abdullahdx212095
TRANSCRIPT
t
REINFORCED CONCRETE BEAMS WITH
STEEL PLATES FOR SHEAR
by
MOND SABRI ABDULLAH, M.Sc (Eng).
A Thesis presented in application for theDegree of Doctor of Philosophy in the
Department of Civil Engineering,University of Dundee,
United Kingdom.
July, 1993
ii
CONTENTS
ACKNOWLEDGEMENTS vi
DECLARATION vii
CERTIFICATION viii
ABSTRACT ix
LIST OF TABLES x
LIST OF FIGURES xi
LIST OF PLATES xiv
NOTATION xv
CHAPTER ONE: INTRODUCTION 11.1 General Introduction 1
1.2 Previous Research on Shear Reinforcement 2
1.2.1 Steel Fibres 2
1.2.2 Welded Wire Fabric 3
1.2.3 Steel Plates 5
1.3 Application of Plate Reinforced Construction 7
1.4 Present Research 81.4.1 Objective of The Research 11
1.5 Outline of The Thesis 11
CHAPTER TWO: REVIEW ON THE THEORY OF SHEAR FAILURE OFREINFORCED CONCRETE BEAMS 132.1 Introduction 132.2 Mechanisms of Shear Resistance 13
2.2.1 Beams Without Web Reinforcement 142.2.1.1 Concrete Tooth Analogy 142.2.1.2 Interface and Shear Compression Zone Theories 16
2.2.1.3 Plastic Analysis 17
2.2.2 Beam With Web Reinforcement 192.2.2.1 The Truss Analogy Method 19
2.2.2.2 The Splitting Method 21
2.2.2 Remarks 252.3 Design of The Ultimate Shear Strength in BS 8110 (1985) 27
2.3.1 Strength Provided by Concrete, V, 272.3.2 Strength Provided by The Shear Reinforcement, V, 30
2.3.3 Remarks 30
CHAPTER THREE: EXPERIMENTAL PROGRAMME AND TEST RESULTS
31
3.1 Introduction
31
31333737383940424242434346464747485151535357576064717177808080848585
949494959596969898
101103104105
iii
3.2 Test Programme3.2.1 Details of Steel Plates
3.3 Materials and Control Specimens3.3.1 Concrete3.3.2 Reinforcements3.3.3 Steel Plate
3.4 Preparation of Test Specimens3.4.1 Casting and Curing
3.5 Test Arrangements3.5.1 Test Set-up3.5.2 Instrumentation3.5.3 Test Procedure
3.6 Test Observation and Results3.6.1 General Behaviour3.6.2 Deflections
3.6.2.1 Mid-span Deflection3.6.2.2 Under Load Deflection
3.6.3 Crack Width3.6.4 Strain Readings3.6.5 Test Response of Individual Beams
3.6.5.1 Beam 1S23.6.5.2 Beam 1S43.6.5.3 Beam 1S63.6.5.4 Beam 1D23.6.5.5 Beam 1D43.6.5.6 Beam 1063.6.5.7 Remarks3.6.5.8 Beam 2S23.6.5.9 Beam 2S43.6.5.10 Beam 2S63.6.5.11 Beam 2S83.6.5.12 Beams 2D2, 2D4 and 2D63.6.5.13 Beams 3D4 and 3063.6.5.14 General Remarks
CHAPTER FOUR: METHOD OF ANALYSIS4.1 Introduction4.2 Mechanism at failure
4.2.1 Flexure4.2.2 Diagonal Splitting4.2.3 Flexural-shear4.2.4 Bearing
4.3 Proposed Method of Analysis4.3.1 Shear Strength
4.3.1.1 Strength of The Web4.3.1.2 The Control of Web Strength4.3.1.3 Mode of Failure4.3.1.4 Contribution of Tensile Reinforcement
iv
4.3.1.5 Ultimate Load 1064.3.1.6 Depth of Compression Zone 1074.3.1.7 Solution Procedures 108
4.3.2 Flexural Strength 1094.3.3 Bearing Strength 113
4.4 Cover to Steel Plate 1144.5 Method of Shear Connection 116
4.5.1 Bond 1164.5.2 Cut-outs as Shear Connectors 118
4.6 Serviceability of The Beams 1224.6.1 Deflection 1224.6.2 Cracking 125
CHAPTER FIVE: FINITE ELEMENT ANALYSIS OF THE BEAMS USING ABAQUS 1285.1 Introduction 1285.2 General Description of ABAQUS 1295.3 Analytical Models of The Test Beams 130
5.3.1 General Consideration and Assumption 1305.3.2 Idealization of The Test Beam 1315.3.3 Constitutive Relationships 132
5.3.3.1 Non-linear Constitutive Relation for Concrete 1355.3.3.1.1 Concrete Input Option 136
5.3.3.2 Constitutive Relation for Steel 1375.3.3.2.1 Steel Input Option 138
5.4 Solution Procedures 1395.5 Analysis results for The Beams 141
CHAPTER SIX: BEHAVIOUR OF THE BEAMS: TEST RESULTS,ANALYSIS AND DISCUSSION 1426.1 Introduction 1426.2 Ultimate Behaviour of Test Beams 142
6.2.1 Mode of Failure 1426.2.1.1 Diagonal Splitting 1436.2.1.2 Bearing 145
6.2.2 Ultimate Strength: Proposed Method 1466.2.3 Ultimate Strength: 'BS 8110 (1985) Method' 1486.2.4 Inclined Cracking Strength 151
6.3 Contribution of Tensile Reinforcement 1516.4 Serviceability Parameters of The Beams 154
6.4.1 Deflection 1546.4.2 Crack Width 158
6.5 Concrete Cover to Steel Plate 1596.6 Bond Stress and Cut-outs 1636.7 Average Shear Stress 1646.8 ABAQUS Program Results 167
6.8.1 Behaviour of The Beams, Failure Load and Mode of Failure 1676.8.2 Deflection 172
V
6.8.3 Strains in Tensile Bars and Steel Plate 1726.8.4 ABAQUS Program Results (Current Version) 177
6.8.4.1 Changes 1786.8.4.2 Results 180
CHAPTER SEVEN: CONSTRUCTION AND ECONOMICS OF THE BEAMS 1897.1 Introduction 1897.2 Economics of The Beams 1897.3 Practicality and Construction of The Beams 191
CHAPTER EIGHT: CONCLUSIONS AND RECOMMENDATIONS FORFURTHER RESEARCH 1968.1 Introduction 196
8.2 Conclusions 1968.3 Recommendations for Further Research 199
REFERENCES 200
APPENDIX
vi
ACKNOWLEDGEMENTS
The author would like to express his sincere gratitude to;
o Dr. N.K. Subedi under whose supervision this research was conducted. His invaluable guidance,
helpful suggestions, constructive advice and continuous supports toward the success of the
research are very much indebted.
o Dr. A. El-Sheikh, Dr. A. Shaat and Mr. I. G. Shaaban who gave assistance on the early stage of
the finite element analysis.
o Dr. C. Randall for advice and ideas on the Chapter Seven of the thesis.
o All the technical staff of the Structural Laboratory and the Workshop, in particular Sandy, Eric,
Ernie, Charlie, Clem, Pat, Alex and Kevin for cooperation in the experimental work.
o The National University of Malaysia (UKM) for sponsoring the study.
o His wife (Rohana) and daughters (Solehah and Salimah) for their patience throughout our stay in
Scotland.
vii
DECLARATION
I hereby declare that the following thesis has been composed by me, that the work of which it is arecord has been carried out by myself and it has not been presented in any previous application fora higher degree.
Mohd Sabri AbdullahJuly 1993
CERTIFICATION
This is to certify that MOHD SABRI ABDULLAH has done his research under my supervision andthat he has fulfilled the conditions of Ordinance 14 of the University of Dundee, so that he is qualifiedto submit the following thesis in application for the Degree of Doctor of Philosophy.
Dr. N.K. Subedi
Department of Civil EngineeringUniversity of Dundee
July 1993
ix
ABSTRACT
The use of vertical stirrups as shear reinforcement is inadequate and create problems whenever high
shear stresses are concerned. Therefore, the application of steel plates in reinforced concrete beams
as an alternative and a solution to the problem of high shear stresses was studied. The system could
provide an efficient composite construction which has a potential application in common or/and
special structural elements.
Tests were carried out on 15 reinforced concrete beams with embedded steel plates as shear
reinforcement. The test specimens had a constant cross section of 100 mm x 400 mm, simply
supported with shear span/depth ratio of 1.0 and subjected to two symmetrical point loads. Steel
plates of different thicknesses, namely 2 mm, 4 mm, 6 mm and 8 mm were used. Seven of the
beams had a single plate and the remaining eight were double plated. Details of the beams, test
procedures, test observation and results are presented.
A method of analysis for the prediction of the ultimate shear strength of the beams is proposed. The
method is based on the concept of equilibrium of forces at the section of the beam between the load
and the support when the splitting occurs. Serviceability requirements and general behaviour of the
beams are discussed.
Test results suggest that plate reinforcement providasan effective solution to the problem of high
shear stresses. An average shear stress up to 16.23 N/mm2 was achieved using a double 6 mm
plate. The value was much higher than the maximum suggested value of 5 N/mm2 (or 0.84ffor
conventional reinforced concrete beams (BS 8110 1985). The diagonal splitting and bearing were
the predominant modes of failure. In general, the predicted failure load and modes of failure of the
beams were in good agreement with the test results.
x
LIST OF TABLES
TABLES PAGE
3.1 Details of test beams 32
3.2 Concrete characteristics 38
3.3 Reinforcement characteristics 39
3.4 Plate characteristics 40
4.1 Control of web strength 104
4.2 Criteria test in determining the mode of failure 105
4.3 Contribution of P and Pp, 106
6.1 Comparison of results 147
6.2 Comparison of predicted shear capacity and cracking strength 150
6.3 Comparison of the contribution of tensile reinforcement 153
6.4 Maximum deflection at failure and service load 158
6.5 Cover to steel plate 161
6.6 Bond stress, number of cut-outs, average shear stressand bearing stress of the beams 165
6.7 Comparison of experimental ultimate loads and modes of failure with thosepredicted by ABAQUS program and the proposed method of analysis 169
7.1 Comparison of the volume of steel required forshear reinforcement (throughout the beams) 190
7.2 Comparison of the volume of steel required forshear reinforcement (at the shear span only) 191
xi
LIST OF FIGURES
FIGURES PAGE
1.1 Lintel reinforcement, including steel plates (Sainsbury & Shipp 1983)
6
1.2 Examples of plate reinforced constructions
9
2.1 Concrete tooth analogy (Kani 1966) 15
2.2 Forces acting on shear span of a beam 17
2.3 Failure mechanisms for shear span subjected to point load 18
2.4 Truss analogy 20
2.5 Splitting cylinder analogy 22
2.6 Meaning of symbols (Kong et. al 1972) 23
2.7 Equilibrium of forces (Subedi 1988) 24
2.8 Shear strength of beams without shear reinforcement (Handbook to BS 8110 1987) 28
2.9 Ultimate shear stresses for beams loaded closeto supports (Handbook to BS 8110 1987) 29
3.1 General arrangement of beam with steel plate 343.2 Typical arrangement of single plated beams 353.3 Typical arrangement of double plated beams 363.4 Test arrangement 443.5 Mid-span deflections 49
(a) Single plated beams(b) Double plated beams(c) For comparison
3.6 Under-load deflections 50(a) Beam 2S2(b) Beam 2D4
3.7 Maximum diagonal crack widths 52(a) Single plated beams(b) Double plated beams(c) For comparison
3.8 Positions of rosettes (Beam 1S2) 553.9 Strains in steel plate and main bars (Beam 1S2) 553.10 Crack pattern at failure (Beam 1S2) 563.11 Positions of rosettes (Beam 1S4) 583.12 Strains in steel plate and main bars (Beam 1S4) 583.13 Crack pattern at failure (Beam 1S4) 593.14 Positions of rosettes (Beam 1S6) 613.15 Strains in steel plate and main bars (Beam 1S6) 613.16 Crack pattern at failure (Beam 1S6) 623.17 Longitudinal crack in Beam 1D2 633.18 Positions of rosettes (Beam 1D2) 653.19 Strains in steel plate and main bars (Beam 1D2) 663.20 Crack pattern at failure (Beam 1D2) 673.21 Positions of rosettes (Beam 1D4) 68
xii
FIGURES PAGE
3.22 Strains in steel plate and main bars (Beam 1D4) 69
3.23 Crack pattern at failure (Beam 1D4) 70
3.24 Crack pattern at failure (Beam 106) 73
3.25 Improved detailing in Second Series Beams 73
3.26 Typical positions of rosettes on steel plate in Second Series Beams 78
3.27 Positions of Demec points in Second Series Beams 78
3.28 Strains in steel plate, main bars and Demec concrete (Beam 2S2) 79
3.29 Crack pattern at failure (Beam 2S2) 81
3.30 Crack pattern at failure (Beam 2S4) 81
3.31 Strains in steel plate, main bars and Demec concrete (Beam 2S4) 82
3.32 Crack pattern at failure (Beam 2S6) 83
3.33 Strains in steel plate (Beam 2S6) 83
3.34 Crack pattern at failure 86(a) Beam 2S8(b) Beam 202(c) Beam 2D4(d) Beam 2D6
3.35 Principal strains in steel plate 87(a) Beam 2S8(b) Beam 202(c) Beam 204(d) Beam 206
3.36 Crack pattern at failure (Beam 304) 88
3.37 Crack pattern at failure (Beam 3D6) 88
4.1 Modes of failures (numbers indicate events) 97(a) Flexure(b) Diagonal splitting(c) Flexural-shear(d) Bearing
4.2 Forces at failure 994.3 Splitting forces 1024.4 Contribution of Pst 1054.5 Determination of the compression depth, dc1074.6 Strain compatibility 1104.7 Elements under the load and above the support 1144.8 Concrete cover preventing the plate from buckling 1164.9 Effective perimeter of steel I-beam in concrete 1174.10 Types of shear connectors in composite constructions (Davies 1975) 1194.11 Cut-outs as shear connectors 1204.12 Perfobond rib connector (Veldanda & Hosain 1992) 1204.13 Determination of the number of cut-outs 1214.14 Deflection of the beam 1234.15 Maximum diagonal crack width 126
FIGURES PAGE
5.1 The idealization of test beams 133(a) Beam idealization(b) Concrete1(c) Concrete2(d) Steel Plate(e) Concrete3
5.2(a) Uniaxial behaviour of plain concrete (ABAQUS 1989) 1345.2(b) Concrete in tension (ABAQUS 1989) 1345.3 Concrete failure surface in plane stress (ABAQUS 1989) 1365.4 Stress-strain relationship for steel 138
6.1 Mechanism of diagonal splitting mode of failure 1436.2 The different of the loaction of P8t 1526.3(a) Mid-span deflection 1566.3(b) Under load deflection 157
6.4 Maximum diagonal crack width 1606.5 Concrete cover in double plated beams 1626.6 Applied load transferred indirectly 1666.7 Crack pattern development in Beam 2S2 as predicted by ABAQUS 1706.8 Crack pattern at failure of Beam 2S2 according to ABAQUS 1716.9 Typical deformed shape of the beams 1736.10 Tension bar's strain 1746.11(a) Strain in steel plate of Beam 282 (positions of rosettes are shown in Fig. 3.26) 1756.11(b) Starin in steel plate of Beam 2S4 (positions of rosettes are shown in Fig. 3.27) 1766.12 Idealization of test beam in Version 5.2 1796.13 Uniaxial stress-strain curve of the concrete 1816.14 Typical deformed shape of the test beams (using Version 5.2) 1846.15 Principal compressive stress in concrete (Beam 2S2) 1856.16 Principal tensile stress in concrete (Beam 282) 1866.17 Principal compressive stress in steel plate (Beam 2S2) 1876.16 Principal tensile stress in steel plate (Beam 2S2) 188
7.1 Beam under two point loads
192
7.2 Cantilever beam and beam under a point load
192
xiv
LIST OF PLATES
PLATE PAGE
3.1 Typical arrangement of strain gauges on steel plate 41
3.2 Test arrangement 45
3.3 At failure (Beam 1S2) 74
3.4 At failure (Beam 1S4) 74
3.5 At failure (Beam 1S6) 75
3.6 At failure (Beam 1D2) 75
3.7 At failure (Beam 1D4) 76
3.8 At failure (Beam 106) 76
3.9 At failure (Beam 2S2) 89
3.10 At failure (Beam 2S4) 89
3.11 At failure (Beam 2S6) 90
3.12 At failure (Beam 2S8) 90
3.13 At failure (Beam 202) 91
3.14 At failure (Beam 204) 91
3.15 At failure (Beam 206) 92
xv
NOTATION
a shear span, measured from centre of load to centre of support
acclear shear span, measured from centre of load to the edge of support
/kph area of steel plate crossing the diagonal crack in horizontal projection
Apy area of steel plate crossing the diagonal crack in vertical projection
A'y' statical moment of transformed concrete area about the neutral axis of thecomposite section
A 17A21A31A4 factors
Ast area of tensile reinforcement
Asv area of stirrup
Aw area of web bar
b breadth of the beam
C flexural compression force
Cl ,C2 ,C3 constant
d effective depth of the beam
d' distance from top surface of the beam to the centre of flexural compression bar
cl, depth of compression zone
d of cut-out
d of the concrete cylinder
dpeffective depth of the plate
dp, depth of the plate which crosses the diagonal crack
dt depth of the diagonal crack
Ec elastic modulus of concrete
Ep elastic modulus of the plate
xvi
Es elastic modulus of the reinforcement
fc concrete cylinder strength
f compressive strength
fp plate stress
fr modulus of rupture of concrete
f, stress of the reinforcement
ft cylinder tensile strength of concrete
ftc limiting tensile of concrete in biaxial compression-tension, fej21
fy yield stress of the reinforcement
f stress of the plate
fy, yeild stress of stirrup
G aggregate interlock action
G, shear modulus of concrete
h overall depth of the beam
I, second moment of area of the transformed composite section
I, moment of inertia of cracked section transformed to concrete
I, effective moment of inertia
I gmoment of inertia of gross uncracked section
I,ylength of the concrete cylinder
L length of the beam
m modular ratio
Ma maximum moment in member at which the deflection is being computed
M, moment at first cracking
M, ultimate moment at which concrete teeth break away
xvii
M, flexural capacity of the cross section
N, number of shear connectors
N„ number of cut-out
o' effective perimeter of the steel I beam and steel plate above neutral axis of the beam
P diametral compressive force
P failure load of the beams predicted by ABAQUSBIN
Pc concrete compressive force
P„ diagonal cracking load of the beams
P, total of the concrete splitting force
Ph horizontal forces
P force in steel plate in bending
Pph horizontal force due to the steel plate
P force in steel plate in bending
Ppu strength of the shear connector
P force due to the steel plate
P, force in reinforcement
Pst horizontal tensile force due to tensile reinforcement
Psc force in compressive reinforcement
Pu the ultimate load
P, vertical forces
s effective depth of the concrete teeth, length of the diagonal crack
sb applied bond stress
S, stirrup spacing
tPthickness of the plate
t. thickness of the concrete cover
T flexural tensile force
V shear force
V, shear strength provided by concrete
Vc1 shear force in compressive zone
Vd dowel action
Vh horizontal shear stress
V, ultimate shear strength of beam
V, shear strength provided by web reinforcement
V9, capacity of the steel plate in shear at the diagonal crack
wd relative displacement rate at yeild line
Wdv relative vertical displacement rate at yeild line
w/c water-cement ratio
Yt distance from centroidal axis of gross section to the extreme tension fibre
x compression depth of the section in bending
Xd diagonal length of the shear panel
a stirrup inclination angle to the beam axis
ad inclination of the displacement rate
13 ratio of the shear span/length of the beam, strut inclination angle to the beam axis
cl•steel parameter
8Bdeflection due to bending
ST horizontal force
ar total deflection
8, deflection due to shear force
xix
width of the concrete teeth
ympartial safety factor
A, the inclination of 'cylinder' failure surface to the horizontal
e strain of the plate in compressionpc
e pt strain of the plate in tension
e bars strains
e in compressive bars
est strain in tensile bars
e plate strainP
alcompressive stress acting in concrete
o3tension stress acting in concrete
Q percentage of tensile reinforcement (100A9/bd)
(0 width of the diagonal crack
tc, txy shear strength of concrete
vcPoisson's ratio for concrete
v Poisson's ratio for steel plateP
0 inclination of yeild line
1
CHAPTER ONE
INTRODUCTION
1.1 General Introduction
One of the types of structural failure that can occur in reinforced concrete structures is 'shear failure'.
Such failure may occur below the flexural capacity of the structural elements and considerably
reduce the ductility of the members. Especially for the latter reason, shear failure is generally
considered undesirable. To prevent such failure, reinforced concrete beams are usually reinforced
with vertical stirrups or bent-up bars.
The conventional types of web reinforcement, however, result in severe congestion and create
problems whenever high shear forces are involved. A practical example where shear becomes a
major problem is the coupling beams situated at about one third of the height of the building in shear
wall structures. Another example is where ever the use of deep beams is involved. The applications
ranges from offshore structures, floatation units for housing in marshy land to floating hotels (Subedi
eta! 1992).
The congestion of stirrups will create difficulties in placing and compacting the concrete. It is also
time consuming in fixing the stirrups as a large number of individual links which must be assembled
and fixed. In one instance, it was reported that in a comparatively modest six storey structure,
25,000 stirrups were required for the slab alone (Clapson 1990). The quantity would be much higher
if the stirrups for the beams were also taken into account. In such cases, the probability for error and
omission will be high. Additionally, the conventional method requires an element of skill and
2
experience which might not always be readily available. In essence, the use of shear links is far from
being efficient, especially in an era of high labour costs.
The traditional alternative of increasing the beam's depth may not always be a feasible solution, as
the depth of the beams are fixed by aesthetic considerations and the need to maintain the constant
storey height. To prevent such problems, an alternative solution must be found, and this will be
discussed in the following section.
1.2 Previous Research on Shear Reinforcement
Research on the alternatives to the use of stirrups and bent-up bars as shear reinforcement has
been carried out by many investigators for the past 20-30 years. Several methods and possibilities
have been tried and proposed. Some are claimed to offer advantages over the others and
vice-versa.
1.2.1 Steel Fibres
One of the alternative solutions to the use of vertical stirrups as shear reinforcement is the use of
steel fibres. The steel fibres of various shapes, namely, round, flat and crimped with various sizes
and volume concentrations have been used as shear reinforcement. Batson et. al (1972) and later
works by Sharma (1986) have shown that the steel fibres can be effectively used as shear
reinforcement in reinforced beams. They also showed that steel fibres have some advantages over
vertical stirrups.
3
Firstly, the fibres are randomly distributed through the volume of the concrete at much closer spacing
than can be obtained by the smallest reinforcing bars. Secondly, the first crack tensile strength and
the ultimate tensile strength are increased by the inclusion of steel fibres. The first crack tensile
strength is increased by the 'crack-arrest' mechanism of closely spaced fibres and the ultimate
strength is increased because of the additional energy that is required to pull the fibres out of
concrete.
Many other researchers (Swamy & Al-Ta'an 1981, Mansur et. al 1986, Victor et. al 1992) worked
on similar topics and concluded that the inclusion of steel fibres in the concrete mix provides an
effective solution as shear reinforcement. The steel fibres have also been applied in the deep beams
(Swaddiwudhipong & Shanmugam 1985, Narayanan & Darwish 1988), where they have been
provided to act as web reinforcement. The results have shown that the shear stress and spalling of
concrete are improved by the use of steel fibres.
Although steel fibres appear to be suitable for shear reinforcement, in a finding by Lim et. al (1987)
it shows that not all types and sizes of fibres can simply be used as shear reinforcement in replacing
stirrups either partially or wholly in reinforced concrete beams. From the result of his investigation,
it is suggested that the stirrups can only be replaced by steel fibres as long as the parity in shear
reinforcement factor is maintained, i.e only fibres of sufficient length with good and stable bond
should be used.
1.2.2 Welded Wire Fabric
Welded wire fabric, both plain and deformed, as well as wire mesh as shear reinforcement have
4
been investigated by a few investigators (Pincheira et. a11989, Taylor & Hammasi 1980, Mansur et.
all 987, Ghosh & Mukhopadhyay 1977). A number of beams containing welded wire fabrics and wire
mesh were tested, and it was found that this type of materials appeared to be suitable as shear
reinforcement in reinforced concrete beams. The use of wire fabrics has also been extended in the
ferrocement beams (Mansur & Ong 1987, 1991). The results showed that the diagonal cracking
strength of the beam was increased as the increases in the volume of the wire fabrics.
The welded wire fabrics has been claimed to be extensively used in the building industries, because
of its advantages over the stirrups. The prime advantage is that it is relatively cheaper and it can be
easily incorporated in construction. It is also reported to have the advantage of reducing the crack
width of the elements (Atlas et. al 1965)
Although all the types of materials discussed above appear to be suitable for shear reinforcement
in the lower range of shear stress (less than 5.00 Nllme), their applicability as shear reinforcement
in resisting high shear stresses, to the best of authors knowledge, has not been researched.
Reinforced concrete beams are being increasingly used as structural elements required to resist not
only flexural stresses but also combined with high shear stresses. As a result, it has become very
important to investigate how the performance of reinforced concrete beams can be improved when
high shear stresses are involved. Therefore, it is pertinent to investigate another type of shear
reinforcement which could be used not only in replacing the conventional stirrups, but also capable
of resisting high shear stresses.
5
1.2.3 Steel Plates
Over the last few years there has been a systematic and planned research at Dundee University to
evaluate the possibility of using steel plate as shear reinforcement. This new innovation is hoped to
eventually provide the solution to the problem of shear in reinforced concrete beams both in the
range of high and low shear stresses.
