Paper2ACIShearAruna

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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 NSFI/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 committeesincluding 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.

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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

members. Most of the research currently available in the literature focused on the use of high

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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. The beams, shown in Table

1, are identified by three parameters: the first two characters indicate the group to which the beam

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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 3f'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 48 in. (102204 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.

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

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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 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)

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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 failures.

CRACK PATTERN

The general crack patterns observed for all beams within the same group were identical.

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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 flexural-

shear cracks. For beams without transverse reinforcement (i.e. G1-M0, G2-M0, G3-C0 and G3-

M0), 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.

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

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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:

( 2 0.5 )sin ( 0.5 ) cos = + D v g ct v g ct

w l l

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 crackwith 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 selected design strength of 80 ksi and 100 ksi used in high strength

stirrups, beams G1-M80, G2-M80 and G3-M80 had a larger crack width in comparison to beams

G1-C60, G2-C60 and G3-C60 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-

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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 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-

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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 V c3 = 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 V c2 = 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 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

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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 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

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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.

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.

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http://www.mmfxsteel.com/http://www.mmfxsteel.com/


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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.

TABLES AND FIGURES

List of Tables:

Table 1: Reinforcement details of beams

Table 2: Load location and a/d details

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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

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Table 1: Reinforcement details of beams

Group ID

Target

Shear

capacity

Cross-

sectiona/d

Design

flexura

l stress

Flexural SteelDesign

Stirrup

StressStirrup

Size

Spacing

tr

in Ten. Comp in

1

G1-M0

Min.

'3 cf bd24 x 28 3.1

100 ksi 4 # 11 2 # 9 - - - -

G1-C60 CONV

60 ksi6 # 11 2 # 9 CONV.

60 ksi# 3 8.0 0.11

G1-M80 100 ksi 4 # 11 2 # 9 80 ksi # 3 10.0 0.09

G1-M100 100 ksi 4 # 11 2 # 9 100 ksi # 3 13.0 0.07

2

G2-M0

Min.

'3c

f bd24 x 28 3.1

100 ksi 4 # 11 2 # 9 - - - -

G2-C60 CONV

60 ksi6 # 11 2 # 9 CONV.

60 ksi# 3 8.0 0.11

G2-M80 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

3

G3-C0

Max.

'7 cf bd16 x 22 3.0

CONV60 ksi

7 # 11 4 # 10 - - - -

G3-M0 100 ksi 5 # 11 4 # 10 - - - -

G3-C60 CONV

60 ksi7 # 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

1 in. = 25.4 mm; 1 ksi = 6.895 MPa

Table 2: Load location and a/d details

GroupTarget Shear

Capacity

Cross-

Section Loaded

Span

Test configuration Effective

Depth a/db h l1 l2 l3 l4

in in ft in in in in in

1 '3 cf bd 24 28 19.0 15 79 155 15 25.4 3.1

2 '3c

f bd 24 28 13.2 3 79 85 97 25.4 3.1

3'

7 cf bd 16 22 14.8 15 54 129 66 18.0 3.0

1 in. = 25.4 mm; 1 ft = 304.8 mm

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Table 3: Service Loads

Group IDb d f'c Stirrup

size

Spacing Vc Vs Vn Vn(avg) VserviceTheta

No. of

Cracks

in in psi in kip Kip kip kip kip

1

G1-C60

24 25

4710 # 3 8.0 84 42 126

128 77

32 1

G1-M80 4710 # 3 10.0 84 45 128 35 3

G1-M100 4950 # 3 13.0 86 43 129 41 1

2

G2-C60

24 25

4710 # 3 8.0 84 42 126

128 77

27 1

G2-M80 4710 # 3 10.0 84 45 128 36 1

G2-M100 4950 # 3 13.0 86 43 129 40 1

3

G3-C60

16 18

5090 # 4 4.5 41 96 137

143 86

47 1

G3-M80 5240 # 4 5.5 42 105 146 38 1

G3-M100 5840 # 4 7.0 44 103 147 49 2

1 in. = 25.4 mm; 1000 psi = 6.895 MPa; 1 kip = 4.4482 KN

Table 4: Code Comparisons for Vc

Group IDS Vc1 Vc2 Vc3

ACI CSA AASHTO

Vc Vc(exp) /Vc VcVc(exp)

/VcVc Vc(exp) /Vc

in kip kip kip kip ratio kip ratio kip ratio

1

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

2

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

3

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

Average 1.11 1.10 1.06

1 in. = 25.4 mm; 1 kip = 4.4482 KN

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Table 5: Code Comparisons for Vs

Group IDS Vs(exp)

ACI CSA AASHTO

Vs Vs(exp)/ Vs Vs Vs(exp)/ Vs Vs Vs(exp)/ Vs

in kip kip ratio kip ratio kip ratio

1

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

2

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

3

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

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

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Figure 1: Typical cross sections for beams of Group 1, 2 and 3

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Figure 2: Typical section and test setup of beams

Figure 3: Stress-strain relationship for #3 and #4 high strength and Grade 60 steel

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Figure 4: Instrumentation

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A: Strain gages

B: Rosettes Confi uration

C: Transverse PI Gages Configuration


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Figure 5: Applied shear v/s deflection for beams of Groups 1, 2 and 3

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Figure 6: Failure for beams of Groups 1 and 2

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G1-M0 & G2-M0

G1-C60 & G2-C60

G1-M80 & G2-M80

G1-M100 & G2-M100


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Figure 7: Crack width v/s applied shear for beams of Groups 1, 2 and 3

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Figure 8: Applied shear v/s transverse strain for beams of Groups 1, 2 and 3

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