BEHAVIOR OF CONCRETE BEAMS REINFORCED WITH
ASTM A1035 GRADE 100 STIRRUPS UNDER SHEAR
by Aruna Munikrishna, Amr Hosny, Sami Rizkalla and Paul Zia
ACI Member Aruna Munikrishna received her B.E from R.V. College of Engineering, India in
2005 and M.Sc. degree from North Carolina State University, Raleigh, NC 2008. Currently she
is a practicing engineer in the Raleigh, NC area.
ACI Member Amr Hosny is a PhD candidate in structural engineering North Carolina State
University, where he also obtained his M.Sc. in 2007. He received his B.Sc. from Ain Shams
University, Egypt in 2004.
ACI Fellow Sami H. Rizkalla is a Distinguished Professor of Civil and Construction Engineering
in the Department of Civil, Construction, and Environmental Engineering, North Carolina State
University, where he also serves as the Director of the Constructed Facilities Laboratory and
NSF I/UCRC in Repair of Structures and Bridges. He is also a fellow of ACI, ASCE, CSCE,
EIC, and IIFC.
ACI honorary member Paul Zia is a Distinguished University Professor Emeritus at North
Carolina State University. He served as ACI President in 1989, and is a member of several ACI
committees including ACI 363, High-Strength Concrete; joint ACI ASCE 423, Prestressed
Concrete; ACI 445, Shear and Torsion; the Concrete Research Council; and TAC Technology
Transfer Committee, serving as chairman of its ITG-6.
ABSTRACT
This paper presents the results of an investigation of shear strength of large-sized
concrete beams reinforced with ASTM A10352 Grade 100 bars. The performance of these beams
is compared to that of similar beams reinforced with ASTM A6151 Grade 60 bars. The results
indicate that by utilizing the higher yield strength of ASTM A1035 bars with reduced
reinforcement ratio, the beams can achieve similar shear strengths as the beams reinforced with
Grade 60 bars. The results also show that cracking and deflection under service load of the beams
with reduced reinforcement ratio are within acceptable limits.
1
Keywords: beam; cracking; deflection; high strength reinforcement; shear strength; stirrup; web
reinforcement.
INTRODUCTION
Reinforcing bars conforming to ASTM A10352 are characterized by their high tensile
strength and enhanced corrosion resistance in comparison to ASTM A6151 Grade 60 bars. Use of
these high strength steel bars offers several advantages such as reduction of the reinforcement
ratio, less cost for reinforcement placement, reduced reinforcement congestion, better concrete
placement, and increase in service life due to enhanced corrosion resistance. The high strength
reinforcing bars used in this investigation3 exhibit a non-linear stress-strain curve without a
distinct yield plateau reaching a stress of 100 ksi (690 MPa) at 0.35% strain. One major concern
with using this high strength steel bar is whether the larger induced steel strains under service
load could cause unacceptably large cracking and deflection of the reinforced concrete beam and
whether the beam would achieve adequate ductility under ultimate load.
The objective of this research is to examine the behavior of concrete beams reinforced
with different reinforcement ratios of high strength steel stirrups up to yield strength of 100 ksi
(690 MPa) and to evaluate the serviceability and effectiveness of using high strength steel as
transverse reinforcement in flexural members. The paper also examines the ability of current
codes to predict the contribution of transverse steel to the shear capacity of reinforced concrete
flexural members.
RESEARCH SIGNIFICANCE
There are no experimental data or design guidelines for the use of high strength steel as
shear reinforcement with yield strength of 100 ksi (690 MPa) for reinforced concrete flexural
2
members. Most of the research currently available in the literature focused on the use of high
strength steel as flexural reinforcement 4,5,6,7,8,9. This paper will provide much needed information
on the behavior of high strength steel stirrups designed for yield strength of 80 ksi (550 MPa) and
100 ksi (690 MPa) for reinforced concrete members. It also provides an evaluation of the current
ACI 318-0810, CSA A23.3-0411 and AASHTO12 code provisions in predicting the contribution of
transverse steel to the shear capacity of reinforced concrete flexural members.
