bearing strength of cold formed steel bolted connections .../67531/metadc115135/m2/1/high_res... ·...

APPROVED: Cheng Yu, Major Professor Diane Desimone, Committee Member Haifeng Zhange, Committee Member Leticia Anaya, Committee Member Enrique Barbieri, Chair of the

Department of Engineering Technology

Costas Tsatsoulis, Dean of the College of Engineering

James D. Meernik, Acting Dean of the Toulouse Graduate School

BEARING STRENGTH OF COLD FORMED STEEL BOLTED

CONNECTIONS IN TRUSSES

Mark Panyanouvong

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

May 2012

Panyanouvong, Mark. Bearing Strength of Cold Formed Steel Bolted

Connections in Trusses. Master of Science (Engineering Systems – Construction

Management), May 2012, 109 pp., 9 tables, 14 figures, 11 references.

The existing design provision in North American Specification for Cold-

Formed Steel Structural Member (AISI S100) for the bearing strength of bolted

connections were developed from tests on bolted connected sheets which were

restrained by bolt nut and head with or without washers. However, in the cold-formed

assemblies, particularly in trusses, the single bolt goes through both sides of the

connected sections, making the connected sheets on each side unrestrained. The

warping of the unrestrained sheet may reduce the bearing strength of the bolted

connection. This research investigates the behavior and strength of bearing failure in

bolted connections in cold-formed steel trusses. Tensile tests were conducted on

trusses connections with various material thicknesses. It was found that the AISI

S100 works well for thick connections but provides unconservative predictions for

thin materials. Based on the experimental results, a modified bearing strength

method is proposed for calculating the bearing strength of bolted truss connections.

The proposed method can be used for any cold-formed steel connections with

unrestrained sheet.

Mark Panyanouvong

ACKNOWLEDGEMENTS

I am heartily thankful to my supervisor, Cheng Yu, whose encouragement,

guidance and support from the initial to the final level enabled me to develop and

gain greater understanding of the subject. I would like to acknowledge my family and

Denial Pisuc who gave me the moral support and for being my back bone. I would

also like to give recognition to Stephen Triplett, who was able to help me through

composition of this thesis.

Many thanks go to Marcus Sanchez and Roger Rovira, whose efforts made

this thesis possible. Lastly, I offer my regards and blessings to all of those who

supported me in any aspect during the completion of the project.

TABLE OF CONTENTS

Page ACKNOWLEDGMENTS ............................................................................................ iii LIST OF TABLES ...................................................................................................... vi LIST OF FIGURES ....................................................................................................vii CHAPTER 1 INTRODUCTION ................................................................................... 1 CHAPTER 2 BACKGROUND, RESEARCH OBJECTIVES ....................................... 3

2.1 Background ........................................................................................... 3 2.2 Research Objectives ............................................................................. 4

CHAPTER 3 LITERATURE REVIEW ......................................................................... 7

3.1 Research Work and Types of Failure Mode .......................................... 7 3.1.1 Longitudinal Shearing of Steel Sheets (Type I Failure) .............. 7 3.1.2 Bearing or Pilling Up of Steel Sheet (Type II Failure) ................. 8 3.1.3 Tearing of Sheet in Net Section (Type III Failure) ...................... 8 3.1.4 Shearing of Bolt (Type IV Failure) .............................................. 9

3.2 AISI Design Criteria for Bolted Connections ....................................... 10 3.2.1 Bearing Strength Proposed Methods ....................................... 10

CHAPTER 4 TESTING ............................................................................................. 13

4.1 Testing of Specimens ......................................................................... 13 4.2 Testing Equipment .............................................................................. 15 4.3 Specimens .......................................................................................... 16 4.4 Specimens Preparation....................................................................... 17

CHAPTER 5 TEST RESULTS ................................................................................. 19

5.1 Specimen Labeling ............................................................................. 19 5.2 Characterization of Typical Bearing Failure Mode .............................. 20

5.2.1 Material Properties ................................................................... 22 5.3 Discussion Proposed Design Method ................................................. 23

CHAPTER 6 CONCLUSIONS .................................................................................. 29

APPENDIX A: DIMENSIONS AND RESULTS OF BOLTED CONNECTIONS IN THE EVALUATION OF EXISTING DATA ........................................................................ 30 APPENDIX B: PHOTOGRAPHS AND SPECIMEN CONFIGURATION ................... 33 REFERENCES ....................................................................................................... 109

LIST OF TABLES

2.1 Bearing factor C, for bolted connections (AISI S100-2007) ........................... 11

3.2.2 Modification factor 𝑚𝑓, for type of bearing connection .................................. 11

4.1.1 Bolt diameter and sizes of bolt holes, inches ................................................. 14

4.1.2 Test matrix of the research project ................................................................ 14

5.2.1 Material properties of specimens ................................................................... 22

5.3 A. Proposed bearing factor, C, for bolted connection .................................... 24

B. Proposed modification factor 𝑚𝑓, for bolted connection ............................ 24

C. Test-to-predicted ratios for sheet bearing strength ................................... 25

D. Resistance factors and AISI factor of safety for proposed design methods for bearing in bolted connections ................................................................... 27

LIST OF ILLUSTRATIONS

2.1 Typical failures of bolted CFS connections ...................................................... 3

2.2 A. Typical sheet to sheet connections ............................................................. 5

B. Typical truss connections ............................................................................ 5

4.2 A. Instron 4482 Universal .............................................................................. 15

B. Hydraulic cylinder testing machine ............................................................ 15

4.3 A. Specimen set up for testing ....................................................................... 16

B. Specimen after testing .............................................................................. 16

4.4 Steps to setup the experiment ....................................................................... 17

5.1 Specimens labeling for sheet bearing and shear specimens ......................... 19

5.2 A. Typical curve bearing failure of a bolted connection ................................. 20

B. Typical bearing failure of a bolted connection without washers................. 20

C. Unchanged shape the bearing strength failure of a bolted connection without washers (118mil) ............................................................................... 21

5.3 A. Test results vs. design methods AISI S100 for bearing strength of bolted connections ................................................................................................... 23

B. The proposed design vs. design methods AISI S100 for bearing strength of bolted connections ......................................................................................... 25

CHAPTER 1

INTRODUCTION

Cold-formed steel (CFS) is a feasible material in buildings, home, office

furniture, automobiles, equipment, utility poles, highway products, drainage

facilities, and bridges. The popularity of CFS can be ascribed to ease of mass

production and prefabrication, uniform quality, lightweight designs, economy

in transportation and handling, fast and simple up righting or installation.

