the influence of concrete strength and longitudinal
TRANSCRIPT
THE INFLUENCE OF CONCRETE STRENGTH AND LONGITUDINAL NITWORCEMENT RATIO ON THE SHEAR STmNGTH OF LARGE-SIZE REINFORCED CONCRETE BEAMS VVITH, AND WITHOUT, TRANSVERSE
REINFORCEMENT
Dino Angelakos
A Thesis submitted in conforrnity with the requirements for the Degree of Master of Applied Science Graduate Department of Civil Engineering
University of Toronto
O Copyright by Dino Angelakos, 1999
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The Infïuence of Concrete Strength and Longitudinal Reinforcernent Ratio on the Shear S trength of Large-Size Reinforced Concrete B a s With, and Without, Transverse Reinforcement, M.A.Sc. 1999. Dino Angelakos, Department of Civii Engineering, University of Toronto
ABSTRACT
Concern about the shear capacity of large, lightly reinforced hi@-strength
concrete beams was the motivation for this investigation. The objectives of this study
were to investigate the influence of concrete strength and main longitudinal
reinforcement ratio on the shear capacity of large, Iightly reinforced concrete members
with, and without, transverse reinforcement. In addition, the test results were used to
assess the performance of the North Arnerican code provisions, AC1 318-95 and CSA
A23 -3-94 (General Method).
The following observations and conclusions resulted fiorn this study :
(i) Overall, the General Method yielded much better predictions than the AC1
approach. For the 12 tests, the average ratio of the experirnental shear failure load to the
predicted shear failure load for the AC1 Methoci and the General Method was 0.74
(Coefficient of Variation = 23%) and 0.98 (C.O.V. = 15.3%), respectively.
(ii) The five beam specimens constructed with 1% longitudinal reinforcement,
without stirrups, and concrete strengths of 20 MPa, 32 MPa, 38 MPa, 65 MPa, and 80
MPa, respectively, had essentiaily the same ultimate shear capacity. No benefit was
realized in the shear capacitywfor the higher stnngth concrete beams. In fact, the bearn
specimen with the 80 MPa concrete had the lowest shear capacity.
(iii) The implementation of high-strength concrete proved to be beneficial only when
transverse reinforcement was utilized
ACKNOWLEDGEMENTS
1 would like to thank my supervisor, Professor M.P. Collins, for his support and
guidance t hroughout this project.
1 would also like to thank Mr. Peter Leesti for al1 his help.
Thanks are also due to the following coileagues and fiiends:
Evan B e n e Stephen Cairns, Amr Helmy, Young-Joon Kim, Jason Muise, Marco Petretta,
Terry Rarnlochan, and Joel Smith.
1 would like to thank the staff of the Civil Engineering Stmctural Laboratones at
the University of Toronto for al1 their help and expertise; Joel Babbin, Remo Basset,
Giovanni Buueo, Mehmet Citak, Peter Heliopoulos, John MacDonald, and Alan
McClanneghan.
To my parents, I would like to express my sincere gratitude for d l their support
and continued encouragement throughout my Iife-
Constantina, thank you for aIways laughing at my jokes.
Dimitra, thank you for being in my life and entering it at the perfect time.
Finally, to my brother Bill, thanks for your unconditional support and your
invaluable advice.
TABLE OF CONTENTS
ABSTRACT
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
LIST OF APPENDICES
NOMENCLATURE
1. BACKGROUND
1.1 Introduction
1.2 Research Objectives and Layout of Work
2. REVIEW OF RELATED WORK AND CODE PROVISIONS
2.1 Review of Related Work
2.2 Review of Code Provisions
2.2.1 AC1 3 1 8-95
2.2.2 CSA -A23 -3-94 (General Method)
3. EXPERIMENTAL TEST PROGRAM
3.1 Specimen Details
3.2 Material Properties
3 -2.1 Concrete Properties
3 -2.2 Steel Properties
3.3 Specimen Construction
3.4 Test Rig Details
3.4.1 Test Set-Up
3 -4.2 Instrumentation and Data-Acquisition
3.5 Load Procedure
Page
ii
iii
iv
vi
vii
TABLE OF CONTENTS (Cont'd)
4. TEST RESULTS AND DISCUSSION
4.1 Effect of Concrete Strength
3.1.1 Reinforced Concrete Bearns Containing 1 % Longitudinal
Reinforcement and no Transverse Reinforcement
4-16 Comparison of Beam Specimens BD0.530 and
BRU 00 (Stanik 1998)
4.1.3 Reinforced Concrete Beams Containing 1 % Longitudinal
Reinforcernent and Transverse Reinforcement
4.2 F.ffects of Transverse Reinforcement
4.2.1 Reinforced Concrete Beams Containing 1% Longitudinal
Reinforcement and Transverse Reinforcement
4.2.2 Comparison of Beam Specimens DB0.530 and DB0.530M
4.3 Effect of Main Longitudinal Reinforcement
4.4 Prediction of Beam's Ultimate Shear Capacity using the AC1 3 18-95
and CSA AS3 -3-94 (General Method) Procedures
5. CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions
5 -2 Recommendations
REFERENCES
APPENDICES
Page
30
LIST OF TABLES
Page
2.1 Values of 8 and p for Sections Not Containing Transverse Reinforcement 15
(CSA A23.3-94)
2.2 Values of 8 and P for Sections With Transverse Reinforcement 17
(CSA A23.3-94)
3.1 Test Specimen Details 19
3 -2 Reinforcing Bar Properties 20
4.1 Experimentd Results for Bearns Containing 1% Longitudinal Reinforcement 3 1
4.2 Experimental Results for Specimens DB0-530 and BRLLOO 36
4.3 Experirnental Results for Beams Containing 1% Longitudinal Reinforcement 37
and Transverse Reinforcement
4.4 Required Amount of Minimum Transverse Reinforcement 44
4.5 Experimental Results for Specimens DB0.530 and DB0.530M 45
4.6 Experimental Results for Bearns Containing OS%, 1%, and 2% 48
Longitudinal Reinforcement
4.7 Ultimate Shear Capacity for Beams Containing 1% Longitudinal 51
Reinforcement and no Stirrups
4.8 Ultimate Shear Capacity for Beams Containing 1% Longitudinal 52
Reinforcement and Transverse Reinforcement
4.9 Ultimate Shear Capacity for Bearns Containing OS%, 1%, and 2% 53
Longitudinal Reinforcement and no Stirrups
4.10 Ultimate Shear Capacity for Specimens DB0.530 and DB0.530M 54
LIST OF FIGURES
Page
Experimentally Determined Cornponents of Shear Resistance at a Cracked
Section (Taylor 1 970)
Shear Stress, v, Normal Stress, a, and S hear Displacement at different
constant crack widths, IV, for 59 MPa and 1 15 MPa concrete (Walraven 1995)
Values of 0 and p for Sections Not Containing Transverse Reinforcement
(CSA A23 3-94)
Values of Band P for Sections With Transverse Reinforcement
(CSA A23 3-94)
Geometric Details of Specimens
Forrn-work for Specimens
Experimental Test Set-Up
LVDT Layout
Diai Gauge Layout
Zurich Target Layout
S train Gauge Layout for Longitudinal Reinforcement
Strain Gauge Layout for Transverse Reinforcement for DB 120M
Strain Gauge Layout for Transverse Reinforcement for DBO.5 3OM, DB l4OM,
DB 16M, and DB 180M
Load vs. Deflection for Beams with 1% Longitudinal Reinforcement and
no Transverse Reinforcement
Crack Surface Roughness for Concrete Strengths Exarnined
Photograph of Specimen DB 120 d e r Failure
Photograph of Specimen DB 130 after Failure
Photograph of Specimen DB 140 after Failure
Photograph of Specimen DB 165 after Failure
Photograph of Specimen DB 1 80 after Failure
Load vs. Deflection for Beam Containing 1% Longitudinal Reinforcement
and Transverse Reinforcement
vii
LIST OF FIGURES (Cont'd)
4.9 Photograph of Specirnen DB 120M at Failure
4.10 Photograph of Specimen DB 140M at Failure
4.1 1 Photograph of Specimen DB 165M at Failure
4.12 Photograph of Specimen DB 180M at Failure
4.1 3 Load vs. Midspan Deflection for DB 120 and DB 120M
4.14 Load vs. Midspan Deflection for DB 140 and DB140M
4-1 5 Load vs- Midspan Deflection for DB 165 and DB 1 6SM
4.16 Load vs. Midspan Deflection for DB 180 and DB 180M
4.17 Load vs. Midspan Deflection for DB0.530 and DB0.530M
4.18 Photograph of Specimen DB0.530 after Failure
4.19 Photograph of Specimen DB0.530M after Failure
4.20 Load vs. Midspan Deflection for 32 MPa Specimens with Varying
Page
38
39
39
40
42
42
43
43
- 45
46
46
47
Longitudinal Reùiforcement
4.21 Load vs. Longitudinal Strain for 32 MPa Specimens with Varying 48
Long itudinal Reinforcement
4.22 Photograph of Specimen DB0.530 after Failure
4.23 Photograph of Specimen DB 130 after Failure
4.24 Influence of Concrete Strength on Shear Capacity of Beams with 1% 55 Longitudinal Reinforcement and no Stimps
5.1 Ratio of Expenmental Shear Capacity to Predicted Shear Capacity versus 58 Longitudinal Reinforcement Ratio and Compressive Concrete Strength for Specimens without Stimps.
LIST OF APPENDICES
Page
A Sample Calculations of AC1 3 18-95 and CSA A23 3-94 (Generd Method) 6 1
code predictions
B Response of Beam Specimens Containing OS%, 1% and 2% 68
Longitudinal Reinforcernent
C Response of Beam Specimens Containing 0.5% and 1% Longitudinal 124
Reinforcement and Transverse Reinforcernent
D Material Properties 171
E Dia1 Gauge Data 176
F Mix Designs for Concrete Used in Expenmental Study 182
CHAPTER 1
BACKGROUND
1.1 Introduction
High-strength concrete is a more sensitive materid than normal strength wncrete
and it must be treated with care both in design and in constmction. The more brittle
nature of high-strength concrete means that if cracks form, they may propagate more
extensively than they would in traditional concrete. This may lead to premature shear
failures in large, lightly reinforced beams. In designing structures utilizing hi&-strength
concretes, questions arise as to the applicability of traditiona! design procedures, which
were developed for much lower strength concretes (Collins et al 1993). Extrapolation to
higher strength material is unjustified and may be dangerous (Carrasquillo et al 198 1).
Princi~le Mechanisms of Shear Resistance
It is necessary to identifjr al1 externd and intemal actions which rnay be present for
a loaded reinforced concrete beam. The shearing force V may be resisted by (Fenwick
and Paulay, 1968): the shearing stresses across the compression zone, the transverse
component of the force resulting fiom interlocking of aggregates, the transverse force
induced in the main flexural reinforcement by dowel action, and the tensile force induced
in the transverse reinforcement (stirrups).
Figure 1.1 shows a graphical representation of the relative contributions of the
concrete compression zone, aggregate interlock action, and dowel action in the shear
resistance of a reinforced concrete beam at a cracked section.
Figure 1 .l Experimentally determined components of shear resistance at a cracked section for a beam without stimps (Taylor t 970)
1.2 Research Objectives and Layout of Work
The aim of this study is to examine how the percentage of main longitudinal
reinforcement and the concrete compressive strength influence the shear capacity of large,
lightly reiriforced concrete beams with and without transverse reinforcement.
Chapter 2 contains a review of the relevant studies previously done pertaining to
mechanisms of shear resistance in reinforced concrete beams as weil as factors influencing
these mechanisms. Experimental programs involving shear tests of reinforced concrete
beams are also reviewed and discussed.
The experimental program in this study involved testing twelve large, lightly
reinforced concrete beams in 3-point loading. The shear span-to-depth ratio for al1 the
tests was approximately 3. Details of the test program for the beam specimens are given
in Chapter 3. The experimentd results for the specimens tested in this study, dong with
discussion, are given in Chapter 4.
Chapter 5 summarizes the conclusions of the study and offers recommendations.
CHAPTER 2
REVIEW OF RELATED WORK AND CODE PROVISIONS
2.1 Review of Relattd Work
Concrete Stren~th and Crack Rouehness
Cracks in concrete can transmit shear forces by virtue of the roughness of their
interfaces. Wit h regard to this roughness, the aggregate particles protruding f?om the
crack faces play an important role. In high-strength concrete, however, the matrix is
stronger than in concrete of normal strength, so that interlocking capacity is reduced. In
concrete with normal and low strengths, the cracks intersect the cement mat* but
propagate around the relatively strong aggregate particles. In a concrete with high
strength concrete, however, the cracks intersect, and pass through the aggregate particles,
such that the roughness of the crack faces is considerably different; the number of contact
areas can be significantly reduced, thus reducing the capability of transmitting shear forces
(Walraven et al 1987, and Walraven, 1995).
Shear transfer across cracks by interlocking particles was first looked at, in detaii,
by Fenwick and Paulay in the late 1960's (Fenwick and Paulay, 1968). This was
aggregate interlock action, and shear displacement (or shear slip) parallel to the direction
of the crack was a prerequisite of shear transfer by aggregate interlock. The authors
examined the principal mechanisms of shear resistance in reinforced concrete beams. Two
of the parameters studied were the concrete strength and the crack width. The concrete
strength rmged fiom about 20 MPa to 60 MPa. Based on tests done on concrete shear
blocks, the authors found thar there was a substantial reduction in shear transmitted by
aggregate interlock action when the crack width was increased. Also, as the concrete
strength was increased to 60 MPa, the shear transmitted across the cracks increased.
However, it is important to note that the crack width for the latter tests was fixed at about
0.2 mm and there was no occurrence of the aggregate interlock action breaking down.
The concrete shear blocks exhibited both shear and flexural cracks.
Carrasquillo et ai (1981) examined the behaviour and microcracking of high-
strength concrete subjected to short-term loading. The authors concluded that high-
strength concrete has much less microcracking at al1 stress levels than normal strength
concrete, but fails more suddenly with fewer planes of failure. The authors looked at the
differences in the mechanical properties of 30, 50 and 70 MPa concretes in terrns of
formation and propagation of microcracks. They found that under uniaxiai compression,
normal strength concrete developed highly irregular failure surfaces including numerous
instances of bond M u r e between the coarse aggregates and mortar. Medium strength
concrete developed a rnechanism sirnilar to the normal strength concretes but at a higher
strain. The failure mode of high-strength concretes was typical of that of a nearly
homogeneous material. Failure occurred suddenly in a venical, nearly Rat plane passing
through the aggregate and the mortar.