EXPERIMENTAL PROGRAM
The experimental program included eighteen tests using nine large-sized reinforced
concrete beams, tested under static loading up to failure. All beams were 22 ft. (6.7 m) long, and
were designed using nominal concrete compressive strength of 4000 psi (28 MPa). The beam
length was chosen such that each beam could be tested twice, and thus doubling the amount of
collected data. The shear span to depth ratio, a/d, of all specimens was kept constant.
The nine beams were classified into three groups based on their shear resistance. The
spacing of the shear reinforcement was varied to reflect a minimum and maximum level of shear
resistance allowed by ACI 318-08. Test specimens were designed to induce stresses of 80 ksi
(550 MPa) and 100 ksi (690 MPa) in the high strength stirrups. Within each group, the beams
were geometrically similar and the shear reinforcement was designed to achieve the same
nominal shear capacity. Hooks were provided at both ends of the longitudinal tension
reinforcement to prevent anchorage failure. The transverse reinforcement consisted of #3 (No.
10) and # 4 (No. 13) closed stirrups designed according to ACI 318-08 requirements, with a bend
radius equal to six times the bar diameter and an extension of six times the bar diameter past the
90-degree bend. Figure 1 shows the elevation and cross section of the beams in Groups 1, 2 and
3. The cross-sections and reinforcement details of all the specimens are summarized in Table 1.
3
The beams, shown in Table 1, are identified by three parameters: the first two characters indicate
the group to which the beam belongs, i.e. G1 is Group 1. The second parameter specifies the
longitudinal and transverse steel type using C for conventional steel and M for high strength
steel. The third parameter is the specified design yield strength in the stirrup, 0 indicates no
transverse reinforcement, 60 indicates 60 ksi (415 MPa), 80 for 80 ksi (550 MPa) and 100 for
100 ksi (690 MPa) design stress in the stirrup based on ACI 318-08. The beams were tested with
a targeted shear span to depth ratio a/d = 3. For the first 4 beams of Group 1 with target shear
capacity of 3f'cbd, the beams were tested with a loaded span equal to 19.0 feet (5.8 m) as
detailed in Table 2. The same four beams were then rotated and tested with a loaded span equal
to 13.2 feet (4 m) while maintaining the same shear span to depth ratio of 3. This set of tests is
identified as Group 2.
With the smaller sectional dimensions of the remaining 5 beams
compared to the first 4 beams, it was possible to test these beams twice using the same setup
configuration. For the replicate tests, an additional letter ‘R’ was added at the end of the
identification to differentiate the second test from the first test of the specimen. In each group,
the beams reinforced with high strength stirrups were compared with beams reinforced with
Grade 60 steel stirrups. Also, beams G1-M0, G2-M0, G3-C0 and G3-M0 were designed without
shear reinforcement and were used to determine the nominal concrete contribution to the shear
strength, Vc.
MATERIAL PROPERTIES
Local ready-mixed concrete using Type I cement and a maximum aggregate size of 3/8”
(9.5 mm) was used to construct all specimens. Three 4×8 in. (102×204 mm) concrete cylinders
were used to determine the compressive strength of concrete in accordance with ASTM C39, at
the time of testing as shown in Table 3.
4
Tension coupons from the reinforcing steel were used to determine the stress-strain
characteristics. Samples of #3 and #4 Grade 100 and Grade 60 bars were taken from the supply
used to fabricate the beams. The stress-strain relationships for #3 and #4 Grade 100 bars and
Grade 60 bars are shown in Figure 3. The Grade 60 bars used in this research program had yield
strengths greater than 60 ksi (415 MPa) and did not exhibit typical yielding plateau. The #3 bars
had yield strength of 80 ksi (550 MPa) compared to 69 ksi (475 MPa) for the #4 bars. Both bars
had ultimate strength of approximately 100 ksi (690 MPa) as shown in Figure 3.
In general, the Grade 100 bars exhibit a linear stress-strain relationship up to a stress level
95 ksi (655 MPa) for #3 and #4 bars. This linear behavior is followed by a nonlinear behavior
and reduction in the modulus of elasticity up to an ultimate strength of 155 ksi (1070 MPa) for #3
bars and 160 ksi (1105 MPa) for #4 bars. The stress of 100 ksi (690 MPa) at a strain of 0.35%
was taken as the yield strength according to the recommendations of ACI 318-08 Section 3.5.3.2.
