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2.5 Shear Reinforcement 2.5.2.1 Test Specimens and Experimental Program
The use of A1035 steel as transverse reinforcement for flex- Specimen Details. The five reinforced-concrete test
ural members was examined experimentally. The experimen- beams (designated by SR_) were all 12 in. wide by 24 in. deep.
tal data from full-scale testing of reinforced and prestressed The first four of these specimens (SR1 through SR4) were
beams were augmented by the results from analytical studies. designed based on a nominal concrete strength of 10 ksi and
The performance of high-strength steel as shear reinforce- included #3 A1035 stirrups along with #4 A615 stirrups,
ment is evaluated in this section. placed in either half of the beam. Specimen SR5, however,
was designed based on a 15 ksi nominal concrete strength and
contained only #3 A1035 stirrups throughout the entire
2.5.1 Shear Resistance length of the beam. The spacing of stirrups in specimens SR1,
Under current AASHTO LRFD Bridge Design Specifica- SR4, and SR5 was governed by the amount required to resist
tions, the Sectional Design Model, which was derived from a prescribed value of ultimate shear force. On the other hand,
the Modified Compression-Field Theory (Vecchio and the maximum stirrup spacing currently allowed by AASHTO
Collins, 1986), is prescribed for determining the required LRFD Bridge Design Specifications was used as the basis of
amount of shear reinforcement. The Sectional Design design for specimens SR2 and SR3. For the specimens con-
Model provides strain-based relationships to account for taining both types of transverse steel, the spacing and size of
contributions from the concrete and the transverse rein- stirrups were selected such that the stirrup force as computed
forcement to overall shear capacity. A value for the yield Av f y dv
by Vs = would be nearly equal for the A615 and A1035
strength of the transverse steel is needed in order to apply S
the design equations in AASHTO LRFD (2007) §5.8.3. stirrups reinforcing in either half of the beam. The value of fy
For design of the test specimens, a value of 100-ksi was was taken as 100 ksi and 60 ksi for A1035 and A615 stirrups,
selected as the "yield strength" of the A1035 steel. A com- respectively. All of the specimens were reinforced with #8
plete synopsis of the design steps and equations is provided A1035 longitudinal bars to induce shear failure prior to
in Appendix F. reaching their flexural capacities. Table 16 summarizes spec-
imen details for the reinforced-concrete beams.
2.5.2 Experimental Evaluation The four prestressed AASHTO Type I girders (designated
by SP_) had 7 in. deep by 48 in. wide composite slabs. All of
A total of nine shear specimens were designed, fabricated, the Type I girders were designed based on a nominal concrete
tested, and analyzed. The specimens consisted of five rectan- strength of 10 ksi in the girder and 5 ksi in the slab. Each of
gular reinforced-concrete beams and four AASHTO Type I these specimens had both #3 A1035 and #4 A615 stirrups
prestressed girders. Of the nine specimens, all but one con- along with 0.6-inch low-relaxation strands. The design of SP1
tained both high-strength (A1035) and A615 shear reinforce- and SP3 was controlled by the amount of transverse rein-
ment. The primary goal was to evaluate the performance of forcement required to resist an ultimate shear force. The
high-strength steel as shear reinforcement in comparison to shear capacities of these specimens were expected to be near
that of the commonly used A615 steel. Appendix F provides their flexural capacities given the nature of the loading
detailed information regarding the experimental program as arrangement. Specimen SP2 used the maximum stirrup spac-
well as a complete record of the test data. ing currently allowed by AASHTO LRFD Bridge Design Spec-
Table 16. Shear specimens (reinforced-concrete beams).
Specimen Transverse f'c (ksi) Design
ID Reinforcement Design Measured Criterion
#4 A615 @ 9.5 in.
SR1 10 12.2 As Needed to Resist Vu
#3 A1035 @ 8.5 in.
#4 A615 @ 13 in.
SR2 10 12.9 Max. Allowed Spacing
#3 A1035 @ 13 in.
#4 A615 @ 13 in.
SR3 10 13.0 Max. Allowed Spacing
#3 A1035 @ 13 in.
#4 A615 @ 8.5 in.
SR4 10 13.1 As Needed to Resist Vu
#3 A1035 @ 8 in.
SR5 #3 A1035 @ 8.5 in. 15 16.9 As Needed to Resist Vu
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Table 17. Shear specimens (AASHTO Type I girders).
Specimen Transverse Girder f'c (ksi) Slab f'c (ksi) Design
ID Reinforcement Design Measured Design Measured Criterion
#4 A615 @ 8 in.
SP1 10 11.9 5 7.2 As Needed to Resist Vu
#3 A1035 @ 7.5 in.
#4 A615 @ 24 in.
SP2 10 12.4 5 9.9 Max. Allowed Spacing
#3 A1035 @ 22 in.
#4 A615 @ 11 in.
SP3 10 13.1 5 10.1 As Needed to Resist Vu
#3 A1035 @ 10 in.
#4 A615 @ 16 in.
