significant parameters susceptible to affect the performance of lightweight steel

/250

members. Using advanced calculation models, the fire resistance of lightweight steel studs maintained by plasterboards has been simulated and compared with fire test results. These comparisons show that numerical models is capable of predicting appropriately the structural behaviour of lightweight steel studs and provide a good estimation of their resistance under fire situation in spite of the various uncertainties inherent to test condition. Then, advanced calculation models have been used to perform a very wide range of numerical simulations, with the aim of developing a suitable approximate calculation method. On the basis of corresponding numerical results and using the same type of buckling approach proposed at room temperature in Eurocode 3 (but including modified material properties depending on temperature and taking into account thermal bowing effects), a simple calculation model has been proposed. It have been shown through the comparison with numerical results that the proposed calculation model is suitable to predict with a good precision the fire resistance of cold-formed steel c-section with small temperature gradient. Concerning the case of AWS section and steel section under important temperature gradient, additional theoretical investigation should still be going on in order to develop a calculation models capable of predicting, with an acceptable accuracy, some special phenomena due to sharp temperature gradient of steel studs under fire situation.

/250

6 FIRE BEHAVIOUR OF LOAD-BEARING WALLS, FLOORS AND THEIR ASSEMBLIES

6.1 GENERAL

In previous chapters, the fire behaviour (thermal and mechanical) of cold formed lightweight steel members were investigated mainly on the basis of individual elements. However in real buildings, these elements are more widely used in assembled frames, as it is shown in figure 6-1 to form either vertical or horizontal panels corresponding respectively to partition walls and floors.

Figure 6-1: Building assembly of cold formed lightweight members Nowadays, a number of fire tests have been carried out throughout the world with either horizontal or vertical assembled panels [8, 9]. But the fire test was never performed with global system including both horizontal and vertical panels. As a consequence, a part of work within this project is concentrated on this item in order to get following technical information:

• global behaviour of wall-floor assemblies compared to separate panels under fire situation

• behaviour of joint between wall and floor panels during fire Considering the complexity of the problem as well as time schedule of the project, our attention is paid mainly on experimental investigation. Some numerical simulations were carried out only on floor members because an important numerical work has been already done in previous parts of the project on members used in wall panels.

/250

6.2 EXPERIMENTAL WORK

6.2.1 Testing methodology

In order to get a good comparison between wall-floor assembly and independent wall or floor elements, a test programme was discussed and agreed by all partners and it can be summarised as follows:

• test with floor element based on Finnish construction system • test with wall element based on Finnish construction system • test with floor-wall assembly based on Finnish construction system • test with floor element based on British construction system • test with wall element based on British construction system • tests with floor-wall element based on British construction system

The principle of these tests is illustrated in figure 6-2.

Wall element Floor element Wall-floor assembly

Figure 6-2: Different types of test with load-bearing lightweight steel members

Within this test programme, two European construction systems were investigated and for each construction system, wall, floor and wall-floor assembly have been all tested. This testing procedure allowed study, on the one hand, the difference of fire behaviour between individual members and their assemblies, and observe, on the other hand, the fire performance of two different construction systems. It should be noted that two wall-floor assembly tests have been performed with UK construction system. In fact, different loading conditions have been adopted in these tests in order to obtain different failure mode of the assemblies.

6.2.2 Summary of test results

Within this test programme, seven fire tests have been carried out which can be summarised in following tables (Tables 6-1 and 6-2).

/250

It must be noted that two fire tests were used to investigate the fire performance of floor-wall assembly with UK systems. Only one of them is included in the summary table because of its common failure mechanism. However, some attention should be paid to the second assembly test with UK system in which a special failure mode joists is observed. This failure mode corresponds to squash failure of joists at floor-wall joint caused mainly by concentrated applied load from jacks (see figure 6-12). More discussion will be given in paragraph 6.2.4 about this phenomenon.

6.2.3 Examples of detailed test results

The experimental results obtained on the basis of UK construction system are presented here as an example in order to give a good idea of how elements behaved under various conditions. For more detailed test results, they are given respectively in [10, 11, 12].

6.2.3.1 Experimental results of floor element test (VTT)

The floor element is composed of six studs with a cross section of C250x72/64x2.5. These studs are, in one hand, linked together at both ends by two tracks using joint stiffeners (see figure 6-3), and on the other hand maintained by plasterboards at bottom (two layers of fire boards) and top (two layers of standard boards). The floor occupied a surface of more than 16 m² and supported simply at two short sides, the span of which is 5240 mm. The load was applied on the floor through three jacks and 24 points to simulate uniformly distributed load (see figure 6-3). The total applied load including the self weight of floor components represents a value of 416.7 kg/m² and remained constant during the test. The floor was exposed below to standard fire and the test lasted for about 69 minutes. More than 50 thermocouples were used to measure the heating of floor and the deflection of the floor is measured at 4 points. The typical experimental results from the test are shown in figure 6-4. The behaviour of the floor can be summarised as follows:

• a sudden temperature rise occurred between 40 and 50 minutes of fire at the interface of first and second layers, which means the destruction of the first layer and its detachment from the second layer of plasterboard;

• the deflection of the floor remained relatively weak until 67 minutes of fire and afterwards the collapse occurred quite quickly during a short duration of about 2 minutes;

• just before the collapse, the heating of steel studs was still low at a temperature level of 400 °C.

/250

Assembly Fire test

Floor

Wall Floor Wall

Global size 2.99x5.5 m2 span=5.24 m

2.8x3.0 m² (H x B)

2.99x5.5 m2 span=5.24 m

2.8x3.0 m² (H x B)

Stud section C 250x72/64x21.5x2.5 c/c 600

TC-150x57x1.2 c/c 600

C 250x72/64x21.5x2.5 c/c 600

TC-150x57x1.2 c/c 600

Plasterboards on exposed side

2 x GF15* and steel battens

GN13 + GF15* 2 x GF15* and steel battens

GN13 + GF15*

Internal insulation 70 mm glass wool 150 mm rock wool (30 kg/m3)

70 mm glass wool 150 mm rock wool (30 kg/m3)

Plasterboards on unexposed side

corrugated steel sheet and 2 x GL15*

GN13* corrugated steel sheet and 2 x GL15*

GN13*

Loading

2.50 kN/m

14 kN / stud e=15 mm on the exposed

side

2.68 kN/m

10.2 kN / stud axial load

Test duration 84 min 85 min 58 min Maximum temperature in

steel studs 915 oC** 940 oC** 935 °C in steel studs of floor element

Failure mode Buckling at mid-height towards exposed side

Loss of load-bearing capacity in bending

Loss of load-bearing capacity in bending of floor

Table 6-1: Summary of tests with Finnish system

/250

Assemblies Fire test

Floor

Wall Floor Wall

Global size of specimen 2.99x5.50 m2 span=5.24 m

2.80x3.00 m2 (h x b)

2.99x5.5 m2 span=5.24 m

2.8x3.0 m² (H x B)

Stud section C 250x67x2.0 c/c 600

C-150x1.2 c/c 600

C 250x67x2.0 c/c 600

C-150x1.2 c/c 600

Plasterboards on exposed side 2 x GF15* GN13 + GF15* 2 x GF15* GN13 + GF15*

Internal insulation - - - - Plasterboards on unexposed side 2 x GL15* GN13 + GF15* 2 x GL15* GN13 + GF15*

Loading

2.5 kN/m per stud 33 kN per stud and axial loaded

2.68kN/m per stud of floor 25 kN per stud of wall

Test duration 69 min 87 min 77 min

Maximum temperatures in steel studs

930 oC** 950 oC** 856 °C in studs of floor 427 °C in studs of wall

Failure mode

Loss of carrying capacity in bending

Buckling at mid-height towards unexposed side

Loss of carrying capacity of floor in bending

Table 6-2: Summary of tests with UK system

/250

Figure 6-3: The test set up of floor element

573

600

600

600

3000

5500

200

View1

View1

Joint stiffeners

Two layers of fire boards

D3

D2

D1

D4

Composition of the specimen

Loading condition

A

1310 1310

A - A

F F F

F

5500

B

B

A

3000

B - B

3100

5240

235

600600

600600

600

1460 710 710

F F F 50

150

860 1310 860 1160 1310

/250

0

200

400

600

800

1000

0 10 20 30 40 50 60 70Time (min)

Furn

ace

tem

pera

ture

(°C

)

TC_55 TC_56TC_57 TC_58TC_59 TC_60TC_61 TC_62TC_63 TC_64EN1363-1

0

200

400

600

800

1000

0 10 20 30 40 50 60 70Time (min)

Tem

pera

ture

(°C

)

C

E

B

F

A

D

C

AB

ED

F

Measured furnace temperatures versus EN1364-1 fire curve

Measured temperatures in steel studs and corresponding plasterboards

0

200

400

600

800

1000

0 10 20 30 40 50 60 70Time (min)