Walraven performed experiments on concrete push-off specimens of various
concrete strengths (Walraven et al 1987 and Walraven 1995). The highest concrete
strength examined had a cube strength of 1 15 MPa. The crack width and normal stress
were also varied in the test program to isolate each parameter. Figure 2.1 shows the shear
stress and normal stress versus the shear slip for various crack widths. As can be seen in
the figure, for a crack width of 1 mm and a shear slip of about 2 mm, the shear stress
transrnitted across the crack for the 59 MPa and the 115 MPa concretes was 6 MPa and 4
MPa, respectively. In general, Walraven found that the shear friction capacity of cracks in
high-strength concrete is significantly reduced due to fracture of the aggregate.
It could be expected that the surface of a diagonal tension fracture in a high-
st rength concrete beam would be relatively smooth, as obtained in uniaxial compression,
and the smooth surface might be deficient in aggregate interlock which is an important
component of shear resistance (Elzanaty et al 1986) (see Figure 1.1).
--
r d 1 ( i l U s
Figure 2.1 Shear stress, v, normal stress, a, and shear displacement D at different constant crack widths, w, for 59 MPa (left) and 1 15 MPa concrete (right)
In the present study, it is expected that the shear stress transmitted across the
cracks will decrease as the concrete strength increases, which in turn, May be a prominent
factor in the overall shear capacity of the high strength concrete specimens.
Loneitudind Reinforcement
The percentage of longitudinal reinforcement in a reinforced concrete beam also
has a pronounced effect on the basic shear transfer mechanisms. An important factor that
affects the rate at which a flexural crack develops into an inclined one, is the magnitude of
shear stress near the tip of that crack. The intensity of principal stresses above the flexural
crack depends on the depth of penetration of that crack. The greater the percentage of
longitudinal reinforcement, the l e s the penetration of the flexural crack. The less the
penetration of the fiexural crack, the less the principal stresses for a given applied load,
and consequently a higher shear is required to cause the principal stresses that will result in
diagonal tension cracking (EIzanaty et al 1986).
The General Shear Design Method of the Canadian Standard (CSA A23.3 1994),
which is based on the Modified Compression Field Theory, States that the shear camed by
tensile stresses in the concrete, V, is a fiinction of the longitudinal straining in the web
member As E~ increases, V, decreases. Increasing the magnitude of the moment or
applied axial tension increases E, and hence, decreases V,. Applying axial compression,
or prestressing the beam member, or increasing the area of longitudinal reinforcernent
decreases Er and hence increases V,. A key to the General Method is that it explicitly
considen the influence of shear upon stresses in the longitudinal reinforcernent (Collins
et al 1996).
Increasing the percentage of longitudinal reinforcement aiso affects the aggregate
interlock contribution to shear resistance. Bearns with a low percentage of longitudinal
reinforcement will have wide, long cracks in contrat to the shorter, narrow cracks found
in beams with a high percentage of longitudinal reinforcement. Since the aggregate
interlock mechanism depends on the crack width, an increase in the aggregate interlock - -
force is to be expected with an increase in the percentage of longitudinal reinforcement
(Elzanaty et al 1986).
Increasing the percentage of longitudinal reinforcement also increases the dowel
capacity of the member by increasing the dowel area and hence decreasing the tensile
stresses induced in the surrounding concrete (Elzanaty et al 1986). As mentioned above,
one feature of high-strength concrete that affects structural response is the tendency for
cracks to pass through, instead of around the aggregate. This creates smoother crack
surfaces, reducing the aggregate interlock action, and hence, reducing the shear carried by
the concrete, V,. Because of the reduced aggregate interlock, higher dowel forces occur
in the longitudinal reinforcing bars for high-strength concretes. Fenwick and Paulay
(1968) concluded that the transverse displacement at the level of the main longitudinal
reinforcement, Le., the shear slip across the crack, will be one of the more important
factors that influence dowel capacity in beams without stirnips. These higher dowei
forces, together with the highly concentrated bond stress in higher strength concrete
beams, result in higher bond-splitting stresses where the shear cracks cross the
longitudinal tension bars. These combined effects can lead to brittle shear-splitting cracks
at the level of the bottom bars, which can lead to brittle shear failures (Yoon et al 1996).
Transverse Reinforcement
Stimps perform the dual role of resisting shear as well as enhancing the strength
of the other shear transfer mechanisrns. Providing an adequate arnount of shear
reinfiorcernent can control the horizontal splitting cracks at the level of the longitudinal
reinforcement, increasing the strength of the dowel action, and thereby enhancing the
shear capacity of the member. Along with increasing the strength of the dowel action, the
stimps can lirnit crack propagation and crack widths (Carrasquiilo et al 1986).
For large concrete beams, the possibly unconservative nature of the AC1
expression for calculating the shear strength contribution from the concrete, V,, is
mitigated by the requirement that a minimum area of -stimips be provided should the
factored shear force exceed 0.5&Vc. However, the provision does not apply to slabs and
footings. Such members can often be both very thick and very lightly reinforced, i.e.,
contain small amounts of longitudinal reinforcement. Traditionaily, such members are
constnicted without stirrups and are sized using the AC1 shear strength equation. The
current AC1 shear provisions, which were developed more than 35 years ago, do not take
into account that members without stirmps fail at lower values of shear stress as they
become larger. Larger member have more widely spaced cracks relative to smdler
rnembers and hence are predicted to fail in shear at lower shear stresses for the reasons
discussed above. Thus, if these provisions are used to design large lightly reinforced one-
way slabs or footings, the resulting structure may have an hadequate margin of safety
(Collins and Kuchma 1997).
Shear Tests on Reinforced Concrete Beams
Eizanaty et al (1986) investigated the shear capacity of 18 reinforced concrete
beams (3 of which contained stimps) using high-strength concrete. The variables were
the concrete strength, longitudinal reinforcement ratio, and shear span-to-depth ratio. The
concrete strength ranged from 21 MPa to 83 MPa. The beams without stirrups were
designed to investigate the effects of concrete strength, shear span-to-depth ratio, and
percentage of longitudinal reinforcement. Those with stirrups had a constant value for the
shear span-to-depth ratio and were designed to study the effects of concrete strength on
the shear capacity of the bearns.
The authors concluded that the shear strength of bearns without stirrups increased
when the concrete strength increased. However, they found that the crack surfaces were
distinctively smoother for the higher strength concretes, indicating that the shear force
carried by aggregate interlock decreased with increased concrete strength.
The authors also concluded that for al1 concrete strengths, increasing the
percentage of longitudinal reinforcement increased the shear strength of the test beams
without stirrups. It was observed that beams with hi&-strength concrete and small
amounts of longitudinal reinforcement had deficient dowel action, and splitting dong the
reinforcing bars occurred suddenly.
The AC1 3 18-83 expressions were used to predict the shear capacities of the tested
beams. The AC1 code was seriously unconservative for medium and high-strength
concrete beams without stirrups, low percentages of longitudinal reinforcement, and high
shear span-to-depth ratios. Furtherrnore, the AC1 code underestimated the importance of
both the percentage of longitudinal reinforcement and the shear span-to-depth ratio, and
overestimated the benefits of increasing the concrete strengt h.
Test results showed that the shear strength of beams with stirrups increased with
the increase of concrete strength and the AC1 code equations were conservative in
predicting the shear strength for al1 test beams with stirrups.
Apart fiom varying the shear span-to-depth ratio, the present study examines the
same parameters as the study by Elzanaty et al (1986). It is expected that the results will
be very similar. One significant difference in the two experimental prograrns, however, is
the size of the specimens. The beams tested by Elzanaty et al (1986) measured
approximately 300 mm in height and 175 mm in width- The present study examines beams
with a height of 1000 mm and a width of 300 mm. This size difference in the specimens
will influence the crack widths. Large, lightly reinforced bearns, relative to smaller ones at
the same stress level, exhibit wider cracks. After cracking, shear is resisted by aggregate
interlock, dowel action of the main reinforcing bars, and resistance of the still uncracked
concrete at the top of the beam (see Figure 1.1). If the cracks are wider, the aggregate
interlock mechanism will not be as effective. Also, as the concrete strength increases and
the crack surfaces become smoother and consequently more dowel action is required, the
shear capacity of the large lightly reinforced members may not increase for higher concrete
strength unless the cracks are contained, either by the addition of stirrups, for example, or
increasing the percentage of longitudinal reinforcement.
Yoon et al (1996) conducted an experimental study at McGil1 University in
Montreal, exarnining the adequacy of the minimum shear reinforcement requirements
according to AC1 3 18-83, CSA A23 -3-84, AC1 3 18-89 and CSA A23 -3-94, in beams
constructed with normal, medium, and high strength concretes. The authors found that
even small amounts of shear reinforcement significantly irnproved the duztility and shear
strength of reinforced concrete beams. ConverseIy, specirnens without stimips failed in a
bnttle manner after significant shear cracking. The specimens had heights of 750 mm and
widths of 375 mm. The beams were tested in 3-point loading with a shear span-to-depth
ratio of about 3. Al1 specimens had a longitudinal reinforcement ratio of 0.028. Some of
the notable results were the following:
The authors found that, in general, the AC1 method overestirnated the strength of
specimens without stirrups for the higher concrete strengths.
For specimens containing the minimum amount of stimips (according to AC1 3 18-
AYfY 83, CSA A23 -3-84, and AC1 3 18-89) given by - = 035MPa, and for concrete bus
strengths of 36, 67 and 87 MPa, the ultimate shear capacities did not indicate that there
was a benefit Ekom increasing the concrete strength. The authors found that CSA A23.3-
94, which provides an expression for the minimum amount of shear reinforcement that is a
function of the square root of the concrete compressive strength, provided adequate
reserve afler cracking and the shear capacities increased noticeably with increasing
concrete strengths.
In the present study, the amount of transverse reinforcement was not varied. The
amount of stirrups was kept constant for a11 strengths of concrete, such that
A 4 - = 0.40 MPa . By keeping bws
concrete strengths, the aim was
the amount of transverse reinforcement constant for al1
to isolate the concrete strength and its effect on the shear
capacity of the bearns with transverse reinfiorcement relative to the beams without such
reidorcement. A significant difference between the present study and the study done at
McGill University is the percentage of longitudinal reinforcement considered. Most of
the beams tested in the present study have only 1% longitudinal reinforcement. Also,
they are 250 mm deeper than the bearns tested at McGiII University. Due to the low
percentage of longitudinal reinforcement and large depth of the members in the present
study, it is expected that the predicted shear capacities using the AC1 code provisions will
senously overestimate the shear capacities of the beam specimens without stimips,
especially as the concrete strength increases. Like the McGill tests, it is expected that the
addition of even a small amount of transverse reinforcement will significantiy increase
the shear strength and ductility of the beams.
At the Curtain University of Technology in Western Australia, Kong and Rangan
(1998) performed tests on 48 reinforced concrete high-performance concrete beams. The
test parameters included the percentage of longitudinal reinforcement, the beam depth, the
shear span-to-depth ratio and the concrete strength. Five of the beam specimens had the
following properties : a depth of 350 mm, a width of 250 mm, a longitudinal
reinforcement ratio of 0.0205, a transverse reinforcement ratio of 0.00 157, and a shear
span-to-depth ration of 2.5.
Test results showed that the increase in shear capacity found with increasing the
percentage of longitudinal reinforcement fiom 1.66% to 2.79% was not as significant as
that obtained by increasing it to 3 -69%.
The geometrk properties of the specimens of the present study diRer significantly
fiom those of the study just mentioned. Neveriheless, the results of the study done by
Kong and Rangan (1998) showed that the concrete strength, ranging from 63 -6 to 89.4
MPa, had essentiaily no infiuence on the shear capacity of the five reinforced concrete
beams mentioned.
Preceding the experimental work undertaken for this thesis was a large test
program, which included 22 lightly reinforced concrete beams tested in 3-point loading, at
the University of Toronto (Stanik 1998). Thirteen of the beams were Iarge-scale
specimens. The dimensions of these large, lightly reinforced specimens were identical to
those of the present study; 1000 mm in height and 300 mm in width. The longitudinal
reinforcement in that study varied between 0.5% t o 1.19%. The other parameters studied
were the concrete strength and the addition of transverse reinforcement such that
AvfY - = 0.40MPa. Al1 of the beams failed in shear pnor to flexural yielding of the bws
longitudinal reinforcement.
It was found that there was little gain in shear capacity for the specirnens made
with hi&-strength concrete. For example, specimens B N l O and BHlOO in the study had
concrete strengths 37 MPa and 94 MPa, respectively, and both had a longitudinal
reinforcement ratio of 0.76%. They failed at shear loads of 192.1 kN and 193.1 kN, .. respectively.
To cornpiement the series of beams without s t imps and to provide experimental
evidence regarding the shear strength of beams containing transverse reinforcement, huo
specimens were constnicted with s t imps in the study by Stanik (1998). One of these
specimens, specimen BM100, was identical to BNlOO except for the concrete strength (46
MPa and 37 MPa, respectively) and the addition o f s t imps satisfying the requirement for
bws minimum transverse reinforcernent in CSA A.23.3-94 (Le., AV = 0.06Jf'S-). The
fv shear capacity of BMlOO was 343 kN, 79% greater than that for BN100. Furthemore,
the midspan deflections at the peak load for BNlOO and BMlOO were about 6 mm and 22
mm, respectively. Thus, providing a minimum amount of transverse reinforcement
enhanced both the shear capacity and ductility of the beam specimen.
Stanik (1998) concluded that, in general, as the concrete strength o r member depth
increased or the percentage of longitudinal reinforcement decreased, for bearns without
stirrups o r distnbuted reinforcement, the AC1 predictions were very unconservative.
These observations are especially evident for specimen BRL100. This specimen had a
concrete strength of 94 MPa, 0.5% longitudinal reinforcement and a depth of 1 metre.