CFS structural members shapes are manufactured by pressed-

breaking or roll forming cold-or hot-rolled coils or sheets; both forming

operations being performed at ambient room temperature, that is, without

manifest addition of heat such as would be required for hot forming. Buckling

usually governs the strength of CFS members for construction.

The structural behavior of bolted connections in CFS construction is

somewhat different from that in hot-rolled heavy construction, mainly because

of the thinness of the connected parts. In the U.S., The design provisions for

CFS bolted connections are provided in the North American Specification for

Cold-Formed Steel Structural Member (AISI S100, 2007). Mexico and Canada

have also adopted this specification.

CHAPTER 2

BACKGROUND, RESEARCH OBJECTIVES

2.1 Background

CFS bolted connections may fail in four typical modes as illustrated in

Figure 2.1: shear failure of sheet (Type I), bearing failure of sheet (Type II),

rupture in the net section (Type III), and shear failure of bolt (Type IV). This

research is focused on the Type II bearing failure of the sheet.

Type I Shear Failure of Sheet

Type II Bearing Failure of Sheet

Type III Rupture in the Net Section

Type IV Shear Failure of Bolt

Figure 2.1 Typical Failures of Bolted CFS Connections

The AISI S100 (2007) provides design provisions for these four types

of failure respectively. AISI S100 provisions for the bearing strength of bolted

connections were developed from tests on sheet connections, in which the

connected sheets were restrained by bolt nut and head with or without

washers on both sides of the group of sheets. However in the cold-formed

assemblies, for example trusses, framing, racking, etc., the single bolt goes

through both sides of the connected sections, making the connected elements

on each side unrestrained. The unrestrained elements may yield significant

out of plan deformation under loading; the deformation may greatly affect the

bearing strength of the bolt connection. A comprehensive research project is

needed to investigate the behavior and strength of CFS bolted connections

with unrestrained elements.

2.2 Research Objectives

This research is aimed at investigating the behavior and strength of

CFS bolted truss connections with unrestrained elements. The investigated

truss connections contain three elements. The first element used was the

web. The tests used using webs of seven different thicknesses such as:

27mil, 33mil, 43mil, 54ml, 68mil, 97mil and 118mil. The second element, the

chord had the same seven thicknesses like the web; 27mil, 33mil, 43mil,

54mil, 68mil, 97mil and 118mil. With those 23 same thickness combinations of

web and chords we used for testing our third element, four bolts with different

diameters; 3/8, 1/2, 5/8 and 3/4 inch. To verify that the results are precise and

accurate; the tests used repeated once for each thickness, for a total of 46

tests.

The main objective for this research is to investigate the behavior and

the strength of bearing failure of bolted connections in cold-formed steel in

trusses where the connections in cold-formed steel (CFS) sheets are not

restrained by bolt nut or head on both sides. The bolted connection of the

bearing strength of cold-formed steel bolted without nut is presented with the

testing inside of the web having no nut. To determine through mechanical

method whether or not having a nut on the inside of the web influences the

peak load.

This study focused on the different combination of web and chord

thickness with varying size bolts. This research also determined the how the

failure points vary based on bolt diameter, web and chord with no support or

nut along the inside wall of the web. The experiments conducted were:

• Examine the difference of the two elements between the web and

chord for each configuration.

• Show the result of the reaction of the web and the chord when the bolt

size are different.

Figure 2.2A Typical sheet to sheet connections

Figure 2.2B Typical truss connections

• Use different type the bolt size of 3/8, 1/2, 5/8, and 3/4 inch for

connections.

• Show how the chord and web thicknesses are affected by the lack of

support or use of additional washers or nuts inside the web.

We compared our experiment testing data to the regular 2-sheet connected

with a nut.

CHAPTER 3

LITERATURE REVIEW

3.1 Research Work and Types of Failure Mode

Prior to 1980, the American Iron and Steel Institute (AISI) determined

the design specification of bolted connections. These were developed on the

basis of the Cornell tests supervised under the direction of George Winter and

other institutes. One of the most recognizable works in this area is the

research done by Yu (1982).

3.1.1. Longitudinal Shearing of Steel Sheets (Type I Failure)

Longitudinal shearing of the steel sheet along two almost parallel

planes, where the distance of separation is close to the bolt diameter is a

Type I Failure. It was discovered by several researchers and they found that

the shear strength of the sheet type I failure is the relationship between the

ratio of edge distance 𝑒 and the bolt diameter 𝐶 which indicate the bearing

stress at failure can be predicted by

σ (Eq.3.1A)

where bσ Ultimate bearing stress between bolt and connected part, ksi

Fu Tensile strength of connected part, ksi

e Edge distance, in.

d Bolt diameter, in.