Tem

pera

ture

(°C

)

C

B

D

A

A

BC D

-100

0

100

200

300

0 10 20 30 40 50 60 70Time (min)

Def

lect

ion

(mm

) D1 D2

D3 D4

Measured temperatures in plasterboards Measured deflection versus time

Figure 6-4: Some representative experimental results

6.2.3.2 Experimental results of wall element test (VTT)

The wall element is composed of six studs with a cross section of C150x54x15x1.2. These studs are inserted respectively at bottom and top sides in two lightweight steel tracks (see figure 6-5). The two layers of plasterboards are used at both exposed side and unexposed side of the wall. For exposed side, the directly exposed layer is a fire board of 15 mm thick and the second layer is a standard board of 13 mm thick. The wall has a total height of 2800 mm and its width is 3000 mm. It was supported simply at bottom with a roller and fully restrained at top. The load was applied at the bottom through two jacks (see figure 6-6) without any eccentricity. The total applied load corresponds to a value of 33x4=132 kN (considering only four loaded studs) and remained constant during the test. The wall was exposed to standard fire and the test lasted for about 87 minutes. The typical experimental results from the test are shown in figure 6-7. The behaviour of the wall can be summarised as follows:

• the temperature increased slowly and remained at relative low level (about 100°C) until 45 minutes of fire;

• from 45 minutes of fire, the temperature rise was more rapid and it increased quite linearly until the collapse of the wall;

• at collapse instant, the maximum temperature was about 450°C; • The deflection of the wall remained quite small until 45 minutes of fire and its value

doesn’t exceed 3 mm. At this moment, the axial contraction seems to be only the effect of thermal elongation;

/250

• from 45 minutes of fire, the temperature rise led to a higher increase of lateral deflection and the axial contraction changed the sign due to the loss of stud stiffness at higher temperatures meanwhile the inclination changed also the sign due to more important thermal bowling;

• after reaching a maximum level of about 12 mm towards the exposed side at 65 minutes of fire, the lateral deflection of the wall stayed then at this level until its collapse which occurred on the contrary in the opposite side (unexposed side);

• the failure mode towards unexposed side was exactly the same as that already observed with maintained individual studs which may be caused by an additional eccentricity due to the shift of both hot section gravity centre and redistributed load centre.

3000 573 600 600 600

2800

D4

D2 D1

D5

D3

C1 C2

x

x

x

C1, C2

D4

D1, D2, D3

D5

/250

Figure 6-5: Test set up of wall element

0100200300400500600700800900

1000

0 15 30 45 60 75 90Time (min)

Furn

ace

tem

pera

ture

(°C

)

TC_59 TC_60TC_61 TC_62TC_63 TC_64EN1363-1

0

200

400

600

800

0 15 30 45 60 75 90Time (min)

Tem

pera

ture

(°C

)

Exposed side D

C

B

A

D

C B

A

Measured furnace temperatures versus

EN1364-1 fire curve Measured temperatures in steel studs and

plasterboards at mid-height

B - B A

A

B

3208 3460

50

Steel frame

-

3000

+

600 600 600 600 600

2800

2800

A - A

-

B

+

3208

34

60

3000

Non-load-bearing stud Non-

load-bearing stud

Loading beam

Steel frame frame

Hydraulic jacks

Free edge

Free edge

Rock wool

Four load-bearing studs

/250

0

100

200

300

400

500

0 15 30 45 60 75 90Time (min)

Tem

pera

ture

(°C

)Exposed side

A

BC A

B

C

0

100

200

300

400

500

0 15 30 45 60 75 90Time (min)

Tem

pera

ture

(°C

)

Exposed side

A

BC

AB

C

Measured temperatures in steel studs at the top

Measured temperatures in steel studs at the bottom

0

10

20

30

40

0 15 30 45 60 75 90Time (min)

App

lied

load

(kN

)

Applied load per stud

-5

0

5

10

15

0 15 30 45 60 75 90Time (min)

Late

ral d

isp.

(mm

) D2

D3

D1

D5D4

Applied load per stud versus time Lateral displacement versus time

-10-8-6-4-2024

0 15 30 45 60 75 90Time (min)

Axi

al d

isp.

(mm

)

C1 C2

-0.8

-0.4

0

0.4

0.8

1.2

0 15 30 45 60 75 90Time (min)

Incl

inat

ion

(deg

)

Inclination at bottom

Axial displacement versus time Inclination at bottom versus time

Figure 6-6: Typical experimental results of wall element test

6.2.3.3 Experimental results of floor-wall assembly test (CTICM)

In order to be consistent with floor and wall elements, the assembly is composed of a floor element supported at one side by a wall element (see figure 6-7). The wall element is made of six studs with a cross section of C150x54x15x1.2 inserted respectively at bottom and top sides in two lightweight steel tracks (see figure 6-5). These studs were insulated by two layers of plasterboards at exposed side and only one layer for unexposed side. For exposed side, the directly exposed layer is a fire board of 15 mm thick and the second layer is a standard board of 13 mm thick. The wall element of the assembly has a total height of 2800 mm and a width of 3000 mm. It was placed at bottom on a steel frame. The top of the wall is linked to floor element with the detail shown in figure 6-7.

/250

The floor element of the assembly has total length of 5500 mm, same as the floor test, It is simply placed at one side on a roll and linked to wall element on other side (see figure 6-7). The span of the floor considered from the central line of studs to the roll is 5240 mm which is also the same used in floor test. Concerning the load condition, the wall element was loaded on the top of every studs through three jacks (see figure 6-7) without any eccentricity. The total applied load corresponds to a value of 25x6=150 kN (considering all six loaded studs) and the loads remained constant during the test. The floor was loaded with steel blocks to simulate uniformed distributed load. The total weight of all steel blocks is 5802 kg leading to uniformly distributed load of 369 kg/m². In this case, the applied load on joist is 221 kg/m². The whole assembly was exposed to standard fire according to part1 of EN1.363. The test lasted for 78 minutes. The typical experimental results from the test are shown in figure 6-8. The behaviour of the assembly can be summarised as follows:

• the temperature increased slowly and remained at relative low level (about 100°C) in floor steel joists until 60 minutes of fire;

• the fall of first layer of bottom plasterboards in floor took place near 50 minutes of fire and it seems to occur firstly near simple support and about 20 minutes after at other location;

• after the fall of first layer of bottom plasterboards in floor, the temperature rise began to be slightly more important and it increased then more and more rapid until the collapse of the assembly

• In parallel, the temperature of wall element increased slowly to about 100 °C after 50 minutes of fire and then more rapidly to about 400 °C at collapse;

• The collapse of the assembly was caused by loss of load carrying capacity of floor after 76 minutes of fire. At this instant, the maximum temperature of steel joints is about 300 °C;

• The maximum lateral displacement of wall before collapse is about 10 mm towards the fire and at the moment of collapse, these displacements changed the sign which was apparently caused by the increase of floor deflection turning the wall away from the fire.

floor-wall assembly Detail of floor-wall joint

/250

Support and load condition of floor-wall assembly

Figure 6-7: Test set up of floor-wall assembly using UK system

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Furn

ace

tem

pera

ture

(°C

)

EN 1363-1

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

pera

ture

(°C

) C

A

E

D

B

D

ABC

E

Furnace temperatures according to EN 1363-1 versus time

Measured temperatures in steel joists and plasterboards of floor at midspan

Simple support

Joint

Joint stiffeners

Loading of floor with steel blocks

Loading of wall with jacks

/250

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

pera

ture

(°C

)

C

A

E

D

B

D

A B CD

0

100

200

300

400

0 10 20 30 40 50 60 70 80Time (min)

Tem

pera

ture

(°C

) C

A

E

D

B

DA

B

C

D

Measured temperatures in steel joists of

floor near simple support Measured temperatures in steel joists of floor

near joint

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

prat

ure

(°C

)

Exposed side D

C

B

A

D

CB

A0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

prat

ure

(°C

)

Exposed side D

C

B

A

D

CB

A

Measured temperatures in steel studs of wall at mid-height

Measured temperatures in steel studs of wall at top

0

100

200

300

400

500

0 10 20 30 40 50 60 70 80Time (min)

Tem

prat

ure

(°C

)

CB

A

A B

Cfire

-20

-10

0

10

20

0 10 20 30 40 50 60 70 80Time (min)

Late

ral d

ispl

acem

ent (

mm

)