The test result for this specimen yielded a shear capacity only 41% of the AC1 318-95
code prediction.
The above study also concluded that an increase in the percentage of longitudinal
reinforcement decreased the crack width and significantly increased the shear capacity of
beams that did not contain transverse reinforcement.
It is expected that the beams in the present study will yield results very sirniiar to
those obtained by Stanik (1998). In this study, a wider range of concrete strengths will be
exarnined, relative to that done by Stanik (1998), to try and establish an optimum concrete
strength for the shear capacity of Iightly reinforced concrete beams with and without
stimps. With the addition of transverse reidorcement it is expected that a sharp increase
in strength and ductility will be evident relative to beams without s t imps for al1 concrete
strengths. The variation of the longitudinal reinfowement fiom 0.5 % to 2 % in the
present study may also shed more light on the effects of crack widths on the beam's shear
capacity .
2.2 Review o f Code Provisions
The following section summarizes the shear design provisions contained in AC1
3 18-95, and CSA A23.3-94, which were used to predict the shear capacities of the test
specimens. Sample calculations for predictions of beam shear capacity using both code
procedures are provided in Appendix A.
2.2.1 AC1 318-95
The traditional expression used to predict the nominal shear strength, V,,
of reinforced concrete bearns is given as :
v n = + Y* 2.1
where V, and V. represent the concrete and transverse steel contributions, respectively.
The expression for the concrete's contribution to shear strength is given by :
V. = 0 1 6 6 ~ b d but 5 J6g [mm and MPa] 2.2
The expression giving the transverse reinfiorcement contribution to shear strength is given
by :
A d 4 Y , = - s 0 . 6 6 f i b d [mm and MPa] 2.3
S
When Vu > O.SpVC the ACI Code requires minimum shear reinforcement, AY min, in ail
flexural members such that,
bws A ~ m i n = 035-
fi [mm and MPa]
To take .advantage of concrete strengths greater than 69 MPa when calculating V,,
AC1 3 18-95 ailows for the actuai specified concrete strength to be used in equation 2.2
provided a minimum amount of shear reinforcement is provided , given by :
2.2.2 CSA A23.3-94 - General Method
The General Method is based on the Modified Compression Field Theory (Collins
et al 1996) which is based on equilibrium, compatibility, and stress-strain characteristics of
cracked reinforced concrete. The key feature of this method is that it explicitly considers
the additional tensile stresses in the longitudinal reinforcement due to the presence of
shear.
The nominal shear strength is given by,
v n = v c + Ys where the concrete contribution to shear resistance is given by :
v c = pmbvdv
and the transverse reinforcement contribution to shear resistance is given by :
AYfYdv Vs = - ~ 0 t 8 S
Also, CSA A23.3-94 requires that the minimum amount of shear reinforcement be
provided in al1 regions of flexural members where the factored shear force exceeds OSV,,
and is given as :
[mm and MPa]
The magnitude of the concrete contribution, V,, is controlled bv the value of f l is a rneasure of the ability of the concrete member to cany tensile stresses across potential
diagonal cracks. The angle 8, is the angle of inclination of principal compressive stress in
cracked concrete with respect to the longitudinal axis of member. This angle, 0, also
coincides with the angle of inclination of the diagonal cracks that result fiom shear. Both
p and 8 are based on the crack spacing and longitudinal strain.
The longitudinal strain is calculated for non-prestressed members with no axial
load present, as
The values of 8 and P for a beam without transverse reinforcement, are shown in
Figure 2.2 and Table 2.1,
Figure 2.2 Values of 8 and P for Section Not Containing Transverse Reinforcement
Table 2.1 Values of 0 and for Section Not Containing Transverse Reinforcement
SX
, [mm] Il25
1250
1500
8 P 8 p 8 -
Longitudinal Strain s, XI 000 s 0.0 27"
0-406 30"
0.384 34"
s 1.00 34"
0.214 41"
0.183 48"
s 1.50 36"
0.183 43"
s 0.25 29"
0.309 34"
0.283 39"
12.0 38"
0.161" 45"
r 0.50 32"
0.263" 37"
0.235 43"
0.156 . 51"
0.138 54'
The values in Figure 2.2 and Table 2.1 are based on the assumption that the
spacing of the diagonal cracks is dsin8, where s is the crack spacing parameter. From
Figure 2.2 and Table 2.1, as the longitudinal strain increases and the crack spacing
parameter increases, p, the measure of the concrete' s ability to carry tensile dresses across
po tential diagonal cracks, decreases.
The beta values were derived assuming that the maximum aggregate sue, a, was
19 mm. These Pvalues can be used for memben cast with other aggregate sizes by using
an equivalent spacing parameter, %=, given by :
35 Sxe = Sx -
a+l6
The crack spacing, s, shall be taken as the esective depth of the member, d,, for
members that do not contain stirrups or intermediate layers of crack control
reinforcement. If the member contains intemediate layers of longitudinal reinforcement,
crack spacing shall be taken as the maximum distance between layers of crack control
reinforcement,
It is important to note that for high-strength beams ( fc > 70 MPa), the cracks will
pass through the aggregate and hence the aggregate size, a, should be taken as zero.
Figure 2.3 and Table 2.2 give the P and 0 values for members that contain at least
the minimum amount of transverse reinforcement required by CSA A23 -3 -94.
Figure 2.3 Values of t9 and /3 for Section With Transverse Reinfiorcement
Tabte 2.2 Values of 8 and f l for Section With Transverse Reinforcement
CHAPTER 3
EXPERIMENTAL TEST PROGRAM
Twelve full-scale reiriforced concrete beams were tested under 3-point loading.
The key variables in the experimental study were: the amount of main longitudinal
reinforcement and the concrete strength. The addition of transverse reinforcement was
also investigated. The details for the test program are discussed in this chapter.
3.1 Specimen Details
Twelve reinforced concrete beam specimens were constructed and tested in the
Mark Huggirs Structural Laboratory at the University of Toronto. The specimen
dimensions were 6 metres in length, 1 metre in depth, and 300 millimetres in width.
Table 3.1 provides a sumrnary of the beam specimen detail. Nine of the beam specimens
contained 1% longitudinal reinforcement (four 30M rebars), two of the beam specimens
contained 0.5% longitudinal reinforcement (two 30M rebars), and one beam specimen
contained 2% longitudinal reinforcement (eight 30M rebars). The beam specimens were
narned according to their percentage of main longitudinal reinforcement, concrete
strength, and transverse reinforcement (if present). For example, specimen DBlZOM
contained 1% longitudinal reinforcement, 20 MPa concrete, and approximately the
minimum amount of transverse reinforcement as specified by CSA A23.3-94.
The concrete strength was the key variable and varied from 20 MPa to 80 MPa.
Five different concrete strengths were considered: 20 MPa, 32 MPa, 38 MPa, 65 MPa,
and 80 MPa. The concrete contained crushed limestone coarse aggregate with a
maximum aggregate size of 10 mm. The concrete was provided by DufCerin Concrete, a
local ready-mix plant. The mix designs for the various concretes used in the
expenmental study are given in Appendix F. in most cases MO specimens were tested
for each concrete strength; one without transverse reinforcement, and the other with
Ah transverse reinforcement such that - = 0.40 MPa . b w ~
Table 3.1 Test Specimen Details
Beam specimeni
Test Date Cast Date
DB130 DB230
The shrinkage strain was monitored during the maturing process for the specimens using the average of the readings of the two strain gauges on the longitudinal reinforcement.
Dec. 1/97 Dec, 2/97
Nov- 6/97 II
1
DB120M 1 Feb. 19/98 DB120 1 I l
3.2 Material Properties
DB0.530M
I 1 -
3.2.1 Concrete Propetties
Age at Test Date
(days)
25 26
I 1
May 29/98
Beam Specimens labeled with " M contain transverse reinforcement.
37 39 48 48 55
DB140
Twenty concrete cylinders (1 50 by 300 mm) were cast simultaneously for each of
A#d f', on test
1 .O1 1.01 0.50
Apr. 30198 May 5/98 July 2/98
the six pours in order to determine the concrete properties. For the concrete cylinders
Shrinkage Stnin at
Test Date date
[ M W
32 32
n.a. n a
-140 0.50 DB0.530
38 65 65 80 80
I f
with strengths ranging between 20 and 40 MPa, a load controlled test machine was used
-140
72 77 34 39 I f 1 July 7/98
July 22/98
to obtain the compressive strength. For the 65 and 80 MPa concretes, a displacement
%
1 .O1 2.09
-180
21 21 32 32
1
Aug. 18/98 AU^. 27/98 Sept. 30/98
DB165M DB165
controlled compression test was performed on the concrete cylinders using a 5000 kN
(PE) n a n a
DB140M 1.01 1.01 1-01 1-01 1.01
July 10/98 I r
MTS universal test machine. The results for both testing procedures were assumed to be
3 1 June 15/98 1 Julv 16/98 -180 -190 -190 -350 -350 DBl8O
consistent. The stress-strain responses of the 65 and 80 MPa concrete are presented in
38 , 1.01
I l 1 Oct. 7/98 L
DBl80M
Appendix D.
Aug. 13/98
3.2.2 Steel Properties
Table 3 2 summarizes the reinforcing bar properties. 30M reinforcing bars were
used as the main longitudinal reinforcement. No. 3 reinforcing bars (9.5 mm diameter),
were used as stimps. 15M reinforcing bars were used as top longitudinal reinforcement
for the specimens that contained stinups. The stress-strain responses for the reinforcing
bars are given in Appendix D.
Table 3.2 Reinforcing Bar Properties
Figure 3.1 shows the details of the geomeûic properties of the beam series. The
reasoning behind specimen Di3 l2OM having a different stimp detail than the rest of the
transverse reinforced beams is discussed in Chapter 4. As can be seen in Figure 3.1,
Specimens DB 140M, DB 165M, and DB 18OM have one, single-legged st imp every 300
mm. Specimen DB 120M had one double-legged stirrup every 600 mm.
Details for the construction of the test specimens are given in the next section.
-
Ultimate Stress [ M W
778 643 710
Rebar Type
#3 MIS M30
Cross- Sectional Area
[mm 7 71 500 700
Yield Stress [ M W
508 437 550
Figure 3.1 Geornetric Details of DB Bearn Series Specimens
3.3 Specimen Construction
Two beams were cast simultaneously during each of the six pours. Apart f?om the
first cast on November 6, 1997 when specimens DB 130 and DB230 were cast, for each of
the subsequent pours, one bearn contained transverse reinforcement while the cornpanion
bearn did not. The existing form-work was constnicted fiom 314 inch sheets of plywood.
The bearns were cast side by side and shared a middle wail consisting of plywood
stiffened by two-by-fours (see Figure 3.2). Lateral support for the exterior walis was
provided by steel soldiers bolted to the form-work floor and small steel "1" and "C"
sections m i n g along the entire length of the form-work.
Figure 3.2 Fom-work for Specimens
The preparation of each reinforced concrete beam for casting consisted of the
following procedures:
After the strain gauges were applied to the individuai rebars, the reinforcement
cages were constnicted entirely outside of the forrn-work. Plastic chairs, positioned on
the form-work floor, were used to support the Iongitudinai reinforcement. 300 mm
spacers were tied to the longitudinal rebar to obtain the required spacing. For those
specimens that contained stirmps, steel horses were used to support the top reinforcement
(two MIS rebars) as the stirmps were tied to both the top and bottom longitudinal
reinforcement. A contractors level was used to ensure the stimps were plum. After the
inside of the form-work was oiled, the reinforcement cages were placed inside using with
the aid of a 10-ton crane. The endplates of the fonn-work were then attached to the fom-
work using 11/2" screws. 300 mm wooden spacers were placed in both beam forms to
keep the width uniform during the cast. Threaded steel rods were used to clamp the
beams across their widths dong the entire length of the beams. A final check was made
for plumbness of the stimps. The wooden spacers were removed when the pour was
near completion. A large concrete bucket, maneuvered by the 10-ton crane in the Mark
Huggins Laboratory, was used for the concrete pours.
Both the beam specimens and control cylinders were covered in burlap and plastic
sheets to minimize the moisture loss afier the initial setting of concrete. The beams were
kept under cover for at least four days afier which they were dlowed to air dry until the
day of testing. The specimens were painted white (flat latex paint) to emphasize the
crack patterns in the photographs taken during load stages of the tests. Sixty zurïch
targets were also glued to the south side of each specimen prior to testing. See Figure 3.6
for details of the zurich target layout.
3.4 Tcst Rig Details
The major components of the test facility included the following: two steel
supports, 1.2 Million Pound Force capacity load-controlled actuator (Baldwin), and a
data-acquisition system- These components are discussed below.
3.4.1 Test Set-Up
Figure 3.3 shows a photograph of the test set-up in the Mark Huggins Structural
Lab at the University of Toronto. The Baldwin was used to apply the downward
concentrated point load to the specimens. A rocker, allowing rotation but not
displacement, was used directly under the Baldwin's head to ensure that the load was
applied verticdly. Both ends of the beam specimens rested upon a support assembly
which consisted of a steel beam with a steel roller on top. The steel roller allowed
rotations and horizontal displacements to occur. Mixed plaster was placed at both
supports and under the loading head in order to create smooth surfaces thereby
minimizing stress concentrations due to irregularities on the surface of the concrete.
Figure 3.3 Experimental Test Set-Up
3.4.2 Instrumentation and Data-Acquisition
The fo Ilowing instrumentation was used in this test program:
A 1.2 Million Pound-Force Load Controlled Actuator, five Linear Varying
D isplacement Transfomers (LVDT' s), zuric h gauges, targets, and so hvare, and six dia1
gauges.
Four LVDT's were mounted on the north side of the test specimens as shown in
Figure 3-4 to enable the detemination of the shear strain in the beam. A fifth LVDT was
placed directly under the bearns at the midspan to measure the vertical displacement (see
Figure 3.4).
Figure 3.4 LVDT Layout
Six dial gauges (not shown in Figure 3.4) were also used in the tests. Two diai
gauges were placed on either side of the LVDT at the midspan of the bearn approximately
25 mm in from the beam sides. Two dial gauges were aiso placed 200 mm from the
centreline of the supports on each end of the beam, again, 25 mm in fiom the sides of the
beam (see Figure 3.5). The dia1 gauges were used: to monitor any tilting of the specimen
that may have occurred during the tests, to monitor support displacements, and to obtain
displacements for general cornparison to the LVDT readings. Expenmental data
collected from the Dia1 Gauges are located in Appendix E.