TEST SETUP
The test setup was designed to allow each beam to be tested twice to replicate test data.
Table 2 gives the test setup details including the location of the load from two supports, effective
depth of beams and shear span to depth ratio for each group. All beams were instrumented to
measure applied loads, deflections, crack widths and steel strain. For each beam, a strain gage
was placed on one bar of the bottom layer of the tension reinforcement at the location of the
applied load to measure strains. Weldable strain gages were used to measure strains in stirrups.
The location of the weldable strain gages was determined by estimating the location of the
compressive strut acting from the point of load application to the support. The weldable strain
gages were attached to the stirrups using a spot welder as recommended by the manufacturer.
Three strain rosettes were attached to the front face of the beam to measure the crack widths and
5
the strain in the stirrups after cracking. The rosette consisted of three 7.87 in (200 mm) PI gages,
placed horizontally, vertically and inclined at 45° angles. In addition to the rosettes, six 3.94 in
(100 mm) PI gages were attached to the back face of the beams to measure strain in a stirrup.
Crack comparators were also used to measure the crack width at different load levels in addition
to the rosettes. All instruments were connected to an electronic data acquisition system to
continuously record the data. Figure 4 shows pictures of the instrumentation.
LOAD- DEFLECTION BEHAVIOR
The applied shear versus deflection at the load point, up to failure for beams in Group 1,
2 and 3 are shown in Figure 5. The results indicate that the pre-cracking stiffness of the beams in
each group were almost identical, but there is a reduction in the post-cracking stiffness of the
beams reinforced with Grade 100 bars using design strength of 80 ksi (550 MPa) and 100 ksi
(690 MPa) due to the larger strains in the longitudinal reinforcement and the reduction of the
transverse reinforcement ratios. However, the figures show that despite the lower shear
reinforcement ratio for beams reinforced with high strength stirrups in comparison with beam
reinforced with conventional steel stirrups, all the beams were capable of sustaining similar
loads. This behavior is attributed to the utilization of the higher tensile strength of high strength
steel. The use of the lower longitudinal reinforcement ratio for the beams reinforced with the
high strength steel caused higher deflections compared to the beams reinforced with the
conventional Grade 60 steel at the same load levels. The reduced transverse reinforcement ratio
results in larger crack widths and reduced stiffness of the beams reinforced with high strength
stirrups. The beams without stirrups failed as expected in a brittle manner at much lower load
and significantly less deflection than the beams with transverse reinforcement. Beams reinforced
for shear were capable of sustaining much higher loads and deflections, and showed more ductile
6
failures.
CRACK PATTERN
The general crack patterns observed for all beams within the same group were identical.
The first flexural crack occurred at an applied load of 30 kips (133 KN) and was located near the
location of the applied load and maximum moment. As the load increased the flexural cracks
propagated towards the compression zone and the number of flexural cracks also increased.
Flexural cracks tended to develop at approximately the location of the stirrups. Therefore, the
spacing of cracks was dominated by the location of the stirrups. As additional load was applied,
new flexural cracks began to form towards the support and these cracks developed into flexuralshear cracks. For beams without transverse reinforcement (i.e. G1-M0, G2-M0, G3-C0 and G3M0), further increase in load resulted in the formation of a critical diagonal shear crack and
sudden failure, as shown in Figure 6 for beams G1-M0 and G2-M0 characterized by the
formation of a single critical diagonal crack spanning from the point of load application to the
support. On the other hand, beams with transverse reinforcement were capable of carrying higher
loads and were characterized by the initiation of additional flexure-shear cracks between the
applied loads and the supports. They exhibited fairly ductile response without explosive failure.
As the loading continued, a well-defined shear crack formed at the middle of the shorter shear
span, and propagated towards the support and the loading plates under the load. The shear crack
widened and extended towards the supports at a faster rate than the flexure cracks. All the beams
failed due to crushing of concrete in the nodal zone of the compression strut connecting the
nodes at the support and at the applied load as shown in Figure 6. Failure of beams G3-M80 and
G3-M100 was due to high stresses developed in the stirrups and the high compression stresses in
the strut, leading to crushing at the tip of the strut.