The use of steel plate in structural concrete is not entirely new. It has been used in strengthening
flexurally distressed reinforced concrete beams, since 1960s (Fleming & King 1967). This method
has become increasingly popular in recent years (Solomon et. al 1976, Jones et. al 1982, 1985,
1988, Swamy et. a1 1987, 1989, Roberts 1989, Roberts & Kazemi 1989, Hamoush & Ahmad 1990,
Oehlers 1992). Despite the success of the method in flexural application, surprisingly there has been
virtually no research on the use of steel plate in strengthening the shear resistance.
Amongst the first reported research on the use of steel plate as shear reinforcement was due to
Hermite & Bresson (1967). The steel plate was glued to the sides of reinforced concrete beams to
enhance the shear capacity. Using the same technique, recently, Swamy (1989) reported the use
of steel strips and channels for web reinforcement in the shear span of reinforced concrete beams.
Although this method has increased the shear capacity of the beams by up to 40% (Swamy 1989),
the application is limited by the lack of adequate information and no further research has been
carried out. Bending shear creates resultant diagonal tensile and compressive stresses, and this
might cause buckling of the steel plate in the compression zone. The buckling then would set up
tensile or 'peeling' stress in the glue, and this could lead to premature failure.
6
At Dundee University, steel plates were embedded in the concrete beams. A successful initialprogramme
researchAwas started with coupling beams of shear wall structures (Subedi 1989). The beams were
designed and tested to fail in shear. The results suggested that the use of steel plate as shear
reinforcement was perfectly feasible.
Current codes of practice (BS 8110 1985, ACI 318-83 1983, AS 3600 1988, CAN3-A23.3-M84 1984)
however do not yet cover the use of vertical plates for shear. But it is well known that the vertical
web sections of universal beams and plate girder are designed to carry shear forces.
In practice, embedded steel plates have been used to resist high shear stresses in the lintel beams
in the construction of The National Westminster Tower (Sainsbury & Shipp 1983), as shown in Fig.
1.1. This method, however, has been applied based on the conventional analysis of composite beam
and the engineering judgement of the designers involved, since there had been no research on this
method before.
Fig. 1.1: Lintel reinforcement, including steel plates (Sainsbury & Shipp 1983)
7
Some other examples of the current and future application of steel plate with concrete in construction
will be discussed in the next section.
1.3 Application of Plate Reinforced Construction
Composite members with steel plates and concrete have been applied to port and harbour
construction. A typical example is a breakwater caisson as shown in Fig. 1.2a (Yokota & Kiyomiya
1987). In this structure, reinforcing bars have been replaced by steel plates. It can be seen that the
plates are connected by shear connectors either only on one surface or both surfaces of each slab
and wall. It has been reported that this type of structure considerably reduced the cost and the
period of construction.
Steel plates have also been used as a 'skin' to the concrete core. The structure known as 'dual skin
composite construction' was devised for use in submerged tube tunnels (Wright eta/1991). Fig. 1.2b
illustrates such construction. Shear studs are welded to the plates at regular centres and act as
connectors for the concrete core. This type of construction is also applicable to nuclear containment,
liquid and gas retaining structures and blast resistant shelters. The system results in a strong and
efficient structure that offer many advantages over conventionally reinforced concrete section.
As it has been mentioned earlier, steel plate has also been found perfectly feasible in coupling
beams of shear wall structures (Subedi 1989). The provision of vertical steel plates in the beam
provides a better solution in detailing the reinforcement in the wall if compared with the application
of universal beam section (Fig. 1.2c).
8
In tall building structures, shear walls are usually made of reinforced concrete and in some cases
steel-plate shear walls have been used as an alternative (Elgaaly 1993). It is anticipated that steel
plate could be used in replacing the reinforcement in the conventional shear wall, as visualised in
Fig 1.2d. Such system may result in a solid strong wall that offer some advantages, such as speed
of erection and could reduce the cost.
Steel plate could also be used in reinforced concrete bridges. Under the action of unbalanced one
sided traffic , the cross beam and diaphragm beam will be subjected to high stresses. The use of
embedded steel plate in such situations (Fig. 1.2e) would provide an efficient system that can resist
high shear stresses. For the existing bridges, the plate appears appropriate to be externally applied
for strengthening in shear. The plate could be attached to the sides of the cross member by
mechanical connectors such as bolts and nuts by drilling through the section (Fig. 1.2f).
1.4 Present Research
As it can be seen that there are tremendous scopes for the application of steel plate in construction.
Thus the present research is undertaken to provide a basic understanding of the behaviour of the
system.
The research forms the continuation and detailed study on the application of steel plate in reinforced
concrete beams which has been started by Subedi (1989). This work is concentrated on simply
supported beams. Simply supported beams were chosen as the easiest construction that can
provide such fundamental understanding of the behaviour of the system. With proper perception of
the system it will lead to the development of design criteria/procedures which later can be applied
-A-,---,w•-g-/-4-.,-,...-•-•-wc.....-4,2.,
Stu d s ie..' oho.
P'l l steel ri A 1 e i. - co ncrele F--- -111
LI I I [ 1 1 1 °'A
I
r.j 1 ,. I
•..: ...%\\... \\\ •
RSJ
Main oars
9
(a) Breakwater caisson (Yokota & Kiyomiya 1987) (b) Submerged tube structure (Wright eta' 1991)
0 0 •
R'aie
—1
shearNcil
Wall I Coupling beam Wall
• ' •I: I I 11 .: .•
Bars cannot Bars yet throughget tnrough RSJ around plats
(c) Steel plate in coupling beam of shear wall structure (Subedi 1989)
\\ \ \ \\ \ \
Main bars
(d) Reinforced steel plate shear wall
Fig. t2: Examples of plate reinforced constructions
steelplatediaphragm
pier pier
6.; • 0
reinforcemen .0 0
steeln----- plate
bolt andnut
10
Fig. 1.2: Examples of plate reinforced constructions (cont.)
(e) Bridge diaphragm
(f) Externally plated beam
11
to any type of the structures.
The work incorporates testing of 15 specimens, under two symmetrical point loads with different
plate thicknesses and configurations. The detail of the specimens is given in Chapter Three.
1.4.1 Objective of The Research
The main objectives of this research are;
i)To establish the use of steel plate as shear reinforcement in simply supported reinforced concrete
beams.
ii) To determine the possibility of increasing the shear capacity of the beams beyond those
recommended by British Code BS 8110 (1985).
iii)To study the overall structural behaviour of the beams and consequently to develop appropriate
method of analysis to predict mode of failure, ultimate failure loads, crack widths and other
serviceability requirements.
iv)To assess the suitability of the method with respect to construction and economic application.
1.5 Outline of The Thesis
In the next chapter a critical review of the methods of analysis for shear failure of reinforced concrete
beams is presented. The discussion is developed to bring a clear picture of the current methods of
analysis adopted by many building codes. The current codes are shown to be oversimplified and
inadequate whenever high shear stresses are concerned.
12
In Chapter Three, the experimental programme, materials properties and results obtained from the
tests including information on deformation, crack widths, crack pattern, strain readings of steel and
concrete and the general response of test beams are presented.
The proposed method of analysis for the prediction of the ultimate strength and general behaviour
of the test beams is given in Chapter Four. The serviceability requirements of such beams are also
discussed.
The application of the Non-Linear Finite Element Analysis Package, ABAQUS, to analyse the test
beams is dealt with in Chapter Five.
In Chapter Six the discussion on the behaviour of the beams observed in test and comparison with
the method of analysis is presented.
The suitability of the method with respect to economic and construction consideration is discussed
in Chapter Seven.
Overall conclusions of the study and recommendations for further research in this area are given in
Chapter Eight.
13
CHAPTER TWO
REVIEW ON THE THEORY OF SHEAR FAILURES
OF REINFORCED CONCRETE BEAMS
2.1 Introduction
The progress towards a better understanding of shear failures in reinforced concrete beams is
reviewed and critically discussed. It is considered that this aspect is important for the beams in the
present research which are designed to resist shear stresses.
The chapter begins by looking at the background research on the theory of shear failure in reinforced
concrete beams without and with shear reinforcement. From the discussion on the different available
approaches, it is shown that at present, none of the theories can accurately predict the shear
transfer in reinforced concrete beams. Therefore, there is scope for developing a more rational
unified theory. It is also shown that the method of analysis adopted by the current codes of practice
(BS 8110 1985) developed for the case of stirrups as shear reinforcement, is subjected to limitation
when high shear stresses are involved. In conclusion, the need for a new type of shear
reinforcement and method of analysis is justified.
2.2 Mechanism of Shear Resistance
The mechanism of shear resistance of reinforced concrete beams without and with web
reinforcement is considerably different. Both situations will be discussed in the sections to follow.
14
2.2.1 Beams Without Web Reinforcement
For beams without web reinforcement, various theoretical approaches have been suggested. The
approaches can be divided into three major categories as follows;
i) Concrete tooth analogy,
ii) Interface and shear compression zone theories and
iii)Plastic analysis.
The discussion on these theories are dealt briefly since the details have already been extensively
treated by other researchers for whom the project concentrated on the shear failure of reinforced
concrete beams, for example works by Chana (1986). The purpose of the discussion here is to show
that there are many theories of shear failure and they differ considerably in approach.
2.2.1.1 Concrete Tooth Analogy
Kani (1964, 1966) was the first researcher to introduce this type of approach. He compares the
concrete of a beam containing flexural cracks to a comb, the backbone of which is the compressive
zone while the tooth are the segments of concrete between the flexural cracks, as shown in Fig.
2.1a.
The function of every concrete tooth can be compared to that of a short vertical cantilever anchored
in the compression zone of the beams and acted on by a horizontal force, ST (Fig. 2.1b). As long
as the concrete teeth are capable of carrying the ST forces, the comb-like structures is essentially
15
a beam. Consequently if the flexural stiffness of the concrete cantilever is reduced, then the teeth
will break away which marks the shear failure of the beam.
a
(a)
Fig. 2.1: Concrete Tooth Analogy (Kani 1964)
At failure, the ultimate moment at which the concrete teeth break away is directly related to the
shear span/effective depth ratios (aid) and can be expressed as,
8 xMMa.= A 4 0(-T)(-
a
-1)
where M, is the flexural capacity of the cross section, and (Ox/s) is a factor which depends on the
geometry of the concrete teeth (as shown in Fig. 2.1b).
Kani (1966) considered the average tooth rather than the longest and the weakest one. He also
neglected any shear force transferred across the crack, either by dowel or by aggregate interlock
actions. Later, Hamadi & Regan (1980) used similar model but with the dowel and aggregate
interlock actions taken into consideration. The proposed method of analysis gave a good agreement
(2.1)
16
with the test results. It should be pointed out that this model was only relevant for shear
span/effective depth ratios greater than 3.0, where shear cracks form from the existing flexural
cracks. For smaller aid ratios, others models would be appropriate.
2.2.1.2 Interface and Shear Compression Zone Theories
As the name implies, this theory considers that the shear stress is transferred through two important
ways, namely through the concrete compression zone and across the crack faces by aggregate
interlock and dowel action (Fenwick & Paulay 1968, Hofbeck et. al 1969, Taylor 1974, Millard &
Johnson 1985). Evidence of the contributions to shear transfer is claimed on the basis of the fact
that the critical crack is always inclined in the shear span towards the transverse load. If these
effects are neglected, the critical crack would be almost vertical.
The aggregate interlock and the dowel action are inter-related as a function of crack width across
the cracks. At an early stage when the crack width is small the aggregate interlock is the most
effective, but is slowly dominated by the dowel action as the crack width increase at failure. Next in
order of effectiveness is the concrete compression zone.
Thus, the shear transfer is effectively a combination of three major actions, i.e the action of the
compression zone above the inclined cracking in the shear span, the interface shear transfer by
aggregate interlock, and the dowel action. Fig. 2.2 shows the free body diagram of these
contributions.
Many experimental works have been carried out to quantify the relative contributions of these actions
T
V
C Gh
17
(Houde and Mirza 1974, Taylor 1974, Smith & Fereig 1977). The main conclusion from these works
showed that the contribution of the individual action is approximately in the following proportions;
compression zone 20 - 40%, aggregate interlock 30 - 50 % and dowel action 10 - 30%.
V
(a) Free body diagram (b) Force polygon
Fig. 2.2: Forces acting on shear span of a beam
where V = shear forceC = flexural compression forceT = flexural tension forceVc1 = shear force in the compression zoneVd = dowel action
G = aggregate interlock
2.2.1.3 Plastic Analysis
The theory of plasticity has also been used to explain the shear resistance of reinforced concrete
beams. In Denmark as early as 1966, Nielsen (Nielsen eta! 1978) was the first to use this concepts
18
to study the shear strength of beams.
The theory uses the concept of 'virtual work' in its solution. In the case of reinforced concrete beams
without shear reinforcement when subjected to point loads, it is assumed that the failure
mechanisms is a single yield line running from the load point to the support as indicated in Fig. 2.3
(Nielsen & Braestrup 1978). The relative displacement, wd at the yield line is uniform along the line
and inclined at an angle ad to it. With some assumptions and by minimizing the relationship obtained
by virtual work, the yield shear stress of the beams can be expressed as follows;
= wdv \I 1 +(21)2-(2.1 _2 h wd,„
where fc is concrete cylinder strength, wd,, is relative vertical displacement rate at yield line and .1:1 is
a total tension and compression steel parameter, which is given by astfy/fchb.
Va
CL , b
(2.2)
fa
yield one.
Fig: 2.3: Failure mechanisms for shear span subjected to point load
19
The work was extended with some modifications in United Kingdom by Kemp & Al-Safi (1981). It is
not intended here to give details of their mathematical formulation, but it is worthwhile to note that
this method when compared to the methods suggested by Australian Standard (AS 36001988), ACI
Standard (AC1 318-83 1983) or Canadian Standard (CAN 3-A23.3-M84 1984) has been found to
give a good correlation with the experimental results for both reinforced and prestressed concrete
beams (Rangan 1991). The theory was also proved to be successfully applied for the case of beams
with web reinforcement.
2.2.2 Beam With Web Reinforcement
aThe inclusion of web reinforcement in/reinforced concrete beam will increase the strength of the
beam. Generally the web reinforcement is simply considered as the added contribution to that of the
concrete. There are two main approaches to the behaviour of the beams with web reinforcements.
The first is known as truss analogy method and the second is splitting method.
2.2.2.1 The Truss Analogy Method
For beam with web reinforcement, (in this case the web reinforcement is referred to vertical or
inclined stirrups) the stress in stirrup is analysed by the truss analogy method.
The use of truss analogy to simulate the action of a reinforced concrete beam subjected to shear
and bending was originated over a century ago by Ritter and Morsh (ACI-ASCE Committee 326
1962). This classical analogy assumed the internal structure of a beam as pin jointed truss. The
longitudinal steel in the tension zone is analogous to tension chord, the stirrups are the tension ties
stirrup _,...d
sv
20
whilst the concrete between diagonal cracks acts as compressive struts (Fig. 2.4). By considering
the vertical equilibrium of the free body to the left of the line A-A, the following equation is obtained;
vs = A3vfyv(cosa + sinacot13)(AL4) (2.3)
sv
where Aufr, is capacity of the stirrups, s, is spacing of the stirrups, B and a are the strut and stirrup
inclination angles to the beam axis respectively. For the particular case of vertical stirrup where a
is 90° and recommended 13 of 45° (ACI-ASCE Committee 426 1973), the Equation 2.3 becomes
Vs = Asifyv—dsv
This equation shows that the failure of the beam is governed by the yielding of the stirrups.
(2.4)
Fig: 2.4: Truss analogy
21
The use of fixed angle of 13 = 45° is known as fixed truss model. In recent development, various
attempts have been made to modify this basic model, which is known as variable truss model
(Lampert & Thurlimann 1971, Collins 1978). From the improved truss model, the angle of the
inclination of the concrete struts is found to be lower than 45° (Collins 1978).
This method of design is widely used in codes of practices including BS 8110 (1985). Further
discussion on the shear design method adopted by BS 8110 (1985) will be given in Section 2.3.
2.2.2.2 The Splitting Method
The shear failure mode of a short shear span beam, which is initiated by a diagonal crack joining
the support towards the loading point has been considered analogous to the splitting cylinder test
(Brazillian Test). Thus the shear resistance of the beam is expressed in term of tensile strength of
concrete to resist the splitting along the failure crack.
Brock (1964) was the first to introduce the splitting cylinder analogy. In a cylinder test the tensile
strength, ft is calculated from the equation
2P 4 - Irdcylcy
where P is diametral compressive force, d cy and Icy are the diameter and length of the concrete
cylinder respectively.
(2.5)
By resolving the force along the diameter of 'imaginary cylinder', as shown in Figure 2.5 , Brock
(2.6a)
(2.6b)
b
h
imaginarycylinder
1/.
•
••\
•
22
(1964) produced the following relationship to express the cylinder tensile strength, f1;
—f 2 Vsin A, .t h
II( sinl )17
or the ultimate shear force, V is given by;
V = 3.14ftbh
where 2n. is inclination of failure surface to the horizontal. In this case the active force that causes
the splitting is the diametral compressive force.
Fig. 2.5: Splitting cylinder analogy
‘•
/•
/
The method has been used by Ramakrishnan and Ananthanarayana (1968) in analyzing 26 deep
AbeamsXsimilar expression was used, but the suggested value for the constant was 2.24 instead of
3.14. The lower value was justified by the fact that the splitting strength varies with shape and size
a Vc.
typical web bar(Aw)
/ main tonqitudinat steel
23
of sample. For larger sample.; the splitting strength is lower than that obtained from smaller samples.
This safer value was introduced to fit the experimental results.
theInkBrock (1964) and Ramakrishnan & Ananthanarayanan (1968) methods, it is assumed that the web
steel yieldsat failure. However in a later work by Desayi (1974) who used similar approach, the web
steel was not considered to yield at failure. Desayi (1974) calculated the steel strain using a modular
ratio concept. Nevertheless the proposed formulation produced a prediction which in general did not
correlate well with experimental results.
Kong et. al (1972) improved this basic idea of splitting by including the shear span/depth ratio in the
proposed equation. Kong et. al (1972) produced the following equation to define the ultimate load
(Fig. 2.6);
V = C1 (1 -C3-)fthb + CzE A Zsin2 aw h w
Three numerical coefficient C I , 02 and 03 were introduced in the equation to fit the test data, where
the best value for 03 is 0.35. C i is the coefficient related to type of concrete whilst 02 is coefficient
related to type of web reinforcement. The meaning of other symbols is defined in Fig. 2.6.
(2.7)
Fig. 2.6: Meaning of symbols (Kong eta11972)
14
o
I
h
_
24
The application of this formula is limited to cases where the ajh values does not depart from the
experimental range of 0.23 to 0.70, and where the main longitudinal reinforcement is anchored at
the end.
Later development in the study of deep beams at Dundee University, led to a more realistic
equation in determining the ultimate shear strength (Subedi 1983, 1986, 1988). The method of
analysis developed by Subedi (1988) is based on the concept of equilibrium of forces at failure. The
splitting will occur when the stress of concrete reaches its limiting tensile strength. At splitting, the
forces which keep the section in equilibrium are shown as in Fig. 2.7;
a
bI.4n.,
Fig. 2.7: Equilibrium of forces (Subedi 1988)
25
Thus, the proposed equation takes the following general form;
1V = —
a(iiibftc + A2Pst + A3Ph + A4Pv)
where ft, = limiting tensile strength of concrete in biaxial tension-compression state of stress,Ps, = horizontal tensile force due to main reinforcement,
13, and Ph = vertical and horizontal forces due to web reinforcement,
A I , A2, A3 and A4 are factors which depend upon geometric parameters of the beams. All the factors
which might effect the strength of the beams, such as the strength of materials, the amount of
reinforcement, and the position of loading are taken into account.
The important feature that has been included by Subedi (1988) in his method is the concept of web
strength control. In this concept, if there is insufficient amount of web reinforcement the failure will
happen the moment the concrete splits. However, if the reinforcement is sufficient, then the concrete
will not contribute and the web reinforcement takes over the control of the splitting force. The method
is also able to predict the mode of failure, either flexural shear or diagonal splitting.
This method was used in analyzing the behaviour of coupling beams of shear wall structures (Subedi
1989, 1990, 1991a, 1991b). In almost all cases, the proposed method correlated well with
experimental results.
2.2.3 Remarks
Up to now there have been a vast amount of test carried out in order to support the methods
(2.8)
predicting the shear transfer of reinforced concrete beams. It is profound to note that, in addition
26
to the main approaches which have been discussed in this chapter, there are other approaches
proposed by other researchers that used totally different concepts in predicting the shear in
reinforced concrete beams, for example works by Hawkins et. al (197.
In the case of beams without web reinforcement, it is apparent that, at present, no real agreement
has yet been reached on this problem and none of the existing theories can accurately predict the
shear transfer of the reinforced concrete beams.
In the case of beam with web reinforcement, the classical fixed-angle truss and the splitting analogy
differ in their concepts. The classical fixed angle truss has shortcomings in its approach. Although
conceptually convenient, it presents an over simplified model of reinforced concrete beams in shear.
For instance, it assumes that the failure is initiated by the excessive deformation of the web
reinforcement. Therefore, for the very thin webbed beams, for which failure may be due to crushing,
the method would give unsafe result. The truss method, however, is widely used in codes including
BS 8110 (1985). The likehood of the failure of very thin webbed beams in this case is eliminated by
placing an upper limit on the shear stress acting on the section. The upper limit of shear stress is
5 NI/me (or 0.84f, whichever is smaller). This limit already include an allowance for the partial
safety factor ym of 1.25.
The current method cannot be applied to sections subjected to shear stresses higher than 5 Nirrie
or 0.84f, whichever is smaller. As a result, it is appropriate to study the potential of the use of steel
plate as an alternative to the problem of high shear stresses. It is also necessary to establish more
rational method for the analysis of such beams.
27
The discussion show that the truss analogy method is over simplified in approach. It assumes that
the failure is initiated by excessive deformation of web reinforcement. The splitting method due to
Kong eta! (1972) and Desayi (1974) although do not depend on the strength of web steel at
ultimate, but the method (Kong et. al 1972) was empirically developed. Some factors have been
used to agree with the experimental results. In such cases the method cannot be applied to wide
range of problems. The splitting method developed by Subedi (1988), however, is different as it was
theoretically determined. The method takes account all the factors which might affect the strength
of the beam. The method is also able to predict the mode of failure.
It is clear that there is no fully satisfactory and rational method suitable for determining shear
capacity of reinforced concrete beams. Nonetheless, the systematic application of Subedi Method
(1988) has considerable potential.
2.3 Design of the Ultimate Shear Strength in BS 8110 (1985)
The design practice adopted by BS 8110 (1985) is conventional in its approach. It is assumed that
the ultimate shear strength of the beam is contributed by concrete and shear reinforcement
separately. That is V u = V, + Vs , where V, is the strength provided by concrete and V s is the strength
provided by shear reinforcement.
2.3.1 Strength Provided by Concrete, V,
BS 8110 (1985) uses the following equation to obtain the strength provided by concrete, V0,
4 5
tp fo.01/2 (400)%d
1 32 7 a6 10
9-----
8 o0 c„. o
8....
c:C \C' A0 \ ,
-eCC'C'
00,..+1,.. A'...
v0 sN'‘..,,
00 c!,5,..... 05\GI4.''
5
0
shearstress
— vc (Nimm2)
0 0 C &C A tests• • • other tests
•
28
vc = (=) faiii3 (100As)ir3 ( 400 ) 1/4 bd (2.9)Ym bd d
where b is the breadth of the web, d is the effective depth (in mm) and y„, is the partial safety factor
with regard to the material strength and V, is in Newton (N).
This equation expresses empirically three major parameters influencing the shear strength of the
concrete, namely the ratio of main longitudinal reinforcement, concrete compressive strength and
size of the member. The factor of 0.27 is a constant which takes account of other factors which have
minor influence on the shear strength of beams, such as the influence of the presence of axial
compressive or/and tensile forces in the beam.
This equation is derived based on extensive study of test data as shown in Fig. 2.8 (quoted from The
Handbook to BS 8110 1987).
Fig. 2.8: Shear strength of beams without shear reinforcement (Handbook to BS 8110 1987)
• experiment
— Code line
29
For the case of short shear span or deep reinforced concrete beams, the value of this shear strength
has to be modified. The test data (Fig. 2.9) shows that the shear strength is increased for beams
loaded close to support. In such cases BS 8110 (1985) treats members with aid < 2.0 with an
enhancement factor of 2(d/a). Although BS 8110 (1985) gives special treatment to the beams of
short shear span, but the code does not cover deep beams, for which designers are referred to
specialist literature such as CIRIA Guide 2 (1977).
Fig. 2.9: Ultimate shear stresses for beams loaded close to supports (Handbook to BS 8110 1987)
30
2.3.2 Strength Provided by the Shear Reinforcement, V,.
In BS 8110 (1985), the design procedure assumes that the web reinforcement needs to be designed
to carry only shear stress in excess of the concrete contribution, V. Thus,
V, = Vu — Vc(2.10)
The contribution of the shear reinforcement is calculated using the traditional truss analogy method,
which produces the formula (as previously described in Section 2.2.2.1)shown as below;
V, = Asvf34,11sv
2.3.3. Remarks
Shear design method adopted by BS 8110 (1985) clearly shows that it is over simplified in its
approach. The contribution provided by concrete which is given by Equation 2.9 is empirically in
nature. Even though it was based on large amount of test data, it has to be reminded that the data
was largely based on the test of rectangular sections, having cube strength in the region of 20 to
40 Nime. The disadvantage of empirical (or semi-empirical) expressions is obvious; that they only
cover a limited range of problems.
The contribution of the web reinforcement (stirrups) is based on the classical truss analogy method.