D1 D2 D3

D4 D5 D6

Measured temperatures in steel track at floor-wall joint

Lateral displacement of wall versus time

Figure 6-8: Typical experimental results of UK floor-wall assembly test

6.2.4 Comparison of fire behaviour between elements and assemblies

As it has been explained previously, the floor and wall elements were tested separately at VTT and their assemblies were tested at CTICM. Therefore, it is very useful to compare the fire behaviour between individual elements and their assemblies. In addition, this comparison can be made with two different systems, that is Finnish and UK systems since they have been both investigated in our fire tests. Concerning the Finnish system, VTT carried out tests on individual floor element in 2000 and on wall element within this project. In the fire test performed at CTICM on the assembly of floor and wall element, the failure occurred at about 56 minutes of fire with floor joists. The

/250

comparison here is then focused on the behaviour of this element under two different types of structural systems. In fact, it can be found in summary table given in paragraph 6.2.2 (table 6-1) that the applied load on the floor in both tests is quite close (the applied load in CTICM test is slightly higher than that in VTT test). However, the fire resistance is significantly different (58 minutes in CTICM test and 84 minutes in VTT test). If more attention is paid to the heating regime recorded during these tests, one can observe that this difference of fire resistance is induced by a very different behaviour of plasterboards. In CTICM test, the fall of the first layer of exposed plasterboards happened at only 35 minutes of fire. At mean time, in VTT test, it happened only after 70 minutes of fire. Nevertheless, the measured floor deflections in both tests are not only very small but also very close to each other until 45 minutes of fire. Another phenomenon to mention is the temperature rise of double joists in CTICM test, which is much quicker from 45 minutes of fire compared to single joist. However, in VTT test, no difference of heating between single and double joists is observed until 70 minutes of fire. Apparently, this important temperature rise would increase considerably deflection of the floor element leading to its premature collapse by an earlier fall of the second layer of plasterboard. As a consequence, the behaviour of plasterboard is the determinant parameter for the different fire rating between assembly test and individual floor element. The different behaviour of plasterboards between VTT and CTICM tests could be explained by a different heating regime of two edge steel joists of the floor element. It has been observed during CTICM test that failure occurred at one edge instead of a uniform collapse (see figure 6-10). In reality, this failure mode was due to the fact that the lower flange of one edge steel joist was much more heated than that of other edge joist. In this case, its bowing effect will be amplified compared to other edge steel joist resulting in more important deflection which appears to be the dominant parameter for good maintaining behaviour of plasterboards. In addition, the failure started firstly at the side of more heated edge joist due to its heating regime. It has to be mentioned here that this heating regime could be very different from reality in which steel joists would be homogeneously insulated by plasterboards and the boundary effect should be eliminated by appropriate constructional arrangement.

/250

0

200

400

600

800

1000

0 15 30 45 60 75 90Time (min)

Tem

prat

ure

(°C

)

AC

B

C

BA

CTICM VTT

0

200

400

600

800

1000

0 15 30 45 60 75 90Time (min)

Tem

prat

ure

(°C

)

A C

B

C

BA

CTICM VTT

Comparison of temperatures in plasterboards near simple support

Comparison of temperatures in plasterboards at mid-span

0

200

400

600

800

1000

0 15 30 45 60 75 90Time (min)

Tem

prat

ure

(°C

)

A

C

B

C

B

A

C

B

ACTICM VTT

0

200

400

600

800

1000

0 15 30 45 60 75 90Time (min)

Tem

prat

ure

(°C

)

A

C

B

C

BA

C

B

ACTICM VTT

Comparison of temperatures in single steel joist at mid-span

Comparison of temperatures in double steel joists at mid-span

0

20

40

60

80

100

0 15 30 45 60 75 90Time (min)

Def

lect

ion

(mm

)

L/2

D2 (CTICM)

D1 (CTICM)D1 (VTT)

D2 (VTT)

Simple support D2 (CTICM)

D1 (CTICM)

D1 (VTT)

D2 (VTT)-10

0

10

20

30

40

50

0 15 30 45 60 75 90Time (min)

Late

ral d

ispl

acem

ent (

mm

)

D1

D2

D3

CTICM VTT

D2 D1D3

Comparison of deflection comparison of floor element

Comparison of lateral displacements of wall element

Figure 6-9: Comparison of test results with Finnish construction system

/250

Deformed floor after collapse (view above) Deformed floor after collapse (view below)

0

200

400

600

800

1000

0 15 30 45 60 75 90Time (min)

Tem

prat

ure

(°C

)

AC

B

C

B

A

0

200

400

600

800

1000

0 15 30 45 60 75 90Time (min)

Tem

prat

ure

(°C

)A

C

BC

B

A

Temperature measured in left edge steel joist Temperature measured in right edge steel joist

Figure 6-10: Failure mode of assembly test with Finnish construction system

The fire tests with UK system on floor element, wall element and floor-wall assembly were all carried out within actual project. As it is with Finnish system, VTT and CTICM performed respectively individual element tests and assembly test. In addition two fire tests were carried out by CTICM with floor-wall assemblies. In the first assembly test, the collapse of the specimen was caused by the failure of floor element and in the second one, failure occurred at floor-wall joint by squash of steel joists as well as stiffeners under applied load of jacks. So the comparison between the first UK system assembly test and individual element tests seems to be more interesting and meaningful as well. A brief comparison table, in which the similarities and differences of both VTT individual element and CTICM assembly tests are listed, is given below (table 6-3).

Parameters VTT tests CTICM test Span of floor joist 5240 mm 5240 mm Height of wall stud 2800 mm 2800 mm

Floor simple supported one side simply supported and other side assembled to wall studs

Boundary conditions Wall fully restrained at top and

hinged at bottom bottom inserted in tracks and top side assembled with floor joists

Applied load 2.5 kN/m per joist of floor and 33 kN on each stud of wall

2.68 kN/m per joist of floor and 32 kN on each stud of wall

Table 6-3: Comparison of testing conditions for UK construction system

/250

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

pera

ture

(°C

)

DA

B

C

C

A

B

DCTICM VTT

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

pera

ture

(°C

)

DA

B C

C

A

B

DCTICM VTT

Comparison of temperatures in steel joist near simple support

Comparison of temperatures in steel joist at mid-span

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

prat

ure

(°C

) D

CB

A

Exposed sideDC

BA

CTICM VTT

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

prat

ure

(°C

) D

CB

A

Exposed sideDCBA

CTICM VTT

Comparison of temperatures in steel studs on top side

Comparison of temperatures in steel studs at mid-height

0

200

400

600

800

1000

0 10 20 30 40 50 60 70 80Time (min)

Tem

prat

ure

(°C

) D

CB

A

Exposed sideDCBA

CTICM VTT

0

4

8

12

16

20

0 15 30 45 60 75 90Time (min)

Late

ral d

ispl

acem

ent (

mm

)

D1

D2

D3

CTICM VTT

D3

D1

D2

Comparison of temperatures in steel studs on top side

Comparison of lateral displacements of wall element

Figure 6-11: Comparison of test results with UK construction system

Comparing the temperature rise between individual element tests and this assembly test, one can find (figure 6-11) that the fall of first layer of bottom plasterboards in VTT floor test occurred everywhere (mid-span and near support) between 45 and 50 minutes. However in CTICM assembly test, this fall occurred at about the same time near the simple support but at mid-span and near floor-wall joint between 65 and 70 minutes of fire so much later. This difference may explain why the failure of VTT floor test happened earlier than that of the floor in CTICM assembly test since the temperature rise is quicker if the fall of plasterboard happens earlier which in turn increases the floor deflection creating therefore more cracking in plasterboard as well as higher temperature rise of steel joists. As far as the heating of wall studs is concerned, it does not vary much between wall element test and assembly test.

/250

In this assembly test with UK system, the mechanical collapse occurred once again on floor joists. But contrary to Finnish system, in assembly test with UK system, the floor resisted longer than that in individual floor element test (77 minutes rather than 69 minutes) because of a less heating regime as explained earlier even the steel joists in assembly test are slightly more loaded. In fact all these differences are related directly to the maintaining behaviour of plasterboards to steel joists. As a consequence, an important recommendation which can be drawn from these experimental results is to have absolutely a good design of appropriate attaching system of plasterboards to steel supporting members. Another interesting phenomenon to discuss is the failure mode of second UK assembly system which is the squash of joint under applied load during test (see figure 6-12).

Global view of steel joist squash at joint Detailed view of steel joist squash at joint

0

10

20

30

40

0 10 20 30 40Time (min)

Vert

. dis

plac

emen

t (m

m)

D2

D1

Simple support

D2

D1

State of edge steel track above wall Measured vertical displacement near joint

Figure 6-12: Failure mode of second assembly test with UK construction This collapse occurred at only 36 minutes of fire (see figure 6-12). However, at this instant, the heating of steel joists is still very weak at about 100 °C and the applied load on each joist is also quite low at only 31 kN (see figure 6-13). In fact, this failure mode has been already obtained in room temperature test but the failure load is as high as 65 kN per joist so twice that in fire test. This failure mode shows that it needs to draw more attention to design of load transmission details of lightweight steel structures in order to avoid unpredicted premature collapse of them.