3.1.2 Bearing or Piling Up of Steel Sheet (Type II Failure)

When the edge distance is sufficiently large or when we have large 𝑒 𝐶

ratios, the failure of connections may occur in front of the bolt. The University

of Missouri-Rolla conducted the research on the failure and recognized that

the hole extension prior to reaching the bearing strength, limited a bolted

connection. The limitation of the connection movement was 0.25 in. or (6.4

mm). The deformation around the bolt holes ( ) is a design consideration,

according to the Supplement to the 1996 edition of the Specification [1.333]: is

given by:

Pn = (4.6t + 1.53)dt Fu (with t in inches) (Eq.3.1B.1)

For SI units:

Pn = (0.831t + 1.53)dt Fu (with t in mm) (Eq.3.1B.2)

where: t Thickness of connected part

d Diameter of bolt (in.)

Fu Tensile strength of steel (ksi) or (MPa)

Bearing strength

3.1.3 Tearing of Sheet in Net Section (Type III failure)

Cornell University conducted the tests by using connections under bolt

head and nut to eliminate the stress concentration for the low ductility steel. In

1992, Zadoanfarrokh and Bryan investigated the shear failure and bearing

failure in connections sheets. In order to prevent the rupture failure the width

𝑤 of the specimens’ connection has to be sufficiently large and thus set up

(w=6.25d) for bearing tests with the nominal bolt diameter d ≥ 0.4 in. Besides

finding the type III failure of tearing of sheet in the net section, the effects of

the 𝐶 𝑠 ratio on the tensile strength of bolted connections with washers were

observed.

The following formulas have been developed to predict the failure stress in the

net section:

a) When 𝐶 𝑠 ≤ 0.3, 𝜎𝑛𝑒𝑡 = [ 1- 0.9r + 3r(d/s)]𝐶𝑢 ≤ 𝐶𝑢 (3.1C.A) b) When 𝐶 𝑠 > 0.3, 𝜎𝑛𝑒𝑡 = 𝐶𝑢 (3.1C.B)

Where 𝜎𝑛𝑒𝑡 Failure stress in net section, ksi

r Force transmitted by bolt or bolts at the section considered, divided by the force in the member at that section

d Bolt diameter, in.

s Spacing of bolts perpendicular to line of stress, in.

𝐶𝑢 Ultimate tensile strength of steel sheets, ksi

3.1.4 Shearing of Bolt (Type IV Failure)

The shearing of bolt failure is the type of failure by shearing of the bolt

that occurs at the strength equal to 0.6 times the tensile strength of the bolt

[Yu, 2000]. For the type IV failure, this research was not focus on this mode of

failure.

3.2 AISI Design Criteria for Bolted Connections

The design bearing strength of bolted connections shall be determined

by the design bearing strength of bolted connections by tests,𝑃𝑛, bearing

factor, C, to account for the influence by the bolt diameter to sheet thickness

ratio, 𝐶 𝑡 . A modification factor is used to reflect the washer option as well as

connection type for single shear connections without a washer with standard

holes, ( 𝑚𝑓 = 0.75 ).

3.2.1 Bearing Strength Proposed Methods

The bearing strength of bolted connections with standard holes is

shown in equation 3.2-1 (𝐸𝑞. E3.3.1-1 of AISI S100 2007). When deformation

around the bolt holes is not a design consideration, the nominal bearing

strength [resistance], 𝑃𝑛, of the connected sheet for reach loaded bolt

determined as follows:

𝑃𝑛 = 𝑚𝑓Cdt𝐶𝑢 (Eq. 3.2.1) where

C Bearing factor, which shall be determined according to Table 3.3.1.

d Nominal bolt diameter

t Uncoated sheet thickness

Fu Tensile strength of sheet as defined

𝑚𝑓 Modification factor for type of bearing connection, which shall be determined according to Table 3.2.2.

USA and Mexico Canada Ω (ASD) ɸ (LRFD) ɸ (LSD)

2.50 0.60 0.50

Table 3.2.1 Bearing Factor, C, for Bolted Connections (AISI S100 2007)

Thickness of Connected Part, t,

(inch) (mm)

Ratio of Fastener Diameter to Member

Thickness

0.024 ≤ t < 0.1875

(0.61 ≤ t < 4.76)

d/t < 10 3.0

10 ≤ d/t ≤ 22 4 – 0.1(d/t)

d/t > 22 1.8

Table 3.2.2 Modification Factor, 𝑚𝑓, for Type of Bearing Connection

Type of Bearing Connection 𝑚𝑓

Single Shear and Outside Sheets of Double Shear Connection with Washers under Both Bolt Head and Nut

Single Shear and Outside Sheets of Double Shear Connection without Washers under Both Bolt Head and Nut, or with only one washer

Inside Sheet of Double Shear Connection with or without Washers

CHAPTER 4

TESTING

4.1 Testing of Specimens

We will compare our experiment testing data to the regular 2-sheet

connected with a nut.

• CFS steel sheet nominal thickness range from 27mil to 118mil with

minimum yield strength from 33 ksi to 50 ksi.

• Bolted Connections is referring to the design criteria and the

requirements for the bolted connections used for cold-formed steel

structural members in which the thickness of the thinnest connected

part is less than 3/16 in. (4.76 mm). [1] American Society for Testing

Material (ASTM), A307 (Type A) bolts, carbon steel bolts and studs,

have less than 60,000 PSI Tensile Strength for bolts with nominal

diameters of 3/8, 1/2, 5/8 and 3/4 in.

• Minimum Edge and End Distances according to AISI S100 (2007). The

minimum distance between centers of bolt holes shall provide sufficient

clearance for bolt holes and shall provide sufficient clearance for bolt

heads, nuts, washers. Also the wrench shall not be less than 3 times

the nominal bolt diameter, d. (e=3d).

Table 4.1.1 Bolt diameter and Sizes of Bolt Holes (inches)

Nominal bolt diameter, d (in.)

AISI Standard Hole Diameter d (in.)

3/8 13/32

1/2 9/16

5/8 11/16

3/4 13/16 Note: 1 in. = 25.4 mm.

Table 4.1.2 Test matrix of the research project

Nominal

bold diameter

Web with Chord (mil.)