This method was discussed in detail in Section 2.2.2.1. It is subjected to limitation as far as the
range of application is concerned.
(2.4)
31
CHAPTER THREE
EXPERIMENTAL PROGRAMME AND TEST RESULTS
3.1 Introduction
In order to establish the possibility of using steel plate as shear reinforcement in reinforced concrete
beams, tests were carried out on 15 specimens. In this research, steel plates of different
thicknesses were embedded in the reinforced concrete beams. This chapter presents the details
of test programme, material properties and test results.
3.2 Test Programme
All the beams for test were 100 mm x 400 mm in cross section, with thirteen of them 2500 mm long,
and the remaining two 1800 mm long. The shear span was 400 mm, thus giving the shear span to
depth ratio of 1.0. The beams were provided and designed with high amount of flexural
reinforcement, so that failure would occur in shear. The main reinforcing bars were welded to steel
channel at both ends to prevent anchorage failure (see Fig. 3.1).
The test beams were divided into three series, designated 1, 2 and 3. Table 3.1 shows details of the
test beams. Series 1 consisted of six specimens in which three of them had single plates and the
remaining three were double plated. Each series consisted of beams with different plate thicknesses,
namely 2 mm, 4 mm and 6 mm. The plates used in series 1 were sand blasted. Series 2 consisted
of seven beams; four beams were single plated and the remaining three were double plated. The
specimens in Series 2 were the same as those in Series 1 except that the plates were not sand
32
blasted, instead they were thoroughly degreased. All beams in series 2 were provided with additional
reinforcement for strengthening at the loading points. This measure was introduced to overcome the
possibility of premature failure (i.e bearing followed by peeling-off of the concrete). Bearing failure
was likely to terminate the load carrying capacity of the beams which were otherwise strong in
flexural and shear. Details of strengthening methods employed at the loading point in Series 2
beams will be discussed in Section 3.6.5.7.
Series 3 consisted only of two specimens; one with 4 mm and the other with 6 mm plate. Both were
double plated. The beams in Series 3 were identical to those in Series 2, except that the length was
1800 mm and that there was no additional detailing provided to strengthen at the loading points.
Series 3 beams were used and tested by the undergraduate students as part for their honours
project. The test and laboratory works were carried out under the guidance of the author.
Series Designation* Flexural Reinforcement
Top(No.-Dia.(mm))
Bottom(No.-Dia.(mm))
1 1S2 2-8 2-25154 2-8 2-251S6 2-8 2-32102 2-8 2-25104 2-16 2-32106 2-16 2-32
2 2S2 2-8 2-252S4 2-8 2-252S6 2-8 2-322S8 2-16 2-32202 2-8 2-25204 2-16 2-32206 2-16 2-32
3 3D4 2-8 4-16306 2-16 4-16
Table 3.1: Details of Test Beam
(* Numbering scheme: First number denotes series number, D means double plate, S means singleplate and last number indicates thickness of the plate)
33
3.2.1 Details of Steel Plates
The steel plates were 370 mm deep and embedded along the length of the beams. They were
punched with 80 mm diameter semi circular cut-outs at 160 mm centres along the longitudinal top
and bottom edges. At the bottom cut-outs, additional 42 mm slots were incorporated to
accommodate the main bars within the depth of the cut-out. The cut-outs were provided to act as
shear connectors, to prevent any possibility of horizontal slip in case of insufficient bond between
the plate and the concrete. In the cut-outs, additional links were provided. These links were provided
for ensuring additional bond between the plate and concrete. These also act as shear connectors
in transferring horizontal shear to the main bars.
theFor single plated beams, the plate was embedded between/tensile bars and vice-versa for double
plated beams. Fig. 3.2 and Fig. 3.3 show typical arrangement of single and double plated beams
respectively.
It can be seen from Fig. 3.2, that the encasement of steel plate gives the structure an appearance
of concrete-encased composite I-beams. But, there are differences between the two as in concrete
encased I-beams, the concrete normally act as a protection against fire and/or corrosion to the !-
beams (Johnson 1968, Davies 1975, Johnson & Buckby 1986). In contrast, the encased steel plate
are provided as shear reinforcement and the concrete encasement provides composite action as well
as stability to the beam.
34
cn
cn
_S
0
E E -E--E E -a S' ctscc> CM 'CD -.§ 0
CD =C"x .= 0 -0 c)
--a 8.r.-C::' 0 ...9. CD8 "-Cr, -=CDX CO 0"--. CD se.U) C6 C
EE -r–
cz C c -0,..-- = _, a)
al CD .6 -CI: 4-66- —cl- ua.C16
- tr. 1Da CD C-71 csi -5.-co w
Cl) E - ,-R c6 CLWI -riz --- = _, C 4 _CP-= CtS CD " p 1-5- cr, OD E 0 "
Cl,
c.c7) CA 1D -01 c, ..5 ccre, .a Ccp • - 0 C° C ) CD 'Es-cD = 1.... —,5E .2crs 9 E0 f --7--
c.>
C,,a,_ — = ..... c ›.
CDca. :irc 0 0.15
CC1 4--• ts-jZ ..-: C \I c6
CDCA 0 -C
'
SL-44
35
0047
36
-.I(...) -
37
3.3 Materials and Control Specimens
3.3.1 Concrete
The concrete materials used were uncrushed gravel aggregates with nominal size of 10 mm, natural
river sand of zone 2 and ordinary portland cement. The mix proportion for all batches was
1:1.75:1.90. Water cement ratio (w/c) for the single plated beams was 0.48, whilst for double plated
beams it was increased to 0.5 in order to give more workable concrete.
For every beam, three 100 mm cubes and three 100 mm x 300 mm cylinders were used for
determining the compressive and tensile splitting strengths respectively on or near the day of test.
Cube compressive strength, cylinder splitting tensile strength and modulus of elasticity of concrete
were determined in accordance with Part 116, Part 117 and Part 121 of BS 1881 (1983)
respectively. Table 3.2 gives the characteristics of the control specimens. The variation in concrete
strength was principally due to variation in age at the day of testing.
38
Beam CubeCompressiveStrength(N/m m2)
CylinderSplitt.Strength(Nim m2)
ModulusofElasticity(kNim m2)
Density(kN/m3)
1S2 49.3 2.74 21.5 22.21184 48.3 2.81 21.5 22.241S6 51.0 2.81 21.5 22.17
1D2 32.8 2.46 20.7 21.491D4 34.8 2.69 20.7 21.471D6 32.3 2.60 20.7 21.44
2S2 47.6 2.88 22.3 22.662S4 34.6 2.58 21.7 21.792S6 43.6 2.72 22.3 22.622S8 43.0 2.71 22.3 22.52
2D2 39.0 2.88 22.2 22.862D4 38.9 2.59 22.2 22.652D6 39.2 2.75 22.2 22.53
3D4 42.3 3.10 22.9 Not3D6 45.6 3.03 22.8 available
Table 3.2: Concrete Characteristics
Note:
1. Cube crushing strength, cylinder splitting strength and density were determined at the day of
testing of the beams.
2. Modulus of elasticity was determined at 28 days after casting.
3.3.2 Reinforcements
Reinforcements for Series 1 and 2 beams were deformed high yield bars. For Series 3 beams, high
yield plain round bars were used. The strength characteristics of the bars were determined by tensile
tests of at least three representative samples of each bar size. Tensile test was carried out in
39
accordance with BS 18 (1987). The properties of the bars are given in Table 3.3.
BeamSeries
BarDiameter(mm)
Yield Stress(0.2% Proof)(N/me)
Modulus ofElasticity(kNime)
Yield Strain(micro-strain)
1 8 578 204 283016 518 203 255025 504 200 252032 462 201 2300
2 8 547 200 274016 516 198 261025 500 202 248032 520 199 2610
3 8 443 227 195016 462 209 2210
Table 3.3: Reinforcements Characteristics
3.3.3 Steel Plate
All plates were of mild steel type. The main advantages of mild steel over high yield steel seems to
be that the strength required to develop the full strain of the plate is less, thus making the plate fully
utilised. This will be more economical.
The strengths of the plates were determined by tensile test on at least three representative samples
for each thickness. All tests were carried out in accordance with BS 18 (1987). The strength
characteristic of the plates are given in Table 3.4.
40
BeamSeries
PlateThick.(mm)
Yield Stress(0.2% Proof)(N/mm2)
Modulus ofElasticity(kN/m m2)
Yield Strain(micro-strain)
1 2 218 201 10804 245 199 12306 304 200 1520
2 2 227 204 11304 195 194 10106 306 204 15008 259 205 1260
3 4 294 200 14706 324 165 1960
Table 3.4: Plate Characteristics
3.4 Preparation of Test Specimens
The main tensile bars were first welded to the steel angle at the predetermined positions. The steel
plates were then carefully placed at their positions. The bottom edges of the plates were arranged
to rest on the angles. To hold the plates in position, spot welding between the edges of the plates
and the angles was used. This weld did not give any strength to the beam. Prior to its fixing, the
plates were extensively mounted with electrical resistance strain gauges. Plate 3.1 shows typical
arrangement of strain gauges on the steel plate.
The top bars were then placed at their positions. To hold the reinforcement, a vertical link was used
at both ends of the beam. The assembly was completed by fixing the small links at the cut-outs at
top and bottom.The assembly was then put into the formwork and ready for casting. The formwork
was made of plywood.
41
42
3.4.1 Casting and Curing
The beams were cast from a batch of concrete, produced by a horizontal pan mixer of capacity of
0.1 m3. In some cases three beams of the same series were cast simultaneously requiring four
batches of concrete. From each batch, the sample was taken for the determination of concrete
characteristics (Section 3.3.1).
The concrete was placed in the formwork in layers of approximately 100 mm deep. The formworks
were arranged on a casting table fitted with a vibrator on the underside. The compaction of the
concrete was done by vibrating the table. In casting the beams every effort was made to produce
a uniform concrete.
After casting, the test and control specimens were covered by wet hessian bags for 2 days before
demoulding. They were then cured in the laboratory condition until ready for testing.
3.5 Test Arrangements
3.5.1 Test Set-up
All the beams were tested simply supported over their span, with two symmetrical point loads. The
shear span of the beams was 400 mm. This position of loading was chosen in order to make the
beams critical in shear.
The beams were supported on a roller bearing at each end. Load from the 6000 kN capacity
43
Losenhaousen Compression Testing Machine was applied through a stiffened spreader beam. The
test arrangements are shown in Fig. 3.4 and Plate 3.2.
3.5.2 Instrumentation
Extensive instrumentation was used in each test beam. This consisted of transducers for the
measurement of deformation, electrical resistance strain gauges (ERGs) for the measurement of
strains in steel plate and reinforcement and Demec points for the measurement of surface strain
of concrete (Demec points were used in Second Series beams only). The positions of transducers
are as stipulated in Fig. 3.5, whilst the positions of ERGs will be shown later when the results of
individual beam are described.
The deformations of the beams (vertical and horizontal) and the strains of steel plates and
reinforcements were recorded on a data logger which was connected to an OPUS Computer. In such
a case the load displacement and/or load-strain readings could be displayed and enabled a
continuous assessment of the behaviour of the beam to be made. Surface strains of concrete were
manually measured using a demountable 2" (50 mm) Demec gauge.
3.5.3 Test Procedure
The testing was carried out by applying the loads in small increments in three cycles. In the first two
cycles the loads were applied within the elastic and elasto-plastic range of the structure. In the third
and final cycle the beam was loaded in small steps of increment until failure. The failure load was
the maximum load which the beam would sustain in test.
44
45
Plate 3.2: Test arrangement
46
In the test, the readings for the transducers and strains reading were taken for every increment of
load, whilst Demec readings were taken at a larger interval of load. Throughout the test, the cracks
were marked on the beam. The maximum diagonal crack width was measured at selected load
increment. The measurement of crack width was carried out by using a hand-held microscope with
magnifying power of ten times. Finally, the beam at failure was also recorded in photographs.
3.6 Test Observations and Results
In this section, the observations and results for the test beams are presented. These results will be
presented in graphical forms for easy interpretation. Discussion on the test results is given in
Chapter Six.
3.6.1 General Behaviour
All the beams were tested under similar loading and support conditions. In such a case they will
generally behave in a similar manner. Initially the beams had developed few mapped fine cracks
which were a result of shrinkage or handling. In double plated beams the cracks were more visible
than that in single plated beams. In was believed that these cracks had no effect upon the overall
structural behaviour of the test beams.
The initial behaviour of all the beams started with the formation of tiny flexural cracks originating from
the soffit in the mid-span region. These cracks occurred at a relatively small load compared to the
failure load (about 15%-25% of failure load).
47- ing
As the load was increased, there was no further occurrence of flexural crack. The beams thenTA
started to produce inclined cracks which originated from the edge of the supporting plate running
diagonally towards the loading point. With further increase in load, these cracks propagated and
widened and in some cases the cracks also branched out which normally happened at the middle
of the web. The formation of the inclined cracks was usually accompanied by an audible splitting
sound.
The failure usually happened when diagonal cracks were completed and some concrete crushing
was noticed under the loading points. The actual behaviour of individual beams will be described
in Section 3.6.5.
3.6.2 Deflections
3.6.2.1 Mid-span Deflection
The load mid-span deflections of the test beams are shown in Fig. 3.5. Fig. 3.5a shows the mid-span
deflections of single plated beams and Fig. 3.5b for double plated beams. The deflections of some
of the beams are not shown since their behaviour was the same as those shown in Fig. 3.5.
In general, the graphs indicate only one stage of behaviour. This shows that the beams behaved in
a linear manner. This behaviour reflects that the formation of flexural cracks were very fine which
did not affect the mid-span deflection of the beam. This also signify that the main bars remain
unyielded until failure.
48
Fig. 3.5 also shows that the deflection of the beams with thicker steel plate is less than that of
beams with thinner steel plates, for example the deflection of Beam 206 as compared to that of
Beam 204 or 2D2 (Fig. 3.5b). It can be deduced from this that the steel plate has also contributed
to the bending stiffness of the beams. To show this contribution, the comparison has been made
between Beam 2S4 with 2D2 and between Beam 288 with 2D4 (Fig. 3.5c). In this figure the
deflections between the beams in each pair are almost identical. Therefore, it would be appropriate
if this contribution is taken into account in calculating the flexural capacity of the beams. However,
the main resistance to flexural stiffness of the beam is due to the main tensile bar, which is shown
by the difference in single plated beams (Fig. 3.5a). The beams with 32 mm tensile bars (i.e Beams
2S6 and 2S8) have less deflection compared to that with 25 mm bars (i.e Beams 182, 1S4, 2S2 and
2S4).
3.6.2.2 Under Load Deflection
The typical deflection of the beams under the loading points are shown in Fig. 3.6. Fig. 3.6a shows
the deflection of Beam 2S2 and Fig. 3.6b shows the deflection of Beam 204. The other beams which
are not shown here have also behaved in a similar manner.
As it would be expected, the deflections under the loading point in all cases are lower compared to
their corresponding values at mid-span. These deflections are almost identical at both locations, i.e
on the left hand side and on the right hand side of the beam. This implies that the loads were
applied equally to both sides and consequently it means that the set-up of the test arrangement was
appropriate.
Load (kN)1000 1200
1000
800
600
400
200
0
Loads (kN)
49
(Single Plated Beams)
(Double Plated Beams)
0 2 4 6 8 10 12 14
(G ) Mid—span Deflection (mm)
0 2 4 6 8 10 12 14 16
(b) Mid—span Deflection (mm)
Loads (kN)
800
600
400
200
0
0 Z 4 6 8 10 12 14
(c) Mid—span Deflection (mm)
(For Comparison)
Fig. 3.5: Mid-span deflections
1000
16
600
500
400
300
200
100
Loads (kN)
_
_
Position:
Mid—span
Under Load on LHS
--,1(— Under Load on RHS
-
_
Loads (kN)1000
aoo
600
100
200
50
Loads Vs DeflectionBeam 2S2
0 2 4 6 8 10 12 14
(a) Deflection (mm)
Loads Vs DeflectionBeam 2D4
4 6 8 10 12
14
Deflection (mm)
Fig. 3.6: Under-load deflections
51
3.6.3 Crack Width
The measured maximum diagonal crack widths during the tests are shown in Fig. 3.7. Fig. 3.7a
shows the maximum diagonal crack width of single plated beams whilst Fig. 3.7b shows that of
double plated beams. Single plated beams of Series 1 are not shown here because they also
produced similar pattern as shown by their corresponding beams in Series 2. The double plated
beams in Series 1 are not shown because the measurements were not taken.
The maximum diagonal crack width observed in all the beams generally occurred at the mid-height.
With reference to Fig. 3.7, as far as the shape of the curve is concerned, no appreciable difference
could be observed for the different thicknesses of the steel plates used. However, for the beams
with thinner steel plates, the bigger size of the crack was observed for the same applied loads (the
relationship between the thickness of the plate and width of the crack is discussed in Section 4.5.2).
It also can be seen that after the formation of cracks, the curves maintained a stiff gradient at the
beginning and becoming nearly horizontal towards the end (except Beam 206). This behaviour
indicates the rapid widening of cracks with increasing loads.
3.6.4 Strain Readings
The results of strain readings will be presented in the next section. For each steel plate, the gauges
were placed at various critical locations. In some beams (for example, Beam 102) up to 66 individual
strain readings were obtained at each load level. Because of the large number of readings obtained,
individual gauge readings will not be presented, instead the principal strains calculated from the
400
200
52
Loads Vs Maximum Diagonal Crack Width(Single Plated Beams)
Loads (kN)1000
800
600
(Double Plated Beams)
Loads (kN)
1000
800
600
400
ZOO
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Maximum Diagonal Crack Width (mm)(b)
0
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
(a) Maximum Diagonal Crack Width (mm)
1200
Loads (kN)1000
800
600
400
200
00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Maximum Diagonal Crack Width (mm)
(For Comparison) (c)
Fig. 3.7: Maximum diagonal crack widths
53
measured values will be plotted. In cases where it is believed that the rosette was faulty, the results
will not be presented. In describing the plate capacity, the plate is considered yielded if a certain
region of it is found to be yielding. This assumption is consistent with the assumption made in
determining the capacity of plate girder (Evans 1987).
The surface concrete strains which were measured using Demec points, it has been found that the
readings were very much influenced by their positions relative to the cracks. In such instances,
therefore, the Demec results need to be considered together with the crack pattern. In many cases,
however, the results of Demec readings were unrealistic, hence these will not be included.
3.6.5 Test Response of Individual Beams
In this section, test results of individual beams are presented. For conciseness, only the important
features of the behaviour under load are highlighted. The lengths of the cracks are given as a ratio
of overall depth of the beam. In describing the beams' behaviour, width of the crack will not be given
since it has been presented earlier in Section 3.6.3.
3.6.5.1 Beam 1S2
The first flexural crack for Beam 2S2 was observed at the load of 140 kN. This crack formed at mid
span region extending vertically towards the compression face up to h/5. At 160 kN another crack
formed, adjacent to the first one. There was no further activities of these cracks at further loads. At
about 120 kN a diagonal crack started to form on the left hand side (LHS) of the beam. This crack
originated from the edge of supporting plate extending diagonally towards the loading point, up to
54
h12 height. This crack widened as the load increased. On the right hand side (RHS) of the beam,
also a diagonal crack started to form. At 380 kN, RHS crack branched out as did the LHS crack.
Meanwhile few more flexural cracks formed at the region of maximum bending moment. With further
increases of the load, failure happened suddenly at 580 kN when the inclined cracks reached up to
the loading point.
The positions of rosettes are shown in Fig. 3.8 and the principal strains experienced by the steel
plate are given in Fig. 3.9. The graphs show that many parts of the plate have yielded. It can be
seen that the plate yielded at about 380 kN.
The graph (Fig. 3.9c) also indicates that the plate is in the state of pure shear behaviour. This
behaviour develops when the element is subjected solely to the shear stresses and in which there
is no influence by other stresses. Its behaviour is recognised by the identical results of the principal
tensile and compressive stresses (or strains). At position R11, the principal strains (tensile and
compressive) were almost identical. This shows that the plate is subjected to the state of pure shear.
The tensile strains in the main reinforcement at both locations, namely at mid-span and at the
support, gave a value of about 1700 micro-strain which is far below its yield strain of 2520 micro
strain. At mid-span the graph (Fig. 3.9f) shows a linear relationship up to failure, whereas at the
support the graph changes its gradient at about 220 kN. This change in gradient could be attributed
to the formation of diagonal crack at this location. As expected, the direct strain readings of the plate
at the region of the maximum bending moment (Fig. 3.9e) show the behaviour; the top in
compression, whilst the lower part in tension. These readings indicate that the plate contributes to
the bending resistance to the beam. Fig. 3.10 and Plate 3.3 show the beam at failure.
55
1.00
1450 400
R8 0 R90 OR10
ORliR13
R120 0 0R14
sl -I
-S 2
53 —
2Z-*--1.12 ,„49 90 1,171 *--11,,„1:894b9.L. '3 2,1,,L21.1
RIO R20 R30
R4
R 0 R60 0R7
Locids (OA)
500 1000 1500 2000 2500Principal Tensile Strain (x 10E-6)
600
500
400
300
200
100
Loads (kik!)
Loads (kN)600
500
400
300
200
100
0-2000--1500--1000-500 0 500 1000 1500 200(
Principal Strain (x10E-6)(d)
Loads (ktl)700
R6
R13 (=R6)
500 1000 1500 2000 2500Principal Tensile Strain (x10E-6)
600
500
400
300
200
(c)
Fig. 3.8: Positions of rosettes (Beam 152)
Loads Vs Principal Tensile Strain(Beam 1 S2)
600
500
400
300
200
100
500 1000 1500 2000 2500
(a) Principal Tensile Strain (x10E-6)
(Yield Sirain = 1C80 x10E-6)
Loads Vs Principal Strain
Fig. 3.9: Strains in steel plate and main bars (Beam 1S2) (cont.)
600
500
400
300
200
100
Loads (kN)
0
Loads (kN)
Position:
— S1
32
—4— 33
Position:
— At Support
Mid—span
Fig. 3.9: (cont.)
25oY 3203_0
200
4E01---7z,S-2C0
320 400360
48/0 zoo I
?
320
200220
3 6 0 1 60 , 3802
36
20
56
Loads Vs Direct Strain
Loads Vs Bar's Strain(1s2) (132)
600
500
400
300
ZOO
100
0—1500 —1000 —500 0 500 1000 1500
0 500 1000 1500 2000 2500
(e) Strain (x10E-6)
(fJ Strain (x10E-6)
(Yield Strain = 2520 x 10E-6)
Fig. 3.10: Crack pattern at failure (Beam 1S2)
57
3.6.5.2 Beam 1S4
The flexural cracks started to form at 160 kN. The cracks formed at mid span of the beam and
extended towards the compression face up to h14. At 180 kN, a diagonal crack developed on the
LHS of the beam. At 220 kN, a diagonal crack also formed on the RHS. As the load increased, both
cracks extended and widened. Few more flexural cracks also appeared in the region of bending
moment. At 470 IN, a small crushing of concrete under the load on the RHS was noticed. At 550
kN, there was more concrete crushing on the RHS, and the same phenomenon also happened on
the LHS. As the load increased, a small amount of concrete was observed to be spalling on both
sides. The crushing of concrete was bigger especially on the RHS. At 700 kN, the concrete crushed
under the load on the RHS. The beam failed at 710 kN, when the inclined crack formed fully,
together with the crushing under the load.
The principal strains in the plate are given in Fig. 3.12, the position of the rosettes being shown in
Fig. 3.11. The graphs indicate that yielding has occurred in many parts of the plate, namely at
R7, R6 and R4. These parts yielded at the load of about 650 kN. It is clear that after the yielding of
these parts, the beam failed. The behaviour governed by pure shear in the web of the plate is clearly
shown by the graph (Fig. 3.12d). The tensile strain in the main bars show that the bar did not yield.
The recorded value was 2200 micro-strain. The direct strain values at the region of maximum
bending moment are given in Fig. 3.12f. Fig. 3.13 and Plate 3.4 show the beam at failure.
3.6.5.3 Beam 1S6
The flexural cracks in Beam 186 formed, as in previous cases, at the soffit of mid-span region.
400 149
Position:
R2—4-- R4
R6 (= R10)
500 1000 1500 2000 2500
(C) Principal Tensile Strain (x10E-6)
800
600
400
200
Loads (kN)
58
0 0 0 -7S1 0 0RI R2 R3 R8 R9
0R4I
-rS2
0 0 0 R7L.S3 R10
0 0R11
•-_____rtsft16"—)._
04,294.190!....12242.2.54.
Fig. 3.11: Positions of rosettes (Beam 1S4)
(seam 1S4)
Loads (kN)
0 500 1000 1500 2000 2500(a) Principal Tensile Strain (x10E-6)
(Yield Strain =- 1230 x 10E-6)
Loads (kN)
500 1000 1500 2000 2500Principal Tensile Strain (x1 0E-6)
Loads Vs Principal Strain(IS 4)
Loads (kN)800
600
400
Z00
0-2000-1500-1000-500 0 500 1000 1500 2000
(d) Principal Strain (x10E-6)
Fig. 3.12: Strains in steel plate and main bars (Beam 1S4) (cont.)
Loads Vs Direct Strain(154)
800Loads (kN)
ki
Position:
Si
—÷- 52
- ÷- S3
0—1500-1000 —500 0 500 1000 1500
(f) Direct Strain (x10E-6)
600
400
ZOO
Loads (kN)
Fig. 3.12: (cont.)