Figure 3.5 Dial Gauge Layout
Figure 3.6 shows the Zurich target layout. The rneasurements obtained using
hand-held Zurich gauges were used to obtain horizontal, vertical, and diagonal
displacements For each g-id of zurich targets, the horizontal, vertical, and shear strains
were calculated for each load stage of every test (Appendix B and C) .
1 .a, .sr .a.. .=., . S I . -4s .y .>; 05.. .';3 ..a .C5 . r, -7 c e .-,9 .w -- In: .- xc
Figure 3.6 Zurich Target Layout
In order to monitor the strain in the longitudinal reuiforcement two strain gauges
were placed at the mid-length of the longitudinal reinforcement as shown in Figure 3.7.
Al1 the strain gauges placed on the longitudinal reinforcement were ghed on the side of
each respective bar (as opposed to the top) to avoid strains resulting from rebar bending.
For the specimens containing 0.5% longitudinal reinforcement (two 30M bars),
gauges MN and MS were placed on both bars, respectively. For the specimens containing
1% longitudinal reinforcement (four 30M bars), gauges MN and MS were placed on the
two middle bars. Furthemore, for the specimens containing 2% longitudinal
reinforcernent (eight 30M bars), the gauges were placed on the two middle bars on the
lower level of the reinforcement (see Figure 3.1). The beam specimens were lined up in
the east-west direction during the test. Gauge MN implies the gauge placed at the
midspan of the rebar on the northem side. The strain gauge locations for the stirrups are
shown in Figures 3.8(a) and 3.8(b). Gauges W1 and E l were positioned as shown in
Figure 3.8(b) in order to monitor the strains that would results fiom potential shear cracks
as they propagated towards the main longitudinal reinforcement.
Figure 3.7 Strain Gauge Layout for Longitudinal Reinforcement
Figure 3.8a Strain Gauge Layout for Transverse Reinforcernent for DB 120M
Figure 3.8b Strain Gauge Layout for Transverse Reinforcement for DBOS30M, DB140M,
DB l6SM, and DB 180M
With the exception of the Zurich displacement readings and the Diai Gauge
readings, which were done m a n d l y at the end of each load stage, the data acquisition
system automatically monitored the instrumentation at a pre-selected time interval. The
components of the data acquisition system include a microcornputer, a digital voltmeter, a
scanner, and the data acquisition software-
3.5 Load Procedure
The specimens were tested under 3-point Ioading. The test involved applying a
vertical downward concentrated load at the beant7s midspan until ultimate conditions
were attained. Ultimate conditions were reached when either a significant &op in load
(post peak) occurrec! or when a significant vertical deflection resulted such that the test
had to be stopped to avoid damaging the LVDT's. However, because most of the beam
specimens failed very abruptly, ultimate conditions were distinct. it took approximately
four to six hours to test each beam with the exception of those beams that had a larger
shear capacity thereby requiring more load stages and hence more time. In the initial
stages of the tests, load stages were taken just after the occurrence of the first flexural
crack and just after the appearance of the first flexural-shear crack. In general, however,
load stages were taken at intervals of 100 kN in total load (50 kN shear). The load stages
were taken at smaller intervals if significant activity was observed in crack formation and
propagation,. The applied load was leveled off at each load stage and decreased
approximately 10% in order to safely take the zurich and diai gauge readings. Along with
the zurich and dia1 gauge readings, cracks were outlined with a black felt tip marker and
the crack widths were detennined and labeled with the aid of a crack width comparator.
Photographs were taken at each load stage and a video record was kept for al1 the tests.
In subsequent chapters, total load refers to the downward actuator load at the
beam's midspan and shear load refers to the reaction force at the supports. From Statics,
the shear load is equivalent to one haif of the total load. The shear Ioads Iabeled in the
specimen photographs in Chapter 3 do not take into account the self-weight of the
specimens.
CHAPTER 4
TEST RESULTS AND DISCUSSION
In this chapter the experimental results are presented and discussed. In addition,
shear strength predictions for the test beams using the design provisions contained in ACI
3 1 8-95 and in CS A A23 3-94 (Generai Method based on MCFT) are compared with the
experimental resdts.
4.1 Effect of Concrete Strength
4.1.1 Reinforced Concrete Beams Containing 1% Longitudinal Reinforcement and no Transverse Reinforcement
Five of the twelve bearns in the series contained 1% Longitudinal Reinforcement
(4 No. 30M rebars) and no transverse reinforcement. The compressive strength of the
concrete for each beam varied and was detemiined by testing six by twelve inch diameter
concrete cylinders as discussed in Chapter 2. The concrete strengths at the time of each
respective beam test were 20,32 38,65, and 80 Megapascais (MPa).
Figure 4.1 shows the load versus midspan deflection respmse for the five
specimens. Table 4.1 sumrnarizes the results for these specimens.
1
i O 1 Z 1 4 5 6 7 I O 10
iiiarpul - c-l Figure 4.1 Load versus Deflection for Beams with 1% Longitudinal Reinforcement and
no Transverse Rein forcement
Table 4.1 Experimental Results for Beams Containing 1% Longitudinal Reinforcement
As can be seen in Figure 4.1 and Table 4.1, the concrete strength had no beneficial
influence on the shear capacity of the beam specimens. Specimen DB180 (80 MPa),
which contained a concrete strength 4 times as strong as specimen DB 120 (20 MPa), had
a slightly lower (-5%) shear capacity.
One explanation for this is that due to the relatively smooth crack surfaces
observed at failure for the specimen containing the high strength concrete, DB180,
aggregate interlock may not have been as prominent in the shear mechanism of resistance
for the beam, resulting in the noticeably low shear load obtained in the tests. Figure 4.2
shows a photograph of portions of concrete taken nom the tested specimens surnmarized
in Table 4.1. From Figure 4.2, it appears that the roughness of the failure crack surface
decreased considerably as the strength of the concrete increased.
The beam shear failures were sudden with virtually no warning, with failure
cracks extending fiom the loading point, down along a previously formed f l e d - s h e a r
crack farthest fiom the midspan of the beam, and splitting the bond of the longitudinal
reinforcement al1 the way to the support. Also, the M n measured in the longitudinal
reinforcement at the bearn's midspan at failure for every specimen was at most about
40% of the yield strain (see Table 4.1). Detailed experimental observations for each
beam test are given in Appendix B.
Specimen
Dl3120 DB130 DB 140
Concrete Stre W h
f %
W a l 20 32 38
DB165 1 65 DB180 1 80
1 Vu,, is the test shear load plus the shear load from the self-weight of the beam
Test S hear Load P/2
CkN] 172 178 173
Deflection at Failure
Cm1 6-2 5 4-8
' Ultimate Shear
Load, V,, '
Iw 179.1 185.1 180-1
178
Longitudinal Strain in Reinforcement at Failure - y EYietd
32 % 36 % 36 %
7-1 185.1 33 % 42 % 165 172.1 1 9.3
Figure 4.2 Crack Surface Roughness for Concrete Strengths Exarnined
Figures 4.3 to 4.7 show photographs of the bearns at failure. It is important to note
that the Iabeled shear load at failure, V, does not include the self weight of the bearn.
Figure 4 3 Specimen DB 120 after Faiiure
Figure 4.4 Specimen DB 130 after Failure
3 3
Figure 4.5 Specimen DB140 after FaiIure
Figure 4.6 Specimen DB 165 afier Failure
3 4
Figure 4.7 Specimen DB 180 afier Failure
From Figures 4.3 to 4.7, it can be seen that the specimens had essentially the same
crack patterns at failure. However, bond splitting was more severe for the hi&-strength
beam specimens, DB 165 (65 MPa) and DB 180 (80 MPa).
Appendix B contains the total load versus midspan deflection, shear load versus
shear strain, and total load versus longitudinal reinforcernent strain responses for these
tests; crack patterns and nirich strain plots of every load stage for ail these beam tests are
also given.
4.1.2 Cornparison of Beam Specimens DB0.530 and BRLlOO(Stanik, 1998)
Specimens DB0.530 and BRLlOO were Iarge, lightly reinforced concrete
rnernbers. Both specimens contained 0.5% longitudinal reinforcement. Specimens
DB0.530 and BRLlOO were identical except for their concrete strengths; 32 MPa for the
former, 94 MPa for the latter. BRL100 was cast on July 5, 1996 and tested on August 12,
1996 by Bogdan Stanik. Test results fiorn specimen BRLlOO supported the hypothesis
that Iightly reinforced concrete beams without stimrps and distributed longitudinal
reinforcement do not demonstrate a reliable gain in shear strength with increasing
concrete strength. The shear failure Loads of specimens DB0.530 and BRLlOO were
165.1 and 164.1 kN, respectively. Table 4.2 summarizes experirnental results for
specimens DB0.530 and BRLIOO. Section 4.3 discusses the effect of main longitudinal
reinforcement on the shear capacity of beams without stirrups.
Tabte 4.2 Experirnentaf ResuIts for Specimens DB0.530 and BRL I O0
From Table 4.2, it is evident that the specirnens yielded virtually identical
responses.
Specimen
DB0.530
4.1.3 Reinforced Concrete Beams Containing 1% Longitudinal Reinforcernent and Transverse Reinforcement
Four of the twelve beams in the senes contaïned 1% Longitudinal Reinforcement
and transverse reinforcement such that - A'fv - - OAO MPo . bws
Concrete Strength
f k
W a l 32
These four beams were intended to complement four of the companion specimens
Test Shear
Load Pl2
WI 158
BRLlOO 1 94
Ultimate Shear
load, V,,
[W 165.1
without transverse reinforcement. The concrete strengths examined were 20, 38, 65, and
157 164.1
80 MPa. Section 4.2 compares the shear capacities of the specimens with stirrups to the
companion specimens without stirrups.
Figure 4.8 shows the load versus midspan deflection response for the four beams.
Deflection at Failure
[mm1 7.6
Table 4.3 surnrnarizes the results for these specimens.
Longitudinal S train in Reinforcement at Failure -
ao%ieM
52 % 7.4 64 %
Figure 4.8 Load vs. Deflection for Beam Containing 1 % Longitudinat Reinforcement and Transverse Reinforcement
Table 4.3
S pecimen
Experimentat Results for Beams Containing 1% Longitudinal Reinforcement and Transverse Reinforcement
Concrete Strength
f %
Test Shear Load P/2
CkN] 275
Ultimate Deflection Shear at Failure
Load, Vu,,
Longitudhal Strain in Reinforcement at Failure -
As can be seen in Figure 4.8 and Table 4.3, when transverse reinforcement is
present, the benefits of high strength concrete are realized in the ultimate shear strength.
The lower concrete strength beam specimens, DB120M and DB140M, failed at a
shear Ioad of about 270 W. At that load level, the higher concrete strength beam
specimens, DBl6SM and DB180M, had very similar crack patterns but srnaller cracks
widths when compared to the lower strength concrete specimens. This translates to a
higher reserve capacity in these higher strength concrete beams (see crack patterns;
Appendix C). As can be seen in Table 4.3, in specimen DB165M, the longitudinal
reinforcement nearly yielded prior to failure.
During the maturing process the specimens rnay shrink due to the hydntion
process and the Ioss in moisture in the concrete. As a result, pre-compression may have
been induced in the longitudinal steel, thus giving it that extra capacity for tensile
straining (see Table 3.1).
The experimental shear capacity of DB 1 80M (80 MPa concrete) was less than the
experimental shear capacity of DB 165 (65 MPa concrete). This result may be due to the
reduction in aggregate interlock capacity across the diagonal cracks in specimen
DBl8OM due to fracturing of the aggregate (Figure 4.2). Detailed experirnental
observations for each beam test is given in Appendix C.
Figures 4.9 to 4.12 show photographs of these specimens at failure.
Figure 4.9 Specirnen DB120M after Failure
38
Figure 4.10 Specimen DB l4OM afier Faiiure
Figure 4.1 1 Specimen DB 1 6SM after Failure
39
Figure 4.12 Specimen DB 1 SOM after Failure (Note: error in sign)
Following the construction and testing of specimen DBI20M, the arrangement of
the stirrups was aitered for the remaining specimens (Figures 3.8(a) and 3.8(b)).
Specimen DB120M contained double-legged stirrups spaced at 600 mm. Figure 4.9
shows a photograph of specirnen DB 120M at failure with the stirrup locations shown
with red dotted lines. The failure crack appears to intersect only one stirmp. From this
resuk it was believed that the 600 mm spacing, the maximum spacing allowed by CSA
A23.3-94 (for V P d < O. 1 A&f'J, was too large and that a smaller spacing would better
utiiize the transverse reinforcement. Thus, the remaining three bearns were constructed
with single-legged stirrups to minimize the spacing to 300 mm and stiM maintain the
same transverse reinforcement ratio.
In Figure 4.10, the locations of the stirrups are shown with red dotted lines. The
shear capacity achievéd by specimen DB 140M was dmost identical to that for specimen
DB 120M. The crack spacing, however, was larger in specimen DB 120M (see Figure
4.9). AIso, as a result of using single-legged stimps, more strain gauges were used and
hence a better representation of strain distributions was obtained throughout the specimen
when compared to that for specimen DBIZOM. Signifïcant sliding along die crack
surfaces c m be detected by the offsetting of the drawn Iines crossed by the diagonal
cracks.
Appendix C contains the total load versus rnidspan deflection, shear load versus
shear strain, and total load versus longitudinal reinforcement strain responses for these
specimens; crack patterns and zurich strain plots of every load are also given.
4.2 Effects of Transverse Reinforcement
4.2.1 Reinforced Coocrete Beams Containing 1% Longitudinal Reinforcement and Transverse Reinforcement
Four of the twelve beams in the series contained 1% Longitudinal Reinforcement
- 0.40 WQ. No. 3 reinforcing bars (9.5 mm and transverse reinforcernent such that - - b !*CF
diameter, 71.3 mm2 area) were used for the stimps with a yield strength of 508 MPa.