7
CRACK WIDTH
Crack widths were measured using a crack comparator and PI gages at each load level.
The latter method utilizes the geometry of two PI gages in the rosettes in order to determine the
summation of the shear crack width within the gage length. In the analysis, the vertical and
diagonal gage readings were used to calculate the summation of the crack widths using the
Shehata13 equation:
w  ( 2 D  v  0.5lg  ct )sin   ( v  0.5lg  ct ) cos 
where, V is the PI gage reading in the vertical direction, D is the PI gage reading in the diagonal
direction,  is the measured crack angle to the horizontal beam axis, lg is the gage length of the PI
gage, and ct is the maximum tensile concrete strain taken as 0.1x10-3. The average crack width,
w, was determined based on the number of cracks within the gage length of the rosette.
According to the commentary of ACI 318-08, at the service load level, the acceptable crack
width is 0.016" (0.41 mm). The shear at service load for this analysis was taken as 60% of the
nominal shear strength of the beam predicted using ACI Building Code for the given
reinforcement. Table 3 gives the service shear load for each group, the number of cracks
recorded at service load for each beam and the measured angle of the crack θ with respect to the
beam axis. It should be noted that all beams were designed to achieve the same nominal shear
capacity using different stirrup spacing for the specific yield strength of the steel. Therefore, all
beams within each group have the same service load. It was also observed that, the measured
crack widths by the PI gage and the crack comparator were approximately the same for the
beams within the same group. Therefore, only the crack widths measured using the crack
comparators are presented in this paper. Furthermore, at service, the measured crack width was
less than 0.016" (0.41 mm) for all beams as shown in Figure 7 for Groups 1, 2 and 3. Due to the
8
selected design strength of 80 ksi and 100 ksi used in high strength stirrups, beams G1-M80, G2M80 and G3-M80 had a larger crack width in comparison to beams G1-C60, G2-C60 and G3C60 respectively. Figure 7 shows that beam G1-M100 in Group 1 had no cracks at service load.
This is mainly due to the higher compressive strength of concrete in G1-M100 that provided
greater concrete contribution and delayed the formation of the first shear crack. The first
measured flexural-shear crack width of 0.004" (0.1 mm) was recorded at 76 kip (338 KN) of
shear. The results suggest that using high strength stirrups slightly increased the crack width in
comparison to conventional stirrups.
STRAIN IN STIRRUPS
The strains in the stirrups were measured using the vertical component of the PI gage
rosette, the PI gages on the back side of the beams, and weldable strain gages that were attached
to the stirrups at selected locations for beams G1-M80, G2-M80, G3-C60 and G3-M80. For
Group 1, the measured shear versus transverse strain is shown in Figure 8(a). The figure shows
that the stirrups were stressed only after first cracking. The corresponding shear was taken as the
concrete contribution to shear strength, Vc. The concrete contribution, Vc, was also estimated
from the control specimens. Figure 8(a) indicates that beams G1-C60 and G1-M100 have a
higher Vc, compared with G1-M0. This difference is due to the higher compressive strength of
the concrete used for these beams. It can be seen that at any given load, beams reinforced with
high strength stirrups have a slightly higher strain value due to the reduced transverse
reinforcement ratio in comparison with beams reinforced with Grade 60 stirrups. The test results
indicated that yielding of the transverse reinforcement of beam G1-C60 did not cause failure of
the beam. Instead, failure of the beams was due to crushing of the concrete in the nodal zone of
9
the compression strut.
The shear versus strain relationship for the beams of Group 2 is shown in Figure 8(b).
The same phenomenon was observed where the strains in the beams reinforced with high
strength stirrups were higher at any given load level due to the lower transverse reinforcement
ratio of these beams. It can also be seen that the strains measured from the weldable strain gages,
curve G2-M80-WSG, matched closely the strains measured using the PI gages, curve G2-M80.