..,
180
230\ 0 )30 CO
60 IGO
)233
420/1
320
200
180
230220
59
Loads Vs Bar's Strain(1s4)
800
600
400
200
00 500 1000 1500 2000
(C) Strain (x10E-6)
Yield Strain = 2520 x 10E-6)
2500
Fig. 3.13: Crack pattern at failure (Seam 1S4)
60
These cracks were noticed at about 300 kN. A diagonal crack was also observed at 300 kN on the
RHS. This crack started from the edge of supporting plate towards the loading point extending up
to h14. A diagonal crack appeared on the LHS at 360 kN. At 420 kN, both the diagonal cracks (RHS
and LHS) were observed to extend almost up to the loading points. At 540 kN, an audible splitting
sound was heard. No crushing of concrete was observed. As the load was increased further the
cracks widened. At 700 kN a small area of concrete under the load on the LHS was observed to
crush. The beam failed at 790 kN, when the diagonal crack on the RHS extended fully and the
crushing of concrete under the load occurred.
The principal strains in the steel plate are shown in Fig. 3.15, the positions of the rosettes being
shown in Fig. 3.14. The graphs show that the steel plate has yielded at the positions of R10 and R7.
Like the 1S4 beam, these parts of the plate yielded when the beam reached close to failure. In other
words, when some parts of the plate yielded, the failure happened. The tensile bars, however,
remained unyielded. The principal compressive and tensile strains at the position of R4 are identical
(Fig. 3.15c). This shows that the state of pure shear exist in the steel plate. The direct strain of the
plate at mid-span is given by Fig. 3.15e. Fig. 3.16 and Plate 3.5 show the beam at failure.
3.6.5.4 Beam 1D2
The flexural cracks for Beam 1D2 were observed at 200 kN. These cracks extended up to h/4. As
the load progressed, a few more flexural cracks formed. At 260 kN, a diagonal crack was noticed
on both sides. At 500 kN, the 'crushing sound' was heard under the loading point on the LHS. On
both sides it was noticed that some other diagonal cracks had formed. They were formed individually
and separated from each other. At this stage it was found that the top-cast surface of the beam (i.e
(Beam 1 S6)
Loads (kN)1000
800
600
R1 (= R9)
R3 (= R8)
RIO (= R5)
R7 (= R11)
400
200
1000Loads (kN)
800
600
400Position:•••n•• n R2
R4
R6
200
1000 Loads (kN)
800
600
400
Rossefte R4:
— Prin. Comp
—1— Prin. Tensile
0-1500 -1000 -500 0 500 1000
(C) Principal Strain (x10E-6)
ZOO
1500
61
"•55
1.00.14 1460
r4-
0Ri 0 °R3R2
0 R4R6 0 R60 0 R7
Si--52=S3-
R8 0
R110 R100
R40
r.-1-24H-12-94-H9.12".1Clw '4.10 39 1, .._,,,,„,„.„24,4„,:22.t..,ja.,„
Fig. 3.14: Positions of rosettes (Beam 1S6)
500 1000 1500 2000 2500( )
Principal Tensile Strain (x10E-6)(Yield Strain = 1520 x10E-6)
0 500 1000 1500 2000 2500
(b) Principal Tensile Strain (x10E-6)
Fig. 3.15: Strains in steel plate and main bars (Beam 1S6) (cont.)
1000 Loads (kN)
700
t
Position:
— Si
—1— 52
---4— 33
800
600
400
(1S6)
Loads (kN)800
600
400
Position:
— At Support
---- Mid—span
200
62
Loads Vs Bar's Strain
Loads Vs Direct Strain(1s6)
0 0 500 1000 1500 2000 2500 —1500-1000 —500 0 500 1000 1500
(d) Strain (x10E-6) (e) Strain (x10E-6)
(Yield Strain = 2300 x 10E-6)
Fig. 3.15: (cont.)
t
T
Fig. 3.16: Crack pattern at failure (Beam 1S6)
longitudinalcrack
steelplate
ars
'steelangle
ENDSEC TION
63
near the loading point on the LHS) suffered excessive longitudinal cracking extending to the end of
the beam. As the load progressed further this longitudinal crack widened and some crushing under
the load occurred. The beam then failed at 535 kN. The failure of the beam was due to the
formation of this longitudinal crack and some crushing the under load. The longitudinal crack is
believed to have formed due to probably inadequate detailing under the loading point. The
longitudinal splitting crack in effect caused the potential peeling-off of the concrete cover to the plate.
The beam is treated as prematurely failed. Fig. 3.17 shows the longitudinal crack developed in the
beam.
longitudinal crack
r—loading plate
..4
PLAN
Fig. 3.17: Longitudinal crack in Beam 1D2
64
The principal strains in the steel plates are presented in Fig. 3.19 with the rosette positions shown
in Fig. 3.18a. In this case, rosettes were mounted on both plates (see Fig. 3.18b). Fig. 3.19 clearly
shows that the steel plates have not yielded at failure. The average value of principal tensile strain
was 800 micro-strain, which represents much lower value than its yielding strain of 1080 micro-strain.
The strains in the tensile bar were also found to be much lower than its yielding value, the recorded
value being only 1400 micro-strain at mid-span. The plate was subjected to pure shear behaviour
as shown by Fig. 3.19d. Fig. 3.20 and Plate 3.6 show the beam at failure.
3.6.5.5 Beam 1D4
The initial flexural cracks for 1D4 appeared at 160 kN. They were formed at the soffit of the beam
in region of maximum bending moment. The first diagonal crack formed on LHS of the beam at 260
kN. As the load was increased the diagonal crack extended further. At 340 kN, the crack extended
up to a height of 0.75h. At this load, also a small portion of concrete under the loading point on the
LHS was noticed to crush and spall. At 420 kN, the beam developed a longitudinal crack at its top-
cast surface. The beam failed at 515 kN partly due to the longitudinal splitting and partly crushing
under the load.
The principal strains in the steel plate are shown in Fig. 3.22. The values of the strains indicate that
the plate is far short of yielding at failure. The average recorded value was 500 micro-strain, which
is much smaller than its yield value of 1230 micro-strain. The tensile bars did not yield either. The
recorded strain was of the order of 1000 micro-strain. Again, the pure shear type behaviour was
recorded in the web (at position R13). Fig. 3.23 and Plate 3.7show the beam at failure.
plate 2
0 0R2 R3
O RL,
OR5 0 0RG
1,..22_46194941.,..3z."T:112.54.,
1450 400
R10
551
CRS 0R9 °R10
OR11
R14 0 OR13 OR12
400
t
65
WO
plate-•
8
(a) SEAM SECTION
i) plate 1
( b)
Fig. 3.18: Positions of rosettes (Beam 102)
(1D2)
600 Loads (kN)
500
4.00
300
Position:200
—)K— R3 ( = R8)
100 —1-- R5 ( = R12, R18)
R7 & R14 Faulty
600
500
400
300
200
100
600
500
400
300
200
100
Loads (kN)600
500
400
300
200
100
Loads (kN)
Rosette R4:
- — Prin. Comp.
—I— Prin. Tensile
66
Loads Vs Principal Tensile Strain(Beam 1D2)
Loads (kN)
00 200 400 600 800 1000 1200 1400
(a) Principal Tensile Strain (x10E-6)
(Yield Strain = 1080 x 10E-6)
(102)
0 200 400 600 800 1000 1200 140(
(5) Principal Tensile Strain (x10E-6)
Loads Vs Principal Strain(1D2)
00 200 400 600 800 1000 1200 1400
(C. ) Principal Tensile Strain (x1 0E-6)
0—1500 —1000 —500 0 500 1000 150
( d) Principal Strain (x10E-6)
Fig. 3.19: Strains in steel plate and main bars (Beam 1D2) (cont.)
Loads600
- Position:
— Si (=54)
- 52 (=55)
53 (.56)
0
500
400
300
200
100
600
500
400
300
200
100
Loads (kN)
30420 330
•••521 270
5 5 Cr/ .332703co '70 7,00
/At /(21Pj \Z7° 7 r 21° 7) r"\O
S2
67
Loads Vs Direct Strain(1D2)
–1500 –1000 –500 0 500 1000 1500
( e) Direct Strain (x10E-6)
Loads Vs Bar's Strain(1D2)
500 1000 1500 2000 2500
Strain (x1 0E-6)
(Yield Strain = 2520 x 10E-6)
Fig. 3.19: (cont.)
Fig. 3.20: Crack pattern at failure (Beam 1D2)
400 14)(1 400
\II-- \ -1--._.)----nJ-- \-...)-W \ -1----S1 •=. R80 R3 0
iS27
S3 - R110 0R10
0 00R3R1 R2
OR/.
R50 P60 0R7
-01
9°)I
pa' 1.00 145 0
0R12
OR135 R4 R15
S61
-Cr)-1 1
S4
s5
1747437, ,_69j4 30,, 1490,439:(50.1,1 'It 1 25 7
68
) Plate 1
400>4.
ii) Plate 2
Fig. 3.21: Positions of rosettes (Beam 1D4)
Loads (kN)600
500
400
300
200
100
Loads (kN)600
500
400
300
2.00
100
600Loads (kN)
500
400
300
200
Rosette R4 (= R13):
100 - — Prin. Comp.
Prin. Tensile
Position:
— SI (=S4
—4— 52 (=SS)
—4— S3 (=56)
500
400
300
700
100
Loads (kN)600
69
Loads Vs Principal Tensile Strain(Beam 1D4)
(104)
Position:
— R1 ( = R9, R12)
—4— R3 ( = R8)
R5 ( = R10, R15)
0 200 400 600 800 1000 12001400 1600
(a) Principal Tensile Strain (x10E-6)
(Yield Strain = 1230 x 10E-6)
Loads Vs Principal Strain(1D4)
0 200 400 600 800 1000 1200 1400 160( b) Principal Tensile Strain (x10E-6)
Loads Vs Direct Strain(1D4)
o I 0 I 1 1 1
— 1500 —1000 —500 0 500 1000 1500 —800 — 600 — 4.00 — 200 0 200 400 6(c) Principal Strain (x10E-6) (c.1) Strain (x10E-6)
Fig. 3.22: Strains in steel plate and main bars (Beam 104) (cont.)
340
440 320
260,,, 2
(
2/-340 " y,
280 260
,) ( (
380
180 203360
70
Loads Vs Bar's Strain(1D4)
Loads (kN)
Position:
— At Support
-H— Mid—span
0 200 4.00 600 800 1000 1200
(C) Strain (x10E-6)
(Yield Strain = 2300 x 10E-6)
600
500
400
300
200
100
340 340
Fig. 3.22: (cont.)
Fig. 3.23: Crack pattern at failure (Beam 1D4)
71
3.6.5.6 Beam 1D6
The flexural cracks for this beam started to appear at 220 kN. At 300 kN a diagonal crack formed
near the supporting plate on LHS extending towards the loading point to approximately h13. As the
load increased, the crack extended and widened. A few more flexural cracks also formed in the
region of maximum bending moment. At 430 liN, an audible sound of concrete splitting was heard
on RHS. As the load reached 480 kN, it was found that its top-cast surface developed excessive
longitudinal cracking. This crack was exactly similar to that of Beams 102 and 104 (see Fig. 3.17).
With further increase of loads, the beam then failed at 520 kN. This is considered to be a premature
failure. Fig. 3.24 and Plate 3.8 show the beam at failure.
No strain readings were obtained for this beam. This was due to malfunction of the data-logger
during the test.
3.6.5.7 Remarks
From the strain results in the steel plates, it is evident that the single plated beams achieved their
full capacity, whilst double plated beams failed prematurely. In order to avoid the repeat of premature
failure, in all the Second Series beams, local strengthening of the beams were carried out by
introducing improved detailing under the loading points.
The detail for strengthening used in single plated beams of the Second Series consisted of three
inverted U shaped 6 mm diameter round bars. These bars were placed right under the loading point
and rested on the steel plate, as shown in Fig. 3.25a. In double plated beams, the details consisted
72
of a 100 x 100 x 12 mm steel pad with four legs made of 6 mm diameter round bars welded
vertically onto it. This steel pad was then inserted into the beam, in such a way that its upper surface
formed at the same level with the top surface of the beam (Fig. 3.25b).
As regards to the principal tensile strains of the plates, it is clear that the shape of the graphs is
identical in all beams for each corresponding positions. Likewise, the profile of strain results of
tensile reinforcement, direct strains of steel plate at mid-span and the state of pure shear behaviour
developed in the web area show no differences. The only difference is the magnitude of the strains.
The thinner plates (i.e 2mm) have yielded at all locations, whilst thicker plates have yielded only in
certain positions.
A further observation shows that all the beams in First Series behaved in a similar manner. The
beams were subjected to the same test and loading conditions and consequently identical behaviour
was observed. For Second Series beams, only the important results will be presented. For the first
two beams, the results will be presented in detail. But for the remainder only the principal tensile
strains in the plates will be given. The tensile strains in the main bars and the direct strains in the
steel plates will not be included.
The crack pattern and the general behaviour of the beams in the Second Series were very much
similar to that of their counterparts in First Series (except double plated beam). Therefore, the
descriptions of the behaviour given in the next section will be brief and precise.
In the Second Series beams, the typical arrangements of the rosette on the steel plates are shown
in Fig. 3.26. In this series the measurements of concrete surface strains were also taken. The typical
too 100
loading plate'00x 100 x 20
top ',tar
p awn
tie
top of beam
• 4
c ut-cut
round bar
06 mm
stealplate
beam
,15 5. 26 6 26 G 15
100
top of beam6 G '0
1
weld
Li
(b) Double plated beams
F12stool pad
100030 x 12
cu t-ou t
d 6mm rouna bar
120
1
73
31.07--C180 .50(- 430 380 .e0\%-:.150
360i 535 -.CO
450 450 '-' ,.., 0340 /40 . 00
r° ) /340 \
220)
TFig. 3.24: Crack pattern at failure (Beam 106)
(a) Single plated beams
SEC TION
SECTION
Fig. 3.25: Improved detailing in Second Series Beams
_
7"N'N
"
Cf)
0
74
A
AN4„,
75
76
77
position of the Demec points are given in Fig. 3.27.
3.6.5.8 Beam 2S2
The first flexural cracks for 2S2 appeared at a load of 100 kN. Some more cracks were formed as
the load was increased. At 140 kN a diagonal crack formed on the RHS. At 180 kN a diagonal crack
appeared on the LHS. Both cracks extended and widened as the load increased further. At 320 an
audible splitting sound was heard on LHS. At further increment of load, the diagonal cracks on both
sides started to branch out. At 590 liN failure happened when the diagonal crack was fully formed
and that some concrete crushing had occurred under the load on RHS.
The principal tensile strains in the steel plate are shown in Fig. 3.28. The graphs show that many
parts of the plate has yielded at failure. On average, the plate reached its yield strain at the load of
about 420 kN (Fig. 3.28a). The graph also shows that the tensile bars have not yielded right up to
the failure. The recorded strain value of 1700 micro-strain is less than its yield value of 2480 micro-
strain. The development of the direct strains in steel plate at mid-span is shown in Fig. 3.28b, which
remain below the yield strain.
The principal strains on the surface of the concrete are shown in Fig. 3.28d. The readings were
recorded up to 500 kN only. The strains at higher loads was found to be very much influenced by
the presence of the diagonal crack. The graph shows the existence of tension-compression state
of strain at mid-span. Demec strain readings at Cl, C2 and 03 (Fig. 3.27) were found to be
unrealistic and will not be presented. Fig. 3.29 and Plate 3.9 show the beam at failure.
X
Rosette arrangementshere are slmilarthose shown ooDosite.
78
450 114_
N0 0 OR
)SI
RI P20_, 52 +'
n-( 4
C R5 0R 53--
_1111_F.12 1.89,1591,90.,
90 4_89 4, '19 _11 25 4
Fig. 3.26:3.26: Typical positions of rosettes on steel plate in Second Series Beams
400 1450 400
crt C1 •"7-•
-(11) LH S C2 •-•.-• -4E11)- RHS
Demec Demo('
C3 4-
"11125 221
221 ..5.,c•25,
Fig. 3.27: Positions of Demec points in Second Series Beams
Loads (kii)600
500
400
300
200
100
Loads Vs Bar's Strain(seam 2S2)
Loads Vs Principal Strain(252)
Loads (0) 500
400
300
600
Loads (IN
79
Loads Vs Principal Tensile Strain(2S2)
Loads Vs Direct Strain(2S2)
Loads (IN600
500
400
300
200
100
00 500 1000 1500 2000 —1000
(a) Principal Tensile Strain (x10E-6) (b)
(Yield Strain = 1130 x 10E-6)
_.,
—500 0 500
Direct Strain (x10-6)
100C
500 1000 1500
2000
0 1 2 3 4
5
Bar's Strain (x10E-6)
Principal Strain (x10E-3)
Fig. 3.28: Strains in steel plate, main bars and Demec concrete (Beam 2S2)
80
3.6.5.9 Beam 2S4
Crack pattern of the Beam 2S4 is shown in Fig. 3.30. The beam failed at 605 kN when the diagonal
crack formed fully joining the support and the load. At failure some concrete crushing was also
observed under the load.
The principal strains in the steel plate are shown in Fig. 3.31. The plate has yielded only at position
R6. At other positions the strains are about 700 micro-strain at failure. In the main bars, the strain
are below the yield value. Plate 3.10 shows the beam at failure.
3.6.5.10 Beam 2S6
The crack pattern of the beam at failure is shown in Fig. 3.32. The beam failed at 885 kN. The
mode of failure was similar to that of Beam 284. Fig. 3.33a shows the principal strains in the plate.
From the graphs, it can be seen that, just after the strain in the plate reached its yield value (in this
case, at the positions of R3, R4, R5 and R6), the beam failed. In Fig. 3.33b, the direct strain
readings in the plate and the concrete are shown. The point of interest from this graph is that, the
magnitude of both strain readings at the same position (i.e at Si and C1) are similar and almost
coincide with each other. This implies that no slip occurred in the beam. Plate 3.11 shows the beam
at failure.
3.6.5.11 Beam 2S8
The crack pattern of this beam is illustrated in Fig. 3.34a. The beam failed at 938 kN. The failure
11.0 140/140 10
-\120 180
580
2E0leo
370
r2240
220 140
2co 120
/C0/1°0
81
Fig. 3.29: Crack pattern at failure (Beam 2S2)
Fig. 3.30: Crack pattern at failure (Beam 2S4)
Loads (kN)600
500
400
300
0 ' L
—800 —600 —400 —200 0 200 400 600
( ID) Direct Strain (x1 0E-6)
_
Position:
— Si
—+— 52
* 53 Faulty
200
100
Loads (kN)700 500
Loads (kN)
400
300
200 -
LHS Concrete Demec:
— Prin. Comp.
—+— Prin. Tensile
o—6 —4 —2 0 2 4 6 8
(a) Principal Strain (x1 0E-3)
100
1
1
82
Loads Vs Principal Tensile Strain(2s4)
Loads (kN)
00 500 1000 1500 2000 2500
(a) Principal Tensile Strain (x10E-6)
(Yield Strain = 1010 x 10E-6)
Loads Vs Tension Bar's Strain(Beam 2S4.)
Loads Vs Direct Strain(254)
Loads Vs Principal Strain(254)
0 200 400 600 800 1000 12001400 1600
( C ) Strain (X 10E-6)
(Yield Strain = 2480 x 10E-6)
Fig. 3.31: Strains in steel plate, main bars and Demec concrete (Beam 2S4)
83
T
27
leD 180IN
)60 50 -160 c240 240- \7 152'
140 350F203
140
Loads Vs Direct Strain(256)
Loads (kN)1000
800
600
400
200
0
'\ +\
\\ \\ \\:* \
Position: \
o
—314— SI (Steel Plate)
—I— CI (Concrete)
—43— 52
C2 (Unrealiable)
S3 (Faulty)
C3 (Unrealiable)
—1200 —1000 —800 —600 —400 —200
( b) Direct Strain (x10E-6)
0
Fig. 3.32: Crack pattern at failure (Beam 2S6)
Loads Vs Principal Tensile Strain(256)
Loads (kN)
500 1000 1500 2000 2500
Principal Tensile Strain (x1 0E-6)
(Yield Strain = 1500x10E-6)
Fig. 3.33: Strains in steel plate (Beam 2S6)
84
was very sudden and accompanied by an 'exploding sound' under the load on LHS. As it is noticed,
a significant amount of concrete crushing under load was observed at failure. The failure of this
beam is considered as bearing failure.
The principal tensile strain of the steel plate is shown in Fig. 3.35a. The graphs show that many
parts of the plate have yielded, which occurred virtually at the same time as the failure of the beam.
Plate 3.12 shows the beam at failure.
3.6.5.12 Beams 2D2, 2D4 and 2D6
The behaviour of the beams 2D2, 204 and 206 may be described as similar. As in previous cases,
the behaviour was characterised by the formation of flexural cracks at earlier loads. After that, as
the load increased, diagonal cracks started to develop. During the application of the loads, at about
50-70% of the failure loads, an audible splitting sound was heard in all cases. The failure occurred
when diagonal cracks developed fully and some crushing of the concrete occurred under the loads.
The beams 202, 2D4 and 206 failed at 665 kN, 875 kN and 1120 kN respectively. After failure, the
beams were examined. It was revealed that part of the concrete in the shear panel were beginning
to peel-off from the plate. This feature, however, may have occurred after the beams had failed.
Figs. 3.34b, 3.34c and 3.34d show the crack patterns of the Beams 2D2, 204 and 2D6 at failure
respectively.
The principal strain readings of the beams are shown in Figs. 3.35b, 3.35c and 3.35d. It is clear from
the graphs that only some parts of the plates have yielded at failure (notably at position of R4 and
R6). The plates reached its yield values at about failure, indicating that the beams failed with the
85
yielding of the plate. Plates 3.13, 3.14 and 3.15 show the beams at failure.
3.6.5.13 Beams 3D4 and 3D6
The behaviour of these beams at the early loads were very similar to the beams previously
described. Both beams failed at 660 kN. In these beams, there was no additional detailing under the
loads (because the beams were tested earlier than any other beams). The failure was found due to
concrete crushing followed by peeling-off of the concrete in shear panel area. The failure was
considered to have occurred prematurely. For these beams, no strain readings were taken. Figs.
3.36 and 3.37 show Beams 3D4 and 3D6 at failure.
3.6.5.14 General Remarks
From the description of the behaviour of beams attest, two types of failure were prominent. The first
type of failure is that due to bearing and some local crushing of concrete under the loads. This will
happen when the local area under the load is subjected to high compressive stress. When this
failure occurs, the full load carrying capacity may not be fully utilised (for example Beams 1D2, 1D4,
1D6, 2S8, 3D4 and 3D6). The failure can be avoided by strengthening the local areas under the
loads or above the supports.
The second type of failure was the diagonal splitting. This type of failure is characterised with the
formation of diagonal crack which started from the edge of supporting plate towards the loading
point. The failure will happen when the diagonal crack is fully developed and some concrete crushing
_no 390720
3Cq220
180/
)160
540
403360
340 ,.260 160130
(00
leo 1100
840
cb\''
620(180
260
1
200160
1240
(c) Beam 204
7.00r200
%1101
(d) Beam 206
630
670
34
.3057Q140
to
86
390
'510
240
(a) Seam 2S8
Fig. 3.34: Crack pattern at failure
(2D2)
Position:
— R1
-4— R3
—11*— R4
—43— R5
R6
700
600
500
400
300
200
100
Loads (kN)
Loads (kN)800
600
Position:
— R3
- R4
400
200- R5
—9— R6
1200Loads (kN)
1000
300
Position:
— R3
- R4
—4— R5
-43- R6
87
Loads Vs Principal Tensile Strain Loads Vs Principal Tensile Strain(2S8)
00 500 1000 1500 2000 2500
(a) Principal Tensile Strain (x10E-5)
(Yield Strain = 1260 x 10E-6)
Loads Vs Principal Tensile Strain(204)
00 200 400 600 800 1000 1200 1 400 1600
( 5) Principal Tensile Strain (x10E-6)
(Yield Strain = 1130 x 10E-6)
Loads Vs Principal Tensile Strain(2D6)
0
0 500 1000 1500 2000
(C) Principal Tensile Strain (x10E-6)
(Yield Strain = 1010 x10E-6)
0
0 ZOO 400 600 800 100012001400160C
(d) Principal Tensile Strain (x10E-6)
(Yield Strain = 1500 x 10E-6)
Fig. 3.35: Principal strains in steel plate
88
Fig. 3.36: Crack pattern at failure (Beam 304)
/_----._--- '-'it'Fig. 3.37: Crack pattern at failure (Beam 306)
89
90
91
92
93
will take place under the load or/and above the support. The formation of the crack is usually
accompanied by an audible splitting sound. All the beams, except those which failed in bearing,
failed in this mode.
The graphs of principal tensile strain of the plates also indicate that the beams which failed in this
type exhibited two further contrasting behaviours.
For the beams with thinner steel plate (i.e 1S2 and 2S2), the plate achieved its yield capacity at
earlier loads compared to the failure loads. In such case, the failure happens when the concrete
reaches its capacity at a later stage. For the beams with thicker steel plates (i.e 4 mm, 6 mm and
8 mm), it shows that the concrete reached its capacity earlier than the plates. In such case, when
the plates (or some parts of the plate) started to yield, then the process of failure commence.
Further discussions on the behaviour of beams will be given in Chapter Six.
94
CHAPTER FOUR
METHOD OF ANALYSIS
4.1 Introduction
The aim in this chapter is to present a simplified method of analysis for reinforced concrete beams
with steel plate or plates for shear which could be developed for practical applications in design. In
developing the method of analysis, three main factors have been considered; (a) that the method
should be simple to use, (b) that the method must realistically represent the physical behaviour of
t hesuch beams as observed inxtestsand (c) that the method must yield results within acceptable
theaccuracy as verified by the experiment and by a detail analysis usingkinite element method.