The Canadian Standard, A23.3-94, requires a minimum area of shear reinforcement, A,,,
given by:
AV = 0 . 0 6 m - or a stress, pfi = 0 . 0 6 6 fu
For specimen DBEOM, double-legged stimps (& = Z(7l.3) = 142.6 mm') were
For specimens DB l4OM, DB l6SM, and DB 180M singte-legged stimps
(A, = 71mm2) were spaced at 300 mm yielding the same stress as above. Because
the concrete strength ranged fiom 20 to 80 MPa and the stirrup detail was kept constant
for dl the beams, the minimum amount of stirrup stress at yield, 0.06&, was not
always attained.
Figures 4.13 to 4.16 compare the load versus midspan deflection for the beams
containing transverse reinforcement and their counterparts, which contain no transverse
reinforcement,
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0
Midspan Oeffection [mm]
Figure 4.13 Load versus Midspan Deflection for DB 120 and DB 120M
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0
Midspn D t f l d o n [mm]
Figure 4.14 Load versus Midspan Deflection for DB 140 and DBI40M
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Midspan Defiedion [mm]
Figure 4.15 Load versus Midspan Deflection for DB 165 and DB l6SM
10.0 15.0
Midspan Oeflecîion [mm]
Figure 4.16 Load versus Midspan Deflection for DB 180 and DB 1 80M
A significant increase in capacity and ductility was realized in the specimens with
transverse reinforcement when compared to their counterparts wbich had no transverse
reinforcement. In general, the presence of stirrups increased the beams shear capacity by
58% for specimens DB120M (20 MPa concrete) and DB140 M(40 MPa concrete). The
increase in beams shear capacity due to the presence of stirrups was much higher for the
higher strength concrete beam specimens. Specimens DB 165M (65 MPa concrete) and
DB 1 8OM (80 MPa concrete) showed a 135 to 150 % increase in ultimate shear strength
over their counterparts that did not contain stirrups.
Though at peak load, the midspan deflection of al1 the beams with transverse
reinforcement was three to four tixnes that of their counterparts without transverse
reinforcement, the sudden drop in load beyond peak conditiors indicated that there was
not enough transverse reinforcement provided for post-peak ductility. Table 4.4 shows
the amount transverse reinforcement used in the specimens relative to the requirements
for minimum transverse reinforcement given in the CSA and AC1 codes.
Table 4.4 Required Arnount of Minimum Transverse Reinforcement
4.2.2 Cornparison of Beam Specimens DB0.530 and DB0.530M
Specimen DB0.530M was intended to complement DB0.530 with the addition of
transverse reinforcement. Figure 4.17 shows the load versus midspan deflection response
of specimens DB0.530 and DB0.530M. Table 4.5 sumrnarizes the experimentai results
for specimens DB0.530 and DB0.530M. Further details for these specimens are given in
Appendix C.
specirnen
DB120M DB 140M DB 165M DB 180M
~o&rete Stren@
f'c
W a l 20
A- 38 65 80
Minimum AI- required b*s
by CSA
W a l 0.268 0.370 0.484 0.537
minimum 9 required b a by AC1
W a l 0.35 0.35 0.35 0.35
- AVfY b~
provided
W a l 0.402 0.402 0.402 0.402
AYfY - provided b*s
A$ - req'd - C H b d
1.50 1 .O9 0.83
I
0.75
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 Midspan Oeflection [mm]
Figure 4.17 Load vs. Deflection for DB0.530 and DB0.530M
slab. As observed in Figure 4.17, the addition of stimps considerably enhanced the
strength and toughness of the lightly reinforced f l e d member. Specimen DBOS30M
nearly attained its flexural capacity, whereas DB0.530 achieved only 63% of its Bexurai
capacity. It is evident that the addition of only 0.079% of transverse reinforcement is
very beneficial. Figures 4.18 and 4.19 show photographs of specimens DB0.530 and
DB0530M at failure.
Table 4.5 Experimental Results for Specimens DB0.530 and DB0.530M
Specimen
DB0.530 DB0.530M
The specimens were essentially representative slices of a thick reinforced concrete
Test Shear Load P/2 WI
Longitudinal Strain in Reidorcement at
Failure - " y Eyield
Ultimate Shear L o d Vu,,
[EcN]
52 % -100 %
Deflection at Failure [mm]
7.6 19.5
158 1 165.1 256 263-1
Figure 4.18 Photograph of DBO.530 after Failure
Figure 4.19 Photograph of DB0.530M after Failure
46
4.3 Effect of Main Longitudinal Reinforcement
Specimens DB0.530, DB130, and DE3230 were designed to study the effects of
arnounts of main longitudinal reinforcement on the shear capacity of reinforced concrete
beams. The three specirnens were dl constnicted using 32 MPa concrete. Figure 4.20
shows the ioad versus midspan deflection of the three specirnens. Table 4.6 summarizes
the experimentai results of the specimens.
0.0 1 .O 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0
Midspan Deflection [mm]
Figure4.20 Load vs. Deflection for 32 MPa Beams with Varying Longitudinal Rein forcement
Table 4.6 Experimental Results for Beams Containing OS%, 1%, and 2 % LongitudinaI Reinforcement
Load P/2 load, V,, Deflection at Longitudinal Strain
Failure in Reinforcernent at 1-1 Failure - "-B/
Eyield
7.6 52 %
The post-cracking stiflkess of the beams increased as the amount of main
longitudinal reinforcement increased (Figure 4.20 and 4.21). Specimen DB230 showed
some resiliency recovering fiom two drops in Ioad thus attaining the sarne ductility as
specimen DBO.530. As expected, specimen DB0.530, with oniy 0.5% longitudinal
reinforcement, yielded the sofiest response.
Figure 4.21 shows the strain histories in the longitudinal reinforcement at the
midspan for each specimen.
Figure 4.21 Load vs. Longitudinal Strain for 32 MPa Beams
Figures 4.22 to 4-24 show photographs of the three specimens after failure.
Figure 4.22 Photograph of DBO.530 after Failure
Figure 4.23 Photograph of DB 130 after Failure
Figure 4.24 Photograph o f DB23O after Failure
From the crack patterns shown in Figures 4.22 to 4.24, it appears that tess bond
splitting occurred as the amount of the main longitudinai reinforcement increased. This
may be attributed to an increase in dowel area By the end of the test several small
diagonal cracks had forrned in the zone of the reinforcement at the east end of the beam
adjacent to the support for specimen DB230. The diagonal shear failure crack got steeper
as the amount of main longitudinal reinforcement increased. Further details of these tests
are given in Appendix B.
4.4 Prediction of Beam's Ultimate Shear Capacity using the ACI 318-95 and CSA A23.3-94 (General Method) Procedures
Tt is important to note that for the beams containhg stirrups, it was assumed that
al1 the specimens contained the minimum amount of transverse reinforcement required by
CSA A23.3-94 and thus predictions were based on P and B values fiom Figures 2.3 and
2.3 and Tables 2.1 and 2.2 given in Chapter 2.
Table 4.7 compares the d t h a t e shear strength values obtained fiom the
experimental results for the specimens with 1% Longitudinal reinforcement and no
transverse reinforcernent to those calculated using the AC1 318-95 and CSA A23.3-94
approaches. In the table, Pl2 signifies the half the total load applied by the testing
machine. Vu,,"P is the actual shear load acting on the specimen taking into account the
self-weight of the bearn.
Sarnple calculations used to obtain the values given in the d l the tables in this
section are provided in Appendix A.
Table 4.7 Uttirnate Shear Capacity for Beams Containing 1% Longitudinal Reinforcement and no Stimps
Frorn Table 4.7, the AC1 predictions for shear capacity significantly exceed the
experimental values, especially for the higher concrete strengths. Even with the Iimit of
69 MPa imposed on the compressive strength of the concrete, specimen DB 180 failed at a
load less than one-half of that predicted using the AC1 code.
The General Method fkom the Canadian Code performed much better than the
AC1 method. Predictions, however, grew increasingly unconservative as the concrete
strength increased.
Table 4.8 compares the ultimate shear values obtained fiom the experimental
results, to those predicted using the AC1 3 18-95 approach and CSA A23.3-94 (General
Beam
DB120 DB130
Pl2
twl
DB140 173.0 180.1 0.65 0-1 1 0.08
DB180 165.0 172.1 0.62 0.07 * equivalent crack spacing parameter calculated assurning an aggregate size of zero. Though this criteria
usually applies to concrete strengths greater than about 70 MPa, the crack surface of specimen DB 165 after faiIure was quite smooth so the aggregate size was taken as zero.
VulrW
M
197.6 209.8' 220.9*
172.0 1 179.1 178.0 1 185.1
vhw vuhACi
- VU[[
bd IVpa]
160.9 191.9
vU,,M?
M
281.9 ----P.
373.6 384.9
vutt
b d n W a l
0.65 0.67
O. 14 O. 12
207.2 262.2
FN]
0.91 0.88 0.75
v,,t,q
vit
0.64 0-50 0.45
1 - 1 1 1 0.86 0.96 0.7 1
Method) approach, for those beams containkg 1% longitudial reinforcement and
Avfv transverse reinforcement, such that, - = 0.401MPa . bws
Table 4.8 Ultimate Shear Capacity for Beams Containing 1% Longitudinal Reinforcement and Transverse Reinforcement
From Table 4.8, the AC1 predictions, in general, overestimated al1 the
expenmental shear strengths. The concrete compressive strength was limited to 69 MPa
again for the AC1 predictions because the transverse reinforcement required to use the
specified f'c was not provided. However, the prediction overestimated the capacity of
specimen DB 180M by 20%.
The General Method (based on MCFT) fiom the Canadian Code, yielded better
predictions than the AC1 approach. Both methods proved to be the most unconservative
for specimen DB 140M.
Table 4.9 compares the ultimate shear values obtained from the experimeatal
results of the beams with OS%, 1%, and 2 % longitudinal reinforcement made fkom 32
MPa and 94 MPa concrete to those calculated using the AC1 3 18-95 approach and CSA
A23.3-94 (Generai Method) approach.
Vu,?-'
Wl
318.4 393.1 484.8 496.1
vu?p
M
282.1
Beam
DBl20M
vu,,""
FN]
299 350
V U I ~ ~
vu/tBECm
0-94 0.79 1.12 0.92
- V U I ~
bd Wa]
1 -02 , 1 .O0 DB 140M 1 270.0 1 277.1
P/2
Lw 275-0
401 423
vd- ACI
0.89 0.70 0.93 0.80
v~ir bdJ7'; Pfpa]
0.23 0.16 0.20 0.16
1.63 1.42
DB165M DB180M
445.0 388.0
452.1 395.1
Table 4.9 Ultimate Shear Capacity for Beams Containing OS%, I%, and 2% Longitudinal Reinforcement and no Stirrups
From Table 4.9, as the percentage of main longitudinal reinforcement decreased
the AC1 predictions become increasingly unconservative. Specimen BRL100, a large,
lightly reinforced high-strength concrete beam with no stirrups or distributed
reinforcement, proved to be the worst case for the AC1 Code failing at a 43% of the shear
load predicted by the AC1 code.
Crack widths tend to decrease in magnitude as the amount of main longitudinal
reinforcement increases. Thus, for members with large amounts of longitudinal
reinforcement, the AC1 approach can perform adequately. Test results indicate that when
either iow amounts of longitudinal reinforcement are provided in the beam, or the size of
the bearn is increased, the crack widths increase in magnitude. Predictions using the AC1
approach for such cases yield the poorest results. The General Method predicts shear
capacities taking into account crack spacing and widths as well as the depth of the
member and the amount of longitudinal reinforcement. Thus, experimental results were
predicted quite weli using the General Method.
Table 4-10 compares the ultimate shear values obtained fiom the experimentai
results of specimens DB0.530 and DB0.530M to those calculated using the AC1 3 1 8-95
approach and CSA A23.3-94 (General Method) approach for the bearns containing
transverse reinforcement.
Beam
BRL100 DB0.530 DB130 DB230
V, MckT
FN]
175.0 146.1 191.9 218-1
LPc1
N I
382.1 262.2 262.2 262.2
PO
[W
157-0 158.0 178.0 260.0
- VUII
bd wa1
0.60 0.60 0.67 0.98
v u I l
M
164.1 165.1 185.1 272.1
vuif
b d m w a ]
0.06 0.1 1 O. 12 0-17
vulr=P
~uir~-
0.94 1.13 0.96 1 -25
-
vulr="
Yuh Act
0.43 0.63 0.7 1 1 -04
Table 4.10 Ultimate Shear Capacity for Specimens DB0.530 and DB0.530M
The AC1 predictions for uitimate shear capacity are better when the crack widths
are contained, either with stirmps or distnbuted reinforcement. However, if the amount
of longitudinal reinforcement is low, as for specimen DB0.530M, the code still yields
very unconservative predictions. This is likely because the AC1 code does not consider
the effects of the longitudinal reinforcement on shear strength. In previous test studies
(see Chapter 2), it appeared that the AC1 code yielded conservative results when stirrups
were utilized. However, the AC1 does not perform well for the beams with transverse
reinforcement in this study because the percentage of longitudinal reinforcement is Iow
(Table 4.7and 4.10). The results in Tables 4.7 to 4.10 indicate that the AC1 code
predictions are conservative o d y when there is a relatively high percentage of
longitudinal reinforcement (Specimen DB230 only).
The average ratio of the experimental shear failure load to the predicted shear
failure load for the General Method was 0.98 with a coefficient of variation of 15.3%.
For the AC1 method the average ratio of the experimental shear failure load to the
predicted shear failure load was 0.74 with a coefficient of variation of 23%.