27 x 27 33 x 33 43 x 43 54 x 54 68 x 68 97 x 97 118 x 118

3/8 inch Yes Yes Yes Yes Yes NO NO

1/2 inch Yes Yes Yes Yes Yes Yes Yes

5/8 inch Yes Yes Yes Yes Yes Yes Yes

3/4 inch Yes Yes Yes Yes NO NO NO

We repeat each configuration once, resulting in a total of 46 tests.

4.2 Testing Equipment

The testing was separated by two machines to properly test the varying

web and chord thicknesses. For thickness of 27mil to 97mil, a 20 kip capacity

Instron 4482 universal testing machine was used. For the thickness of 118mil,

the test was performed at the high-bay area by the hydraulic cylinder that is

able to handle over 20 kip as shown in Fig.4.2B. Most tests conducted were

stopped shortly after the deformation point and once maximum load had been

achieved as shown in Fig.4.2A.

Figure 4.2A Instron 4482 Universal Figure 4.2B Hydraulic Cylinder

Testing Machine

4.3 Specimens

The same sheet steel thicknesses were used for the web and the chord

for each of the 46 tests to create the specimens with 4 different kinds of bolt.

A coupon test was performed for every thickness in order to get the yield

stress 𝐶𝑦, ultimate stress 𝐶𝑢, and the thickness of the sheet steel and

percentage of elongation. Each thickness was tested 3 times in order to

achieve the same results and determine that the tests were precise.

Figure 4.3A Figure 4.3B Specimen setup for testing Specimen after testing

4.4 Specimens Preparation

Two sheets steel with the same thickness were cut into 2 pieces,

measurement based upon the testing specifications for each and every test.

The hole punch distance varies with the bolt diameter used as according the

AISI standard hole diameter specification as shown in the Figure 4.4.

Figure 4.4 Steps to setup the experiment

The sheets were then folded using a brake press machine with the web

fold points slight closer so that the web will accurately fit into the chord.

The web and chord were connected by the bolt specimen based on the

test specifications and secured with a nut to insure the body of the bolt

specimen was within the testing area of the web and chord and that the

threads of the bolt would not create a point of failure during the tests. The

testing specimens were connected to the testing machine using mounting

brackets to insure the load of the machine is being evenly distributed across

specimen.

CHAPTER 5

TEST RESULTS

The testing results and the geometric properties can be found in the

Appendices (Table A1, A2, A3 and A4). Here, it is also included the

comparison between the bearing strength of the actual test capacity and the

new bearing capacity calculated with adjustment with preferable the ratio

closest to one (𝑃𝑡𝑒𝑠𝑡 𝑃𝑛𝑒𝑤 =1). The comparisons are shown in the Table A1

(Appendix A).

5.1 Specimen Labeling

The labeling specimens were assigned by the same format to identify the test

specimens:

33-1/2-T1

Figure 5.1 Specimens Labeling for Sheet Bearing and Shear Specimens

Web/Chord Thickness in mil

Nominal diameter of bolt in inches

Test Number

5.2 Characterization of Typical Bearing Failure Mode

The graph below illustrates the typical curve of the bearing failure for

the specimens. With the initial load applied, the sheet steels experienced

slippage against the bolt. With the load still being applied, sheets steel started

yielding at to the maximum load. At which point the specimen continued to

deform and stopped the testing at around 1 or 1.2 inch.

Figure 5.2A Typical curve bearing failure of a bolted connection

Figure 5.2B Typical bearing failure of a bolted connection without washers

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Sheets and Bolt Slippage

Elastic Deformation

Plastic Deformation

Bearing Failure Maximum load

Displacement (inch)

In this research 46 experiments with 4 different sizes of bolts were

conducted. The chord and the web connections when the load was applied

were observed. Since, there was no support along the inside wall of the web,

the testing results showed the reaction of the web conformed to the perimeter

contour after the load applied as shown in Figure 5.2B., resulting in type II

failures or piling during tests. The same reaction also occurred with same

thickness of testing from 27mil until 97mil. In contrast, for the sheets steel

connections of 118mil, the results of the shape remaining unchanged after the

maximum load was reached and the test was stopped here. Great elongation

was observed in this case as shown in Figure 5.2C. Due to the thickness of

the 118mil steel, most failures were type I, (failure of the steel sheet).

Figure 5.2C Unchanged shape the bearing strength failure of a bolted connection without washers (118mil)

5.2.1 Material Properties

Coupon tests were conducted according to ASTM 307 (2007)

“Standard Test Method and Definitions for Mechanical Testing of Steel

Products” to obtain the actual properties of the test materials in this research.

The coupon test results are summarized in Table 5.2. The coating on the steel

was removed by hydrochloric acid prior to the coupon tests. The coupons

tests were conducted on the INSTRON 4482 universal testing machine. An

INSTRON was employed to measure the tensile strain. The tests were

conducted in displacement control at a constant rate of 0.05 in./min. A total of

four coupons were tested for each member, and the average results are

provided in Table 5.2.1

Table 5.2.1 Material Properties of specimens

Nominal

sheet thickness

uncoated thickness

Actual 𝐶𝑦

Actual 𝐶𝑢

𝐶𝑢𝐶𝑦

Elongation on 2-in.

gage length

Ductility

27 mil 0.0227 50.30 57.80 1.15 18.65% high 33 mil 0.0361 44.60 54.10 1.21 18.95% high 43 mil 0.0437 66.00 79.60 1.21 16.75% high 54 mil 0.0566 60.32 78.25 1.30 10.00% high 68 mil 0.0698 46.10 54.50 1.18 15.50% high 97 mil 0.1017 69.92 75.22 1.08 10.00% high

118 mil 0.1305 45.30 52.20 1.15 16.90% high

5.3 Discussion Proposed Design Method

According to previous research (LaBoube and Yu 1995, Wallace,

Schuster, and LaBoube 2001a), the experience adopted the same equations

(Eq. E3.3.1-1) for the bearing failure of bolted connections based on the AISI

S100 (2007) specifications as bearing factor C and the modification factor 𝑚𝑓

listed on Table 3.2.2 and 3.2.3 respectively for bearing single shear and

outside sheets of double connection without washers uses 𝑚𝑓 = 0.75.