Initially, the physical behaviour of the beam including the mechanism at failure is described. Then,
in the next section, a method for the analysis of reinforced concrete beams with plate reinforcement
for shear is proposed. The following sections then discuss the capacity of the beams in flexural and
bearing. The concrete cover to steel plate where it plays an important role in preventing the plate
from buckling is also discussed. The problems of bond stresses between the plate and concrete and
the determination of the number of cut-outs required to act as shear connector in the beams are
discussed in Section 4.5. The serviceability requirements, particularly the deflection and cracking of
the beams are dealt with at the end of the chapter. Discussion on the results by method of analysis
is given in Chapter Six.
4.2 Mechanism at Failure
Failure of the beams may be identified by four different modes. The three basic modes are flexure,
95
diagonal splitting and flexural-shear. A fourth mode of failure which is common in beams when
subjected to high stresses is bearing.
4.2.1 Flexure
Beams with low ratios of main tension reinforcement (under-reinforced) fail in flexure. The crack
formation starts at a relatively small load. The vertical flexural cracks form at the region of maximum
bending moment. With further increase in load, these cracks widen and propagate towards the
compression zone. The failure is characterised by excessive deformation of tensile reinforcement,
progression of vertical cracks upwards and large sagging at the region of maximum bending
moment. Eventually the crushing of a small depth of concrete in the extreme fibres of the
compression zone will take place. Fig. 4.1a illustrates this behaviour.
4.2.2 Diagonal splitting
The diagonal splitting mode of failure occurs in beams with shear span/depth ratio in the range 0.5-
1.0 and with a moderate amount of tensile reinforcement. This failure is the commonest mode of
failure in deep beams (Ramakrishnan & Ananthanarayana 1968, Kong et. a/1970, Subedi 1988,
1992).
Initially some flexural cracks may form in the mid-span region. Then some inclined cracks in the
direction of load and support form in the shear span. The failure is identified with the splitting of the
cracks as the limiting tensile strength of the web is reached. The appearance of the cracks usually
accompanied by an audible sound of splitting. Just before the failure, a dominant crack extends
96
between the support and the loading point. Notional hinges form at the two ends of the splitting
crack. To complete the failure mechanism, the crushing and/or spalling of the concrete will take
place at the notional hinges. The tensile reinforcements do not yield at failure. The mechanism of
diagonal splitting mode of failure is illustrated in Fig. 4.1b.
4.2.3 Flexural-shear
Flexural shear mode of failure occurs within a narrow band between the flexural mode and the
diagonal splitting mode. It occurs when the magnitude of the main tensile force is adequate to
prevent complete flexural failure but not adequate enough to form a clear diagonal splitting mode
(Subedi 1992).
At first, flexural cracks develop on the soffit at or near the mid-span of the beam. As the load is
increased, more flexural cracks follow accompanied by some inclined cracks. Failure occurs as the
inclined cracks penetrates into the compression area which is accompanied by yielding of the main
tensile reinforcement at the edge of support. Large deflection will be noticed causing the crushing
of concrete in compression zone. Fig. 4.1c shows this type of failure.
4.2.4 Bearing
Bearing is a common mode of failure in beams with small shear span/depth ratio as the results of
high compressive stress build up locally. Bearing failure occurs either under the loaded areas or
above the supports (Fig. 4.1d). When bearing failure occurs, the full strength capacity of the beams
may not be achieved.
97
F-7
(b) Diagonal Splitting
(c) Flexural-shear
"V<LI:Ly
(d) Bearing
Spatting & crushing
Fig. 4.1: Modes of failure (numbers indicate events)
98
4.3 Proposed Method of Analysis
In developing the method of analysis a few assumptions are made;
i) Perfect bond exists between the plate and the concrete.
ii) Plate is subjected to in-plane force under the action of shear force.
iii)The concrete cover to steel plate is rigid enough in preventing the plate from buckling.
iv) Plate is resisting shear and flexural stresses.
v) The method of analysis is developed for both single and double plated beams. In double
plate beams, the same formulae are applied but the thickness of the plate is doubled.
during theThese assumptions are, in general, consistent with the observation of the beams/ tests.
4.3.1 Shear Strength
The method proposed in this section is based on the splitting concepts. The method assumes that,
when the concrete reaches its limiting tensile strength, it splits. Consistent with the observation of
the beams during the test, this splitting is noticed with an audible sound. The splitting in the beams
will produce a diagonal crack in the shear panel area. With the gradual increase in loads, the crack
will propagate and some concrete crushing and/or spalling under the load will form to complete the
failure mechanism.
The equilibrium of forces at failure is considered at the failure plane. With reference to Fig. 4.2, the
forces which keep the section in equilibrium are as follows;
a
compression zone
V 1" -r
b
-n11
dcl
dP
I
1CP" 4A t
P
Pu/2
99
1- a diagonal splitting force normal to the failure plane which depends on the limiting tensile strength
of concrete, ft,.
2. the compressive force P,, above the diagonal crack.
3. a vertical shear force, V.
4. a horizontal tensile force, Pm which is the contribution of the main tensile reinforcement.
5. the horizontal and vertical forces, Pph and P to the steel plate.
6. the reaction, Pj2, in which P u is the ultimate load.
Fig. 4.2: Forces at failure
(4.2)=0
100
In Fig. 4.2, dc is depth of the compression zone; dt is depth of the diagonal crack, defined by d-dc;
tp is thickness of the plate; d p is the effective depth of the plate and d p, is depth of the plate which
crosses the diagonal crack. Other symbols have their usual definitions.
In this case, for simplicity, the contribution from the compressive reinforcement and dowel resistance
are neglected since they are too small, and this will be on the safe side.
Horizontal equilibrium;
PC — ftcbd t — PPh — Pst = 0 (4.1)
Moments about 0;
Pua PA ftubce ftcba Pphdpc PpvacPstd t -
2 2 2 2 2 2
By substituting Pc (from equations 4.1) into Equation 4.2, the ultimate load for the beam is expressed
as;
2 bf P acPPu = Rdt + da
Pst—a
+ (dt + (14+ aP atc + (dc + dpu)--Lh + Pv
a a
Equation 4.3 is the general equation. The contribution of the individual parameter, PM, ftcf Pp, and
P and depend on particular case of test beam. The value of these parameters can be
determined by using criteria tests with regard to the strength of the web and mode of failure.
(4.3)
(4.4)
(4.5)
101
4.3.1.1 Strength of The Web
The shear panel of the beam under the action of shear force will develop a state of pure shear
behaviour (consistent with the strain results). The state of pure shear behaviour, in consequent will
produce an equivalent biaxial compression-tension field of stress (Fig. 4.3). When the stress in
concrete in this panel reaches its limiting tensile strength ft,, the concrete will split. In the state of
pure shear behaviour, ft, is given by (Hobbs et. al 1977);
al = fcu — 20a3
a l and a3 are the biaxial compressive and tensile stresses respectively' (Fig 4.3b).
For pure shear situation al
cuf tc =
21
The limiting tensile strength adopted here is only depedent upon the value of f the concrete. This
expression is neglecting other factors which may also affect the limiting tensile strength, such as the
shear span/depth ratio and the presence of vertical compressive stresses (Mau & Hsu 1987, Shahidy
1992).
The Equation 4.5 being adopted by the fact that the beams in this investigation had a constant value
of the shear span/depth ratio (i.e 1.0). In such cases, the shear panel area of the beams is subjected
to the state of pure shear in which no direct compressive (or/and tensile) stresses exist. The principal
strain results in the steel plate (see Chapter Three) supports this behaviour.
=a3=ft,, therefore;
(a) ( b )
102
Fig. 4.3: Splitting forces
The concrete splitting force is equal to ftcbs where s is Ad12+a,2). As the plate in the web undergoes
compatible strain, the total of concrete splitting force, P, is equal to;
Pcs = ftcbs + mftc\I(Al2,h +Apv2 )
where m is the modular ratio and Aph and A the areas of steel plate crossing the diagonal crack
in horizontal and vertical projection respectively.
(4.6)
103
4.3.1.2 The Control of Web Strength
The control of web strength depends on the relative magnitude of the concrete splitting force, Ps,
against the capacity of the steel plate in shear at the diagonal crack, V is given by;
Vsc = fp.1,1(4,1,+ All)
(4.7)
where f equal to fyp/43 (Henclv-Mises Criterion); and fyp is yield stress of the plate.
Depending on the relative magnitude of P. against V possible situations will arise;
i) when P. > V.
This situation arises when the amount of steel plate is 'insufficient'. In this case, the failure of the
beam happens at the instance of splitting, where the concrete reaches its full capacity. As the failure
occurs, strains in the steel plate will suddenly increase. The sudden increase in steel plate strains
is due to the stresses released from the concrete. This situation is known as concrete control.
ii)when P. < V.
When the magnitude of P. is smaller than that of V„, the strength of the web is controlled by the
steel plate. This situation occurs when there is 'sufficient' amount of steel plate in the beam. Under
the application of the load, the concrete will reach its capacity earlier than that of the steel plate. The
plate will take over the splitting force and the beam will be able to work further until the plate yields.
In such cases, strains in the steel plate will gradually increase and the splitting capacity of the
104
concrete will not contribute.
iii) when P. = Vsc
When the capacity of the concrete is equal to that of the steel plate, the failure will happen as either
one of these material reaches its capacity. This situation is known as the balanced section. Ideally,
this situation is the most economical section that the beam will achieve. This is because at the time
of splitting, both materials are being utilised to their maximum capacity.
Table 4.1 summarises the control of web strength of the beams.
P, Control of Web
Strength
> V„
=
<
Concrete
Balanced
Steel Plate
Table 4.1: Control of Web Strength
4.3.1.3 Mode of Failure
The mode of failure, either flexural shear or diagonal splitting depends on the value of tensile strains
in reinforcements, either yielded or not. Diagonal splitting mode of failure happens across a
prominent diagonal crack in which the concrete in the compression area near the load and/or near
105
the support crushes (see Fig. 4.1b). In this case, tensile reinforcement may not yield. In contrast,
the flexural shear mode of failure required the main reinforcement to be yielded (see Section 4.2.3).
The criteria test in determining the mode of failure is given in Table 4.2;
Psi Predicted Mode of Failure
� Astfy
< Asify
Flexural Shear (FS)
Diagonal Splitting (DS)
Table 4.2: Criteria Test in Determining the Mode of Failure
4.3.1.4 Contribution of Tensile Reinforcement
The contribution from tensile reinforcements, P s, depends on the control of web strength. The value
of Ps, is assumed to be equal to the capacity of the horizontal component of the splitting force.
Referring to the idealised diagram in Fig. 4.4, the maximum force that the main reinforcement may
be subjected to, is determined by the magnitude of the horizontal component of the splitting force.
Fig. 4.4: Contribution of 1352
106
Thus, when the mode of failure is diagonal splitting, there are two possibilities for the value of Pst;
i) when concrete controls,
Pst = ftebdt + mftcAph (4.8a)
or ii) when steel plate controls,
P= frisAph (4.8b)
4.3.1.5 Ultimate Load
The ultimate load, P, is determined using Equation 4.3. The contribution of P st, P Pph for
appropriate condition as discussed above is summarised in Table 4.3;
Mode ofFailure*
WebStrengthControl
Pst Pph P pv Comment
FS Steel Plate Astfy Aphfps Vs, f not contribute
FS Concrete Astfy Aphniftc Apvrnftc
DS Steel Plate Aphfps Aphfps Afp, f not contribute
DS Concrete ftsbdt+Aphnific Aphrnftc Apvmftc
Table 4.3: Contribution of Pst , Po and Pp„
(* Note: DS = Diagonal splitting; FS = Flexural shear)
f tdryp p
0.G7f bdCU C fYP t (d -c
P c
Ps t
Bars and Concrete Plate
SECTION FORCE EQUILIBRIUM
dc
d pcplate
thicknesstP
107
4.3.1.6 Depth of Compression Zone
The depth of the compression zone, dc is determined by considering the equilibrium of the horizontal
forces. A rectangular concrete stress block of intensity 0.67f, is assumed. Steel plate is considered
to resist both shear and flexural stresses.
Fig. 4.5: Determination of the compression depth, dc
Fig. 4.5 shows the cross section of the beam and the stress diagrams which are used in determining
the depth of the compression zone d c . For equilibrium;
108 .
Ascfyc + 0.67fbdc + fyp tp (dc —di) = Pe + fyp tpdpc (4.9)
where Aufy, and Pe are the forces due to the compression and tension bars, 0.67f„bd, is the
concrete compression force, and fyptp (dcd,) and fyptpdpc represent the compressive and tensile forces
in the plate respectively. In this case, the value Pm is depedent upon the assumed mode of failure
and web strength control, which is given in Table 4.3.
4.3.1.7 Solution Procedures
The method for determining web capacity of the beams as described above may be summarised as
follows;
1. Find a value of dc. In finding the value of d 0, an initial assumption with regard to the mode of
failure and the control of web strength must be made in order to consider the horizontal forces. The
value of dc may be calculated by the process of trial and error.
2. Find Pm by substituting the value of d c into an appropriate equation (as given in Table 4.3).
3a. Check the control of web strength (using the criteria given in Table 4.1). If the control of web
strength is correct as previously assumed (Step 1) then proceed to the next steps. If not, repeat Step
1 and make another assumption with regard to the control of web strength.
3b. Check the mode of failure (using the criteria given in Table 4.2). If mode of failure is correct as
previously assumed (Step 1), then proceed to the next steps. If not, repeat Step 1 and make another
109
assumption with regard to mode of failure.
4. Calculate the ultimate load by using Equation 4.3. Appropriate values of P so Pph and P given
in Table 4.3. If the web strength is controlled by steel plate, the value of f zero.
The application of the method of analysis is illustrated in Appendix A.
4.3.2 Flexural Strength
Flexural failure of ordinary reinforced concrete beams may be recognised by yielding and final
fracture of tensile reinforcement. Prior to failure, excessive deformation and significant vertical cracks
will be appeared in the maximum bending moment region.
A number of methods are available in predicting the flexural capacity of shallow and deep beams.
The most common method for shallow beams is using the strain compatibility approach. This
approach also has been suggested for application in deep beams (Subedi 1988). This concept is
based on the assumption that the strain at the critical cross section of the beam vary linearly with
the ultimate value of concrete strain of 0.0035 at the outermost of the compression zone.
In deep beams, the recommendations from the European Concrete Committee
(CEB-FIP 1970) is widely used. The recommendations are mainly based on the results of ultimate
load tests. In these recommendations, the flexural strength is assessed on the basis of suggested
expressions for the lever arm, which is expressed in term of depth and span of the beams, and the
area of tensile reinforcement.
force, Pp, and Pp, represent the tensile and compressive forces in the plate respectiveley.
0.0035
0.9x
pti
Ppt 2
t
dx7
dP
110
The beams tested in this project were provided with excessive tensile reinforcement, so the flexural
failure will not be the case. Therefore, it is suggested to use the strain compatibility method in
checking the flexural capacity of the beams.
Fig. 4.6 shows the cross section of a typical beam at the region of maximum bending moment,
together with the strain and stress diagrams which are used in this method. The steel plate is also
considered to resist flexural moment. The analytical procedure starts by using trial value for the
compression depth, x until the equilibrium condition for the horizontal forces in Equation 4.10 is
satisfied.
Psc Pc E Ppc = Pst E
(4.10)
where P„ and P 31 are the forces in the compression and tensile bars, P, is the concrete compressive
concrete & bars plate
SECTION STRAIN STRESS DISTRIBUTION
Fig. 4.6: Strain compatibility
(4.12b)
111
By the concept of strain compatibility, the bar strain in compression and tension and can be
determined from the strain diagram (Fig. 4.6). Thus;
e ss . 0.0035 (x—d1 x
and
est = 0.0035 (d—x)x
(4.11a)
(4.11b)
where es, and est refer to the strains in compression and tension bars. Having determined the strains,
the stresses and resulting forces in the bars can be evaluated by;
(4.12a)
fs = e 8 Es e s e S y
Ps = As fs (4.12c)
where fs , es and Es are bar stress, strain and elastic modulus, whilst As is the area of bars and Ps
is the corresponding force in the bars.
Similarly, the strain in compression and tension part of the plate can be determined. Thus;
112
epc
= 0035( X — dx)
• x
and
e =0• 0035(
dd,, + dx - x
)pt x
(4.13a)
(4.13b)
where ep, and ept are the strain in compression and tension part of the steel plate. The stresses and
forces in the plate are given by;
(4.14a)f = e E e s CP P P P YP
f = fyp e s > eP yp
where fp , ep and Ep are plate stress, strain and elastic modulus respectively.
By using the Equation 4.14, when the entire plate yields, then;
Ppt = fyp tp (dp+dx—x)
and
Ppc = fyp tp (x—dx)
(4.14b)
(4.15a)
(4.15b)
where P P forces in compression and tension part of the plate respectively.
Concrete compressive force, P, at failure can be computed from;
Pc = 0.67fccb(0.9x) (4.16)
The ultimate moment of resistance, M u at the mid-span section can be determined by;
113
= Pd + P (dp+ dx + x
)
Pd' - Pc(0.45x) - Ppc(d)-—+ x
)Pt 2 2
The ultimate load, P u for a two point load beam can be computed by employing;
Mu(4.17)
Pu2g,_
a(4.18)
4.3.3 Bearing Strength
Bearing failure is a common mode of failure in deep beams subjected to point loads. It occurs either
under the loaded areas or above the support, which is due to local high compressive stress. The
concrete directly under the loaded area is subjected to a biaxial compression state of stress, whilst
those above the support will be subjected to a biaxial compression-tension state of stress (Fig.4.7).
Under such conditions, therefore, the concrete's resistance to crushing and spalling is greater under
the load and less above the support. The actual capacity depends on how much strengthening is
provided at these stress concentration areas.
The beams in this project were subjected to very high stresses. In such condition, it is expected that
the failure due to bearing and crushing is most likely, eventhough some strengthening mechanisms
have been provided in these areas. In this case it is reasonable to use the suggested value of
bearing stresses for deep beams to be applied here.
114
comD-ComP
*71-7—o ;ension-comp.
Fig. 4.7: Elements under the load and above the support
The CEB-FIP Recommendations (1970) limit the bearing stress of a deep beams to 1.2f, at interior
supports and 0.8% at exterior supports, where f © is cylinder compressive strength of concrete. Taner
et. al (1977) suggested a lower value for this situation, i.e 0.7% at both under the loaded areas and
above the supports. Subedi (1988) suggested a limiting value of bearing stress of deep beams to
be 0.85f. under the load and 0.7f„ above the support.
A few recommendations above shows that they are not much different in this matter. Since Subedi's
suggestion is in the middle between the other two suggestions, therefore, this recommendation is
used in the case where there was no strengthening added to the bearing areas. When strdngthening
has been employed, a factor of 1.5 is appropriate to be included in the recommended value.
4.4 Cover to steel Plate
The minimum concrete cover to the steel plate seems to be one of the vital criteria in designing the
beams. For the single plated beams, the cover varied from 46 mm to 49 mm, depending on the plate
thicknesses, whilst double plated beams had 15 mm cover.
115
The question of what is the minimum concrete cover to the steel plate at this moment was not
experimentally verified. Nonetheless, from the 'tests, it was observed that in all single plated beams,
the cover was enough. This implies that no beams suffered the peeling-off of concrete at failure. For
the double plated beams, it was noticed that some of the beams had cover concrete peeled-off at
failure. This situation, however, occured at the same time with the existance of longitudinal cracks
in the beams (see Section 3.6.5). The longitudinal cracks is formed probably due to inadequate
detailing under the loading point.
In the proposed method of analysis, it was assumed that the steel plate effectively utilised to its
yielding value. In such assumption, therefore, the concrete cover surrounding it must be stiff in order
to prevent the plate from buckling. The best and simple approximation to quantify the thickness of
concrete cover is by using the concept of rigidity. As it can be visualised from Fig. 4.8, it is clear that,
under the action of the load (the load is idealised as axial compression), both the plate and concrete
tend to bend (buckle). Therefore, to prevent the plate from buckling, the flexural rigidity of the
concrete cover must be at equal or bigger than that of steel plate, thus;
[
Et: [ Et;
12(1 —2
v2)I,„,„c 12(1 — v2)10,0(4.19a)
or the minimum concrete cover, t, required may be expressed as;
32
3 (1 -vo)to � tnto
(1 -Vp2)
(4.19b)
116
Fig. 4.8: Concrete cover preventing the plate from buckling
The calculated value of the concrete cover will be presented in Chapter Six.
4.5 Methods of Shear Connection
When steel plates are embedded in concrete, the composite action between the structural steel and
concrete is necessary to be maintained by the provision of shear connectors. For the case of fully
encased steel I beams in concrete, the natural bond between steel and concrete is also a factor
which has to be considered. The next subsections will discuss these two methods as a means of
shear connection for beams tested in this project. The available literature on the encased steel I
beams in concrete will be appropriate to be used for discussion.
4.5.1 Bond
In encased steel (I beams or steel plate) in concrete without shear connectors, the interaction is
completely reliant upon bond. The transfer of shear by bond takes place in the compression zone,
Elastic
Neutral AxisPerimeter forcalculating bond
stress
Reinforcement
L_.... - - --I
Fig. 4.9: Effective perimeter of steel I-beam in concrete
117
so that the effective perimeter of the steel beam (or steel plate) profile for shear transfer is that
above the elastic neutral axis as shown in Fig. 4.9 (Wong 1963, Hawkins 1973, Davies 1975).
Wong (1963), suggested the allowable bond stress, s h for encased steel joists in concrete for
elastic design may be taken as 80 psi (0.55 Nimm 2). Later, Hawkins (1973) suggested a higher
value for the encased I beams. He suggested the value of 100 psi (0.69 NI/me). The applied
bond stress, sh in the beams is calculated from the following equation;
sb = vhb
oi
where vh is horizontal shear stress of the beam and o' is the steel perimeter above the elastic
neutral axis (Fig. 4.9). vh is given by;
V(a i yl) vh -
1,b
(4.20)
(4.21)
118
where I, is second moment of area of the transformed composite section and A'y' is statical moment
of transformed concrete area about the neutral axis of the composite section.
In British Code BS 5400 Part 5 (1979), the bond stress in encased steel beams is limited to 0.5
NI/me. The bond may be assumed to be developed uniformly only over both sides of the web and
the upper surface of the top flange of the steel beams. The soffits of the steel flange is excluded
from consideration in order to give a safety factor to the possibility of poor compaction of concrete.
These values showed that the bond stress is very small and can only be relied in the beams within
its elastic range (Johnson 1975). At the higher loads the bond stresses have little meaning due to
the development of cracking and local bond failure (Johnson 1968). In this effect, since the beams
in this research were subjected to the loads in excess of its elastic range, therefore, the beams have
to be provided with shear connectors.
4.5.2 Cut-outs as Shear Connectors
The provision of shear connectors in composite beams is for two main purposes;
1) to transfer shear between the steel and concrete (i.e to limit the horizontal movement) and,
ii) to prevent vertical separation between the steel and the concrete.
The detailed make-up of a connector must be such that both functions can be achieved. There are
many type of connectors are available, ranging from the helical, channel, bar, 'tension' and the most
widely used is headed stud connector (Fig. 4.10)
( a ) Helical
(e) Tension
119
:71 J14_ JLLoad
(b) Channel
••••n•
FIT(c) Stud
n.) Loadra-13"`
(d) Sar
Fig. 4.10: Types of shear connectors in composite constructions (Davies 1975)
In this project, the provision of semi circular cut-outs at the upper and bottom edges of steel plate
is to act as shear connector (Fig. 4.11). These cut-outs were similar to the perfobond rib connector
which has been used sucessfully as shear connector in the construction of a composite bridge in
Venezuela (Veldanda & Hosain 1992). As shown in Fig 4.12, this perfobond rib connector is a flat
steel plate containing a number of holes. As it can be seen from both figures (Figs. 4.11 and 4.12),
the concrete plugs in the cut-outs and the holes will provide an effective resistance to the horizontal
shear.
60
120
tp-.._..
Fig. 4.11: Cut-outs as shear connectors
-12
Fig. 4.12: Perfobond rib connector (Veldanda & Hosain 1992)
The number of shear connectors required in ordinary composite beams is based on ultimate
strength behaviour. The strength of connector, P pu is determined by push-out test (BS 5400
NcVh
Ppu(4.22)
a1-
resisting force, applied
V T- \ iorce,V
steel plate,thickness, tp
121
1979). The number of connectors, Nic then defined by;
In this project, there was no push-out test carried out. However, the number of cut-out required can
be determined as follows. Referring to Fig. 4.13, total applied shear force in the region of shear
stress is (virtually the cut-outs are effective only in this region);
V = Vha tp (4.23)
The resistance, Vr to this applied force will be;
V, = Nco doc,tp T c (4.24)
where N, and d„ is the number and diameter of the cut-outs, and T, is shear strength of concrete
under the state of pure shear behaviour which is 0.08f, (Bresler & Pister 1958).
Fig. 4.13: Determination of the number of cut-outs
122
By equating the total applied shear force to the resistance force, the number of cut-out required
is given by;
Vko - ha
0.08 fcc1,1
vha_ 0.068 fcucico
The required number of cut-outs must be evenly spaced in the region of shear force. For the case
of two point loads, where there is a region of zero shear force, it is recommended to use at least
minimum number of cut-outs. BS 5400 Part 5 (1979), recommends that the maximum longitudinal
spacing of shear connectors in ordinary composite beams should be not greater than 600 mm. This
recommendation is suggested to be used in this project. The calculated number of the cut-outs will
be presented in Chapter Six.
4.6 Serviceability of The Beams
Having determined the strength of the beams, checks must be made to ensure whether its
serviceability criteria is within the acceptable limits. Deflection and cracking are two important things
in this case, which will be discussed in the following sub-sections.
4.6.1 Deflection
The deflection of the beams can be calculated using the transformed section method. The use of
transformed method is consistent with the previous calculation which assumed a complete interaction
between the steel and concrete.