These results indicate that the strains in the transverse reinforcement for both beams exceeded
the yield strain; however, the beams continued to sustain increasing loads. Failure was caused
due to crushing of the concrete in the nodal zone of the compression strut. It should be noted that
the results for Beam G2-M100 were not included in this graph as failure occurred due to a
diagonal shear crack that occurred in the longer shear span of the beam where no
instrumentations were provided.
Similar observations can be made for the beams of Group 3 as shown in Figure 8(c). At
any given load level, the strains are higher for beam G3-M100 with the lowest transverse
reinforcement ratio, followed by the strains for beam G3-M80, and beam G3-C60 had the lowest
strains in the stirrups because it had the highest transverse reinforcement ratio. For beams G3M80 and G3-M100, it was observed that, following the formation of the first shear crack the
stirrup reached very high strains, without much increase in the load. It is believed that, once these
stirrups yielded, the increase in the applied load was transferred to the adjacent stirrups and so on
until all the stirrups have yielded. Once all the stirrups in the shear span yielded, the compression
strut carried additional load and failure occurred when the concrete at the nodal zone of the
compression strut crushed. An explosive failure was observed in beams G3-M80 and G3-M100.
Spalling of the concrete cover was also observed during testing. All the stirrups were terminated
10
with 90° hooks. At high stresses these 90° hooks were insufficient in confining the concrete and
opened up, resulting in an explosive failure.
CODE PREDICTIONS
Concrete contribution to the shear strength of each beam was determined by three
methods: Vc1, using the test result from the control specimen without transverse reinforcement;
Vc2, using shear versus transverse strain relationship when strain is first detected in the stirrups;
and Vc3, based on initiation of the first diagonal crack. The concrete contribution determined
from these three methods is compared with the predictions according to ACI, CSA and AASHTO
codes in Table 4. It can be seen that for larger beams, beams in Groups 1 and 2, the concrete
contribution was overestimated by all the codes. This is likely due to the size effect, which is not
accounted for in the code equations. For the smaller sized beams of Group 3, the code equations
underestimated the concrete contribution. Also, there are some differences in the concrete
contribution determined by the different methods. For example, for Beam G1-C60, the control
specimen failed at Vc1 = 51 kips, while Vc2 = 65 kips based on the strain first detected in the
weldable strain gage, and Vc3 = 56 kips was observed at the first diagonal cracking. These
differences are due to the fact that the initiation of the first diagonal crack did not always pass
through the instrumented stirrups with the weldable strain gage. In addition, the diagonal crack
could be too small to be visible, but it can be detected by the strain gages as is the case for Beam
G2-M80, where Vc2 = 63 kips and Vc3 = 68 kips.
The steel contribution Vs to the shear strength is compared to the predicted values
according to ACI, which is based on a 45 degree truss model, CSA, and AASHTO codes, which
are based on the Modified Compression Field Theory, in Table 5. The comparisons between the
experimental and the predicted values by the code equations indicate that the ACI 318 code is
11
most conservative since it underestimates the steel contribution Vs from stirrups especially when
high strength steel is used. The test results also indicate that CSA and AASHTO codes predict
more accurately the steel contribution Vs in all cases except for Beam G3-M100 which is more
heavily reinforced with stirrups using design strength of 100 ksi (690 MPa).
CONCLUSIONS
Based on the tests of large-scale beams reinforced with high strength longitudinal and
transverse reinforcements, the following conclusions can be drawn:
1. The shear strength of flexural members can be achieved by using less number of high
strength stirrups and lower high strength longitudinal reinforcement ratio in comparison
with using Grade 60 reinforcement
2. The use of the lower longitudinal reinforcement ratio for the beams reinforced with the
high strength steel caused higher deflections compared to the beams reinforced with the
conventional Grade 60 steel at the same load levels.
3. The measured shear crack widths for all beams reinforced with high strength stirrups
designed with yield strength of 80 ksi (552 MPa) and 100 ksi (690 MPa) were within the
allowable limit recommended by the ACI Building Code.