Possible discrepancies that exist with predicted values and experimental values
may involve the quality of the aggregate. Though the desired concrete compressive
strengths were obtained, the quality of the aggregate was, in general, poor. With
advances in the quaiity of cement and supplementary cementing materials, concrete as a
whole, can achieve the required strength with poor quality aggregate. However, shear
resistance, and not unixial compressive strength of concrete, is the main concem in a
lightly reinforced concrete beam. Poor aggregates can have a negative effect on the shear
Beam
DBO-530
DB0.530M
Pl2
FN]
t 58.0
256.0
VultaP
[W
165.1
263.1
- V U ~ I
bd WaI
0.60
0.95
V U ~ I
b d f i PfPaJ
0.1 1
V,,Fm
WI
146.1
0.17 1253.0
CW
262.2
373.4
vultCXP
vu1t
1.13
V U ~ I QCP
Vuft A= l
0.63
1 .O4 0.70
fnction dong crack surf'aces. If the development of shear fnction dong the crack surfâce is not as
effective as is irnplicitly assumed in current design code niles, unconservative designs niay result-
Figure 4.25 shows the influence of the concrete compressive strength on the beam shear
capacity for specimens of this series, and two specimens tested in 1996 by Tommi Leinala and
Sinisa Stojicic with 1% longitudinal reinforcement and no stimips (the 36 MPa specimen in 1996
was strapped after Mure and re-tested to produce the two data points shown). The predîctions
made by the AC1 and CSA (General Method) codes are also shown for the various concrete
strengths in Figure 4.25,
It is interesting to note that the specimens tested in 1996 show higher shear capacities
comparai to the specimens testai in the cunent series. However, both test series show that
increasing the concrete strength by a factor of 3 to 4 does not result in a correspondhg increase in
the shear capacity of the beams. in fact, for both senes, the highest strength concrete beams fàiled
at the iowest shear capacities.
Figure 4.25 infiuence of Concrete Strength on Shear Capacity of Beams with 1% Longitudinal Reinforcement and no Stirmps.
As rnentioned previously, the aggregate quality in the current test series \as, in general,
poor. The trend in Figure 4.25 would appear to indicate that, in the last two years, the quality of
the aggregate, in terms of shear resistance, fiom the local concrete plant has deteriorated. It would
sccm that large lightly reinforceci beams are very sensitive to aggregate quality.
CHAPTER 5
CONCLUSIONS AND RECOMMENDATIONS
5.1 Conclusions
1. The concrete strength, which ranged between 20 and 80 MPa, had no significant
influence on the shear capacity of the beam specimens of this test series which
contained 1% (main) longitudinal reinforcement and no transverse reinforcement.
The beam specirnen with the highest concrete strength had the lowest shear
capacity .
2. The impiementation of high strength concrete was oniy beneficial when
transverse reinforcement was utilized. Whereas the beam specimens with the 20
and 40 MPa concretes attained a 60% increase in shear capacity due to the
addition of a small amount of stirrups, an increase in shear capacity of 135 to
150% was attained for the beams with 65 and 80 MPa concretes.
Providing a çmall amount of transverse reinforcement (Le. * = 0.40 ma) to b lis
large, lightly reinforced members resulted in significant gains in terms of reserve
strength and ductility when compared to the cornpanion specimens that did not
contain transverse reinforcement, in some cases, nearing the beam's flexural
capacity. Specimens with stirrups had midspan deflections 3 to 4 times greater
than those for the specimens without stirrups.
4. Increasing the main longitudinal reinforcement ratio, and thus decreasing the
crack widths, increased the shear capacity of beams without transverse
reinforcement.
5. Bond splitting was most severe for the high strength concrete specirnens without
stirrups. Furtherrnore, bond-splitting cracks were controlled with an increase in
the main longitudinal reinforcement ratio or the addition of stirnips.
6 . It is of considerable concem that 11 of the 12 specimens failed at shears less than
the capacities predicted by the AC1 code. Specimen DB230, which contained 2%
longitudinal reinforcement, failed at just 4% above the AC1 code prediction. The
AC1 code predictions were severely unconservative for lightly reinforced (0.5%
and I%), high strength concrete beams without transverse reinforcement- For the
12 tests the average ratio of the experimental shear failure Load to the AC1
prediction for the shear failure load was 0.74 with a coefficient of variation of
23%. See Figure 5.1.
7. The use of the Generai Method for the predictions o f the beams' shear capacities
yielded generally good results. Unlike the AC1 approach, as the percentage of
longitudinal reinforcement decreased, the General Method provided excellent
predictions for the large beams without stirnips. This approach gave somewhat
unconservative results, however, as the concrete strength increased for specimens
without transverse reinforcement. Thus, specimen DB180 failed at 75% of the
General Method prediction. For the 12 tests, the average ratio of the experimental
shear failure Ioad to the General Method prediction for the shear failure load was
0.98 with a coefficient of variation of 15.3%. See Figure 5.1.
Figure 5.1 Ratio of experirnental shear capacity to predicted shear capacity versus -
longitudinal reinforcement ratio and concrete strength for beams without S ~ ~ M P S
5.2 Recommendations
The concrete used in this study was obtauied fiom a major ready-inix plant in Toronto.
For some of the low strength concrcte specirnens, examination of the crack surfàce of tested
specirnens showed that, though the surfafes were, in general, quite "hi11 y" and rough, some of the
coarse aggregates had fractured. Fracturing of the aggregate is usually expected fiom high
strength cuncrete.
As discussed in section 4.4, large lightly reinforceci concrete beams seem to be vecy
sensitive ta aggregate quality (see Figure 4.25). A coordinated program of t e h g should be
perfonned across Canada with standardid specirnens to systernatically study the influence of
local aggregate characteristifs on the shear capacity of large, lightly reinforcecl concrete beam
specirnens.
REFERENCES
1. AC1 Committee 318, "Building Code Requirements for Reinforced Concrete (AC1 318-95) and Commentary AC1 318 R-95", American Concrete Institute, Detroit, 1995,369 pp.
2. Collins, M.P., "Procedures for Calculating the Shear Response of Reinforced Concrete Elements: A Discussion", Journal of Structural Engineering, ASCE, V. 124, No. 12, Dec. 1998, pp. 1485-1488.
2. Collins, M.P., Mitchell, D., "Prestressed Concrete Structures", Response Publications, Canada, 1997,766 pp.
4. Collins, M.P., Mitchell, D., Adebar, P., Vecchio, F.J.? "A Gened Shear Design Method", AC1 Structural Journal, V.93, No. 1, Jan-Feb. 1996, pp. 36-45.
5. Collins, M.P., Mitchell, D., MacGregor, J.G., "Structural Design Considerations for High-Strength Concrete", Concrete International, V. 15, No. 5, May 1993, pp. 27-34.
6 . Collins, M.P., Kuchma, D., "How Safe Are Our Large, Lightly Reinforced Concrete Beams, Slabs and Footings?", Paper published in Concrete Canada Compendium for Technology Transfer Day: The Specifications and Use of HPC, University of Toronto, October 1, 1997, pp. 87-1 16.
7. Collins, M.P., "Reinforced Concrete in Combined Shear and Flexure", Proceedings of the Mark W. Huggins Symposium, University of Toronto, Sept. 1978, pp. 154-171.
8. Carrasquillo, R.L., Nilson, A.H., Slate, F.O., "Properties of High Strength Concrete Subject to Short-Term Loads", AC1 Structural Journal, V.78, No. 3, May-June 1981, pp. 171-178.
9. Carrasquillo, R.L., Slate, F.O., Nilson, A.H., "Microcracking and Behavior of High Strength Concrete Subject to Short-Term Loading", AC1 Structural Journal, V.78, No. 3, May-June 1981, pp. 179-186.
10. CSA Committee A23.3, "Design of Concrete Structures: Structures (Design) - A National Standard of Canada", Canadian Standards Association, Rexdale, Dec. 1994, 199 PP .
1 1. Elzanaty, A.H., Nilson, A H , Slate, F.O., "Shear Capacity of Reinforced Concrete Beams Using High-Strength Concrete", AC1 Structural Journal, V.83, No- 2, Mar.-Apr 1986, pp. 290-296.
12. Fenwick, RC-, Paulay, T., "Mechanisms of Shear Resistance of Concrete Beams", Journal of the Structural Division, ASCE, V.94, No. ST10, Oct. 1968, pp. 2325- 2350.
13. Kong, P.Y.L., Rangan, B.V., "Shear Strength of Hi&-Performance Concrete Beams", ACI Structural Journal, V.95, No. 6, Nov.-Dec. 1998, pp. 677-688.
14. Kuchma, D., Vegh, P., Simionopoulos, K., Stanik, B., Collins, M.P., "The Influence of Concrete Strength, Distribution of Longitudinal Reinforcement, and Member Size on the Shear Strength of Reinforced Concrete Beams", CEB Bulletin No. 237, 21 PP .
15. Stanik, B., "The Influence of Concrete Strength, Distribution of Longitudinal Reinforcement, Amount of Transverse Reinforcernent and Member Size on Shear Strength of Reinforced Concrete Members7', M.A.Sc. Thesis, University of Toronto, Department of Civil Engineering, 1998,7 1 I pp.
16. Vecchio, F.J., Collins, M.P., "The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear", AC1 Structural Journal, V.83, No. 2, Mar.-Apr. 1986, pp. 2 19-23 1,
1 7. Vecchio, F. J., Collins, M.P., "Predicting the Response of Reinforced Concrete Beams Subjected to Shear Using Modified Compression Field Theory", AC1 Structural Journal, V.85, No- 4, May,-June 1988, pp. 258-268.
1 8. Walraven, J-C., "Shear Friction in High-Strength Concrete", Progress in Concrete Research, V.4, TU Delft 1995.
19. Walraven, J.C., Frenay, J., Pruijssers, A., "Influence of Concrete Strength and Load History on the Shear Friction Capacity of Concrete Members", PCI Journal V. , No. , Jan.-Feb. 1987, pp. 66-84.
20. Yoon, Y., Cook, W.D., Mitchell, D., "Minimum Shear Reinforcement in Normaf, Medium and High-Strength Concrete Beams", V.93, No. 5, Sept.-Oct. 1996, pp. 576-584.
SAMPLE CALCULATIONS OF AC1 318-95 AND CSA A23.3-94 (General Method)
CODE PREDICTIONS
Estimation of Shear Failure Load Using the General Method (CSA A23.3-94)
Sarn~le Calculation for Specimen DB 130. V,.,, = 185.1 kN (Table 4.6) -
Concrete; f', = 32 MPa, 10 mm aggregate
Reinforcement; 4-30M rebars with a cover of 75 mm
1. Find the effective shear depth or flexural lever ann;
a dv=d--=925-
550 x 4 x 700 / 0.85 x 32 x 300 = 83 lmm
2 2
2. Calculate the crack spacing parameter
For members that do not contain distributed longitudinal reinforcement or stimips can set crack spacing parameter sx = dv = 83 lmrn
Because the aggregate size is not 19 mm, the aggregate size used to derive the P values, the equivalent crack spacing parameter, ss,, is needed. Le.,
3. Guess a value for the longitudinal strain, 4, to obtain Vu and calculate Mu using equation for q. Check ratio of moment to shear at critical section.
The shear capacity, Vu, is given fiom equation 2.7 in chapter 2 as:
Assume = 0.001. From Table 2.1, 8 = 57.2" , P = 0.1 14 Therefore, Vu = (1410)0.114 = 161.2 kN
The longitudinal strain, c, is calculated as:
Longitudinal Strain, = M u / dv + OSVucott9
EsAs
The criticai section is taken 4. away from the applied load where the moment to shear ratio is approximately 1.8 metres.
M u 422 - - - - 2.62 > 1.8 This indicates that our assumption was too Vu 1612
conservative. We must choose a smaller magnitude of the longitudinal strain, gx.
4. Second iteration
Try E, = 0.0005 - Frorn Table 2.1, O= 52O , P= 0.159
Therefore, Vu = (14 1O)O. 159 = 224 kN
E x = MU / 83 1 + O5(224OOO) cot 52
= 0,0005 (200000)(2800)
1.8--7 14 Using Linear Interpolation, VU = 224 - (224 - 16 1.2) = 1882k.N
2.62--7 14
Prediction overestimates the section shear capacity, 1 85.1 W, by about 2%.
Estimation of Shear Failure Load Using the AC1 Approach (ACI-318-95)
Sample Calculation for S~ecimen DB 130, V,,,, = 185.1 kN (Table 4-61 -
The concrete's contribution to shear strength fiom equation 2.2 în chapter 2 is given by:
Predicüon overestimates the section shear capacity, 185.1 kN, by about 42%.
Estimation of Shear Failure Load Using the General Method (CSA A23.3-94)
Sarnple CalcuIation for Specirnen DES 120M- V..,. - = 282.1 kN (Table 4-71
Concrete; - f, = 20 MPa, 10 mm aggregate
Reinforcement; - 4-30M rebars with a cover of 75 mm - #3 Stirrups at 600 mm
S hear,
= p & x 3 0 0 ~ 8 3 1 + 2(7 l3)(5O8) (83 1) cot 9 600
v Using Table 2.2, assume gX r 0.00 15 and - 1 0.075 . This yields 8 = 40" , P = 0.158
f'.
Therefore, Vu = ( 1 1 130.158 + 100.3cot40 = 295.7 khi
MU / dv + 05Vu CO^ 0 Longitudinal Strain, a =
Eds
MU / 83 1 t O.S(2957OO) cot 40 a = = 0.00 15
(200000)(2800)
The critical section is taken dv away from the applied load where the moment to shear ratio is approximately 1.8 metres.
Mu 551.6 -- _-- - 1.87 > 1.8 This indicates that our assumption was a little too Vu 295.7
conservative. We must choose a smaller magnitude o f the longitudinal strain, E,.
v Try E, I; 0.001 and - 10.075- From Table 2.2, O= 36 ,P= 0.179
f'.
Therefore, Vu = (1 1 15)O. 179 + 100.3cot36 = 337.6 IrN
v 337600 / 300 x 83 I -= = 0.068 < 0.075 okay. f 'c 20
MU / dv + 05Vu~0t0 Longitudinal Strain, ~r =
E d s
MU / 83 1 + O5(33 7600) cot 36 E r = = 0.00 1
(200000)(2800)
Using Linear Interpolation, VU = 33 8 - (338 - 296) 1.8 - 0.805 = 298.8kN 1.87 - 0.805
Prediction overestimates the section shear capacity, 282.1 kN, by about 6%.
Estimation of Shear Failure Load Using the AC1 Approach (ACI-318-95)
Samde Calculation for S~ecimen DB 140M- V,,,, - = 282-1 kN (Table 4.7)
The concrete contribution to shear capacity, V,
The stirrup steel contribution to shear capacity, as:
fiom equation 2.2 in chapter 2 is given as:
V,, from equation 2.3 in chapter 2 is given
So, Vc = 0167$E(300)(925) = 2 0 7 W
and Vs = î (7 l3)(508)(925)
= 1 1 1.7kN 600
Therefore, Vu = Vc + Ys = 3 19kN
Prediction overestimates the section shear capacity, 282.1 kN, by about 13%.