/250

0

40

80

120

160

200

0 10 20 30 40Time (min)

Tem

pera

ture

(°C

)

D

A BC

E

D

A

E

B

C

0

20

40

60

80

0 10 20 30 40Time (min)

App

lied

load

(kN

)

Temperature evolution of steel joist near floor-wall joint

Measured applied load of all jacks (two studs by jack)

Figure 6-13: Heating of steel joist as well as applied load in second assembly test with UK

construction system

6.3 NUMERICAL INVESTIGATION OF FIRE BEHAVIOUR OF JOISTS IN FLOOR

Until now in the project, the numerous numerical modelling performed already was applied only to cold formed lightweight steel members with compressive force as principal load. However, for joists in various floors tested in this part of work, they were mainly subjected to bending. In order to check the validity of advanced numerical models, numerical analysis has been carried out and corresponding results are presented below.

6.3.1 Assumption of numerical modelling

In the numerical modelling, for joists of both floor elements and floor-wall assemblies, they are modelled as individual simply supported members under uniformly distributed load applied over the upper flange. As the joists are fixed with plasterboards at both lower and upper flanges, they are considered therefore as laterally restrained in displacement. In addition, the two edges of the joist are laterally restrained also for account of joint steel tracks. All these modelling details are also illustrated in figure 6-14. In order to take account of possible local buckling of joists, before the analysis of joist under fire situation, an eigenvalue analysis was performed for the purpose of applying an initial geometry imperfection to the joist, the shape of which is shown in figure 6-15. As far as material model is concerned, the reduction factors proposed in Chapter 2 for Type B steel are adopted because that the steels used in all tests involving floor elements are from the same manufacturers. Another important assumption necessary to mention is the heating condition of joist used in numerical modelling. Considering that the temperature of joists was measured during the tests on several cross sections along their length, it is so possible to attribute real temperature field to modelled steel joist based on experimental results. This rule has been applied throughout all numerical simulations of steel joist presented hereafter.

/250

Figure 6-14: Boundary conditions as well as loading condition of joist in numerical modelling

Shape of initial geometry imperfection affected

to steel joist based on eigenvalue analysis Temperature filed according to test results

Figure 6-15: Initial geometry imperfection and temperature field attributed to steel joists

6.3.2 Comparison of numerical modelling with test results

The numerical modelling presented above is then applied to simulate the behaviour of floor joists. In figure 6-16 is given a comparison between numerical calculations and experimental results for two structure systems. It can be found that the agreement is quite satisfactory not only for deflection but also for failure time. This good agreement shows that the numerical modelling with advanced calculation models is fully capable of predicting the mechanical performance of joists exposed to fire. It should be noted that joists are subjected only to bending and theoretically their behaviour is less complicated compared to studs which are subjected to both bending and buckling. Nevertheless, the good results of numerical simulation give once again the proof about the validity of used material model proposed in chapter 2.

/250

0

20

40

60

80

100

0 15 30 45 60 75 90Time (min)

Def

lect

ion

(mm

)

L/2

D1 (CTICM)D2 (VTT)

Simple support

D2 (ANSYS)

D2 (Test)

D1 (Test)

D1 (ANSYS)

-20

0

20

40

60

0 10 20 30 40 50 60 70Time (min)

Def

lect

ion

(mm

) D1 D2

D3 D4

ANSYS

Finnish system in both floor and assembly

tests UK system in floor test

Figure 6-16: Comparison of floor deflection between numerical modelling and test

6.4 CONCLUSIONS

The work presented in this chapter is mainly dealing with fire behaviour of cold formed lightweight steel panel structure systems, such as floor, wall and their assemblies. In studies carried out correspondingly, emphasis is firstly made on experimental investigation by means of several types of fire tests on two European lightweight steel structure systems. In addition to above experimental work, numerical simulations have been performed to analyse the floor behaviour under fire situation. The results obtained in these studies lead to following conclusions:

• The wall panels behave very similarly as individual studs maintained by boards presented in chapter 5;

• The fire resistance of floor panels is related directly to maintenance performance of plasterboards;

• The behaviour of plasterboards at floor-wall junction in assembly tests is very satisfactory and no disorder appeared during fire tests;

• The fall of plasterboards in floor panels occurred always. However, the first fall was located on the side of simple support due to apparently more important deflection of supporting steel joists;

• If collapse of floor-wall system was caused by failure of floor panel, the failure mode is very similar to that of individual floor panel;

• Failure may occur by local squash of steel joists due to important descending load from above floors so attention must be paid to the local resistance design of joists under concentrated load;

• The numerical modelling is capable of predicting, in a good way, the fire behaviour of floor joists.

/250

7 FIRE RESISTANCE ASSESSMENT OF HIGH NON LOAD-BEARING PARTITION WALLS BUILT WITH COLD FORMED LIGHTWEIGHT STEEL MEMBERS

7.1 GENERAL

The actual testing configuration for the investigation of partitions submitted to fire is limited by the height, as the tests performed show a height about 3 meters. However, in reality, they can be applied to the height up to fifteen even twenty meters. Therefore, question arises about how to extend the test results obtained on small size partition walls to very high partition walls. Some assessment methods exist already [7-1, 7-2], but either they are based only on the mechanical resistance of lightweight steel studs or they require a quite complicated analysis procedure based on advanced numerical models. As a consequence, within the project, a simple extrapolation method using only handle calculations is proposed which tries to combine deformation compatibility criteria of plasterboards and the mechanical resistance of lightweight steel members. A full explanation of this method is then given together with some validation cases against test results.

7.2 TESTING CONFIGURATION AND SAFIR SIMULATIONS

Based on the tests performed by CTICM [5-2], the fire behaviour of steel studs in medium section 13x 57x150x57x13 (1.2 mm thick) has been modelled with SAFIR using beam rather than shell elements. This step has the aim to calibrate the F.E. model based on test results in order to perform further simulations for taller partitions. The static system used in these simulations is a "fixed-hinged" system (see figure 7-1).

Figure 7-1: Test configuration, system and section geometry

Stud 13 x 57 x 150 x 57 x 13 (thick. 1,2mm)

Plasterboard facings

Supporting platein the lower part

13 mm

13 mm

1,2 mm150 mm

57 mm

57 mm

2.80

m

/250

Figure 7-2: Imposed temperature distribution according to test results The heating up of the stud section follows the curves given in figure 7-2 which were measured during the test for the stud at the location 1, 3 and 5 (see figure 7-3). In order to consider the self weight of the plasterboards (4*25mm) a continuous load of 75kg/m has been applied over the stud length corresponding to a plasterboard weight of 1200 kg/m3. The static system used in our F.E. model has "fixed-hinged" end conditions. The measurements performed at H/4, H/2 and 3H/4 for the horizontal displacement are compared with SAFIR simulations (see figure 7-3) and show a quite good agreement which gives an evidence about the validity of used model. These simulations have been performed in order to establish a good basis of SAFIR model for further calculations to be performed in relation with the development of new simplified methodology.

2.80

m

0

10

20

30

40

50

60

70

80

0 1200 2400 3600 4800 6000

Time [sec]

Dis

plac

emen

t [m

m]

H/2 (3)

H/4 (5)

3H/4 (1)

SAFIRTest

h/4

Stud

s lo

catio

n

Stud

s lo

catio

n

1

h/2

3h/4

3

5

2

4

6

Figure 7-3: Comparison between measured and calculated displacements at different heights of studs

Hot face temperature

Cold face temperature

Mid face temperature

/250

7.3 SIMPLIFIED METHODOLOGY

7.3.1 General features

The final goal will be to determine the failure time of a taller partition based on the test results on partitions with same geometry but a reduced height. The simplified methodology will be based on: • a "hinged-hinged" end condition system (see figure 7-4) in order to simplify the

deformations and by the way to achieve symmetrical deformations over the length

Figure 7-4: Boundary conditions of lightweight steel stud in partition walls

• the possibility to consider a free head elongation until a defined value and a blocked

elongation after having reached this value. In this way one can simulate the fact that the system can't go up anymore after having reached the ceiling

• the calculation of reference failure criteria according to the data recorded during a small scale fire test

• simplified calculation rules in order to determine the deformation (horizontal displacement values) of the extended partition in function of time

Initial simulations have been performed with SAFIR in order to analyse the end condition configuration and compare them with the test results. Hereafter we can see the comparison between • the measured horizontal displacements in function of time obtained from the test • the "fixed-hinged" system • and the "hinged-hinged" system with a free allowable elongation of 10 mm.

/250

Figure 7-5: Comparison between measured and calculated displacements with different

systems

The results obtained with the "hinged-hinged" system configuration (see figure 7-5) are on the safe side since the horizontal displacements are more important than the experimental ones obtained in fire test. Nevertheless the shape of the curves is quite similar. Based on the results with the "hinged-hinged configuration, the simplified method will be validated against further F.E. calculations.