4. The ACI, CSA and AASHTO LRFD design codes can all be used to predict the shear
strength of concrete beams reinforced with high strength stirrups with the ACI Buidling
Code being most conservative. The predictions by the CSA and AASHTO codes are quite
accurate and are very close to each other. Yield strength up to 100 ksi (690 MPa) can be
used in design of high strength transverse reinforcement for flexural members without
impairing the ultimate load carrying capacity and not exceed the limits of the crack width.
But the stirrups should have 135° degree hooks to provide better anchorage when it is
12
designed for such high stresses. More testing to validate this detail is recommended.
5. The ultimate load-carrying capacities recorded for all the beams were at least five times
the service load specified by the ACI Building Code.
ACKNOWLEDGEMNETS
The authors would like to thank MMFX Technologies Corporation for their financial support for
the research. They are also indebted to several members of Constructed Facilities Laboratory
including Jerry Atkinson, Bill Dunleavy, Greg Lucier, and Lee Nelson for their help with beam
fabrication and laboratory testing.
REFERENCES
1. ASTM A615, “ASTM A 615/ A 615M - 09: Standard Specifications for Deformed and Plain
Carbon-Steel bars for Concrete Reinforcement,” ASTM International, West Conshohocken,
PA, 2009, 6 pp.
2. ASTM A1035, “ASTM A 1035/ A 1035M - 07: Standard Specifications for Deformed and
Plain, Low Carbon, Chromium, Steel bars for Concrete Reinforcement,” ASTM
International, West Conshohocken, PA, 2007, 5pp.
3. MMFX Technologies Corporation, "MMFX Steel Technologies," 2005. (Retrieved from:
http://www.mmfx steel.com/).
4. Briggs, M., Miller, S., Darwin, D., and Browning, J., “Bond Behavior of Grade 100 ASTM A
1035 Reinforcing Steel in Beam-Splice Specimens,” SL Report 07-01, The University of
Kansas Center for Research Inc., Lawrence, KS, Aug. 2007 (Revised Oct. 2007), 83 pp.
13
5. Glass, G. M., “Performance of Tension Lap Splices with MMFX High Strength Reinforcing
Bars,” M.Sc. Thesis, University of Texas at Austin, Austin, TX, 2007, 141 pp.
6. Hosny, A., “Bond Behavior of High Performance Reinforcing Bars for Concrete Structures,”
M.Sc. Thesis, North Carolina State University, Raleigh, NC, 2007, 150 pp.
7. Seliem, H. M., “Behavior of Concrete Bridges Reinforced with High-Performance Steel
Reinforcing Bars,” Ph.D. Dissertation, North Carolina State University, Raleigh, NC, 2007,
259 pp.
8. Seliem, H. M., Hosny, A., and Rizkalla, S., “Evaluation of Bond Characteristics of MMFX
Steel,” Technical Report No. RD-07-02, Constructed Facilities Laboratory (CFL), North
Carolina State University, 2007, 71 pp.
9. El-Hacha, R., El-Agroudy, H., and Rizkalla, S., H., “Bond Characteristics of High-Strength
Steel Reinforcement,” ACI Structural Journal, V. 103, No. 6, Nov.-Dec. 2006, pp. 771-782.
10. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-08) and
Commentary (318R-08), American Concrete Institute, Farmington Hills, MI., 2008.
11. CSA Committee A23.3, Design of Concrete Structures, CSA A23.3-04, Canadian Standards
Association, Rexdale, Ontario, Canada, 2004..
12. AASHTO LRFD, Bridge Design Specifications and Commentary (3rd Ed.), American
Association of State and Highway Transportation Officials, Washington, DC, 2004..
13. Shehata, E.F.G., “Fibre-Reinforced Polymer (FRP) for Shear Reinforcement in Concrete
Structures,” PhD thesis, University of Manitoba, Winnipeg, Manitoba, Canada, 1999.
14. Munikrishna, A., “Shear Behavior of Concrete Beams Reinforced with High Performance
Steel Shear Reinforcement” M.Sc. Thesis, North Carolina State University, Raleigh, NC,
2008, 167 pp.