RESPONSE OF BEAM SPECIMENS CONTAINING O.SO/o, le/. AND 2%
LONGITUDINAL REINFORCEMENT
Total Load versus Midspan Deflection
Shear Load versus Shear Strain
Total Load versus Longitudinal Reinforcement Strain
Crack Patterns and Surface Strain Profiles
Specimen DB 120
The first flexural crack occurred at a total load of 150 kN (75 kN shear) at the
beam's midspan, extending approxirnately 350 mm into the specimen (the loads
mentioned are the test loads and do not consider self weight). At a total load of about 220
kN (1 10kN shear) the Eirst flexural-shear crack formed on the West side of the specimen.
At Load Stages 2 and 3 (total loads of 224 kN and 300 IrN respectively), several flexurai
and flexural-shear cracks formed on either side of the beam's midspan. The spacing of
these cracks was about 300 to 400 mm. At a total load of 350 kN (Load Stage 4), the
flexural-shear cracks on both ends of the specimen had turned over with crack tips
directed towards the loading point. On the West side, the cracks extended diagondly
towards the loading point approximately 700 mm into the beaxn (perpendicular distance
from the bottom). Upon reloading, the specimen failed abruptiy in shear at a load less
than the Ioad attained at load stage 4. The failure shear load was 172 W. The failure
crack extended Erom the loading point diagonaIIy dong a flexurai-shear crack that had
forrned at a shear load of about 170 kN on the West side of the beam. The failure crack
also split the bond between the longitudinal reinforcement and the concrete and extended
passed the support into the overhanging portion of the bearn..
The deflection at the peak load of 175 kN was 5.7 mm and the defiection at the
failure load was 6.2 mm. The strain in the longitudinal reinforcement at the beam's
midspan peaked at approximateiy 900 microstrain, about 33% of the yield strain.
The totai load versus midspan deflection, shear load versus shear strain, total load
versus longitudinal reinforcement strain responses, and crack patterns and zurich strain
plots for every load stage, are given in the following figures.
180 -t OB1 20 - Shear vs. Shear Strain
4 -/ r WEST
EAST
0.20 0.30 Sheir Stnin ( 111000)
DE120 - Load vs Longitudinal Reinforcement Strain
200 4m 600 800 Stmin Gauge Reading [mierastrain]
i-S/-&i 4 - - P a . a . X
Specimen DB 130
The first flexural crack occurred at a total load of 170 k N (85 kN shear) and
extended halfway up the beam. At load stages 2 and 3, (total loads of 200 kN and 250 kN
respectively) new flexural cracks formed on both sides of the beam's midspan. The
cracks on both the West and east sides showed signs of tuming over following Load Stage
3. Load Stage 4 was taken at a total load of 300 )cN (1 50 kN in shear). New flexural-
shear cracks formed forming a symmetric pattern about the beam's midspan and the
existing flexural cracks at the beam's midspan had extended as far as 700 mm into the
beam. The final load stage was taken at a total load of 350 kN. At this stage, fiexural-
shear cracks extended 500 to 600 mm into the beam depth. On the west side, the
flexural-shear cracks extended approximately 400 mm into the beam depth.
The beam failed in shear, on the east side, at a shear load of 178 kN. Again, tike
specimen DB120, the shear crack extended fiom the loading point to the level of the
longitudinal reinforcement where bond splitting occurred al1 the way to the support and
beyond into the overhang of the beam.
The longitudinal strain in the reinforcement at the beam's midspan at fadure was
approximately 1000 microstrain (36% of yield) and the midspan deflection of the
specimen at failure was approximately 5 mm.
The total load versus midspan deflection, shear load venus shear strain, total load
venus longitudinal reinforcement strain responses, and crack patterns and zurich strain
plots for every load stage are given in the foIlowing figures.
OB1 30 - Load vs. Daflection -l-
DM30 - Shear vs. Shear Strain 3
11 t ---- a --- Lm- . ,
0.2 0.3 0.4 Shear Strain [111000]
081 30 - Lord vs. Longitudinal Reinforcement Stnin
MN
460 600 800
Strain Gu- Reading (rnkrostr8inl
& B r . b-&\
Specimen DB 140
The first flexural cracks formed at a total load of approximately 142 kN (71 kN
shear). The first flexural-shear crack formed at a load of about 250 kN (125 kN shear), at
which point the second load stage was taken. Load Stage 3 was taken at a total load of
300 kN by which time several f l e d - s h e a r cracks had formed on both sides of the
beam's midspan, Flexural-shear cracks had extended about 700 mm into the beam depth
on both the east and West sides.
Faiture occurred at a total load of 346 kN (173 kN in shear) on the west side.
Like the 20 and 30 MPa specimens, the shear crack extended fiom the loading point,
along an existing flexural-shear crack, do wn to the level of the longitudinal reinforcernent
where bond splitting occurred al1 the way to the support and beyond into the overhang of
the beam.
The strain in the longitudinal reinforcement at the bearn's rnidspan at failure was
approximately 1000 microstrain (36% of yield). The midspan deflection of the specimen
at failure was approximately 4.8 mm at failure.
The total load versus rnidspan deflection, shear load versus shear strain, total load
versus longitudinal reinforcement strain responses, and crack patterns and ninch strain
plots for every load stage are given in the following figures.
DBl4û - Load vs. Deflection
DBl4O - Shear vs. Shear Strain
0.30 0.40
Shear Strain [ 111000)
08140 - Load vs. Longitudinal Reinforcement Stnin
O 400 600 800
Strain Gauge Reading [microdrainJ
Specimen DB 165
The first indication of cracking was at a total load of 186 kN (93 kN s h e d . Upon
reaching a total load of 250 kN, the existing flexurai cracks had extended about 700 mm
into the beam depth and the outermost flemral-shear cracks had began to turn over. At a
total load of 3 10 kN, a new flexural-shear crack had propagated about 650 mm into the
beam on the West side. A load stage was taken at a total load of 320 kN (160 kN in
shear). The flexural cracks extended about 850 to 900 mm into the specimen.
At a total load of 350 kN (175 kN shear), a large shear crack formed on the east
side. The crack extended fiom the loading point down to the level, and dong the
longitudinal reinforcement nearly reaching the support through bcnd splitting. The crack
tvidth of this diagonal crack on the east side (not measured and marked at a load stage)
appeared to be approximately 0.3 to 0.4 mm. The load dropped approximately 60 kN
(17% drop) in total load when this crack formed.
With only about a 1 mm increase in midspan deflection, the beam recovered the
load in approximately two minutes, followed by a shear failure, on the West side, at a total
load of 356 kN (178 kN in shear).
The strain in the longitudinal reuiforcement at the beam's midspan at failure was
approximately 920 microstrain (33% of yield). The midspan deflection of the specimen
at failure was approximately 7.1 mm.
The total load versus midspan deflection, shear load versus shear strain, total load
versus longitudinal reinforcement strain responses, and crack patterns and nuich strain
plots for every load stage are given in the following figures.
DBl6S - Load vs. ûeflection
DB165 - Shear vs. Shear Strain
0.60 0.80 1 .O0 1.20 t -40
Shear Strain ( 1/1000]
Specimen DB 180
The first flexural cracks occurred at a total load of 170 kN with the first crack
extending about 650 mm into the specimen. At a total load of 250 kN, load stage 2 was
taken. At this point, the outerrnost flexural cracks had tumed over. At this point the
existing flexural cracks at the midspan extended 900 mm into the beam. Load stage 3
was taken at a total load of 300 kN. The crack pattern was syrnmetric about the beam's
midspan and d l the outerrnost cracks had tumed over.
At a total load of 322 kN (16 1 kN in shear), a Iarge diagonai crack formed on the
West side. The crack extended form the loading point down to the level of the
longitudinal reinforcement, splitting some of the bond of the longitudinal reinforcement.
Like specimen DB 165. the load dropped approximately 60 icN (19% drop) without a large
increase in deflection.
The beam recovered the load and failed in shear on the east side of the specimen
at a total load of 330 kN (165 kN in shear) - the lowest shear capacity of ail the
specimens tested.
n i e strain in the longitudinal reinforcement at the beam's midspan at failure was
approximately 1 150 microstrain (42% of yield). The midspan deflection of the specimen
at failure was approximately 9.3 mm.
The total load versus rnidspan deflection, shear load versus shear strain, total load
venus longitudinal reinforcement strain responses, and crack patterns and zurïch strain
plots for every load stage are given in the following figures.
DB18O - Load vs. üeflection
OB180 - Load vs Longitudinal Reinforcernent Strain
3501
$90 600 800 1000 Strain Gauge Reading [microdrain)
Specimen DBO-530
The first cracks occurred at a total load of 144 kN (72 kN shear) extending 600
mm into the specimen at midspan. The second load stage was taken at a total load of 220
kN where the flexural cracks began to turn over into flexural-shear cracks. Much like the
beams with 1% longitudinal reinforcement, at a total load of 300 kN (150 kN in shear;
Ioad stage 3), a symmetric pattern of flexural shear cracks existed about the beam's
midspan. At this point the west side of the beam showed greater distress than the east
with a relatively flat diagonai crack extending towards the Ioading point.
The specimen failed abruptly in shear on the West side at a total load of 3 16 kN
(1 58 kN in shear). Unlike the 1% and 2% longitudinally reinforced beam specimens with
32 MPa concrete, DB130 and DB230, respectively. the failure crack was relatively flat
extending fiorn the ioading point diagonally to the level of the reinforcement and splitting
the bond a11 the way passed the support into the overhang of the beam.
The strain in the longitudinal reinforcement at the beam's midspan at failure was
approximately 1430 microstrain (52% of yield). The midspan deflection of the specimen
at failure was approximately 7.6 mm.
The total load versus midspan deflection, shear load versus shear strain, total load
versus Longitudinal reinforcement strain responses, and crack patterns and zurich strain
plots for every load stage are given in the following figures.
080.530 - Load vs. lkfkction
0.0 1 .O 2 0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11 .O
Midspan Delkction (mm]
080.530 - Shear vs. Shear Strain
0.2 0.3
Shear Strain [ 111000]
080.530 - Load vs. Longitudinal Reinforcement Stnin
O 200 400 600 800 lm 1200 1400 1600
Strain Gaugc Reaâing [microstrain]
a f !-,h-=--8- 0
1 O i - 1 L * - e t g 2 s 2 : ,t
Specimen DB230
The first crack occurred at the high total load of 200 kN (1 00 kN in shear).
Significant cracking did not occur until a total load of about 324 kN (162 kN shear)
where three other flexural cracks formed at the midspan area. The cracks in the shear
spans of the beam appeared to begin tuniing over into flexural-shear cracks at a total load
of about 400 kN (200 kN shear)at which tirne a load stage was taken. Following this load
stage, at a total load of 450 kN (225 kN shear), no new cracks had formed and the
existing flexural-shear cracks had extended about 600 mm into the beam. At a total Ioad
of 500 kN (250 kN shear), few new cracks formed but existing flexurai-shear cracks on
the east side had extended al1 the way up to the Ioading point. The cracks were steeper,
wider and spaced farther apart than those for the 1 % and 0.5 % longitudinally reinforced,
32 MPa specimens, DB 130 and DB0.530, respectively.
Specimen DB230 failed in shear at a total load of 520 kN (260 kN in shear)- The
diagonal crack was steep extending from an existing flexurai-shear crack on the east side
from the loading point to the level of the reinforcement. Unlike specirnens DB 130 and
DB0.530, there was not a significant amount of bond splitting, though several small
diagonal cracks fomed at the Ievel of the two layers of main longitudinal reinforcement
at the east end of the beam, adjacent to the support.
The strain in the longitudinal reinforcernent at the beam's midspan at failure was
approximately 770 microstrain (28% of yield). The midspan deflection of the specimen
at failure was approximately 7.6 mm.
The total load versus midspan deflection, shear load versus shear strain, total load
versus longitudinal reinforcement strain responses, and crack patterns and zurich strain
plots for every load stage are given in the following figures.
08230 - Load vs. ûeflection
WEST
0.2 0.4 0.6 0.8 1 1 -2 1.4 Shear Strrin [1/1000]
08230 - Load vs. Longitudinal Reinforcement Stnin
200 400 600 800 Io00 Strain Guage Reading [mkrostrainJ
LOADSTAGE: 6 SHEAR FORCE V = 250 kN
APPENDIX C
RESPONSE OF BEAM. SPECiMENS CONTAINIBIG O.SO/., 1% LONGITUDINAL
REINFORCEMENT AND TRANSVERSE REINFORCEMENT
Total Load versus Midspan Deflection
Shear Load versus Shear Strain
Shear Load versus Transverse Reinforcement Strain
Total Load versus Longitudinal Reintbrcement Strain
Crack f attems and Surface Strain Profiles
Specimen DB 120M
The first flexurd crack occurred at a total load of approximately 148 kN (74 kN in
shear). At a total load of 400 kN (200 kN shear), there was a symmetric pattern of
flexural-shear cracks about the beam's midspan. Diagonal crack widths on the West and
east sides of the bearn ranged from 0.4 to 0.6 mm and 0.1 to 0.3 mm, respectively.
At a total load of 500 kN (250 kN shear), the diagonal cracks on the west side had
extended al1 the way up to the loading point and smail diagonal cracks had formed at the
level of the reinforcement adjacent to the support. The diagonal cracks on the West side
measured about 3.0 to 3.5 mm in width whereas on the east side they measured about 0.2
to 0.5 mm in width.
Failure occurred very suddenly on the east side at a total load of 550 kN (275 IcN
in shear). The diagonal failure crack extended fiom the loading point to the level of the
longitudinal reinforcement dong a flexural-shear crack that had previously formed.
The midspan deflection of the specimen at failure was approximately 15 mm and
the strain in the longitudinal reinforcement at the beam's midspan peaked at 1450
microstrain (53% of yieId).
The total load versus midspan deflection, shear load versus shear strain, total load
versus longitudinal and transverse reinforcement strain responses, and crack patterns and
zurich strain plots for every load stage are given in the following figures.