7.3.2 Assumptions concerning the new methodology

7.3.2.1 Background

In order to create a link between performed test data and calculations, two acceptance criteria based on the minimum radius of curvature ρ and maximum relative elongation ε at failure time tfail for a performed test have been considered, the most unfavourable value being relevant. The failure time tfail corresponds to the moment in which the plasterboards fall. Both

yall

0

10

20

30

40

50

60

70

80

0 1200 2400 3600 4800 6000

Time [sec]

Dis

plac

emen

t [m

m]

H/2

H/4

3H/4

SAFIR(max. elongation =10mm)

SAFIRTest

/250

values obtained at failure time tfail will be used also as the failure criteria for extended partitions. The curvature radius ρ is determined with the Lagrange formula (see figure 7-6).

Figure 7-6: Lagrange formula The maximum relative elongation ε is defined as: ε = system length at failure time / initial system length

7.3.2.2 Working steps for the determination of the curvature radius ρ

From a given test, the heating up curves for the section as well as horizontal deflection measurements (bowing) must be known at different heights of partitions. A minimum of 3 horizontal measurements must be known, 5 values are recommended (see figure 7-7). The stud is divided into 4 elements, the Lagrange formula is applied for 2 consecutive elements (starting at AB), for which 3 horizontal displacements are known (1, 2 and 3). Further division of this segment into 6 equal elements and calculation of the curvature radius ρ at the points a, b, c, d, e. For the segment AB, the curvature radius ρAB is the minimum of ρa, ρb, ρc, ρd, ρe. The same is done for the consecutive element CD for which the correction value ρCD is determined. The smallest of both values corresponds to the reference value ρref = min(ρAB, ρCD).

5

4

3

2

1

D

C

B

A

3

2

1

B

Aa

b

c

d

e

Figure 7-7: Discretization steps

2

3

4

5

n

y

x

At a given abscisse x of a curve y=f(x), the curvature is given by :

2/32))'y(1((''y1

+=

ρwhere ρ is the radius for curvature.

For calculating y’ and y’’, the Lagrange formula is used :

32313

212

321231

1312132 y

)xx()xx()xx()xx(y

)xx()xx()xx()xx(y

)xx()xx()xx()xx()x(y ⋅

−⋅−−⋅−

+⋅−⋅−

−⋅−+⋅

−⋅−−⋅−

=

32313

212

321231

1312132 y

)xx()xx()xx()xx(y

)xx()xx()xx()xx(y

)xx()xx()xx()xx('y ⋅

−⋅−−+−

+⋅−⋅−

−+−+⋅

−⋅−−+−

=

32313

23212

13121

y)xx()xx(

2y)xx()xx(

2y)xx()xx(

2''y ⋅−⋅−

+⋅−⋅−

+⋅−⋅−

=

/250

7.3.2.3 Working steps for the determination of the elongation ε

• From a given test, the heating up curves for the section as well as horizontal deflection measurements (bowing) at failure must be known at different heights of partitions. A minimum of 3 horizontal measurements must be known, 5 values are recommended.

• The elongation of the system has to be calculated. Here every element is divided into 3 sub-elements and the relative axial elongation εax defined as the element length at failure time over the initial length can be calculated (see figure 7-8).

• In order to consider the relative elongation at the external fibre due to the bowing, (see fig. 2.7) the axial elongation εax is increased by the factor εrot = b/2ρref.

• The value of ρref corresponds to the minimum curvature radius determined into the previous chapter.

• The reference εref, is defined as an addition of the axial elongation εax plus the elongation at the external fibre εrot.

εref = εax,i + εrot

• The axial elongation εax,i is determined for every meshed element and the maximum value is retained εax = max (εax,a, εax,b, …εax,c, εax,l)

• The axial elongation εax,i is defined as follows:

iL

Liax,ε =

with L = length of the element at failure and Li = initial length of the element

5

4

3

2

1

εrot

b

Li

L

ρref

Figure 7-8: Discretization steps

7.3.2.4 Reference values for the test

For our reference test following values have been calculated for tfail = 59 minutes:

ρref = 34.507 m εref = 1.002724

Both values determine the acceptance criteria for other taller partitions, meaning that for a given partition height both criteria dominate the partition wall stability.

/250

An Excel sheet has been developed in order to define the maximum relative elongation εref and the minimum radius of curvature ρref at failure time tfail simply by entering the measured deflection values at their given height as well as the stud depth b.

7.3.2.5 Assumptions concerning the deformations of extended partitions

In order to determine the deflection of a partition in a simplified way considering the thermal and mechanical properties of the system, the boundary conditions of the analysed system are "hinged-hinged" meaning that a sinusoidal shape of the deformation is adopted. Step 1 Calculation of the weight ω of wall per square metre i.e. (kg/m2) x 9.81, and selection of a height L (mm) Step 2 Definition of a stud thickness t (mm), stud spacing m (mm), stud depth d (mm), flange width fw (mm). The yield stress σ should be taken as the value appropriate to the quality of steel being used e.g. 210, 280 or 350 MPa. The Young’s modulus E is assumed to follow the shape (see figure 7-9) defined according to CSM proposal within this project (see chapter 2).

Young Modulus in function of temperature

0

0.2

0.4

0.6

0.8

1

1.2

0 200 400 600 800 1000 1200Temperature [°C]

redu

ctio

n fa

ctor

New developed curve

EC3-1-2

Figure 7-9: Young Modulus in function of temperature

It must be noted that SAFIR simulations have been performed with the curve from EC3 1.2. Step 3 Definition of hot flange temperature Th in °C and cold flange temperature Tc in °C in function of time. The temperature is assumed as constant over the whole length Step 4 Calculation of the reduction factor for proportional limit k defined for sections with Type A steel (see figure 7-10) as:

/250

Proportional limit in function of temperature for small sections

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 100 200 300 400 500 600 700Temperature [°C]

redu

ctio

n fa

ctor

kh = 1 for Th ≤ 100°C

500T

56k h

h −= for 100°C ≤ Th ≤ 600°C

kh = 0 for Th ≥ 600°C

kc = 1 for Tc ≤ 100°C

500T

56k C

c −= for 100°C ≤ Tc ≤ 600°C

kc = 0 for Tc ≥ 600°C Figure 7-10: Strength reduction factor for

Type A steel

k = kc - kh and calculation of the reduction factor for proportional limit k defined for sections with Type B steel as:

Proportional limit in function of temperature for medium and large sections

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 100 200 300 400 500 600 700 800 900Temperature [°C]

redu

ctio

n fa

ctor

kh = 1 for Th ≤ 100°C

700T

78k h

h −= for 100°C ≤ Th ≤ 800°C

kh = 0 for Th ≥ 800°C

kc = 1 for Tc ≤ 100°C

700T

78k c

c −= for 100°C ≤ Tc ≤ 800°C

kc = 0 for Tc ≥ 600°C Figure 7-11: Strength reduction factor for

Type B steel

k = kc - kh Step 5 Calculation of the neutral axis yn from the cold end:

fw .(kh . d + kc . t/2) + d2 .(k/6 + kh/2) yn =

(kh + kc ) . (fw+ d/2) Step 6 Calculation of e = d - yn and calculation of the second moment of area of the stud Ih at elevated temperature:

Ih = t.( fw . (kh . e2 + kc . yn2 ) + e3 .(kh /3 + k . e/(12.d)) + yn

3 .(kc /3 - k . yn/(12.d)))

Step 7 Calculation of the Euler height under the above conditions:

Le = ((2. π2 . E . Ih . 106 )/(ω . m))0.3333

/250

Step 8 The height L should be lower than the Euler height Le. If it is not the case, the partition will be unstable regardless of any thermal bow. Otherwise it can be proceeded to step 9. Step 9 Calculation of the load Pe:

Pe = π2. E.Ih.1000/(L2 . m) Step 10 Calculation of the total weight P per meter width:

P = ω . L/1000 Step 11 Calculation of the thermal bow b:

b = ((14x10-6 ) . L2 . (Th-Tc))/(8.d) Step 12 Calculation of the additional bow be due to self weight from

1P

2Pbbe

e

−=

Design Aspects of Fire Rated Partitions within Buildings There are various design aspects which must be considered such as the total movement due to the bow and the movement limit at the head of the partition. The extent of the head movement depends on the net result of the vertical upward expansion due to temperature and the drop caused by the thermal bow. The thermal expansion coefficient of steel is approximately 14 x 10-6 (between 100 and 700 °C) and therefore the upwards expansion at the head yu mm of the partition is: Step 13

yu = ( 14x10-6 ) . L . Ts Ts = stud average temperature in °C (above ambient) If the cladding material does not protect the steel studs adequately, then quite large expansion at the head is possible and clearly therefore, it is best not to allow the metal to get too hot! This upward deflection however could be reduced by the effect of thermal bowing (and self weight) of the partition and when a large bow is expected then the head detail might need to accommodate the partition dropping at the head and yet still be adequately restrained laterally. Step 14 The head drop yd mm caused by the bow is:

/250

3L)b8(by2

ed

+=

L

y all

y fix

y u

y d

∆y fi

x

be+b+bimp btot

Figure 7-12: Definition of deformations Step 15 The system will expand until having reached a determined height defined as the addition of the initial length L and an allowed elongation yall. In case that the elongation due to the heating yu is more important than the allowed value yall, a restrained in elongation yfix has to be considered as well as the supplementary bowing caused by this effect (see figure 7-12).

yfix = yu - yall

As the head drop yd caused by the bow also has to be considered for this matter, following configurations are possible and define an effect of the restrained elongation or not. If yfix ≤ 0 or yfix ≤ yd no consideration of this effect If yfix > 0 but yfix ≤ yd no consideration of this effect If yfix > 0 and yfix > yd calculation of the bowing caused by this effect Step 16 Calculation of the additional bowing badd caused by the restrained elongation:

∆yfix = yfix - yd

badd = 8

L*y3 fix∆

/250

Step 17 Calculation of the total bow btot. In order to consider an initial imperfection, the total bow has been increased by bimp = L/1000

btot = b e + b +badd + bimp

Step 18 In order to check the stability of the wall, the moment capacity Mr of the stud at elevated temperature is compared with the moment produced by the self weight acting eccentrically Ms. The condition is Mr > Ms. Calculation of the moment capacity MR of the stud at elevated temperature:

MR = t. (fw .( kh . e + kc. yn )+ e2 .(kh /2 + k . e/(6.d))+ yn2 .(kc /2 - k . yn /(6.d))). σ

Step 19 Calculation of the moment capacity Mr of the stud frame per meter width:

Mr = MR .1000/m

Step 20 Calculation of the moment Ms produced by the self weight acting eccentrically:

Ms = (ω. L2 . α . (1 - cos α ) ) / (4 .1000. sin2 α)

where L

2b2Atanα tot= ( in radians)

Step 21 The acting moment MS should be lower than the resisting moment Mr in order to ensure the wall stability. Step 22 Calculation of the curvature radius ρ as well as the elongation ε for the threaten configuration in function of time. Supposing that the shape of the curve is sinusoidal, supplementary horizontal displacements are calculated over the height at different points with the Lagrange Formula (see figure 7-6). The system to analyse has been divided into 20 equidistant elements independently from its length (see figure 7-13). The values ρ and ε are calculated with the assumptions defined in paragraphs 7.3.2.2 and 7.3.2.3 for the treated length and with the configuration following the figure underneath (figure 7-13).

/250

Figure 7-13: Comparison between SAFIR results and simplified methodology

The behaviour rules have been put into an Excel sheet (see figure 7-14) in order to determine the deformation shape.

21

4

3

2

1

C

B

A

btotL

1

20

/250

Figure 7-14: Excel sheet for the determination of the horizontal displacements at mid height

/250

7.3.3 Simplified methodology results

In order to check the validity of the obtained results, the horizontal displacement at mid height btot has been plotted for stud heights from 3 m up to 10 m and has been compared with F.E. SAFIR results. The different lengths consider allowable elongations from 15 mm to 20 mm. The comparison is shown in following figures (figures 7-15 to 7-23).

Horizontal displacements for L = 3m

0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR

Figure 7-15: Comparison between SAFIR results and simplified methodology (L=3m)


0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR


yall=15m

yall=15m

/250


0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR



0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR


yall=15m

yall=15m

/250


0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR



0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR

Figure 7-20: Comparison between SAFIR results and ARCELOR simplified (L=8m)

yall=15m

yall=20m

/250


0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR

Figure 7-21: Comparison between SAFIR results and ARCELOR simplified (L=9m)


0

25

50

75

100

125

150

0 10 20 30 40 50 60 70 80 90 100time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR

Figure 7-22: Comparison between SAFIR results and ARCELOR simplified (L=10m) The results plotted show that a failure occurs at a given time. This failure can be represented in a good manner by the simplified methodology. Hereafter you can see the results obtained for the radius of curvature ρ and the elongation ε for all the lengths treated. The reference value has been determined within paragraph 7.3.2.4. The match point between this value and the value for the considered length determines the failure time for this system, the smallest value between curvature radius and elongation being relevant.

yall=20m

yall=20m

/250

Variation of the radius of curvature ρ for different heights of the stud

0

50

100

150

200

250

0 10 20 30 40 50 60

time [min]

ρ [m

]

3m4m5m6m7m8m9m10m12m

ref. value ρref = 34.507 at time t = 59 min.

Figure 7-23: Failure time for extended partitions in function of the curvature radius ρ

Variation of elongation ε for different heights of the stud

1.0000

1.0005

1.0010

1.0015

1.0020

1.0025

1.0030

1.0035

1.0040

0 10 20 30 40 50 60 70

time [min]

ε [-]

3m4m5m6m7m8m9m10m12m

ref. value εref = 1.002724 at time t = 59 min.

Figure 7-24: Failure time for extended partitions in function of the elongation ε

7.4 DEVELOPED TOOL GUIDANCE

As already explained, the developed tool has been simplified in such a way that a user friendly excel sheet is obtained, the input data are:

/250

• For the calculation of the reference criteria ρref and εref: the section depth b and the horizontal displacement measurements "y" at their relative coordinates "x" at failure time tfail (see figure 7-25)

Figure 7-25: Excel sheet for calculation of reference criteria

• For the analysis of the defined tall partition: the section geometrical and mechanical values, the temperature curve in function of time, the section size and the allowed elongation yall (see figure 7-26).

Figure 7-26: Excel sheet for calculation of extended sections • Based on these values, the elongation ε as well as the curvature radius ρ in function of

time is obtained. Both curves can be plotted. The reference values ρref and εref are

/250

constant values. The match point of the calculated values in function of time determines the failure time of investigated taller partition.

In case that the conditions in step 8 or step 18 aren't anymore fulfilled, the calculation for the investigated taller partition is stopped at the critical time (see message in figure 7-25). If the obtained critical time doesn't exceed the reference failure time tfail, the extended stud length has to be reduced or a different stud section has to be chosen.

7.5 SUPPLEMENTARY VALIDATION TEST

In order to increase the validation field of the new methodology and to prove its good behaviour, a supplementary test has been analysed. The test data has been furnished by CTICM from a test performed during a previous project (see figure 7-27).

7.5.1 Testing configuration and SAFIR simulations for the test 2

Figure 7-27: Test configuration, system and section geometry The system used for the SAFIR simulations is identical to the previous test meaning "hinged-hinged" end conditions with a free allowable elongation of 20 mm.

4.50

m0.

02m6 mm

6 mm

0,6 mm70 mm

50 mm

50 mm

/250

Time-Temperature Plot

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70 80

Time [min]

Tem

pera

ture

[°C

]

Figure 7-28: Imposed temperature distribution following test

The temperature curves chosen have been measured during the test and correspond to the curves at mid height (see figure 7-28).

Horizontal displacement for L=4.50m (allowed elongation = 20mm)

0

20

40

60

80

100

120

140

160

180

200

0 10 20 30 40 50 60 70 80

time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR

Test

Figure 7-29: Comparison between measured and calculated displacement at mid height

The results about displacement obtained are plotted into the figure 7-29. The comparison between SAFIR and the simplified methodology shows the good correlation.

HOT face temperatureMID face temperature

COLD face temperature

y all

/250

7.5.2 Reference values for the test 2

Following the working steps explained in paragraphs 73.2.2. and 7.3.2.3, the reference values have been calculated for tfail = 76 min:

ρref = 10.492 m εref = 1.016

7.5.3 Simplified methodology results for the test 2

The following displacement-time curves at mid height have been plotted for SAFIR and for the simplified methodology. As the results following the simplified methodology weren't good compared to the SAFIR results and as the thermo-mechanical assumptions developed during this project for the simplified methodology are more severe (see paragraph 7.3.2.5 step 2 and step 4) compared to Part 1.2 of EC3 [2], it has been decided, but only for comparison reasons, to plot the simplified methodology curves with the assumptions following Part 1.2 of EC3 [2]. The results are very good validating again the simplified methodology (see figures 7-30 to 7-35).