(4.25)
P/201. (1-23)L /2 ft
bending deformation
shear deformation
123
The classical Moment Area Method can be used in calculating the deflections due to bending 88,
both under the load and at mid span. Since the beams are subjected to high shear force, the
deflection due to shear force 8,„ has also to be considered. For the rectangular beam subjected to
two symmetrical point loads, P/2 (shown in Fig. 4.14), total deflection ST under the load is given by;
a,
_ L _
8V
t 3v
Fig. 4.14: Deflection of the beam
124
EIT = 5B + 81,
8 _ P(1342 1 L (DL) + 3)93 L
r Ecl. [4 3 f 5Gcbh(4.26a)
and deflection at mid span is given by (since the shear force at mid span is zero, the deflection due
to shear is same as under the load);
o r -
(0.125 - 112-)P13L36 + 3R3L
2EG./e 5 Gcbh
(4.26b)
where E, and G, are elastic and shear modulus of concrete respectively, and I, is effective moment
of inertia of the section.
The effective moment of inertia in calculating the deflection varies a great deal throughout the
member and received significant study (Yu & Winter 1957, Branson 1972). It has been shown (Park
& Paulay 1975, Wang & Salmon 1985), that the actual deflection of reinforced concrete beams lies
within the computed values based on I transformed cracked section and I gross uncracked section.
The use of transformed cracked section overestimates the deflection and the use of gross section
underestimates the deflection. ACI Code 318-83 (1983) recommends the following expression for
the effective moment of inertia, I, to be used in calculating the deflection;
MIe = (
M—E)3 I + 1 - (—E-r)3 I 1Ma g [
Ma cr
where
1 9 = moment of inertia of gross uncracked section,
I,= moment of inertia of the cracked section transformed to concrete,
(4.27)
125
I cr= moment of inertia of the cracked section transformed to concrete,
Ma = maximum moment in member at stage at which the deflection is being computed and
Mcr= moment at first cracking, is given by frldy,
where fr is modulus of rupture of concrete and y, is distance from centroidal axis of gross section to
the extreme tension fibre. Modulus of rupture of concrete, fr can be taken as 1.5f, (Kong & Evans
1989).
The above suggested formula for moment of inertia will be used in calculating the deflection of the
beams in this project.
4.6.2 Cracking
The maximum width of cracks is one of the major serviceability requirements for concrete and
encased steel structures. Wide cracks are aesthetically unpleasant and may impair durability of the
structures by exposing the steel to corrosive agents.
To the best of author's knowledges, there has been no research on control of cracking in encased
beams. For consistency, the rule for such beams is the same as that in BS 8110 (1985) for the
reinforced concrete beams.
This section will propose a simple method in calculating the maximum diagonal crack width of the
beams in this project. The shear panel area is shown in Fig. 4.15. When the crack starts to appear,
concrete will relieve the strain and the applied force is taken up by the steel plate. Provided the bond
between the concrete and plate is sufficient (which is consistent with previous assumptions), the
.2'T
xY
t
(b) element at the centre
126
width of the crack, co will be equal to the total elongation of steel plate in the direction normal to the
crack, thus;
(0 = Xdep
XdO
(4.28)_
EP
where ; is strain of the steel plate in direction normal to the crack and x d is diagonal length of shear
panel as shown in Fig. 4.15.
(a) Shear panel area
Fig. 4.15: Maximum diagonal crack width
TxY
(4.29)
127
If the maximum crack width is assumed to occur in middle of shear panel (this assumption is
consistent with observation), then the shear stress at this location is given by;
where dp and tp are effective depth and thickness of the plate respectively.
In the state of pure shear behaviour, ; I, is equal to ay, hence from Equations 4.28 and 4.29, the
maximum diagonal crack width may be expressed as;
3 Pxd_4 Ed t
P P
co (4.30)
128
CHAPTER FIVE
FINITE ELEMENT ANALYSIS OF THE BEAMS USING ABAQUS
5.1 Introduction
Following its appearance in the mid 1950s (Clough 1980), the finite element method (FEM) has
become the most widely used numerical technique in engineering analysis. A decade after its
inception, this powerful computational tool began to be applied to the analysis of concrete structures.
The earliest published application of the FEM to reinforced concrete was by Ngo and Scordelis in
1967, where linear elastic analysis was performed to simple beams. With the development in
understanding the behaviour of plain and reinforced concrete under multiaxial stress states together
with the advent of powerful computers, the method has made a substantial progress on the non-
linear analysis. Of the many outstanding research works in this respect were, for example those
accomplished by Nielson (1968), Kupfer et. al (1969, 1973), Jofriet and McNeice (1971), Hand et.
al (1973), Suidan and Schnobrich (1973), Phillips and Zienkiewicz (1976), Vecchio (1989). The
successful application of non-linear FEM to the analysis of reinforced concrete structures depends
on realistic descriptions of constitutive relations for elastic and inelastic response under combined
stress state, and failure criteria for the concrete, steel, bond and aggregate interlock. An excellent
discussion of the application of FEM to reinforced concrete structures is given in the State-of-Art
Report by the ASCE Task Committee on Finite Element Analysis of Reinforced Concrete Structures
(1982) which will not be repeated here.
For this study, the application of non linear finite element analysis to the test beams was carried out
by using a software package named ABAQUS (1989). The main objectives of this work are to
129
acquire a working knowledge on the theory of FEM and to study the response of the beams by using
this method, in comparison with those obtained experimentally. The work was only a supplementary
work, therefore, the presentation of this chapter is limited within that scope.
The next sections will discuss the general description of the package, idealization of the test beams,
constitutive relationships of the materials and solution procedures. Analysis results for the beams
will be given in Chapter Six.
5.2 General Description of ABAQUS
ABAQUS was developed by Hibbitt, Karlsson & Sorensen Inc. (1989). It was designed as a flexible
tool for numerical modelling of structural response. The ABAQUS system is capable of analysing
linear, non-linear, dynamic, heat transfer and pore fluid diffusion problems. The package contains
many type of elements in its library, such as truss element, plane stress and plane strain elements,
beam element, axisymmetric element, membrane element and user defined element. ABAQUS also
contains a wide range of both linear and non-linear material types which cover most engineering
materials. In such situation, the package is capable of handling virtually almost all types of structural
problems.
In using ABAQUS, a user has to provide a 'data deck' which will describe the problem so that
ABAQUS can provide an analysis. The data deck contains 'model data' and 'history data'. Model
data define a finite element model: the elements, nodes, element properties, material definition,
boundary conditions and so on-any data that specify the model itself. History data define what
happens to the model, i.e the sequence of events or loadings for which the model's response is
130
sought. This history is divided, by the user, into 'steps'. Each step is a period of response of a
particular type of the load. For output request, ABAQUS can provide the printed results of element
variables (i.e stress, strain etc.) and nodal variables (i.e displacements and reaction forces). The
contour plots showing the variation of stress concentrations of the structures can also be produced.
For linear problems, the analysis is straight forward, but for non-linear analysis, some control
theparameters have to be included to ensure thatAnon-linear problem is satisfied. For non-linear
analysis, it is usually necessary to divide the step into a number of increments during which the
loads are changed gradually. The accuracy in which the equilibrium must be satisfied at each node
in non-linear analysis is specified by force and/or moment tolerance options. Choosing these
tolerances is absolutely critical in obtaining good, and at the same time economical results. Very tight
tolerances will cost more iterations, while loose tolerances will give bad answers.
Further details on non-linear analysis implemented in the package, especially the non-linearity of the
materials, will be described through the discussion of its application to the test beams.
5.3 Analytical Models of The Test Beams
5.3.1 General Consideration and Assumption
It was considered that the stress variation across the thickness of the beam is negligible, i.e the state
of plane stress conditions exists. This condition is practically achieved when the thickness of
structural member is small compared with other dimensions. Perfect bond between the concrete and
the steel plate was further assumed (this assumption is consistent with method of analysis). In such
131
assumption, therefore, the idealisation meshes of steel plate will be overlapping and coincide with
those of the concrete. Since all the beams in this project were subjected to symmetrical loading
conditions, hence, the model only consists half of the beams.
5.3.2 Idealization of The Test Beams
From the extensive element library available in ABAQUS, only one particular type of element has
been selected, since it is proved to be satisfactory to model the concrete and steel plate. This
element, named as CPS4 is a four node bilinear plane stress element. The basic formulation of the
element is given in many finite element text books (Zienkiewicz 1977, Cook 1981, Rockey et. al
1983, Dawe 1984). The tensile and compressive reinforcements were modelled by using a REBAR
option. In ABAQUS, REBAR option is used to model the reinforcement . Rebar isia‘one dimensional
strain element which is defined in embedded surface to model the reinforcement. This element is
superimposed on the mesh of plain concrete elements, and used with standard metal plasticity
models that describe the behaviour of the rebar material. The effects associated with the
rebar/concrete interface, such as bond slip and dowel action, can be modelled approximately by
introducing some 'tension stiffening' to simulate load transfer across crack through rebar.
The finite element idealisation for all the beams is shown in Fig. 5.1. As it is seen from the figure,
the average size of an element in shear panel area is 50 mm x 51 mm. At the stress concentration
areas (i.e under the load and above the support), finer meshes have been employed to allow a more
detail study of these regions. The meshes for steel plate overlap with those of the concrete in which
they were share the same nodes but with different element numbers.
132
In this case, both sides of concrete cover were combined together (Fig. 5.1a) The concrete element
were numbered from 1 to 124 (Fig. 5.1b). In the input data, this is known as CONCRETE. Steel plate
elements were numbered from 142 to 231, in which they share the same nodes with the concrete
at node numbers 19 to 117 (Fig. 5.1d). Figs. 5.1c and 5.1e show the elements and nodes numbers
of the concrete below and above the plate (see Fig. 5.1a). In the input data, these were known as
CONCRETE2 and CONCRETE3 respectively. However, their material descriptions were same as
those of CONCRETE. Tensile reinforcements were superimposed at the position of node numbers
19 to 36, whilst compressive reinforcements were at the position of nodes 117 to 134. The presence
of the cut-outs in the plate was ignored.
The idealization adopted here is one of the approach which can be handled by ABAQUS. This
approach is simple and easy to use in which perfect bond has to be assumed between the plate and
the concrete. Another approach is by using an option MPC (Multi-point Constraints). This option
allows constraints to be imposed between different degrees of freedom of the model. Details of this
approach will not be discussed here.
5.3.3 Constitutive Relationships
The basic information required in modelling of non-linear behaviour of the beams in this project is
the constitutive relations and failure theories which adequately describe the characteristics of
concrete, steel plate and reinforcement upon loading.
133
CONCRETE 3
PLATE(a) Beam idealization
CONCRETE 1
CONCRETE 2
Element number
44
Node nuf
8050,4c25 00 110 135 165 175
.) @ (17:9)li
108 109 110 111
(-,-3-0 0/) g (139) (11 (41) (142) (:
112 113 114 115 120 121 12 2 123124
i,
' '3 94 95 96 97 98 99 100 101 102 103 104 105 106 107I'
h ,79 BO 81 82 83 84 85 86 87 88 89 90 91 92
I(
63 64 65 66 67 613 69 70 71 72 73 74 76 76 77
49 49 50 51 52 53 54 55 56 57 58 59 GO GI 62f
)
33 34 35 36 37 38 33 40 41 42 43 44 45 46 47I
18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
010 C)(7) 5 6 7. 8 (9) 10) 11 (12) 63) (14) 65) OW (12) (
1175 mm
(b) Concretel
129 130 131 132 133 134 135 136 137 138 139 140 141
D
(c) Concrete2
217 218 219 220 221 222 223 224 225 226 227 228 229 230 231
202 203 204 205 206 207 208 209 210 211 212 213 214 215 216
187 188 189 190 191 192 193 194 195 196 197 198 • 199 200 201
172 173 174 175 176 177 178 179 180 181 182 183 184 185 186
157 158 159 160 161 162 163 164 165 166 16 7 168 169 170 171
142 143 144 145 146 147 148 149 150 151 152 153 154 155 156
(d) Steel plate
233 2475
— 232 234 235 _236 237 238 239 CNI 0.1 244 I 245 246 248
(e) Concrete3
Fig. 5.1: The idealization of test beams
Start of inelasticbehavior
Unload /reload response
Idealised ( elastic) unload! reload responseStrain
strain
Softening Cracking failure
Stress
Strain, eeut E
"tension stiffening"curve
134
stress
(
Failure point incompression(peak stress)
Fig. 5.2a: Uniaxial behaviour of plain concrete (ABAQUS 1989)
Stress,
7
Failure point
Fig. 5.2b: Concrete in tension (ABAQUS 1989)
135
5.3.3.1 Non-linear Constitutive Relation for Concrete
The tensile and compressive responses of concrete that are incorporated in the model are illustrated
by the uniaxial response of a specimen as shown in Fig. 5.2a.
When concrete is loaded in compression it initially exhibits elastic response. As the stress is
increased some non-recoverable (inelastic) straining occurs, and the response of the material
softens. After the material softens, an ultimate stress is reached where it can no longer carry any
stress. The behaviour of concrete in tension is shown by its elastic response up to about 7%-10%
of ultimate compressive stress, after which the cracks will form. Fig. 5.2b shows the behaviour of
concrete in tension.
Under the action of multiaxial stress states, the behaviour of concrete was modelled by the failure
surface. The concrete failure surface in plane stress analysis is shown in Fig. 5.3. This model is
intended for the application of relatively monotonic loading cases only.
A "compression" failure surface forms the basis of the model for the non-linear response when the
principal stresses are dominantly compressive. In tension (including tension-compression zone),
cracking is assumed to occur when the stress reaches a failure surface which is called the "crack
detection" surface. Once the crack occurs, ABAQUS uses a smeared crack approach in which
constitutive calculations are performed independently at each integration point of the finite element
model, and the presence of cracks enters into these calculations by the way that the cracks effect
the stress and material stiffness associated with integration points.
136
"crack detection" surface
uniaxial tension
biaxialtension
//II
compressicn /surface
biaxial compression
Fig. 5.3: Concrete failure surface in plane stress (ABAQUS 1989)
5.3.3.1.1 Concrete Input Option
In ABAQUS, three material properties options are required for non-linear analysis of concrete. The
ELASTIC option is used to give elastic properties, the CONCRETE option is used to describe
compressive stress-strain relationship outside the elastic range and the TENSION STIFFENING
option is used to define the concrete's post failure behaviour after cracking. This TENSION
STIFFENING option is primarily intended to allow some effects on the interaction of reinforcement
with concrete and to allow the smearing of cracking in the model. The SHEAR RETENTION sub-
option was also used in the input data to describe the reduction of shear modulus associated with
crack surfaces as a result of aggregate interlock and the effect of dowel action. Shear retention
option assumes that the shear stiffness of open cracks reduces linearly to zero as the crack opening
increases.
137
The list of concrete input data for Beam 1S4 is given below as a typical data of all other beams.
*MATERIAL, NAME=CONCRETE*ELASTIC, TYP E=ISOTROP IC21500,0.15*CONCRETE20.0,0.048.3,0.00105*FAILURE RATIOS1.125,0.08,1.20,0.333*TENSION STIFFENING0.0,1.0E-3*SHEAR RETENTION1.0,0.0,1.0,0.0
This example presents that the elastic modulus of concrete is 21500 N/rnm 2 and Poisson's ratio is
0.15. The uniaxial compressive strength is 48.3 Nimm 2 and the corresponding plastic strain is
0.00105. On the uniaxial stress-strain curve of the concrete, the relationship is assumed linear until
the stress reaches 20.0 Nime, at which plastic strain is zero. The input data in FAILURE RATIO
represent that the biaxial to uniaxial compressive strength ratio is 1.125, the uniaxial tension to
uniaxial compressive strength ratio is 0.08, the ratio of plastic strain in biaxial compression to uniaxial
compression is 1.20, and the cracking failure ratio in plane stress with one principal stress at
compressive failure is 0.333. The TENSION STIFFENING data denote that the fraction of remaining
stress to stress at cracking is zero, whilst the absolute value of the direct strain minus the direct
strain at cracking is 1.0 x 10E-3. The values of the maximum direct strain across the crack, e a' for
dry and wet concrete are zero and their corresponding values of (1-e/ema ) are 1.0. In many cases,
when the actual data was not available, the default values were used.
5.3.3.2 Constitutive Relation for Steel
The behaviour of both steel plate and reinforcing bar are approximated by an elastic-perfect plastic
138
stress-strain relationship. ABAQUS recognises the effect of strain hardening of the steel, however,
since the data from the test could not define the curve precisely, therefore an elastic-perfect plastic
relationship was adopted. The stress-strain relationship of this model is shown in Fig. 5.4.
_
Stress1
0.- Strain
Fig. 5.4: Stress-strain relationship for steel
5.3.3.2.1 Steel Input Option
For non-linear analysis of the steel, two material properties are required. The ELASTIC option is
used to define linear elastic modulus and the PLASTIC option is required to specify the yield value
of the material. The list of steel input option is for Beam 1S4 is given below as an example;
*MATERIAL, NAME=STEEL*ELASTIC
199000, 0.30*PLASTIC245.0
139
The example indicates that the elastic modulus of the plate is 199 kN/me, the Poisson's ratio is
0.30 and the yield stress is 245 N/mrre.
5.4 Solution Procedures
ABAQUS uses Newton's Method as a numerical technique for solving non-linear equilibrium
equations. The non-linear solution is then obtained by performing a succession of linear
approximation until the constitutive relationships and conditions of equilibrium are satisfied within an
acceptable error.
In ABAQUS, the problem of getting a convergent solution at minimum cost for non-linear analysis
is handled by 'automatic control of time stepping'. The user only defines a step and certain tolerance
or error measures. The step is divided into increments, by user control or by automatic program
control. In each non-linear increment, ABAQUS iterates for equilibrium.
A static stress analysis was adopted to the test beams in which the loads were automatically applied
in increments until the 'ultimate' load is achieved. The force tolerance (PTOL option) which is the
basic tolerance measure for the solution of equilibrium equations at each increment, was taken as
approximately 1% of the experimental failure load. The maximum number of iteration in an increment
was specified to 6, and the maximum number of increment allowed was 70. The load proportionality
factor was set at 1.20 of the experimental failure load, in which the analysis will end when it reaches
this factor.
140
The example of solution control parameters for Beam 1S4 is given below;
*STATIC, PTOL=4000, RIKS0.2,1.0„1.20*STEP, INC=70, SUBMAX*DLOAD116,P3,38117,P3,38
118,P3,38119,P3,38240,P3,38241,P3,38
242,P3,38243,P3,38
In this case, the ultimate failure load of the beam is 790 kN, so that the load on the half model will
be 395 kN. The value of PTOL is set to 4 IN (4000 N) which is about 1% of the actual force. Since
considerable non-linearity is expected in the response, including the situation when the concrete
cracks, the RIKS option is used with automatic incrementation. With the RIKS option, the load data
and solution parameters serve only to give an estimate of the initial increment of load. In this case,
it seemed reasonable to apply an initial load of about 8 Nime over the loading patch of 100 mm
x 100 mm (equivalent to a point load of 80 kN). This can be accomplished by specifying a distributed
load (known as P3) of 38 Nime over the elements number 116 to 119 and 240 to 243 and an initial
time increment of 0.2 for a time period of 1.0. The analysis is terminated when the load
proportionality factor reaches 1.20, corresponding to a total load on the beam of 912 kN. The
distributed type of load is chosen over the point load in order to avoid a premature local crushing
under the load. The SUBMAX parameter is also included on the STEP card. This option forces
ABAOUS to continue iterating up to the maximum iterations allowed before it subdivides the
increment because of failure to achieve equilibrium.
The load level at which the analysis was terminated as the solution failed to converge due to
141
numerical instability is regarded as the analytical failure load of the beam.
5.5 Analysis Results for The Beams
The analysis results of the test beams such as deformations, stresses, strains and the ultimate loads
will be discussed in Chapter Six.
142
CHAPTER SIX
BEHAVIOUR OF THE BEAMS:
TEST RESULTS, ANALYSIS AND DISCUSSION
6.1 Introduction
This chapter presents a detail discussion on the test results of the beams. The discussion includes
the modes of failure, ultimate strength, cracking strength, beams' deformation, crack width and other
related factors. The discussion is carried out through comparison between the results determined
by the proposed method of analysis (see Chapter Four) with those experimentally obtained. The
results of finite element analysis of the beams are also discussed.
6.2 Ultimate Behaviour of Test Beams
6.2.1 Mode of Failure
Table 6.1 shows the observed and predicted mode of failure for each beam. In general, the predicted
mode of failure is in good agreement with those observed from the test. The observed modes of
failure that have been identified are;
i) diagonal splitting,
ii) bearing and
iii) bearing with the longitudinal cracks (along the top-cast surface of the beam and peeling-off of
concrete).
t
(a) Formation of diagonal splitting crack
........... -
notional hinge
I
1
I
I
1- - _
143
6.2.1.1 Diagonal Splitting
The diagonal splitting mode of failure is a common mode of failure in deep beams (Subedi 1988,
1992). It occurs in beams with shear span/depth ratio in the range of 0.5-1.0 and with a moderate
amount of web reinforcement. The failure is identified with the splitting of inclined crack between the
support and the loading point, as the limiting tensile strength of the web is reached. The appearance
of the cracks is usually accompanied by an audible sound of splitting. Just before the failure, a
dominant crack extends between the support and the loading patch. Notional hinges form at the two
ends of the splitting crack. To complete the failure mechanism, the crushing and/or spalling of the
concrete will take place at the notional hinges. The tensile reinforcements do not yield at failure. The
mechanism of diagonal splitting mode of failure is illustrated in Fig 6.1.
(b) Completion of failure mechanism
Fig. 6.1: Mechanism of diagonal splitting mode of failure
144
Diagonal splitting was the primary cause of failure of the beams 1S2, 1S4, 2S2, 2S4, 2D2, 2D4.
Three other beams, namely 1S6, 2S6 and 2D6 were also observed to follow the diagonal splitting
failure criterion until the last stage. At the last stage, instead of the notional hinges being formed due
to flexure and shear, crushing due to excessive bearing stress was observed. This is evident from
the failure loads for these beams. For 1S6 and 206 the failure loads are between the predicted
range of bearing and shear. For 2S6 the failure load is closer to both bearing and shear capacities.
They are identified as failing in diagonal splitting and bearing modes.
The results of strains in tensile reinforcements for these beams (see Section 3.6.5) indicate that the
reinforcements were not fully stressed near the support, when the maximum shear capacities for
beams were reached. The range of tensile strain in the main bars were measured between 1900
micro strain to 2100 micro strain as compared to the yield strain of the bars, 2300 micro strain
(Beam 1S6) and 2610 micro strain (Beams 2S6 and 206). This agrees well with the concept of
diagonal splitting.
The strength of the web in diagonal splitting mode of failure may be controlled by either concrete
or steel plate. In order for the steel plate to control the web strength, a sufficient amount of steel
plate will be required. Beams 1S4, 2S4, 2S6, 202 and 2D4 satisfy this condition. The control of web
strength by steel plate means that at the time of splitting, the splitting force is taken by steel plate.
The failure occurs when the plate (or some parts of the plate) reaches its yield capacity. This
behaviour is characterized by the increase of principal strain in the web area of steel plate. The
measured strain behaviour of the steel plate in these beams (shown in Section 3.6.5) reflects this
behaviour. For example in Beam 1S4, the principal strain for the plate at position R7 (see Fig. 3.12b)
was measured to be 2000 micro-strain.
145
In the case of concrete control, once the concrete reaches its tensile strength capacity in biaxial
tension-compression, the splitting will occur and this will determine the ultimate strength of the beam.
According to analysis, this would mean that at the occurrence of the splitting, there will be a large
increase in strain in the steel plate. However, as it can be seen from the load-strain curve of the
Beams 1S2 and 282 (see Figs. 3.9 and 3.28 respectively), this behaviour was not clearly shown.
However, the graphs do show that in many parts of the plate, yielding had occurred earlier before
the failure load was attained. But the strain increment was gradual rather than sudden.
6.2.1.2 Bearing
Bearing is a common mode of failure in beams with small shear-span/depth ratio (Kong et. al l 970,
Subedi et. al l992) as the results of high compressive stress build up locally. When bearing failure
occurs, the full strength capacity of the beams may not be achieved. Beam 288 failed in bearing
under the loading area. Beams 186, 2S6 and 206 also have been observed crushing locally (i.e
under the loads and above the support). However, in all these beams, this situation was observed
simultaneously as the beams would fail in diagonal splitting.
The predicted mode of failure of the beams 1D2, 1D4, 1D6, 3D4 and 3D6 were bearing. From the
observations, this was not solely the cause of failure of these beams. As described in Section 3.6.5,
Beams 102, 104 and 1D6 failed by the formation of longitudinal cracks along the top-cast surface
of the beam and consequently some concrete crushing under the load. The peeling-off of the
concrete took place as the result of this longitudinal crack. This behaviour, however, was observed
at the later stage. At the beginning, the beams had developed the diagonal splitting cracks between
the supports and the loading points. The beams failed earlier than expected due to inadequate
146
detailing provided under the load.
One way of avoiding such failures, is by improving detailing at these stress concentration areas, as
was carried out in Second Series Beams. As a result, all the beams in this series had improved their
capacity compared to their counterparts in the first series.
6.2.2 Ultimate Strength: Proposed Method
The ultimate strength of the beams is given in Table 6.1. As it can be seen, where bearing failure
is prevented, the failure load of the beam is increased as the thickness of the plate increased.
The table also shows the predicted ultimate loads of test beams.The prediction of these loads was
carried out by comparing the strength of the beams in different modes of failure, namely flexural
capacity, bearing capacity and shear capacity. The lesser of these values is considered as the
predicted ultimate load of the beams. The individual load carrying capacities of the beam was
determined according to the methods of analysis presented in Chapter Four. In determining the
capacity of the double plated beams, the same formulae was applied but the thickness of the plate
was doubled.