14
TABLES AND FIGURES
List of Tables:
Table 1: Reinforcement details of beams
Table 2: Load location and a/d details
Table 3: Service Loads
Table 4: Code Comparisons for Vc
Table 5: Code Comparisons for Vs
List of Figures:
Figure 1: Typical cross sections for beams of Group 1, 2 and 3
Figure 2: Typical section and test setup of beams
Figure 3: Stress-strain relationship for #3 and #4 high strength and Grade 60 steel
Figure 4: Instrumentation
Figure 5: Applied shear v/s deflection for beams of Groups 1, 2 and 3
Figure 6: Failure for beams of groups 1 and 2
Figure 7: Crack width v/s applied shear for beams of Groups 1, 2 and 3
Figure 8: Applied shear v/s transverse strain for beams of Groups 1, 2 and 3
15
Table 1: Reinforcement details of beams
Group
Crosssection
Flexural Steel
Ten.
Comp
100 ksi
4 # 11
2#9
-
-
-
-
CONV
60 ksi
6 # 11
2#9
CONV.
60 ksi
#3
8.0
0.11
100 ksi
4 # 11
2#9
80 ksi
#3
10.0
0.09
100 ksi
4 # 11
2#9
100 ksi
#3
13.0
0.07
100 ksi
4 # 11
2#9
-
-
-
-
CONV
60 ksi
6 # 11
2#9
CONV.
60 ksi
#3
8.0
0.11
100 ksi
4 # 11
2#9
80 ksi
#3
10.0
0.09
G2-M100
100 ksi
4 # 11
2#9
100 ksi
#3
13.0
0.07
G3-C0
CONV
60 ksi
7 # 11
4 # 10
-
-
-
-
100 ksi
5 # 11
4 # 10
-
-
-
-
CONV
60 ksi
7 # 11
4 # 10
CONV.
60 ksi
#4
4.5
0.31
G3-M80
100 ksi
5 # 11
4 # 10
80 ksi
#4
5.5
0.25
G3-M100
100 ksi
5 # 11
4 # 10
100 ksi
#4
7.0
0.20
ID
a/d
in
G1-M0
Min.
G1-C60
1
G1-M80
'
c
3 f bd
24 x 28
3.1
G1-M100
G2-M0
Min.
G2-C60
2
G2-M80
G3-M0
3
Design
Stirrup
Stress
Design
flexura
l stress
Target
Shear
capacity
G3-C60
'
c
3 f bd
24 x 28
3.1
Max.
7 fc' bd
16 x 22
3.0
Stirrup
Size
Spacing
tr
in
1 in. = 25.4 mm; 1 ksi = 6.895 MPa
Table 2: Load location and a/d details
Group
Target Shear
Capacity
CrossSection
b
h
in
in
Test configuration
Loaded
Span
Effective
Depth
l1
l2
l3
l4
ft
in
in
in
in
in
a/d
1
3 f c' bd
24
28
19.0
15
79
155
15
25.4
3.1
2
3 f c' bd
24
28
13.2
3
79
85
97
25.4
3.1
3
7 fc' bd
16
22
14.8
15
54
129
66
18.0
3.0
1 in. = 25.4 mm; 1 ft = 304.8 mm
16
Table 3: Service Loads
b
Group
d
in
in
G1-C60
1
2
3
f'’c
Stirrup
size
ID
Spacing
psi
Vc
Vs
Vn
in
kip
Kip
kip
Vn(avg)
kip
Vservice
Theta
No. of
Cracks
32
1
35
3
kip
4710
#3
8.0
84
42
126
4710
#3
10.0
84
45
128
G1-M100
4950
#3
13.0
86
43
129
41
1
G2-C60
4710
#3
8.0
84
42
126
27
1
4710
#3
10.0
84
45
128
36
1
G2-M100
4950
#3
13.0
86
43
129
40
1
G3-C60
5090
#4
4.5
41
96
137
47
1
5240
#4
5.5
42
105
146
38
1
5840
#4
7.0
44
103
147
49
2
G1-M80
G2-M80
G3-M80
24
24
16