Horizontal displacement comparison for L = 6m

0

100

200

300

400

0 10 20 30 40 50 60 70 80time [min]

disp

lace

men

t [m

m]

Simplified MethodSAFIRSimplified Method EC3


yall=30m

/250


0

200

400

600

800

0 10 20 30 40 50 60 70 80time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR

Simplified Method EC3



0

200

400

600

800

1000

1200

1400

1600

0 10 20 30 40 50 60 70 80time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR



yall=30m

yall=40myall=30m

/250


0

400

800

1200

1600

0 5 10 15 20 25 30 35 40time [min]

disp

lace

men

t [m

m]

Simplified Method

SAFIR



Simplified MethodEvolution of ε in function of the time

0

50

100

150

200

0 10 20 30 40 50 60 70 80time [min]

ε [-]

L=6mL=8mL=10mL=12m

ρref = 10.5

Figure 7-34: Failure time for extended partitions in function of the curvature radius ρ

yall=40m

/250

Simplified MethodEvolution of ε in function of the time

1

1.01

1.02

1.03

0 10 20 30 40 50 60 70 80time [min]

ε [-]

L=6mL=8mL=10mL=12m

εref = 1.016

Figure 7-35: Failure time for extended partitions in function of the elongation ε

7.5 CONCLUSIONS

A simplified method has been developed in order to determine the failure time of taller partitions. Here for a reference test for which the temperature plot over the time, the horizontal displacements at failure time and the failure time tfail must be known. These values are defined as failure criteria. The failure time tfail corresponds to the moment in which the plasterboards fall. The Young modulus E has been considered as function of temperature according to the development presented in chapter 2. The system considers a free allowed elongation yall which can be chosen by the user. The developed tool considers two instability criterias determined in function of time: • The height L must be lower than the Euler height Le. • The moment Ms produced by the self weight acting eccentrically must be lower than the

moment capacity Mr of the stud frame. In case that one of both criteria isn't anymore fulfilled, the calculation is stopped at the critical time. Nevertheless, the behaviour of the stud can be plotted until this time. In order to increase the critical time, a larger stud section has to be defined or the length of the stud has to be reduced. The strength reduction factor k defined on step 4 of paragraph 7.3.2.5 considers two different shapes in function of types of steel. The results obtained in paragraphs 7.3.3. and 7.5.4 show a good correlation between simplified methodology and SAFIR results.

/250

Test 1 The direct comparison between the test result with a failure at 59min and the simplified methodology is given in the figure above. Following the simplified methodology, the failure of the reference stud occurs after 57.5 min against 59 min obtained in reality. The correlation to reality is very good.

1

1.005

1.01

1.015

1.02

0 10 20 30 40 50 60 70 80 90 100time [min]

ε

εref = 1,0027Fa

ilure

tim

e =

59'

57.5min

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100time [min]

ρ [m

]

ρref = 34,507

Failu

re ti

me

= 59

'

57.5min

Figure 7-36: Comparison between calculated and measured failure time following reference

criteria In order to give an idea about the failure time obtained for extended taller partitions in function of the length, following table has been drawn (Table 7-1). The results show that determinant criteria for every length.

/250

Reference : L= 2,8m tfailure = 59 min εref = 1.0027 ρref = 34.5m

Length tfailure in function of ε

tfailure in function of ρ

Determinant failure time

Allowed elongation yall

[m] [min] [min] [min] [mm]

2.8 Ref. 57.5 57.5 57.5 10

3 65 65 65 15

4 59 57 57 15

5 55 57 55 15

6 53.5 57 53.5 15

7 52 56.5 52 15

8 51 56 51 20

9 50 55 50 20

10 49 54.5 49 20

12 47 52 47 30

Table 7-1: Failure time in function of length In order to improve the obtained results a correction factor can be foreseen. For the reference test with a length of 2,8m and a failure time of tfailure = 59 minutes the reference criteria are as follows: εref = 1.0027 and ρref = 34.5 m. The simplified methodology reaches these values for ρ at tsimp = 57,5 min and for ε at tsimp = 59 minutes.

The correction factor is calculated as follows: 026.157.559)

tt;

ttmin(χ

simp

fail

simp

failcorr === .

The determinant failure value given in the table above (see table 7-1) is multiplied by this value. Test 2 The same has been done for the second reference test with a failure at 76 minutes. According to the simplified methodology, the failure of the reference stud occurs after 65 minutes based on the critical curvature radius criteria (see figure 7-37).

/250

1

1.01

1.02

1.03

0 10 20 30 40 50 60 70 80time [min]

ε [-]

εref = 1.016

Failu

re ti

me

= 76

'

0

20

40

60

80

100

0 10 20 30 40 50 60 70 80time [min]

ε [-]

ρref = 10.5

65min

Failu

re ti

me

= 76

'

Figure 7-37: Comparison between calculated and measured failure time following reference criteria

/250

Reference : L= 4,5 m tfailure = 76 minutes εref = 1.016 ρref = 10,492 m

Length tfailure in function of ε

tfailure in function of ρ

Determinant failure time

Allowed elongation yall

[m] [min] [min] [min] [mm]

4.5 Ref. 76 65 65 20

6 59 59.5 59 30

8 34.5 48.5 34.5 30

10 28.5 36 28.5 30

12 26.5 30.5 26.5 40

Table 7-2: Failure time in function of length The correction factor as explained before can be calculated for this test. The simplified methodology reaches the reference values for ρ at tsimp = 65 minutes and for ε at tsimp = 76 minutes.

The correction factor is calculated as follows: 169.16576)

tt;

ttmin(χ

simp

fail

simp

failcorr === .

The determinant failure value given in the table above (see table 7-2) should be multiplied by this value.

/250

8 GENERAL CONCLUSIONS

During the last three and half years (from the first of July 2000 until the end of 2003), a research project, sponsored mainly by ECCS, dealing with the fire performance of cold formed lightweight steel structures has been completed by the following partners:

• CTICM (France - Coordinator of the project) • CORUS (United Kingdom) • CSM (Italy) • LABEIN (Spain) • ProfilArbed (Luxembourg) • VTT transport and building (Finland)

A detailed description of all investigated technical features of the project has been provided in previous chapters, which have been arranged to meet the following principal objectives:

• to increase understanding of the fire behaviour as well as failure mechanisms of lightweight steel structures under fire exposure by performing both fire resistance tests and numerical simulations on small and full scale specimens, including heating condition under natural fire developments;

• to obtain accurate data on the mechanical properties of cold formed steel at elevated temperatures;

• to check the ability of existing advanced calculation models to simulate the experimental behaviour of lightweight steel elements;

• to develop simple calculation models on the fire behaviour of lightweight steel structures on the one hand for fire assessment of their load-bearing capacity, and on the other hand for extrapolating test results on small size lightweight steel partitions to real building partition walls of very large size.

In order to reach above aims, the project has been divided into several tasks of which the leadership is shared between all involved partners. The main activity of each task as well as its outcome can be summarised as follows:

• Material properties of cold formed lightweight steels at elevated temperatures o As part of the fundamental data for mechanical resistance assessment, the material

properties of cold formed lightweight steels were determined by conventional tests on three different steels at both room and elevated temperatures. The corresponding experimental results have been fully analysed and the strength reduction factors of studied steels have been derived. In order to incorporate these results into future fire part of Eurocode, all corresponding reduction factors are given in such a way that they can be used directly in Eurocode mathematical model for describing stress-strain relationships of steel at elevated temperatures. In addition, the above results have been applied to the numerical modelling parts of this research for mechanical analysis of lightweight steel structures under fire situation.

• Mechanical behaviour of cold formed lightweight steel members as well as their assemblies at room temperature

o Fire resistance assessment of structural members usually needs to be referred to room temperature performance. As a consequence, a relative important part of the research work was focused on mechanical behaviour of cold formed lightweight steel members at room temperature. A full testing programme was carried out on the same types of studied elements under fire situation such as short stub columns, tall isolated studs, studs maintained by boards in various arrangements, floor and wall panels, as well as their assemblies. The experimental results were then compared to both

/250

standard design rules and numerical modelling with advanced calculation models. This comparison shows that standard design rules give, in general, conservative load-bearing capacities of lightweight steel members and that advanced calculation models are capable of predicting their failure loads within acceptable limits and can be used in parametric studies.

• Mechanical behaviour of lightweight steel members fully engulfed in fire o In some cases, lightweight steel members are used as load-bearing elements without

any fire protection and still need to provide certain level of fire resistance. In the project, this situation has been dealt with by means of both experimental and numerical approaches in which lightweight steel members subjected mainly to compression were examined. The fire tests carried out on both short stub columns and tall studs under compression provide valuable information not only on the local buckling behaviour of lightweight steel members but also on their overall instability failure at elevated temperatures. Based on relevant experimental results, numerical modelling has been performed to validate the capability of advanced numerical model to simulate the fire behaviour of lightweight steel members. Finally, simple calculation models have been developed on the basis of results of parametric numerical studies on heated isolated lightweight steel members under compression. These models can be applied manually to assess the fire resistance of lightweight steel members engulfed in fire.