Table 6.1 shows a good agreement between the predicted and the observed ultimate load of the
beams. The mean value and coefficient of variation (CV) of the ratios of the predicted/measured
ultimate loads are 0.82 and 14.89% respectively.
A close examination of Table 6.1 shows that the predicted failure loads of the Beams 1S2 and 2S2
147
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148
are less about 40% than that of the test results. In both cases, the predicted mode of failure was
diagonal splitting with concrete controlling the web strength. This discrepancy means that the method
of analysis underestimates the ultimate load when the concrete control concept is used. As pointed
out in Section 6.2.1.1, according to the concept, at the time of splitting there should be a sudden
large increases in strain in steel plate, but from the strain results this was not the case. This
disagreement would possibly affect the predicted ultimate load. This, however, needs further
verification.
The predicted ultimate loads for other beams compare well with the test results.
6.2.3 Ultimate Strength: 'BS 8110 (1985) Method'
The ultimate strength of the beams were also calculated by the method suggested by BS 8110
(1985). It should be emphasized that, BS 8110 (1985), however, does not give any recommendation
for the analysis of the types of beam investigated in this study. The method adopted here is only
based on the general concept of determining shear capacity of reinforced concrete beams as
suggested in the BS 8110 (1985).
The ultimate shear strength of reinforced concrete beam is a direct summation of V, and V,, where
V, is the strength provided by concrete and V, is the strength provided by shear reinforcement. The
concrete contribution, V, can be calculated by using the suggested expression (as given in Chapter
Two (Section 2.3.1));
149
Vc0.27 f) 113 100As
) ir3 400
cu (--1 )1I4bdYm bd 7
The enhancement factor of 2(d/a) is applicable in the equation since the aid <2.0.
In BS 8110 (1985), the strength provided by shear reinforcement is calculated by the truss analogy
method which requires the stirrup to be yielded (see Section 2.3.2). By using the same philosophy,
accordingly, the strength provided by steel plate, Vsp may be taken as the full capacity of the plate
in shear, which is given by (Hencky-Mises Criterion);
= ( -113-)dptp (6.1)
where fyp is yield stress of the plate, and d p and tp are effective depth and thickness of the plate.
Table 6.2 gives predicted shear capacity of the beams as calculated by this approach. Predicted
ultimate load obtained by the proposed method of analysis is also given for comparison. In general,
a good correlation is obtained between the experimental ultimate load and the loads predicted by
the BS 8110 Method. The ratios of P uanalysifiutem obtained by both analytical methods in many cases
are almost identical. For example the ratios of P ua,4sis/Putest of Beams 184 is 0.75 in both cases. This
suggests that, the 'BS 8110 Method' is capable of predicting the shear capacity of the beams.
However, the assumptions with regard to the mode of failure and method of resistance in BS 8110
(1985) need to be examined for plate reinforced beams.
(2.9)
150
Beam TEST ANALY. 'BS 8110 METHOD' 2V,/
Pcr
P, amy/
Pu test
Fail.LoadP
Diag.CrackLoadP„ (kN)
ShearLoad
Pu3(kN)
V,(kN)
V(kN) Load
Pu4=2(V,i-Vs„)
Pro-posed
BS811C
1S2 580 1 20 316 93 78 342 1.55 0.54 0.59
1S4 710 180 530 93 175 536 1.0 3 0.75 0.75
1S6 790 300 860 110 325 870 0.73 1.09 1.10
1D2 535 260 445 78 156 468 0.60 - -
104 520 260 913 91 350 882 0.70 - -
1D6 515 300 1497 89 651 1480 0.59 - -
2S2 590 140 302 92 81 346 1.16 0.51 0.59
2S4 605 200 426 83 139 444 0.83 0.70 0.73
2S6 885 220 892 104 327 862 0.95 1.01 0.97
2S8 938 390 1003 104 370 948 0.53 - -
202 665 220 473 82 162 488 0.75 0.71 0.73
2D4 875 300 798 94 278 744 0.63 0.91 0.85
206 1120 340 1529 94 655 1498 0.55 1.36. 1.34.
304 660 240 978 81 386 934 0.68 - -
306 660 300 1591 83 637 1440 0.55 - -
ean= 0.79C.V=. 2 7. 19 %
Table 6.2: Comparison of predicted shear capacity and cracking strength
Note:Comparisons for Beams 1D2, 1D4, 1D6, 2S8, 304 and 3D6 cannot be made because they failedin different mode of failure.
*Comparisons are not strictly correct because the beam failed in combined mode of failure.
151
6.2.4 Inclined Cracking Strength
Results of the diagonal cracking strength of the beams are tabulated in Table 6.1. The figures in
brackets alongside the cracking load are the percentage of the experimental failure loads. From the
table it can be seen that the diagonal cracking is found to vary between 24 and 58 percent of the
failure load for all beams. In general, the diagonal cracking load increases with the increase in the
failure load of the beam.
In designing conventional reinforced concrete beam without web reinforcement, the diagonal
cracking load is generally considered as the ultimate load. This is simply because the margin of
safety above the cracking load is highly inconsistent and unpredictable. If the same design basis is
applied to the beams in this investigation, it is desirable to predict the diagonal cracking load. In this
case, therefore, expression to evaluate shear capacity of the concrete (Equation 2.9) suggested by
BS 8110 (1985) is taken as diagonal cracking strength of the beam. The computed values are
presented in Table 6.2.
From the table, it is evident that the predictions made by BS 8110 (1985), are on the safe side
(except Beams 1S2 and 2S2). The mean value for all beams is 0.79 while the coefficient of variation
is 27.19%.
6.3 Contribution of Tensile Reinforcement
One of the main features in determining the shear capacity of the beam according to the proposed
method of analysis is a need to calculate the contribution of tensile reinforcement, P r In diagonal
measuredhere
t analysis here
Nc—different in length
152
splitting mode of failure, Psi is assumed to be equal to the horizontal component of the splitting force
at failure (Section 4.3.1.4).
A comparison is made between the calculated and measured value of P failure (Table 6.3). The
measured values are determined from the strain reading in the bars at the location exactly above
the support.
The results clearly show that in all cases, the predicted values were lower compared to the
measured values. The ratio of predicted/measured is ranging from 0.42 to 0.84. The general
tendency is that the predicted value is compared reasonably well with the measured value for the
beams with bigger size of the bars. For example, the results of beams 1D4, 2D4 and 2D6 in which
32 mm diameter bars were used.
It, however, needs to be emphasized that the comparison made in Table 6.3 is not strictly correct.
This is because the position of measured Pst is exactly above the support, whereas the calculated
P the value considered at the interface of the diagonal crack and the bar (as shown in Fig. 6.2).
The difference in the location may affect the results.
Fig. 6.2: The different of the location of Pst
153
Beam Contribution of TensileReinforcement, Pst
Predicted!Measured
Measured(kN)
Predicted(kN)
1S2 183 88 0.48
1S4 306 145 0.47
1S6 552 232 0.42
102 294 123 0.42
104 307 249 0.81
1D6 Gauge faulty 389 -
2S2 184 85 0.46
2S4 220 113 0.51
2S6 388 226 0.58
2S8 491 267 0.54
2D2 283 131 0.46
204 327 217 0.66
2D6 479 401 0.84
304 Not 246 -
3D6available
398 -
Table 6.3: Comparison of The Contribution of Tensile Reinforcement, P.
154
6.4 Serviceability Parameters of The Beams
The main parameters governing the behaviour of beams in service are the maximum deflection and
crack width. In order to satisfy the design requirements, both must remain within the prescribed
limits.
6.4.1 Deflection
The load versus mid-span and under-load deflections for the Beams 2S4, 1S6 and 2D6 as typical
samples are presented in Fig. 6.3a and Fig. 6.3b respectively. In each graph the comparison is
made between the measured and calculated values. The result from the elastic theory using
Equation 4.26 (Section 4.6.1) is referred as 'calculated' in the plots. The graph is a straight line. The
deflections obtained by ABAQUS Program have also been superimposed in the same graphs. A
discussion on the ABAQUS Program results is treated in Section 6.8.
The typical load-deflection characteristics from the test, Fig. 6.3, indicate that the behaviour is almost
linear. There is only a light reduction of stiffness probably as a result of the formation of cracks as
load is increased. The behaviour is typical of a shear dominated structure.
From the graphs, it is clear that there is a reasonable agreement between the calculated and the
measured values. From Fig. 6.3b, the measured and calculated values at the positions under the
load are practically overlapping (Beam 2S4 and 1S6), showing a good agreement. In deflection at
mid-span (Fig. 6.3a), however, a small deviation is observed between the calculated and measured
values. The calculated values overestimate the deflection but remain within an acceptable range of
155
about 10-20%.
The load-deflection characteristics provide an evidence that the composite action is realised between
the plate and concrete. The calculated deflection is based on the transformed I value for the beams
assuming the full composite interaction between the two materials.
From this study, the maximum deflection for the beams occur, as expected, at mid-span. The
maximum deflections measured at test and the corresponding loads for the beams are shown in
Table 6.4. Assuming that the service load for the beams are 0.6 times the ultimate or failure load,
the maximum deflections at service will be as shown in column (4) in the table. These values are
below the prescribed limit of span/250 (BS 8110 1985) (column 5). It would appear that the
serviceability requirements for deflection will be well within the prescribed limits for the plate
reinforced construction.
/
/1//
.1
600
400
200
300Load (kN)
(156)
— Experiment
Calculated
ABAQUS
700Loads (01)
200 — Experiment
600
500
400
300
Load Vs Mid—span Deflection(Beam 2S4)
156
Calculated
100ABAQUS
0 Z 4
( a) Mid—span Deflection (rnm)
126 8 10 12
2 4 6 8 10
(b)
Mid—span Deflection (mm)
(1D6)
Load (k11)1200
100 0
800
600
4.00
2.00
/
//.•
/
/
,
P.
Experiment
-÷".- Calculated
ABAQUS
2 4 6 8 10 12 14 16
(C)
Mid—span Deflection (mm)
Fig. 6.3a: Mid-span deflection
Load ( kN)
Load Vs Under—load Deflection
(Beam 2S4)
400
300
2 4 6 8 10
Under—load Deflection (mm)
4 6 a, 10
( b) ljncier —load Deflection (mm)
700
500
— Experiment
Calculated
ABAOUS
(156)
300Load (kN)
600
400
I /
/200
.11 ./
/ 0
157
Experiment
Calculated
—K— ABAOUS
Load ( kN)
800
600
400
ZOO
4i4 /
,
//
—"4--
1200
1000
//
Experiment
Calculated
ABAOUS
0 2 4 6 8 10 12
(c) Under—load Deflection (mm)
Fig. 6.3b: Under load deflection
158
Beam FailureLoad*(kN)
MaximumDeflection(mm)
Max. Def. atService Load (0.6 xFail. Load)(mm)
Span/250(mm)
1S2 580 (348) 8.27 4.27 9.0
1S4 710 (426) 10.87 6.06 9.0
1S6 790 (474) 6.78 4.56 9.0
1D2 535 (321) 7.80 4.25 9.0
1D4 515 (309) 6.90 3.20 9.0
1D6 520 (312) not available 9.0
2S2 590 (354) 8.76 4.60 9.0
2S4 605 (363) 9.89 4.76 9.0
2S6 885 (531) 10.01 5.72 9.0
2S8 938 (563) 10.12 6.28 9.0
2D2 665 (399) 10.62 5.40 9.0
2D4 875 (525) 10.86 5.84 9.0
2D6 1120 (672) 11.67 6.84 9.0
304 660 (396) 7.49 3.30 6.4
3D6 660 (396) 5.49 3.05 6.4
Table 6.4: Maximum deflection at failure and service load
(* Figures in brackets represent load at service (i.e 0.6 times failure load))
6.4.2 Crack Width
The load versus calculated and measured maximum diagonal crack widths for the Beams 2S2, 2S8,
159
2D2 and 2D6 are plotted in Fig. 6.4. These beams are chosen to represent the typical results of all
the beams. Calculated values were determined using the proposed equation in Section 4.6.2, in
which the width of the crack is proportionally expressed as a function of the strain of steel plate in
diagonal direction. Hence, the graph of the calculated value is a straight line.
In general, the test results show that the beam with thinner steel plate produces a wider crack than
that of the beam with thicker steel plate (for the same applied load). Fig. 6.4 shows clearly that the
development of crack width is non-linear for most part of the curve. Diagonal crack width also
increases at a faster rate, towards the last stages of loading before failure. There is also more
ductility with the single plate system than with the double plate. The maximum width of the crack
near failure for the double plate system varies between 0.4 to 0.75 mm. For the single plate system
the maximum crack width is about 1.5 mm. The calculated values overestimates the width of the
crack and the linear prediction is an over simplification of the real behaviour. The prediction needs
further refinement.
6.5 Concrete Cover to Steel Plate
The thickness of the concrete cover required to prevent the possibility of buckling of steel plate is
given in Table 6.5. The value were determined by a simple concept of rigidity as described in
Section 4.4.
600 Load (kN)
1
//
Measured
Calculated
500
400
300
200
100
(233)
1000Load ( kN)
800
600
400 r/
Measured
—1— Calculated
Load (kN)700
600
500 t-
Measured
Calculated
100
300
ZOO
100
- /
Load (kN)1000
I /
600 /
//
/400 -
•
200 / Measured
—4— Calculated
800
160
Load Vs Max. Diagonal Crack Width(Beam 2S2)
0 0.5 1 1.5 2
0 0.5 1 1.5
(o) Max. Diagonal Crack Width (mm)
( b) Max. Diagonal Crack Width (mm)
(2D2) (2D6)
0 0.2 0.4. 0.6 0.8 1 0 0.2 0.4. 0.6 0.8
C) Max. Diagonal Crack Width (mm)
( d) Max. Diagonal Crack Width (mm)
Fig. 6.4: Maximum diagonal crack width
161
PlateThickness(mm)
CoverRequired(mm)
Cover Provided(mm)
Single Plated Beam Double Plated Beam
2468
591318
49484746
late 151515
::
_
late•111 cover COVET
Table 6.5: Cover to Steel Plate
The cover required to prevent the buckling of steel plate varies from 5 mm to 18 mm depending on
the thickness of the plate. These values are apparently less than that provided in all single plated
beams. Thus, it is expected that in single plated beams, peeling-off of concrete will not occur as was
the case observed in the test.
In the case of double plated beam, the cover of 15 mm seems to be just over the minimum required
for up to 6 mm plate. In the last stages of the Beams 1D2, 1D4 and 1D6 failure was accompanied
by the concrete peeling-off. The condition was much improved in the Second Series double plated
beams, 2D2, 2D4 and 2D6, by the improvement of detailing under the load and at the support.
Therefore, it is clear that both factors, (i) adequate cover, over the minimum required and (ii) proper
detailing are important to prevent the concrete separating from the sides of the plates.
The proposed method of determining the cover is difficult to verify from the current test alone. The
observation of the Beams 1D2, 1D4 and 1D6 cannot be taken as evidence of the inaccuracy of the
method. This is because other factors might also influence the behaviour; for example the small links
in the cut-outs. As it is shown in Fig. 6.5, the edge of the links is very near to the outer face of the
the separation of concrete from the plate.
100
6
154
steel
plate
154- it 14-
15 15
162
concrete, i.e about 5 mm. A second factor might be the initial imperfection of the plate which may
have reduced cover less than 15 mm. The presence of a bundle of wires which were used to
connect the strain gauges might have also contributed in reducing the thickness of the cover. There
is scope for further research in this area.
BS 5400 Part 5 (1979), however, has made recommendation with regard to the minimum cover
required for the steel I beams in encased concrete beam. The suggested cover is 50 mm in all
direction. This value was suggested in order to prevent the possibility of spalling and peeling-off of
concrete and also for the protection of the steel against fire. It is believed that the requirement for
fire protection was the most important consideration in recommending a minimum cover of 50 mm.
Research works on concrete encased I beams by Wong (1963), Procter (1967) and in Australia by
Hawkins (1973) also showed that the cover of 2 inches (50 mm) was sufficient for preventing the
beams from premature failure by spalling and peeling-off of concrete. In fact one of the beams tested
by Hawkins (1973) had only 1 inch (25 mm) cover which also proved to be sufficient.
It is suggested that further tests to be carried out to establish the minimum cover required to prevent
edge of the small link is very near
to the outer face of concrete
Fig. 6.5: Concrete cover in double plated beams
163
6.6 Bond Stress and Cut-outs
The calculated bond stress between the plate and concrete at failure is tabulated in Table 6.6. The
values range from 0.13 Nime to 0.57 NI/me.
In this investigation, no pull out test was carried out to quantify the ultimate bond stress between the
plate and concrete. Due to the absence of test data, it would be unjustifiable to draw any rigid
conclusion whether the bond was sufficient or not.
The British Code BS 5400 (1979), however, limits the bond stress in encased steel beam to 0.5
Nime. If this value is taken as a guide, it is clear that in some of the beams in this investigation,
the bond stress has exceeded the permissible value. These were Beams 1S6, 2S6 and 2S8. The
bond stress of other beams were lower than 0.5 NI/me. Since the bond can only be relied in the
beams within its elastic range (Johnson 1975), thus the steel plates were provided with cut-outs.
These cut-outs were designed to act as an effective shear connector in the beams.
The theoretical number of the cut-out required by the beam in order to effectively act as shear
connector is determined by the suggested expression as given in Section 4.5.2. The calculated
numbers are presented in Table 6.6. It is seen from this table that the number of cut-out required
in all beams is three, except Beam 2D6 which requires four, and Beams 104, 1D6 and 3D6 need
two cut-outs. The cut-outs are required in the shear panel area. In the region of zero shear force,
only a minimum number is required.
In all the test beams, the number of cut-out provided in shear panel area was three. Therefore, it
164
is considered that the beams have acted compositely and no slip has occurred. The direct strain in
steel plate and surface Demec strain of the concrete at the same location as shown by the results
of the Beam 2S6 (Fig. 3.42) supports that there was little or no slip between the steel and concrete.
This results also indicate that the influence of sand blasting on the steel plate upon the bond in this
case is insignificant when compared with the degreased plate. This is because the Second Series
Beams which were only degreased, have shown that there was no or little slip between the steel and
concrete (result of the Beam 2S6-Fig. 3.42). This result, however, is difficult to be justified from this
investigation as the beams also have been provided with the cut-outs. Therefore, a separate test to
study the effect of sand blasting on steel plate upon the bond is recommended.
6.7 Average Shear Stress
In Table 6.6, the average shear stress of the beam at failure load is tabulated. The value is
calculated by the expression V/bd. The stress varies from 7.46 N/mm 2 for Beam 1D4 to a maximum
value of 16.23 N/me for Beam 206. These values in general represent a high value of shear stress
and in excess of the upper limit for ordinary reinforced concrete beam which is 5 N/me (or 0.84f„
which ever is lesser) as suggested by the code (BS 8110 1985). This indicate that the application
of steel plate in reinforced concrete beam is perfectly feasible to resist high shear stress.
A closer examination of Table 6.6 suggests that Beams 2S6, 2S8, 2D4 and 2D6 have resisted very
high average shear stresses, between 12.26 to 16.23 N/me. In all these beams, the failure
mechanism was a well developed diagonal splitting mode. The final stages was characterised by
the crushing of concrete at the notional hinges due to what can be described as excessive bearing
165
Beam TEST
(kN)
Han-zontalshearstressatfailurevh(N/m m2)
BondStress,sb(N/mm2)
No. ofcut-outsrequired
Averageshearstress,v (N/mm2)
Bearingstressunderload &abovesupport
(N/mm2)
FailureLoad
ShearForce, V
1S2 580 290 1.40 0.43 3 7.96 29.0
1S4 710 355 1.56 0.49 3 9.74 35.5
1S6 790 395 1.57 0.50 3 10.94 39.5
1D2 535 267.5 1.16 0.18 3 7.60 26.8
1D4 515 257.5 0.93 0.15 2 7.46 25.8
1D6 520 260 0.80 0.13 2 7.54 26.0
2S2 590 295 1.44 0.45 3 8.09 29.5
2S4 605 302.5 1.34 0.42 3 8.30 30.3
2S6 885 442.5 1.80 0.57 3 12.26 44.3
2S8 938 469 1.78 0.57 3 13.00 46.9
2D2 665 332.5 1.44 0.23 3 9.45 33.3
2D4 875 437.5 1.63 0.25 3 12.68 43.8
2D6 1120 560 1.75 0.29 4 16.23 56.0
304 660 330 1.25 0.20 3 9.19 33.0
3D6 660 330 1.15 0.19 2 9.19 33.0
Table 6.6: Bond Stress, Number of Cut-outs, Average Shear Stress and Bearing Stress of The Beams
/
166
rather than due to flexure and shear. It is clearly evident that even higher shear stresses can be
resisted if adequate precaution is taken against bearing failure. Some of the methods that can be
suggested are (i) proper detailing at the loading patch; making it part of the design requirement for
such beams (ii) partial transfer of the applied load indirectly; for example by using concrete bracket
attached to the side of the beam (Fig. 6.6), and (iii) using very high strength concrete, say 80
Nime.
It is envisaged that the proposed improvement in the design of beam will make the use of steel plate
in concrete beams a very attractive and economic proposition for general application.
C_
concretebracket/// ,
/ ol// 1/ /
\ . I loadpath
reinforcemetie/ /
)7
47
///
A/ //
\
NN
SECTION
Fig. 6.6: Applied load transferred indirectly
167
6.8 ABAQUS Program Results
The application of the finite element ABAQUS Program to the test beams, is demonstrated by
carrying out the comparison of the test results with those from the analysis. The results discussed
in Section 6.8.1 to 6.8.3 was obtained using Version 4.8 of the ABAQUS (1989).
6.8.1 Behaviour of The Beams, Failure Load and Mode of Failure
The response to load for all the beams started with the formation of flexural cracks at the region of
maximum bending moment (element numbers 12, 13, and 14 - see Fig. 5.1). These cracks appeared
at the load of about 15%-30% of the 'failure' load. With further increases of the load, the cracks
extended up to about half of the height of the beam (up to element 57, 58 and 59). A diagonal crack
also formed, starting from the support (elements 2, 3 and 4) extending towards the loading point
(elements 84, 85 and 100). Diagonal crack usually formed at the load of about 25% of the 'failure'
load.
The development of the cracking pattern of the Beam 2S2 as predicted by ABAQUS is shown in Fig.
6.7. This beam represents a typical behaviour for all beams. The ABAQUS Program that was used
in the analysis is incapable of plotting cracking pattern, so the figures were produced manually based
on tabular results from the output file. The cracking pattern at failure of this beam is shown in Fig.
6.8. In general, the analytical cracking pattern is in good agreement with those observed from the
test (see Fig 3.29 for comparison).
Depending on individual characteristics of the beam, in some beams the plate yielded (Beams 1S2,
1 6 8
1 D2, 2S2, 2S4 and 2D2) and followed concrete crushing at the support (elements 2,3,4 and 5) at
'failure'. For these beams, the failure is regarded as the diagonal splitting mode of failure. In other
beams, the plates did not yield, but the concrete was found crushed at the support at 'failure'. These
beams are considered as failed in bearing. The strain results of the tensile bars were also examined
and were found to be not fully strained at 'failure'. This interpretation of the behaviour justify that the
correct modes of failure have been adopted. Further discussion on the mode of failure of the beams
will be presented in Section 6.8.4.2
Failure for both cases were assumed when the computer run was terminated due to numerical
instability (i.e failed to converge). The load at this level is considered as the failure load for the
beam.
The ABAQUS's failure load and modes of failure of the beams are presented in Table 6.7. The
modes of failure and failure load obtained from the test and by the method of analysis are also
presented for comparison. As it is seen from the table, the failure loads and the modes of failure
correlate well between the prediction and the test results. The ABAQUS failure loads, in general,
give lower estimation than that obtained from the test (except for Beams 1 D4 and 1 D6). This result
was expected; because in ABAQUS, once the beam has developed excessive cracking and the
concrete has started to crush, the solution will create numerical instability with the result of the run
being terminated. This level was considered as the ABAQUS's 'failure' load, whereas the actual
capacity of the beam is higher than this. The results, however, are on the safe side.
It is considered that the above assumption of failure had in the analysis can be improved with
refinement in mesh around local areas and also by redefining the control parameters. This, however,
is a matter of available time and effort set aside for this part of the work.
169
Beam TEST(kN)
ANALYSIS(kN)
13,/
P,ABAQUS FiniteElement(kN)
Pabl/
PU
Fail.LoadP,
Mode ofFailure
Fail.Load
PU4
Mode ofFailure
'Fail.LoadP aha
'Mode ofFailure'
1S2 580 DS 316 DS (Conc.)
•
0.54 462 DS* 0.80
1S4 710 DS 530 DS (Plate) 0.75 522 Bearing** 0.73
1S6 790 DS-Bearing 714 Bearing 0.90 722 Bearing 0.91
102 535 Diagonal splitting andexcessive longitudinalcracks, followed bypeeling-off of cover& bearing under load
445 DS-Bearing 0.83 490 DS 0.92
1D4 515 487 Bearing 0.95 556 Bearing 1.08
106 520 452 Bearing 0.87 550 Bearing 1.06
2S2 590 DS 302 DS (Conc.) 0.51 480 DS 0.81
2S4 605 DS 426 DS (Plate) 0.70 438 DS 0.72
2S6 885 DS-Bearing 892 DS-Bearing 1.01 684 Bearing 0.77
2S8 938 Bearing Under Load 903 Bearing 0.96 675 Bearing 0.72
2D2 665 DS 473 DS 0.71 490 DS 0.74
204 875 DS 798 DS-Bearing 0.91 550 Bearing 0.63
206 1120 DS-Bearing 823 Bearing 0.73 650 Bearing 0.58
3D4 660 Diagonal splitting and 592 Bearing 0.90 - - -
306 660bearing followed bypeeling-off of cover 638 Bearing 0.97 - - -
Table 6.7: Comparison of Experimental Ultimate Loads and Modes of Failure with Those Predicted by ABAQUSProgram and The Proposed Method of Analysis
Note:DS refers to Diagonal Splitting Mode of Failure
•DS Mode of Failure according to ABAQUS is considered when the beams have developed a complete diagonal crack,followed by yielding of steel plate and some crushing of concrete at the support/under the load.