After the test results achieved and compared to the current AISI S100

predictions are lower than predictions when the ratio of d/t had a big number.

In order to accurately predict the bearing strength, the research revised the

formula of the bearing factor, C, and the modification factor, 𝑚𝑓.

Figure 5.3A Test Results vs. Design Methods AISI S100 for Bearing Strength of Bolted Connections

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00

Data Testing

Current AISIS100 Design

A new bearing factor and modification factor (Table 5.3A) were

proposed in order for the test results to be more in line with the original AISI

S100 standard. The Y-axis represents the normalized peak loads, 𝑃𝑡𝑒𝑠𝑡/(𝐶𝑢𝐶𝑡),

which is equivalent to the value of the bearing factor and modification factor

(C 𝑚𝑓). The new proposed method adopted a non-linear curve for the C factor

in order to get the factor of safety and resistance factor approach to AISI S100

values.

Table 5.3A Proposed Bearing Factor, C, for Bolted connection

Ratio of fastener diameter to member thickness, d/t New Method for Bearing Factor C

d/t < 5 3

5 ≤ d/t ≤ 28 0.33 + 13.33/(d/t)

d/t > 28 0.81

Table 5.3B Proposed Modification Factor,𝑚𝑓, for Bolted Connection

Type of Bearing Connection 𝑚𝑓

Single Shear and Outside Sheets of Double Shear Connection without

Washers under Both Bolt Head and Nut

Figure 5.3B The Proposed Design vs. Design Methods AISI S100 for Bearing Strength of Bolted Connections

The ratio for the new design method is 𝑃𝑡𝑒𝑠𝑡/𝑃𝑛𝑒𝑤. The new method

gives an average test ratio of 1.05, with a standard deviation of 0.28 and

coefficient of 0.24.

Table 5.3C Test-to-Predicted Ratios for Sheet Bearing Strength

Hole config.

No. of tests

𝑃𝑇𝑒𝑠𝑡/𝑃𝐴𝐼𝑆𝐼 𝑃𝑇𝑒𝑠𝑡/𝑃𝑁𝑒𝑤 Avg. Std.

dev. COV Avg. Std.

dev. COV

Trusses connections

46 0.66 0.25 0.38 1.16 0.28 0.24

Current AISI Proposed Design Data from Testing

𝑃 𝑛/(𝐶𝐶𝐶 𝑢

Proposing bearing strength method, the resistance factor ɸ for (LRFD)

and factor of safety Ω (ASD) were determined according Chapter F of AISI

S100 (2007), with a target reliability index 3.5 for connections for the LRFD.

Considering the equation Eq.5.3A and from AISI S100 (2007) Eq. F1.1-2 the

resistance factor ɸ can be determined as follows:

ɸ = 𝐶ɸ(𝑀𝑚𝐶𝑚𝑃𝑚) 𝑒−𝛽0𝑉𝑀2 + 𝑉𝐹2 + 𝐶𝑃𝑉𝑃2 + 𝑉𝑄2 Eq.5.3A

where:

𝐶ɸ Calibration coefficient 1.52 for the United States

𝑀𝑚 Mean value of material factor, M, listed in Table F1 for type of component involved (AISI S100-2007)

𝐶𝑚 Mean value of fabrication factor, F, listed in Table F1 for type of component involved (AISI S100-2007)

𝑃𝑚 Mean value of professional factor, P, for tested component

𝛽0 Target reliability index 3.5 for the United States

𝑉𝑀 Coefficient of variation of material factor listed in Table F1 for type of component involved

𝑉𝐹 Coefficient of variation of fabrication factor listed in Table F1 for type of component involved

𝐶𝑃 Correction factor (1+1/n)m/(m-2) for n≥4

𝑉𝑃 Coefficient of variation of test results, but not less than 6.5%

m Degree of freedom (n-1)

n Number of tests

𝑉𝑄 Coefficient of variation of load effect 0.21

𝑒 Natural logarithmic based 2.718

According to the AISI, by knowing the resistance factor, ɸ, the

corresponding safety of factor can be computed as follows:

Ω = 1.533ɸ

Eq.5.3B

The resistance factor ɸ and the factor of safety Ω can be determined

based upon the test results and the calibrations AISI S100 (2007), Table F1 of

the bolted connections with and without washers

Table 5.3D: Resistance Factors and AISI factor of Safety for Proposed Design Methods for Bearing in Bolted Connections

Number of Specimens 46 Mean 1.16 Std. Dev. 0.28 COV (𝑉𝑃) 0.24 𝑀𝑚 1.10 𝑉𝑀 0.08 𝐶𝑚 1.00 𝑃𝑚 1.16 𝑉𝐹 0.05 m 45 𝐶𝑃 1.07 β(LRFD) 3.5 𝑉𝑄 0.21 AISI S100 ɸ (LRFD) 0.6 0.6 Ω (ASD) 2.56 2.50

The new method yielded an equivalent resistance factor of 0.6

compared to AISI S100 standard, while the safety factor was slightly higher

than the AISI S100 standard value. Based on the testing value and similar

equation values, the AISI S100 would be acceptable to adapt to the same

type of connection.

CHAPTER 6

CONCLUSION

A total of 46 CFS bolted truss connections were tested in this research.