OB1 20M - Lord vs. Dafkction m-.
500 - -
400 - - L. z s r 300.-
I A
t
7" r
DB120M - Shear vs. Shear Stmin
1
1 1.5 2 2.5 Strain Gauqe Reiding microd drain^
DB120M - Shear vs. T nnsverse Reinfoicement Strain
0.0 500.0 1000.0 1500.0 2mO.O 2500.0 3000.0
S h i n Gauge Reading [microdrain]
DB120M - Lord vs. Longitudinal Reinforcement Strain
6 0 0 1
400 800 1200
Strain Gauge Reading [microstrain]
SPECIMEIY : DB12OM Si-IEAR FORCE V = 92 kN
Specimen DB 140M
The first flexural crack occurred at a total load of 154 kN (77 kN). At a total load
of 440 kN (220 kN shear), the diagonal cracks on the West and east sides had maximum
widths of 0.5 mm and 0.35 mm, respectively.
New diagonal cracks formed at a total load of 520 kN (260 kN shear) and
extended fiom the edge of the both supports, 600 mm into the specimen depth. The
flexural-shear cracks at this load had extended al1 the way up to the loading point and
diagonal cracks had a maximum widths of 1.5 mm and 0-7 mm on the West and east
sides, respectively.
A shear failure occurred at a total load of 540 ICN (270 kN shear) on the east side,
A stimp approximately 1.5 metres from the midspan, on the east side, fmctured.
Leading up to failure the strain histories of the gauges attached to the stirrups on the east
side indicated much more straining than the gauges attached to the stirrups on the west
side of the beam (see the Ioad versus transverse reinforcement strain response).
The midspan deflection of the specimen at failure was approximately 13.5 mm
and the strain in the longitudinal reuiforcement at the beam's midspan peaked at 1540
microstrain (56% of yield).
The total load versus midspan deflection, shear load versus shear strain, total load
versus longitudinal and transverse reinforcement strain responses, and crack patterns and
nuich strain plots for every load stage are given in the following figures.
DB140M - Shear vs. Shear Strain
?
1 -5 2 Shear Stnin [111000]
DB14OM - Shear vs. Tnnsverse Reinforcement Strain
O 500 1000 1500 2oOo 2500 jdOO
Stnin a u g e Reading [microdrain]
08140M - Load vs. Longitudinal Reinforcement Strain 600
O 200 400 600 800 lm 12w 1400 1600 Strain Gauqe Rcaâing [microdrain]
L I - & = O d s rS d o ! d
LOADSTACE: 3 SIIEAR FORCE V = 160 klY
Specimen DB 165M
The first flexural crack occurred at a total load of 182 kN (91 kN in shear).
According to stirmp gauges W3 and E3, the transverse steel 1 metre on either side of
midspan began straining at a total load of about 360 kN (180 kN shear). At a total load of
560 kN (280 kN) as new diagonal cracks formed, the stirrups approx. 2 metres on either
side of midspan, with gauges W2 and E2 attached, began to strain significantly.
From a total load of 450 kN (225 kN) to the failure load, few new cracks formed.
Existing f l e d shear cracks extended towards the loading point and continued to widen-
At a Ioad of 520 kN (260 kN shear), a stimp, with gauge E3 attached, approximately 1
metre ezst of the midspan, yielded. At a total load of 650 kN (325 kN shear), srnall
diagonal cracks formed at the level of the longitudinal reinforcement adjacent to the
supports. The maximum diagonal crack widths prior to failure were 3.0 mm and 2.5 mm
on the W e s t and east sides respectively.
A shear failure occurred on the West side at a total load of 890 kN (445 kN shear)
- far greater than any beam examined in the series. The failure crack was steeper than
those for specimens DB120M and DBl40M and propagated dong a wide flexural-shear
crack on the West side.
The rnidspan deflection of the specimen at failure was approximately 22 mm and
the strain in the longitudinal reinforcement at die bearn's midspan peaked at 2400
microstrain (87% of yield).
The total load versus midspan deflection, shear load versus shear strain, total load
versus longitudinal and transverse reinforcement strain responses, and crack patterns and
zurich strain plots for every load stage are given in the following figures.
DB16SM - Load vs. Defkction
DB165M - Shear vs. Shear Strain
DB165M - Sherr vr. Tmnsverse Reinfortement Stnin
DB165M - Load vs. Longitudinal Reinforcement Stmin
SPECIMEN : DB165M LOADSTAGE: 2 SHEAR FORCE V= 12s kN
4.w I aor l P Y'
SPECIMEN : DB16SM LOADSTAGE: 3 SHEAR FORCE V = 175 kN
' I I 'IZ -11 * l 4
025 *?b -27 -28 O 1 0 O 1 9 ' 4 0 ' 4 1 Or,?
'41 4 4 '46 33 *36 '31 '36 '59 ' b O
v
LOADSTAGE: 4 SI1EAR FORCE V = 225 W
LOADSTACE: 7 SHEAR FORCE V = 325 kN
'II ' 2 ' I l
'26 *27 '20
-- n i -
Specimen DB 1 80M
The first flexwal crack fonned at a total load of 176 kN (88 kN shear). The
gauged transverse steel about 1 rnetre on each side of midspan, with gauges E3 and W3
attached, began straining at a totai load of about 350 kN (175 kN shear). At a total load
of approximately 460 kN (230 kN) as new diagonal cracks formed, stimrps about 2
metres on either side of midspan, with gauges E2 and W2 attached, began to strain
significantly. At a total load of approximately 400 kN (200 kN shear), there was a
symmetric distribution of flexural-shear cracks about the beam's midspan.
At a totai load of 436 kN (218 kN shear), a large diagonal crack formed on the
east side approximately 1 mm in width extending 800 mm into the specimen's depth
followed by, at a total load of 466 kN (233 kN shear), a shear crack forming on the west
side approximately 0.5 mm in width extending about 350 mm into the specimen depth.
At a total load of about 494 kN (247 kN shear); just prior to a load stage, new diagonal
cracks formed just adjacent to the eastem support with hairline widths extending 350 mm
into the specimen depth. At a total load of 600 kN (300 kN shear), previously formed
diagonal cracks continued to propagate towards the toading point, and small diagonal
cracks formed at the level of the longitudinal reinforcement adjacent to the support on the
West end.
The maximum crack widths for the diagonal cracks prior to failure were 3.0 mm
for the West side and 2.5 mm for the east side- The bearn failed in shear at a total load of
776 kN (388 k N in shear) on the West side. As with DB 165M, the failure crack was steep
and had propagated fiom a previously formed flexural-shear crack.
At failure, the midspan deflection of the specimen was approximately 22 mm and
the strain in the longitudinal reinforcement at the beam's rnidspan peaked at 2275
microstrain (83 % of yield).
The total load versus midspan deflection, shear load versus shear strain, and total
load versus longitudinal and transverse reinforcement strain responses, and crack patterns
and zurich strain plots for every load stage are given in the following figures.
06180M - Lord vs. Daflection 8001
DB18OM - Shear vs. Shear Strain
0.00 0.50 1 -00 1 -50 206 250 3.00 3.50 4.00 4.50 5.00 Shmr Strain [111000]
SQO lm0 1500 2000 2500 Strain Gauge Reiding (microstrain]
DBf 8OM - Lord vs. Longitudinal Reinforcement Strain
SPECIMEN : DBllOM LOADSTAGE : 1 SIIEAR FORCE V = 00 kN
SPECIMEN : DBl8OM LOADSTACE: 6 SHEAR FORCE V = 350 kN
* I I ' 1 2 'Il ' 3 ' C I
' 2 6 ' 2 7 *al ' 4 2
T V
ND (iRICH M T A C a L C C l L D
Specimen DB0.530M
The first flexural crack formed at a total Ioad of 140 khi (70 kN). The transverse
steel about 1 metre on each side of rnidspan with gauges E3 and W3 attached began to
strain at a total load of about 280 kN (140 W shear). At a total load of 400 kN (200 kN
shear), the stimps approximately 2 metres on each side of midspan, with gauges E2 and
W2 attached, began to strain significantly.
It is worth noting that relative to the specimens containing 1% longitudinal
reinforcement and stirrups the flexurai cracks were wider and spaced farther apart.
Prior to failure, the maximum diagonal crack width on the West side was 2.0 mm
and 1.0 mm on the east side. The beam exhibited a very ductile response. The beam
failed in shear at a total load of 512 kN (256 kN shear) on the West side. The rnidspan
deflection at the peak load was about 21 mm. M e r the shear failure, the specimen
achieved a rnidspan deflection of 38 mm sustainhg a total of 400 kN (200 kN shear).
The strain of the longitudinal reinforcement at the beam's midspan, at the peak
shear failure load of 256 kN, was 2750 microstrain, equivalent to the yield strain of the
reinforcement.
The total load versus midspan deflection, shear load versus shear strain, and total
Ioad versus longitudinal and transverse reinforcement strain responses, and crack patterns
and zurich strain plots for every load stage are given in the following figures.
Unfortunately, photographs for the first five load stages for specimen DB0.530M
were unrecoverable and thus, crack patterns and are not available.
DB0.530M - Load vs. Ocfiection 600
OB0.530M - Shear vs. Sheat Stnin
L EAST
DB0.530M - S hear vs. Tmnsverse Reinforcernent Stmin
DB0.530M - Load vs. Longitudinal Reinforcernent Strain
1000 1500 2000
Stilin Gauge Reading (microdrain]
APPENDLX D
MATERIAL PROPERTIES
Load versus Displacement Curves for Tension Tests on Reinforcing Bars :
USA No.3
1 SM
30M
Load versus Displacement Curves for Uniaxial Compression Tests on Concrete Cylinders :
65 MPa
t . . - 1 . . . :
APPENDIX E
DLAL GAUGE DATA
( ALL VALUES IN mm)
S H M DUL GAUGE R W N G S Laad SI- LOAD vusrt-mh we81.roulh AVG. Change
O 0.00 0.00 0.00 1 74 0.40 0.31) 0.39 2 92 0.54 0,50 0.13 3 140 0.89 0.77 0.32 4 200 1.47 1.11 O,* 5 250 1.91 1 AS 0.39
SHEAR DUL OUAOE RUDINOS Load Stage LOAD ml-narth weat-wth AVO. Change
O O O O
( ALL VALUES IN mm)
SHEAR DlAL OAWE READINOS Load Stage LOAO Ii(M wnt.nocth west-south AVG. Change
O 0.00 0.00 0.00
Failura 1 7 1
SHE AR MAL OAUOE READINOS Load Sbgo LOAD FN] wost-nonh wt.souîh AVG. Change
O 0.00 0.00 0.00
srstmrth east-south AVG, C h r w 0.00 0.00 0 .O0
east-nomi east-south AVG, Chonga 0.00 0.00 0.00 0.16 0.23 0.19 0.41 0.46 0.24 0.66 0,61 0, lS
m l h a diil 9.- nui the supports m r a plrd 200 mm Rom h. conûellna of fh. suppoft
In th0 noim-w diraAh, îho dial gaugm won pl~ced 25 mm in hom elch hce of the barn.
wost-nomi, for ritimpie, Impiies the west slde of the barn near tha northem lace.
DB16SM = DEFLECf IONS (dmwards) ( ALL VALUES IN mm)
SHEAR DlAL OAUOE READINOS Loûd Sîage LOAD wesî.north md-souh AVG. Change
O 0.00 0.00 0.00 east-south AVG, Chanjp -
0.00 0.00 0.32 0.32 0.44 0.14 0.71 028 1 .O0 0.34 1.32 028 1.47 0.2 1 1.71 0.23 2.10 O,«) 2.W 0 3
mlddle-notth mlddle-sauth AVG. Change O .al 0.00 O .OO 1 .O9 1 .O7 1 .OB 2 .O0 1 -99 0.92 3,91 3.91 1.91 6.56 6-55 2 -64 8,46 8.48 1.91 11 -07 11.11 2-63 12.70 12,78 1.64 15.33 15.34 2.60 18.00 1 7.90 2.65
ûBl60 -MF LECTWS (dommrds) ( ALL VALUES IN mm)
SHEAR M L OAWE READINOS L W load Stage L O N wnt-nwih umt.south AVG. Change ead-rrocrn e i i d . M AVG. Chiiip r miâdknotîh r n l d d k M AVG, Chrnpb mldrpn M. ' Anpk (âqrm)
O 0.00 0.00 0.00 0,OO O .O0 0.00 0.00 0.00 O. O0 0.00 n a
Failum
p m 1 ~ h e di4 gauges n u i h a wppoib r i e plmced 200 mm hom n* centrelino d me suppo<l.
In tha norlhmuîh dlrdon, the dlai giuges wsre p l i c d 25 mm ln IWtl ~h hce d Ihe krm.
( ALL VALUES IN mm)
SHEAR D l A l OAüûE REAMNOS LVDT Load Stage LOAD mt-nah mrt-south AVG. Change
O 0,00 0.00 0.00
( ALt VMUES IN mm)
In îb norai-roccai dimaori, îb dirl garr0.s mro placod 25 mm In tram a h face dlhe k r m .
mlddle-noriil mlddk-roulh AVG. Cham 0.00 0.00 0.00
mlddbnorth m)bdk.souîh AVG. Chwipr 0.00 0.00 0.00
LVDT
DB0.630M DEFLECTlûNS (downwards) ( ALL VALUES IN mm)
SHUR DlAL OAWJE REAMNOS Loid Skga LOAD wosî-nofîh vmt-south AVG, Chsnge ead-narth errt-south AVG. Chinpe middbnorth mlddle-wuîh AVG. Chrnga
O 0.00 0.00 0.00 0.00 0 .O0 0.00 0.00 0.00 0.00
DBO,S~O - MRECTMS (dommrds) ( ALL VALUES IN mm)
S W DUL OAWE REAUNOS Load Stip. LOAD wost-notai wmt-iou(h AVG, Chrnps aid-noRh rashouni AVG. Chinpr middkroim middio-souîh AVG. C h r w
O 0.00 0.00 0.00 0.00 0.00 0.w 0.00 0.00 0.00
midsprn [W. Anqla (dogrim) 0.00 O
APPENDIX F
MIX DESIGNS FOR CONCRETE USED IN EXPERIMENTAL STUDY