**Bearing Mode of Failure according to ABAQUS is considered when the beams have developed diagonal cracks andthen followed by crushing of the concrete at the support/under the load; without yielding of steel plate.
(a) at 165 kN
(b) at 217 kN
rL
(c) at 290 kN
170
n
(d) at 400 kN
Fig. 6.7: Crack pattern development in Beam 2S2 as predicted by ABAQUS
171
LOO
.165-165165 155
t1140050000
1L0
( 240 140 460
Li 140;CO
Fig. 6.8: Crack pattern at failure of Beam 2S2 according to ABAQUS
Fig. 3.29: Experimental crack pattern at failure of Beam 2S2 (for comparison)
172
6.8.2 Deflection
The typical deformed shape of the beam is shown in Fig. 6.9. The predicted deflections from
ABAQUS at mid-span and under the load of the chosen beams were presented earlier in Fig. 6.3.
For comparison purposes, the corresponding measured values were also plotted in the same graph.
As it is seen, the ABAQUS prediction gave a lower estimate of deflection between 10% to 35%
compared with the measured values. This discrepancy could be due to many reasons. One of the
reasons could be the fineness of the mesh may not have been adequate.
In using ABAQUS, the termination of the run in some cases occurred at a fairly early stage, but the
results indicate that the deflected shape of the curves were progressing towards the plot of the
measured values. It is envisaged that, had it been possible to achieve convergence for the actual
failure load, the maximum deflection would compare much better.
6.8.3 Strains in Tensile Bars and Steel Plate
Load versus strain in tensile bars for Beams 2S2 and 2S4 as samples are plotted in Fig. 6.10. The
comparisons are made between the strains obtained from the ABAQUS Program and the measured
values both at the support and mid-span. The results compare much better in the case of 2S4 than
2S2. However, the shape of the curves are similar, indicating that the predicted behaviour is similar.
Fig. 6.11 shows the load versus principal stresses (and also load versus direct strain) of the Beams
2S2 and 2S4 at selected positions as obtained by the ABAQUS and from the test (the positions of
the rosette are given in Fig 3.26).
173
Co
a)_oCD
a)
CO.c
-o
8a)-o
0.
t-
it;Co
Position:
— Mid —span (Test)
Mid —span (ABACUS)
At Support (Test)
At Support (ABACUS)
100
Loads (kN)
200
600
500
400
500
700
600
500
400
300
200
100
Loads (kN)
+
/
•
/
...".
-1-,V
Mid—spun (Test)
MId—span (ABACUS)
--I— At Support (ABACUS)
—4— At —Support (Test)
174
Loads Vs Tension Bar's Strain(Beam 2S2)
500 1000 1500 2000
( a ) Strain (x10E-6)
Loads Vs Tension Bar's Strain(Beam 254)
0 200 400 800 800 Ian 1200 1400 1600
( b)
Strain (X 10E-6)
Fig. 6.10: Tension bars strain
.d
/4- //
//
//
7 7,e/
Position:
R5 (Test)
—4— R5 (ABA0US)
Loads ( kN600
500
400
300
ZOO
100
HOLoads (kN)
a—1000 —500 0 500 1000
Direct Strain (x10-6)
500
00
400 I-
300 PtIc rt:
—6— Si
--I--2.00 -
—is—
•
\
(Test) A
S2 (Test) \
53 (Test) \
S1 (ABAQUS)
52 (ABAQUS)
S3 (ABAQUS)
175
Loads Vs Principal Tensile Stress(2s2)
(2.S2)
0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 400
(a ) Principal Tensile Stress (N/mm2) ( b) Principal Tensile Stress (N/mmZ)
Loads Vs Direct Strain
(232)
(232)
0 50 100 150 ZOO 250 300 350
(c)
Principal Tensile Stress (N/mm
Fig. 6.11a: Strain in steel plate of Beam 2S2 (positions of rosettes are shown in Fig. 3.26)
200 I-I ositicn:
100 _ m3 (Test)
-14- R3 (ABACUS)
176
Loads
Load
600
500
400
300
Vs Principal Compressive Stress(Beam 2S4)
(k N)
700
600
500
400
300
Loads (
(Beam 2S4)
\\ \
/
41/
4/51
41-
Position:
R4 (Test)
-4- R4 (ABACUS)
-160-140-120-100-80 -60 -40 -20 0 0 50 100 150 200 250 300(a) Principal Comp. Stress (N/mm2) (b) Principal Tensile Stress (N/rnm2)
Loads Vs Direct Strain(2S4)
600Loads (kN)
500
400
300
Position: •\
200 •-•41-n 5.1 (Test)'
SZ (Test)
100 Si (ABACUS)
-4- S2 (ABACUS)
0-800 -600 -400 -200 0 200 400 600
( c) Direct Strain (x1 0E-6)
Fig. 6.11 b: Strain in steel plate of Beam 2S4 (positions of rosettes are shown in Fig. 3.26)
177
From 6.11 it is observed that a very good agreement is found between the analytical results and the
measured values. The graphs of steel plate's principal stresses show almost identical results. This
reinforces that the ABAQUS is a good tool which can be used to study the overall behaviour of the
beams.
A very good correlation was also obtained in the case of direct strain results in the steel plate
between the analysis and the test. This also provides the evidence that the beams were acting
compositely. The analysis was carried out based on the assumption that a full composite action
occured between the steel and the concrete.
6.8.4 ABAQUS Program Results (Current Version)
This section will discuss some changes on the data and results obtained by using the ABAQUS
Program Version 5.2 (1993). This version has superseded the old version 4.8 (1989) which had been
used earlier in this research. While the research was underway, the new version of the software was
introduced. The new version was mounted on a new machine, SunSparc, using DUX System. The
old version was mounted on the PRIME machine.
Some of the results which had yet to be obtained were the plot of principal stresses of the concrete
and the plate in the beams. These plots are believed to be useful in the verification the proposed
concept of diagonal splitting.
In using the current version, the same data file which had been created in the old version is
transferred to the DUX system and then the analysis is carried out. However, in running The
178
Program, some changes in input data were made to incorporate with the new version.
6.8.4.1 Changes
After it was found that the run (hence, represent the 'failure load') in using the current version was
terminated earlier than that previously obtained for the same data file, the data was modified. This
modification was made in order to incorporate with the new version in which the CONCRETE input
data has to be defined accurately. Besides this modification, some changes on the idealisation of
the beams which was believed to have affected the run in the new version were also made. The
changes are including the following;
i) The node numbers 20, 22 and 126 and 128 (see Fig. 5.1b) were found not connected to the
neighbouring nodes. Therefore, these nodes had to be connected to their adjacent nodes. The node
20 was connected to nodes 37 and 38, node 22 was connected to nodes 38 and 39, node 126 was
connected to nodes 109 and 110, while node 128 was connected to nodes 110 and 111. The
changes were affected by the introduction of identical triangular elements replacing the original
elements 18,19,101 and 102 as shown in Fig. 6.12.
ii)The support condition at nodes 1,2, 3 and 4 were changed to represent a 'true' simply supported
system by allowing a free movement in horizontal and vertical directions. This was made possible
by defining the support only at node 3 which is in contrast to the previous case (old version), where
nodes 1,2,3 and 4 were defined as a support. In previous case, these nodes were defined as
supports in order to avoid high concentrated stress which in turn wouiciterminate the run earlier. This
situation, however, was overcome in the current version by introducing an 'equal pressure' at these
) (3E) (131) (12..0 ( 139) Q4 9)(141) Q42 ) ( 1:)1) Em Q49) 050) i (51)11!„ 108 -109 110 111 112 113 114 115 -̀21'.---1?=.1 cZ' 120 121 12 2 123
124
94
111
95 96 97 98 99 100 101 102 103 10 4 105 10G107
li.,„
79 eo 81 82 83 84 85 96 87 BB 89 90 91 92
A l, -- 64 65 66 47 68 69 70 71 72 73 74 75 76 77 1
,c,., ,0 49 50 51 52 53 54 55 56 57 58 59 GO GI 62
' 43 34 35 36 27 38 23 0 41 42 43 1.4 :5 46 47
2 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
73)..., 1 2 314 5 6 7 a g 10 11 12 13 14 15 16 17
C(D(10. (5) 5) (7) (e.-1) (2) OM '. 11 ) ( 12) (13 ) (14) lj5) (16) ,111)
5
fi)
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8050'CED2q • 5 175
179
Element number
Noce num
00 '10 135
1175 mm
Fig 5.1b: Idealization of test beam in Version 4.8 (showing element and node numbers)
3-node plane stress elements
Fig. 6.12: Idealization of test beam in Version 5.2
180
nodes. This pressure which is always equal to the applied load was distributed at the nodes (i.e
1,2,3 and 4), and hence the high concentrated stress was not allowed to build up locally.
iii) In the current version, the CONCRETE input data had to be defined accurately. In previous case,
two points on the uniaxial stress-strain curve were found 'enough' to defined the non-linearity of the
concrete (see Section 5.3.3.1.1), but in the current version more points were required (Fig. 6.13).
Therefore, under the CONCRETE option, the input data was;
*CONCRETE20.0,0.025.0,0.0001230.0,0.0002235.0,0.0004440.0,0.0007245.0,0.0010245.5,0.0010846.0,0.0011246.5,0.0011647.0,0.0012447.6,0.00150
The example given is for Beam 2S2, which represents the typical data of other beams. In this data,
the first figure represents the compressive stress of the concrete, while the second figure is the
corresponding value of the plastic strain which is defined by the stress-strain curve. In defining this
curve, the value of elastic modulus of the concrete, Ec has also to be adjusted accordingly. For
example, the adjusted E c value in this case is 33000 Nimm2 while the measured value was 22300
Nime.
6.8.4.2 Results
The typical deformed shape of the beams from Version 5.2 analysis is shown in Fig. 6.14. This plot
181
fcU 10 11
9
stress i
point 1
.—strain
Fig. 6.13: Uniaxial stress-strain curve of the concrete
Note:
* In ABAQUS Version 4.8, the CONCRETE input data was defined by points 1 and 11 only.
* In ABAQUS Version 5.2, points 1 to 11 were used to define the non-linearity of the concrete.
182
is for Beam 2S2 at the load increment 20 (i.e at 0.735 of the total applied load). It can be seen that
the edge of the beam (at nodes 1 and 2) is free to move in horizontal and vertical directions. This
is in contrast with the previous plot (Fig. 6.9) where this edge was 'fixed' in vertical direction. The
values of the deflection obtained by the current version, however, do not differ significantly with those
obtained earlier, hence they will not be presented.
In using the current version, the plot of principal tensile and compressive stresses of the concrete
and plate were obtained. Figs. 6.15 and 6.16 show the principal compressive and tensile stresses
in the concrete of Beam 2S2 respectively, while Figs 6.17 and 6.18 show the corresponding stresses
in the plate. These figures are the typical examples of other beams. These plots were obtained at
the load increment of 20 which represents 0.735 of the total applied load.
These plots are further evidence to the proposed concept of diagonal splitting mode of failure.
According to the concept, the failure happens as the limiting tensile strength of the concrete in shear
panel area is reached. It can be seen from Fig. 6.16, the value of principal tensile stress at this area
is obviuosly higher than its limiting value of 2.27 Nime. In this figure, the principal tensile stress at
the shear panel area is about 2.79 N/me and at two places, the value is reached up to 3.84 Nimm2
(shown by a green contour). This contour clearly shows that the splitting is in progress.
On the other hand, the plot of compressive principal stress in concrete (Fig. 6.15) indicates that at
the shear panel area, the value is less than its compressive strength (i.e 47.6 Nimm 2), indicating that
the failure is not by the compression at this area. The highest recorded value (at this load increment)
is 38.75 Nime which occurs under loading point (node 145), indicating that some concrete crushing
will happen in this area.
183
Figs. 6.17 and 6.18 show the behaviour of the plate. The plots show that the plate behaved as
expected; the top part in compression, while the bottom in tension. The recorded maximum principal
tensile value of 270 NI/mm2 which is higher than its yield value of 227 NI/me indicates that the plate
is yielding at failure.
The results from this study verify that the concept of diagonal splitting of concrete at failure is a valid
assumption.
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189
CHAPTER SEVEN
CONSTRUCTION AND ECONOMICS OF THE BEAMS
7.1 Introduction
One of the objectives of this study is to evaluate the suitability of the beams from the economics and
construction consideration. This aspect cannot be neglected especially in the era of high construction
cost. This chapter will discuss on the subject by making a direct comparison between the beams in
this investigation with the conventional stirrups' beams.
The construction problems and cost implications for this part of the research were studied in
consultation with the Department's Construction Management Research Unit.
7.2 Economics of the Beams
The benefit derived from the usage of steel plate as shear reinforcement in reinforced concrete
beams is believed to be the reduction of the amount of steel.
To assess this advantage, a comparative study is made between the beam in this project with the
conventional stirrups' beams. Table 7.1 presents the amount of the steel required as shear
reinforcement between these two type of beams. The beams were designed with similar dimensions,
loading condition and subjected to the same magnitude of load with the same flexural
reinforcements.
190
Beam DesignShearForce
(I(N)
Volume ofsteel required(x 10-3 m3
web Percentage ofloss of steelplates againststirrups
Stirrups SteelPlates
2S2 295 1.666 2.142 28.571S4 355 1.915 3.752 95.932S6 442.5 2.412 5.362 122.31238 469 2.661 6.973 162.04
Table 7.1: Comparison of the volume of steel required for shear reinforcement (throughout the
beams).
The table shows that the volume of web steel required in steel plated beams is more compared to
that of conventional stirrups' beams. The result is expected for this particular loading arrangement.
This is because the use of minimum shear reinforcement is not applicable due to the continuous
nature of the plate in the beams. In conventional beam, the minimum links are provided in the region
where shear stress, v is less than 0.5v. This condition contributes to the saving of steel. On the
other hand, the provision of the plate in between the loading points in plate reinforcement approach
is virtually redundant (Fig. 7.1).
This situation, however, might change if different loading arrangements are adopted. The examples
are a cantilever beam with a point load at the end and a beam subjected to a single point load (Fig.
7.2). In both cases, the shear forces exist throughout the section, hence the use of steel plate seems
economical. To support this judgement, the same comparison is made on the volume of web steel
required at the shear span only.
191
Beam Volume of websteel required(x 10-3 m 3 )
Percentageof saving ofsteel plateagainststirrup
Stirrup SteelPlate
2S21S42S62S8
1.4931.7422.2392.488
0.7111.2021.6912.185
52.3831.0024.4821.02
Table 7.2: Comparison of the volume of steel required for shear reinforcement (at the shear span
only).
The comparison given in Table 7.2 clearly shows that the steel required in the plated beams are less
compared to that of conventional stirrup beams. In this particular example, a saving as much as 52%
is obtained in 2 mm plated beam (i.e Beam 2S2). This result is in total contrast with that in Table
7.1.
From this point of consideration, it can be deduced that the steel plate approach is economical when
the beam is subjected to high shear stress that exist throughout the beam. There are other factors
which also influence the economics of the beams. These factors will be discussed in conjunction with
the practicality and construction of the beam in the next section.
7.3 Practicality and Construction of The Beam
From the practicality and construction consideration, the plate reinforcement could be effective in
many aspects.
• ••40;•
192
(a) Beam
at this section,
plate provided is redundant
(b) Shear force diagram
Fig. 7.1: Beam under two point loads
(a) Beam
(b) Shear force diagram (shear force exists throughout the beam)
Fig. 7.2: Cantilever beam and beam under a point load
193
It can be anticipated that the steel plate approach could reduce the time and consequently the cost
of preparing and fixing if compared to the conventional stirrups. This is because the plate could be
obtained directly from the manufacturers to the required size and profile and brought to the
construction site by a truck. Even though the cost of manufacturing and transporting the plate may
be high, but it is deemed that the overall cost is still small when compared with the cost of preparing,
fixing and tying numerous individual links.
The need of semi-skilled labour to fix the stirrups is eliminated as the plate can be simply assembled
in the beams. In such situation, the time of fixing will be reduced, hence increasing the speed of
construction. The ease in the construction and detailing will further contribute to the saving of cost.
The shorter the time required in preparing the beam, the greater the saving to the overall cost of the
project.
The use of steel plate as shear reinforcement in the beam will eliminate the possibility of error or
omission. In many cases, the stirrups' placement is often not thoroughly inspected on construction
sites. A brief check of stirrups' placement is insufficient to adequately inspect the many important
placement details. The possibility of errors, such as improper bending and/or omissions of the
stirrups are high in the conventional approach. The use of steel plate, on the other hand, provides
the opportunity to increase the quality control on sites. Since the plate is prefabricated in plants, the
chance of missing and/or improper bending some stirrups is virtually eliminated. In addition, the use
of steel plate also eliminates the possibility of misplacement since only one layer of plate is used on
a given section.
The plate reinforcement approach, may also have disadvantages. In handling the plate on site, a
194
crane is needed. This is for (i) unloading from a truck to a storage warehouse (ii) transporting of the
plate onto the formwork and (iii) placement of the plate into the section (either by crane or could be
done by hand). In conventional stirrup approach, the use of crane is unnecessary, unless the amount
of the stirrups is very large.
Another problem that was encountered in steel plated beams in this investigation is due to the
presence of small links in the cut-outs (refer to Figs.3.2 and 3.3). These links are comparatively
strenuous to be prepared.
The above problems, however, could be overcome. In handling on site, a small mobile crane is
seems able to place the plate in most situations. Different types of cranes are available depending
on the accessibility of the site and the size of the project. The small links in the cut-outs also could
be eliminated, for example by the provision of shear hooks incorporated as part of the plate itself.
As conclusion, before the plate reinforcement could be used on site, the factors which need to be
considered are;
i) Manufacturing the plate in factory
ii) Transporting to the site
iii) Storage
iv) Handling and lifting of the plate at the site
v) Placement and fixing onto the formwork
These factors vary depending on the individual situation of the site. The actual cost involving
195
material, labour and equipment have to be determined accordingly.
From the discussion, it seems that the new approach promises a bright future ahead. The
attractiveness of the method is not only confined to the practicality in construction, but also provides
a better solution to the problem of high shear stress.
196
CHAPTER EIGHT
CONCLUSIONS AND RECOMMENDATIONS FOR FURTHER RESEARCH
8.1 Introduction
The objective of the research was to study the structural behaviour of reinforced concrete beams
with steel plate as shear reinforcement. This system was designed to provide an efficient solution
for the problem of high shear stresses. Tests were carried out on fifteen simply supported reinforced
concrete beams with embedded steel plate as shear reinforcement. Steel plates with different
thicknesses and configurations were used.
8.2 Conclusions
Based on the experimental results and the analysis, the following general conclusions can be drawn;
1. Reinforced concrete beams with steel plate have a potential application both for common and
special structural members, especially when high shear stresses are concerned.
2. Under the adopted loading arrangement (i.e the shear span/depth ratio of 1.0), diagonal splitting
and bearing are the predominant modes of failure of the beams.
The diagonal splitting mode of failure occurred when the inclined crack between the support and the
loading point splits, as the limiting tensile strength of the concrete in the web is reached. Notional
hinges form at the two ends of the crack, and consequently the crushing and/or spalling of the
197
concrete will take place at the hinges for completion of the failure. Tensile reinforcements was not
fully stressed at failure. Bearing failure occurred under the loads (or above the supports) due to over
stressing of concrete. When bearing failure occurs, the full strength of the beams may not be
achieved.
3. A proper detailing at the loading patch and adequate concrete cover to steel plate are necessary
in order to avoid premature failure of the beams.
4. A method of analysis for the prediction of the shear strength and mode of failure of the beams
was proposed. The method adopts the concept of equilibrium of forces at the section when the
splitting occurs. The method is capable of taking account the influencing parameters on the strength
of the beams, such as the strength of material (%Co ftc, fyp , fy), the amount of bar and plate (A9t, tp),
the geometry of the beam (d, b) and the position of loading (a, c).
5. The predicted failure load and modes of failure of the beams were in good agreement with the
test results. The mean value and coefficient of variation of the ratios of the predicted/measured
ultimate loads were 0.82 and 14.89% respectively.
6. Shear strength and inclined cracking strength of the beams were also calculated by the method
based on the general concept as suggested by BS 8110 (1985). In general, a good correlation was
obtained between the experimental ultimate and cracking loads, and the loads predicted by 'BS 8110
(1985) Method'.
7. Shear strength of the beam increased as the thickness of the plate increased. The average shear
198
stress up to 16.23 Nimm 2 was achieved using a double 6 mm plate.
8. The behaviour of the beams with two plates was similar to that of single plated. The ultimate
strength of double plated beams was about the same as the beams with single plate of the double
thickness.
9. Deflection of the beams calculated by elastic theory gave a reasonable agreement with the
experimental results.
10. A method for determining the maximum diagonal crack width of the beams was also proposed.
The diagonal crack width of the beams was proportional to the total elongation of the steel plate in
the diagonal direction. The predicted values overestimated the width of the crack. In general, the
beam with thinner steel plate produced a wider crack than the beam with thicker steel plate.
11. A simple method of estimating the required concrete cover to prevent the buckling of steel plate
was put forward. The method was based on the concept of rigidity. The reliability of this method
against the test results, at this moment, cannot be fully justified. From the test, however, the cover
of 46 mm or more seemed adequate.
12. The provision of semi circular cut-outs at the top and bottom edges of the plate was effective
as the shear connector in the beams. Test results and analysis suggest that there was little or no
slip between the steel plate and concrete.
13. An estimate suggests that plate reinforcement for shear provides an economic solution in term
199
of the volume of steel when the beam is subjected to shear stress that exists throughout the span.
8.3 Recommendations for Further Research
1. Verification on the proposed method of analysis by additional test data. Hence, the beams with
different geometry, loading conditions and concrete strength are of immediate importance to be
experimented.
2. The use of high strength concrete, say 80 Nime or more in the test beams. In such a case,
bearing failure could be delayed and the beam may achieve its full capacity.
3. The behaviour of the beams with steel plate provided only at the region of shear stress.
4. A separate push out test to determine the capacity of the cut-outs.
5. A detail and separate study on the concrete cover is required in order to prevent the plate from
buckling and from the possibility of being peeled-off.
6. Development of a design method for such beams to be applied in construction. This involves
recommendations with regard to serviceability limits, ultimate limit and proper detailing.
200
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APPENDIX
APPENDIX A
Determination of the web capacity: Example Beam 2S2
Data:
f„ = 47.6 N/me;a = 400 mm;d = 364.5 mm;
A5 = 101 me;Am = 982 me;tp = 2 mm;
modular ratio, m =
ft, = f,j21 = 2.27 N/meb = 100 mm; acdp = 309 mm; dxfy, = 547 N/mefyt = 500 N/mef 227 N/mre
Ep/E, = 204/22.3 = 9.15
= 350 mm= 35 mm
Find the depth of compression zone, dc (see Fig. 4.5)
Assuming that the mode of failure is diagonal splitting and the web strength is controlled by theconcrete.
Thus;
Pm = ftcbdt + mftcAph (Eqn. 4.8a)
= ftcb (d-d,) + mft,(dp+dx-d„)tp
= 2.27x100(364.5-do) + 9.15x2.27(344-d)x2
(*)
Then, for horizontal equilibrium of forces (see Fig. 4.5),
Pm + fyptpdpc = Ascfy, + 0.67fcubdc + fyptp(dedx)
[2.27x100(364.5-dc) + 9.15x2.27(344-Qx2] + [227x2(344-c1,1 = [0.67x47.6x100dj + [227x2(d,-35)]
solve this equation by trial and error, then;
d, = 47 mm
Subtitute cl, = 47 mm into (*), then;
Pm = 84.41 kN
Check the control of web strength
(i) Concrete capacity, P,
P, = kips + mf1c4(Aph2 + Ap„,2)
where
Aph = (344-dc)x2= (344-47)x2= 594 mm2
Ap,, = at= 350x2= 700 mm2
and
s = 4(a,2 + d12)= 4(3502 + 317.52)= 473 mm
(Eqn. 4.6)
subtituting the values into (Eqn. 4.6), then;
P, = 126.43 kN
(ii) Steel plate capacity, Vso
V„ = fpsq (Aph2 + A 2pv)
= (227/43)x(4(5942 + 7002)
= 120.32 kN
Since Pm > V„ therefore, the web strength is controlled by the concrete.
Hence, the initial assumption with regard to the web strength control was correct.
Check the mode of failure
ktfyt = 982x500 = 491 kN > Pa (84.14 kN)
Therefore, the bars are not fully stressed at failure. Hence, the mode of failure is the DiagonalSplitting.
Calculate the ultimate load, Pu (Eqn. 4.3)
PL, = (24 + dc) Pisi t + (Cif + d4+ ac2)1131c + (dc + dpc)_,P + a cPapv
(4.3)
where
(it = d-d,= 364.5-47= 317.5 mm
Pph = Aphrnftc (see Table 4.3)= 592x9.1 5x2.27= 12338 N
and
Ppv = Apvnific (see Table 4.3)= 700x9.15x2.27= 14539 N
subtitutes the values into (Eqn. 4.3), then Pu;
Pu = [(2x317.5) + 40(84410/400] + [(317.52 + 317.5x47 + 3502)x1 00x2.27/400]+ [(47 + (344-47))123381400] + [350x14539/400]
= 302 kN.
Therefore, shear strength capacity of the beam is 302 kN.