The specimen parameters include the thickness of the material and the bolt

diameter. The experimental results show that the truss connections with thick

materials (118mil and 97mil) do not demonstrate significant out of plan

deformation in the unrestrained elements. The existing AISI provisions give

good prediction for the beating strength of those connections. However for

thin materials (68 mil or thinner), significant out of plane deformation was

observed, the test results of those connections are lower than the AISI

predictions. On average, the ratio of test to AISI predicted is 0.66 for all 46

specimens.

Based on the test results, new equations for the bearing factor, C, and

new value for modification factor, 𝑚𝑓, are proposed to add to the existing AISI

bearing equation. The new factors can be used to predict the bearing strength

of bolted connections with unrestrained elements including truss connections,

framing connections, racking system connections, etc. the proposed new

factors were adjusted so that the existing resistance factor and safety factor in

AISI S100 for bearing strength shall also be permit for the connections with

unrestrained elements.

APPENDIX A

DIMENSIONS AND RESULTS OF BOLTED CONNECTIONS

IN THE EVALUATION OF EXISTING DATA

27Mil,33Mil,43Mil, 54Mil, and 68Mil with 3/8" Bolt

No. Speciment Uncoated Uncoated Bolt Bolt d/t e Yield Tensile Fu/Fy Pn(AISI) P (Test) Elongation Δ Δ Shape P(test)/P(AISI) P (0.25") Pn(AISI) P(new) P(test)/Label Thickness Thickness Type Dia. Stress Strength without defo. for one side 2 in. gage at peak After Test without for two with mf = 0.675 P(New)

Sheet#1 (in.) Sheet#2 (in.) d (in.) (in.) Fy (ksi) Fu (ksi) Ratio (lbf) (lbf) length (%) (in.) deformation sides deformation1 27-3/8-T1 0.0227 0.0227 A307 0.375 16.520 1.125 50.30 57.80 1.15 866.46 619.60 18.65 0.9515 Changed 0.715 687.78 804.62 377.58 1.6412 27-3/8-T2 0.0227 0.0227 A307 0.375 16.520 1.125 50.30 57.80 1.15 866.46 572.00 18.65 0.6610 Changed 0.660 653.42 804.62 377.58 1.5153 33-3/8-T1 0.0361 0.0361 A307 0.375 10.388 1.125 44.60 54.10 1.21 1626.55 1173.00 18.95 1.0610 Changed 0.721 1449.67 1243.22 797.51 1.4714 33-3/8-T2 0.0361 0.0361 A307 0.375 10.388 1.125 44.60 54.10 1.21 1626.55 1280.00 18.95 0.8690 Changed 0.787 1397.05 1243.22 797.51 1.6055 43-3/8-T1 0.0437 0.0437 A307 0.375 8.581 1.125 66.00 79.60 1.21 2935.00 1454.25 16.75 0.6485 Changed 0.495 2865.50 2260.30 1658.33 0.8776 43-3/8-T1 0.0437 0.0437 A307 0.375 8.581 1.125 66.00 79.60 1.21 2935.00 1376.10 16.75 1.1060 Changed 0.469 2115.43 2260.30 1658.33 0.8307 54-3/8-T1 0.0566 0.0566 A307 0.375 6.625 1.125 60.32 78.25 1.30 3736.93 2430.35 10.00 0.9390 Changed 0.650 4509.00 2977.29 2625.50 0.9268 54-3/8-T2 0.0566 0.0566 A307 0.375 6.625 1.125 60.32 78.25 1.30 3736.93 2572.10 10.00 0.3435 Changed 0.688 5093.15 2977.29 2625.50 0.9809 68-3/8-T1 0.0698 0.0698 A307 0.375 5.372 1.125 46.10 54.50 1.18 3209.71 3719.75 15.50 0.5440 Changed 1.159 4687.79 2644.62 2706.90 1.374

10 68-3/8-T2 0.0698 0.0698 A307 0.375 5.372 1.125 46.10 54.50 1.18 3209.71 3510.05 15.50 0.3925 Changed 1.094 4942.28 2644.62 2706.90 1.297

27Mil,33Mil,43Mil, 54Mil, 68Mil, 97Mil and 118Mil with 1/2" Bolt

No. peciment Labe Uncoated Uncoated Bolt Bolt d/t e Yield Tensile Fu/Fy Pn(AISI) P (Test) Elongation Δ Δ Shape P(test)/P(AISI) P (0.25") Pn(AISI) P(new) P(test)/Thickness Thickness Type Dia. Stress Strength without defo. for one side 2 in. gage at peak After Test without for two with mf = 0.675 P(New)Sheet#1 (in.) Sheet#2 (in.) d (in.) (in.) Fy (ksi) Fu (ksi) Ratio (lbf) (lbf) length (%) (in.) deformation sides deformation

1 27-1/2-T1 0.0227 0.0227 A307 0.5 22.026 1.5 50.30 57.80 1.15 885.64 647.00 18.65 0.9515 Changed 0.731 722.69 1072.82 414.12 1.5622 27-1/2-T2 0.0227 0.0227 A307 0.5 22.026 1.5 50.30 57.80 1.15 885.64 631.50 18.65 0.6610 Changed 0.713 760.81 1072.82 414.12 1.5253 33-1/2-T1 0.0361 0.0361 A307 0.5 13.850 1.5 44.60 54.10 1.21 1915.14 1435.00 18.95 1.0610 Changed 0.749 1182.28 1657.62 851.89 1.6844 33-1/2-T2 0.0361 0.0361 A307 0.5 13.850 1.5 44.60 54.10 1.21 1915.14 1425.50 18.95 0.8690 Changed 0.744 1412.08 1657.62 851.89 1.6735 43-1/2-T1 0.0437 0.0437 A307 0.5 11.442 1.5 66.00 79.60 1.21 3725.28 1634.00 16.75 0.6485 Changed 0.439 2467.65 3013.73 1755.18 0.9316 43-1/2-T1 0.0437 0.0437 A307 0.5 11.442 1.5 66.00 79.60 1.21 3725.28 1607.50 16.75 1.1060 Changed 0.432 1886.71 3013.73 1755.18 0.9167 54-1/2-T1 0.0566 0.0566 A307 0.5 8.834 1.5 60.32 78.25 1.30 4982.57 2808.00 10.00 0.9390 Changed 0.564 3682.15 3969.72 2748.82 1.0228 54-1/2-T2 0.0566 0.0566 A307 0.5 8.834 1.5 60.32 78.25 1.30 4982.57 2696.50 10.00 0.3435 Changed 0.541 3509.80 3969.72 2748.82 0.9819 68-1/2-T1 0.0698 0.0698 A307 0.5 7.163 1.5 46.10 54.50 1.18 4279.61 3537.00 15.50 0.5440 Changed 0.826 3807.78 3526.16 2812.82 1.257