• Mechanical behaviour of lightweight steel members maintained by boards (as gypsum/calcium silicate boards or glazed panels), at elevated temperatures

o The majority of lightweight steel members are used together with boards to form floor, walls etc. In this case, they are generally maintained by these boards which provide additional restrain to lightweight steel members leading to higher fire resistance. This common design situation is extensively investigated within this research project. Once again, both experimental and numerical approaches are used. A large number of fire tests have been carried out in which various parameters of maintained lightweight steel members, such as type of sections (dimension and section shape), loading conditions (eccentricity and applied load level), heating condition (standard and natural fire as well effect of internal insulation), nature of boards (standard and fire boards), maintained condition (one side or two sides maintained) were investigated in detail. In parallel, an important numerical modelling investigation was performed on both the thermal and mechanical behaviour of lightweight members associated with boards in which the validity of advanced calculation models was fully checked. Numerical parametric studies were carried out which allowed development of simple calculation models to assess the fire performance of lightweight steel members maintained by boards.

• Fire behaviour of load-bearing walls, floors and their assemblies o This part of research work is dedicated to the global behaviour of lightweight steel

frame systems, such as floor, wall and their assemblies. The work was focused mainly on experimental investigation in which several large scale of fire tests were carried out on both individual lightweight steel panel systems and assembled panel systems. These tests showed clearly that individual panels made of lightweight steel frames behaved in a very similar way to with the fully assembled panels. The junction between horizontal and vertical boards did not suffer from the deformation of floor or the wall. The panel failure modes, if they occurred in panels, were also exactly the same as the isolated tests. However, more attention must be paid to local squash failure of floor-wall joint which apparently could occur with largely reduced concentrated load in fire situation. The performance of steel joists in floor panels was numerically studied and the good agreement with experimental results shows that

/250

advanced numerical models is fully convenient for prediction of lightweight steel members under pure bending.

• Fire resistance assessment of high non load-bearing partition walls built with cold formed lightweight steel members and plasterboards

o There is a limit to the size of non load-bearing partition walls which can be tested with existed testing facilities. However, the size of real partition walls are often much greater than this limit (up to several times of tested size). Therefore the last part of the research concentrated on development of a simple extrapolation method of this special application case of lightweight steel structures. The proposed method is based only on simple calculations for ease of application and is easily amenable to spreadsheet use (consisting of just one Excel page). It covers both mechanical resistance prediction of lightweight steel supporting members and deformation compatibility criteria of plasterboards so that the time to fall of plasterboards can be taken into account.

After a global review of the results obtained during this research project, it can be considered that the whole of the objectives initially predicted for this project have been satisfactorily reached. The behaviour of lightweight steel structures at elevated temperatures has been largely investigated not only by means of tests but also with advanced numerical models. Although all the features of lightweight steel members under fire situation were not covered because of the complexity of all possible cases encountered in real buildings with lightweight steel structures, simple calculation models have been developed for the most common types of application conditions of lightweight steel structures, which can be easily incorporated in future fire part of Eurocode for steel structures. Moreover, according to the outcome of this project, the following observations should be noted:

• In the fire part of Eurocode 3, a fixed critical temperature of only 350 °C is proposed for steel members with class 4 cross sections. However, the results of this research show that very slender thin wall steel members could have a critical temperature exceeding easily 400 °C under quite high load level. As a consequence, the critical temperature of 350 °C could lead to very conservative design and penalize consequently the use of steel. Therefore, it is so necessary to make available detailed design rules for fire assessment of thin wall steel members, not only for cold formed but also for hot rolled elements;

• Existing European design rules for steel members are based only on uniform heating condition related to steel elements fully engulfed in fire. However, if the steel cross section is exposed partially to fire, an important temperature gradient arises across the steel section. This kind of heating regime could significantly modify the fire performance of steel structural members, in particular when they are subjected to compression. In this case, steel members will be unsafely designed if average temperature in the cross section is used whereas they will be very conservatively assessed if the maximum temperature is adopted. Therefore, it is necessary to provide additional design rules for steel members under compression with varying temperature gradient.

/250

9 REFERENCES

[1] CEN “General rules, Supplementary rules for cold-formed thin gauge members and sheeting”, English version of part 1.3 of Eurocode 3, 27th September 2002

[2] CEN “Design of steel structures, general rules, Structural fire design”, part 1.2 of

Eurocode 3, 27th April 2003 [3] J. Outinen “Transient state tensile results of structural steels S235, S355 and

S350GD+Z at elevated temperatures”, Helsinki University of Technology, 1995 [4] ECSC “Development of the use of stainless steel in construction (contract 7210-

SA/842)”, work package 5.1 of final report, 1999 [5] CTICM “Calculation Rules of Lightweight Steel Sections in Fire Situation”, Appendix A

of Second annual technical report, 27th March 2001 [6] CTICM “Calculation Rules of Lightweight Steel Sections in Fire Situation”, Appendix A

of Second semester technical report, 24th September 2001 [7] CEN “General rules, Rules for buildings”, English version of part 1.1 of Eurocode 3,

27th September 2002 [8] Alfawakhiri, F. and Sultan, M.A. “Fire Resistance of Load-Bearing Steel-Stud Walls

Protected with Gypsum Board”, Proc. Fire and Materials ’99, Interscience Communications Ltd., San Antonio, TX, USA, 1:235-246, 1999

[9] CTICM “Fire resistance of a tall distributive partition wall of type PREGYMETAL

D106/70 – 50/40A”, Test report, 17th of March 1999 [10] CTICM “Fire Resistance of an assembly consisted of a partition and a floor, each of

them made of steel frameworks and plasterboard facings”, Test report 03-U-163, 30th April 2003

[11] CTICM “Fire Resistance of an assembly consisted of a partition and a floor, each of

them made of steel frameworks and plasterboard facings”, Test report 03-U-334, 2nd October 2003

[12] CTICM “Fire Resistance of an assembly consisted of a partition and a floor, each of

them made of steel frameworks and plasterboard facings”, Test report 03-U-392, 12th November 2003

[13] PR 254 N 83 "Test report on fire tests of lightweight steel sections maintained by

plasterboards", VTT [14] Fire test of building elements "Test report 02-U-007", CTICM [15] PR 254 N 92 - Appendix D "Summary of fire test results with steel studs maintained

by plasterboards", CTICM [16] PR 254 N 72 Appendix G "Calculation rules of lightweight steel sections in fire

situation, validation study of mechanical behaviour of steel stud maintained by board, ANSYS results", CTICM, B. ZHAO

/250

[17] PR 254 N 72 Appendix H "Calculation rules of lightweight steel sections in fire situation, Numerical analysis of a steel stud at room and under elevated temperatures with the software SAFIR", ProfilARBED

[18] PR 254 N 87-C "Validation study of the mechanical behaviour of a steel stud -

ABAQUS results ", VTT, Olli Kaitila [19] PR 254 N 72 Appendix F "Calculation rules of lightweight steel sections in fire

situation", LABEIN [20] PR 254 N 93-A "Lightweight steel sections maintained by boards at elevated

temperature: Numerical simulation of fire tests", CTICM, C. RENAUD [21] PR 254 N 95-A "Lightweight steel sections maintained by boards at elevated

temperature: Numerical simulation of two fire tests", CTICM, C. RENAUD [22] PR 254 N 122-A "Numerical simulations of VTT fire Tests 13, 14 and 15 on C250-80-

21.5/2.5 - steel sections maintained by plasterboards", VTT, Olli Kaitila [23] PR 254 N 107-A "Numerical simulations of VTT fire Tests 3, 5 and 18 and CTICM fire

tests 2 and 5 on lightweight steel sections maintained by boards", VTT, Olli Kaitila [24] PR 254 N 108-A "Numerical simulations of VTT fire Tests 10, 11 and 12 on AWS -

steel sections maintained by plasterboards", VTT, Olli Kaitila [25] PR 254 N 88-C «Parametric study of studs maintained by boards", CTICM, C.

RENAUD [26] PR 254 N 109-A "Parametric study of AWS sections maintained by boards in fire",

VTT, Olli Kaitila [27] PR 254 N 113-A "Comparison between simple calculation rule and ANSYS results ",

CTICM, C. RENAUD [28] French methodology for extended application of partition test results for tall partitions

INC-02/147-JK/IM [29] Group of notified bodies-Fire Sector Group - Rules for extended application of fire

resisting elements FSG N162 [30] CTICM “Calculation Rules of Lightweight Steel Sections in Fire Situation”, Appendix K

of Fourth annual technical report, 30th March 2004 [31] VTT “Mechanical Behaviour of Lightweight Steel Sections at Elevated Temperatures”,

test report, 29th November 2002 [32] CTICM “Mechanical Behaviour of Tall Lightweight Steel Studs at Elevated

Temperatures”, test report, 29th March 2004

calculation rules of lightweight steel … · ... more and more lightweight steel structures are...

Documents