25
25
18
G3-M100
128
128
143
77
77
86
1 in. = 25.4 mm; 1000 psi = 6.895 MPa; 1 kip = 4.4482 KN
Table 4: Code Comparisons for Vc
ACI
S
Group
1
2
Vc1
Vc2
CSA
Vc3
ID
AASHTO
Vc
Vc(exp) /Vc
Vc
Vc(exp)
/Vc
Vc
Vc(exp) /Vc
in
kip
kip
kip
kip
ratio
kip
ratio
kip
ratio
G1-C60
8.0
51
65
56
84
0.61
104
0.50
97
0.53
G1-M80
10.0
51
52
52
84
0.61
89
0.58
97
0.53
G1-M100
13.0
51
67
59
86
0.60
96
0.54
100
0.51
G2-C60
8.0
75
77
60
84
0.90
98
0.77
97
0.77
G2-M80
10.0
75
63
68
84
0.90
85
0.88
90
0.84
G2-M100
13.0
75
70
68
86
0.88
87
0.87
92
0.82
G3-C60
4.5
62
62
56
41
1.50
44
1.39
44
1.41
G3-C60-R
4.5
62
68
54
41
1.50
45
1.37
44
1.41
G3-M80
5.5
63
54
59
42
1.50
37
1.67
41
1.51
G3-M80-R
5.5
63
52
58
42
1.50
38
1.64
41
1.51
G3-M100
7.0
63
52
53
44
1.42
42
1.48
44
1.43
G3-M100-R
7.0
63
53
56
44
1.42
42
1.49
44
1.43
3
Average
1.11
1 in. = 25.4 mm; 1 kip = 4.4482 KN
17
1.10
1.06
Table 5: Code Comparisons for Vs
ACI
S
Group
1
2
CSA
AASHTO
Vs(exp)
ID
Vs
Vs(exp)/ Vs
Vs
Vs(exp)/ Vs
Vs
Vs(exp)/ Vs
in
kip
kip
ratio
kip
ratio
kip
ratio
G1-C60
8.0
82.8
50.3
1.65
71.2
1.16
76.8
1.08
G1-M80
10.0
72.5
44.7
1.62
60.1
1.21
68.3
1.06
G1-M100
13.0
61.2
43.0
1.42
58.8
1.04
65.7
0.93
G2-C60
8.0
78.9
50.3
1.57
69.8
1.13
76.8
1.03
G2-M80
10.0
59.8
44.7
1.34
59.1
1.01
60.3
0.99
G2-M100
13.0
61.3
43.0
1.43
56.7
1.08
58.0
1.06
G3-C60
4.5
149.9
108.8
1.38
129.7
1.16
156.1
0.96
G3-C60-R
4.5
145.1
108.8
1.33
130.2
1.11
156.1
0.93
G3-M80
5.5
149.4
104.7
1.43
131.9
1.13
135.1
1.11
G3-M80-R
5.5
143.0
104.7
1.37
132.8
1.08
135.1
1.06
G3-M100
7.0
126.3
102.9
1.23
133.0
0.95
132.7
0.95
G3-M100-R
7.0
129.4
102.9
1.26
132.5
0.98
132.7
0.98
3
Average
1.42
1.09
1.01
Standard deviation
0.13
0.08
0.06
Coefficient of variation
0.09
0.07
0.06
1 in. = 25.4 mm; 1 kip = 4.4482 KN
18
a
b
c
Figure 1: Typical cross sections for beams of Group 1, 2 and 3
19
Figure 2: Typical section and test setup of beams
Figure 3: Stress-strain relationship for #3 and #4 high strength and Grade 60 steel
20
A: Strain gages
B: Rosettes Configuration
C: Transverse PI Gages Configuration
Figure 4: Instrumentation
21
a
b
c
Figure 5: Applied shear v/s deflection for beams of Groups 1, 2 and 3
22
G1-M100 & G2-M100
G1-M80 & G2-M80
G1-C60 & G2-C60
G1-M0 & G2-M0
Figure 6: Failure for beams of Groups 1 and 2
23
a
b
c
Figure 7: Crack width v/s applied shear for beams of Groups 1, 2 and 3
24
a
b
c
Figure 8: Applied shear v/s transverse strain for beams of Groups 1, 2 and 3
25