10 68-1/2-T2 0.0698 0.0698 A307 0.5 7.163 1.5 46.10 54.50 1.18 4279.61 3321.00 15.50 0.3925 Changed 0.776 4807.52 3526.16 2812.82 1.18111 97-1/2-T1 0.1017 0.1017 A307 0.5 4.916 1.5 69.92 75.22 1.08 8606.11 8370.00 10.00 1.0860 Unchange 0.973 3844.30 7657.10 7745.50 1.08112 97-1/2-T2 0.1017 0.1017 A307 0.5 4.916 1.5 69.92 75.22 1.08 8606.11 8830.00 10.00 0.9605 Unchange 1.026 6405.90 7657.10 7745.50 1.14013 118-1/2-T1 0.1305 0.1305 A307 0.5 3.831 1.5 45.30 52.20 1.15 7663.61 9570.96 16.90 1.0745 Unchange 1.249 5424.18 7273.69 6897.25 1.38814 118-1/2-T2 0.1305 0.1305 A307 0.5 3.831 1.5 45.30 52.20 1.15 7663.61 9724.69 16.90 1.0226 Unchange 1.269 9560.67 7273.69 6897.25 1.410

Table A1: Test Results of Bolted Connections

27Mil,33Mil,43Mil, 54Mil, 68Mil, 97Mil and 118Mil with 5/8" Bolt

1 27-5/8-T1 0.0227 0.0227 A307 0.625 27.533 1.875 50.30 57.80 1.15 1107.05 514.90 18.65 0.9515 Changed 0.465 683.49 1341.03 450.65 1.1432 27-5/8-T2 0.0227 0.0227 A307 0.625 27.533 1.875 50.30 57.80 1.15 1107.05 521.90 18.65 0.6610 Changed 0.471 616.92 1341.03 450.65 1.1583 33-5/8-T1 0.0361 0.0361 A307 0.625 17.313 1.875 44.60 54.10 1.21 2076.93 1225.50 18.95 1.0610 Changed 0.590 1314.90 2072.03 906.27 1.3524 33-5/8-T2 0.0361 0.0361 A307 0.625 17.313 1.875 44.60 54.10 1.21 2076.93 1133.40 18.95 0.8690 Changed 0.546 1098.53 2072.03 906.27 1.2515 43-5/8-T1 0.0437 0.0437 A307 0.625 14.302 1.875 66.00 79.60 1.21 4190.19 1348.40 16.75 0.6485 Changed 0.322 2284.56 3767.17 1852 0.7286 43-5/8-T1 0.0437 0.0437 A307 0.625 14.302 1.875 66.00 79.60 1.21 4190.19 1357.05 16.75 1.1060 Changed 0.324 2531.54 3767.17 1852 0.7337 54-5/8-T1 0.0566 0.0566 A307 0.625 11.042 1.875 60.32 78.25 1.30 6011.80 1734.50 10.00 0.9390 Changed 0.289 2821.48 4962.15 2872.1 0.6048 54-5/8-T2 0.0566 0.0566 A307 0.625 11.042 1.875 60.32 78.25 1.30 6011.80 1786.85 10.00 0.3435 Changed 0.297 3559.73 4962.15 2872.1 0.6229 68-5/8-T1 0.0698 0.0698 A307 0.625 8.9542 1.875 46.10 54.50 1.18 5349.52 3472.20 15.50 0.5440 Changed 0.649 4463.90 4407.70 2918.7 1.190

10 68-5/8-T2 0.0698 0.0698 A307 0.625 8.9542 1.875 46.10 54.50 1.18 5349.52 3329.95 15.50 0.3925 Changed 0.622 3926.98 4407.70 2918.7 1.14111 97-5/8-T1 0.1017 0.1017 A307 0.625 6.1455 1.875 69.92 75.22 1.08 10757.64 8384.50 10.00 1.0860 Changed 0.779 2901.48 9571.37 8065.2 1.04012 97-5/8-T2 0.1017 0.1017 A307 0.625 6.1455 1.875 69.92 75.22 1.08 10757.64 7677.05 10.00 0.9605 Changed 0.714 8811.81 9571.37 8065.2 0.95213 118-5/8-T1 0.1305 0.1305 A307 0.625 4.7893 1.875 45.30 52.20 1.15 9579.52 9309.00 16.90 1.0745 Unchanged 0.972 8948.44 9092.11 8621.6 1.08014 118-5/8-T2 0.1305 0.1305 A307 0.625 4.7893 1.875 45.30 52.20 1.15 9579.52 9579.00 16.90 1.0226 Unchanged 1.000 7550.03 9092.11 8621.6 1.111

27Mil,33Mil,43Mil, and 54Mil with 3/4" Bolt

1 27-3/4-T1 0.0227 0.0227 A307 0.75 33.04 2.25 50.30 57.80 1.15 1328.46 590.35 18.65 0.9515 Changed 0.444 673.82 1609.24 487.18 1.2122 27-3/4-T2 0.0227 0.0227 A307 0.75 33.04 2.25 50.30 57.80 1.15 1328.46 599.45 18.65 0.6610 Changed 0.451 578.26 1609.24 487.18 1.2303 33-3/4-T1 0.0361 0.0361 A307 0.75 20.776 2.25 44.60 54.10 1.21 1977.42 1290.75 18.95 1.0610 Changed 0.653 1234.36 2486.43 960.65 1.3444 33-3/4-T2 0.0361 0.0361 A307 0.75 20.776 2.25 44.60 54.10 1.21 1977.42 1410.20 18.95 0.8690 Changed 0.713 1583.35 2486.43 960.65 1.4685 43-3/4-T1 0.0437 0.0437 A307 0.75 17.162 2.25 66.00 79.60 1.21 4468.55 2041.10 16.75 0.6485 Changed 0.457 2394.63 4520.60 1948.9 1.0476 43-3/4-T1 0.0437 0.0437 A307 0.75 17.162 2.25 66.00 79.60 1.21 4468.55 2180.65 16.75 1.1060 Changed 0.488 2457.45 4520.60 1948.9 1.1197 54-3/4-T1 0.0566 0.0566 A307 0.75 13.251 2.25 60.32 78.25 1.30 6663.97 2631.70 10.00 0.9390 Changed 0.395 2152.48 5954.58 2995.5 0.8798 54-3/4-T2 0.0566 0.0566 A307 0.75 13.251 2.25 60.32 78.25 1.30 6663.97 2455.30 10.00 0.3435 Changed 0.368 2453.43 5954.58 2995.5 0.820

Table A1: Test Results of Bolted Connections (Continued)

APPENDIX B

PHOTOGRAPHS AND SPECIMEN CONFIGURATION

TESTING # 1

27Mil, 33Mil, 43Mil, 54Mil and 68Mil

WITH 3/8” BOLT

Test Label: 27-3/8-T1

Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results: 27mil/24gage Test#1

Maximum load = 1.2392e+003 Displacement = 0.9585

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

(Continued: Test Label: 27-3/8-T1)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-200

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

Displacement (inch)

Specimen Configuration Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 54mil/16gage Test#2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

Displacement (inch)

TESTING # 2

27MIL, 33MIL, 43MIL, 54MIL, 68MI, 97MIL and 118MIL

WITH 1/2” BOLT

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

Maximum load = 2.7941e+003 Displacement = 869.0100e-003

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

Displacement (inch)

Maximum load = 3.2150e+003

Displacement = 648.5000e-003

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

Displacement (inch)

Maximum load = 3.1613e+003 Displacement = 1.1060e+000

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

Displacement = 0.9390

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

Displacement (inch)

Specimen Configuration

Chord : 4.00 inches X 9.00 inches Web : 4.00 inches X 8.00 inches Test Results : 68mil/14gage Test#2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-5000

Displacement (inch)

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-5000

Displacement (inch)

TESTING # 3

68Mil, 97Mil and 118Mil

WITH 5/8” BOLT

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-5000

Displacement (inch)

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-5000

Displacement (inch)

TESING # 4

27Mil, 33Mil, 43Mil and 54Mil

WITH 3/4” BOLT

0 0.05 0.1 0.15 0.2 0.25 0.3 0.350

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.40

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

Displacement (inch)

0 0.2 0.4 0.6 0.8 1 1.2 1.4-500

Displacement (inch)

Displacement = 0.5190

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

Displacement (inch)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

Displacement (inch)

REFERENCES

ASTM A370 (2007). “A370-07b Standard Test Methods and Definitions for Mechanical Testing of Steel Products,” American Society for Testing and Materials, West Conshohocken, PA.

Chong, K.P., Matlock, R. B. (1975). “Light-Gage Steel Bolted Connections without Washers,” Journal of the Structural Division, ASCE, vol 101.

Gilchrist, R.T., Chong, K. P. (1979). “Thin Light-Gage Bolted Connection without Washers,” Journal of the Structural Division, ASCE, vol 105.

Winter, G. (1956a), “Light Gage Steel Connections with High-Strength, high-Torqued Bolts,” Publications, IABSE, Vol. 16, 1956.

Winter, G (1956b), “Tests on Bolted Connections in Light Gage Steel,” Journal of the Structural Division, ASCE, Wol.82, No. ST2, February 1956.

LaBoube, R. A., Yu, W. W. (1995). “Tensile and Bearing Capacities of Bolted Connections,” Final Summary Report, Civil Engineering Study 95-6, Cold-Formed steel Series, Department of Civil Engineering, University of Missouri-Rolla.

NAS (2007). “North American Specification for the Design of Cold-Formed Steel Structural Members, 2007 Edition,” American Iron and Steel Institute, Washington, DC.

Wallace, J., Schuster, R., and LaBoube, R. (2001a). “Testing of Bolted Cold-Formed Steel Connections in Bearing (With and Without Washers),” Research Report PR01-4, American Iron and Steel Institute, Washington, DC.

Wallace, J., Schuster, R., and LaBoube, R. (2001b). “Calibrations of Bolted Cold-Formed Steel Connections in Bearing (With and Without Washers),” Research Report PR01-5, American Iron and Steel Institute, Washington, DC.

Yu, W. W. (1982). “AISI Design Criteria for Bolted Connections,” Proceeding of the 6th International Specialty Conference on Cold-Formed Steel Structures, University of Missouri-Rolla.

Zadanfarrokh, F., Bryan, E. R. (1992) “Testing and Design of Bolted Connections in Cold Formed Steel Sections,” Proceedings of Eleventh International Specialty Conference on Cold-Formed Steel Structures, St. Louis, Missouri.

bearing strength of cold formed steel bolted connections .../67531/metadc115135/m2/1/high_res... ·...

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