SP4 10 10.5 5 6.3 Under-Designed A1035
#3 A1035 @ 18 in.
ifications, and was expected to fail in shear. By selecting dif- sure load, deflection, and both steel and concrete strains in
ferent bar sizes and spacing in these three specimens, the given locations.
amount of shear force provided by A615 and A1035 stirrups
was kept nearly identical. Specimen SP4, on the other hand,
2.5.2.2 Results and Discussions
was designed such that the A615 shear capacity exceeded the
A1035 shear capacity in order to induce shear failure on the The measured and observed responses are used to assess
A1035 side. Table 17 summarizes specimen details. The mate- the performance of various specimens as described in the fol-
rial properties of transverse reinforcement are summarized in lowing sections.
Table 18. Appendix A provides an in-depth discussion of
material properties. 2.5.2.2.1 Observed Failure Modes. Both specimens SR1
and SR2 failed in shear on the side reinforced with #4 A615
Testing Program. Three different loading arrangements stirrups. Figure 17 displays specimen SR2 after failure. In
were selected to test the specimens. Specimens SR1, SR2, and terms of strength, the failure on the portion of the beam using
SR5 were all 13.5 ft long and were tested over an 11-ft simple A615 transverse reinforcement suggests satisfactory perform-
span in three-point bending. Specimens SR3 and SR4 were ance of the A1035 stirrups. The side of specimen SR3 with
both 26 ft long and tested as a simply supported beam with a A1035 stirrups was loaded first before testing the A615 side to
6-ft overhang where the load was applied 1 ft from the tip of failure. The failure load was higher than what was applied to
the overhang. Specimens SR3 and SR4 were tested in two the A1035 side; hence, no conclusion regarding performance
phases such that one test isolated the loading to just one type of A1035 stirrups versus A615 stirrups can be drawn from
of stirrup. The side of specimen SR3 reinforced with A1035 specimen SR3. The order of testing of specimen SR4 was
stirrups was tested first. For specimen SR4, the side using reversed from SR3; therefore, the A615 side was loaded short
A615 stirrups was tested first. The side tested first was not of failure. The failure on the A1035 side could be character-
loaded to failure in order to be able to reposition the speci- ized as flexural. The observed failure mode was unexpected
men and load the other side. The prestressed specimens (SP1 according to the computed capacities. Loading of specimen
to SP4) were all 30 ft long and tested over a 26.5-ft simple SR5 had to be stopped prior to failure after reaching the load-
span in four-point bending with a constant moment region ing apparatus' capacity, which was 20% larger than the best-
of 11 ft. For each test, specimens were instrumented to mea- predicted capacity (based on compression field theory) and
Table 18. Measured properties of transverse reinforcement.
Calculated Ultimate Yield Strength (ksi)
Rupture
Stirrup Specimens Modulus of Strength @ Strain = @ Strain = 0.2%
Strain
Elasticity (ksi) (ksi) 0.0035 0.0050 Offset
#4 A615 SR1-SR4 n.r. 26934 100.7 62.6 64.2 63.5
#4 A615 SP1-SP3 n.r. 27596 105.4 86.3 88.2 88.2
#4 A615 SP4 n.r. 23945 105.0 83.4 92.9 90.2
#3 A1035 SR1-SR5 0.111 29800 156.0 95.0 112.0 130.0
#3 A1035 SP4 0.070 27740 164.1 93.0 117.2 131.9
Notes:
There are no sample data for #3 A1035 stirrups used in SP1-SP3; n.r. = not reported.
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capacity computed according to AASHTO provisions. The
failure load was also 51% and 25% larger than the capacity of
#4 A615 stirrups depending on whether AASHTO capacity or
compression-field theory is used.
Capacity. Capacities were computed according to the
Sectional Design Model in the AASHTO LRFD Specifications
using as-built material properties. A program called Response
2000 (Bentz 2000), abbreviated as R2K in Table 19, also was
used to compute the capacities. This program is a non-linear
sectional analysis program for the analysis of reinforced-
concrete elements subjected to shear based on the modified
Figure 17. Failure mode of SR2 (A615 side). compression-field theory. As shown in Appendix F, load-
deflection responses from Response 2000 are reasonably close
to the experimental results. A summary of the measured
67% larger than the capacity computed based on AASHTO and computed capacities for the shear specimens is given in
equations. The behavior of specimens SR4 and SR5 suggests Table 19. This table also provides the ratios of measured
that the shear strength of members reinforced with A1035 capacities to the computed capacities. All of the specimens far
appears to be appreciably larger than what is computed. exceeded the predicted capacities based on AASHTO. Even
Specimen SP1 was designed with the highest shear capac- Response 2000 underestimates the shear capacities in most
ity and failed in a flexural manner with no signs of excessive cases. The only specimen for which Response 2000 was found
shear cracking. Specimen SP2, which had the least amount to be slightly unconservative was specimen SP1, which failed
of shear reinforcement, failed in shear. The failure, which in a decidedly flexural manner. The large ratios of measured
occurred on the A615 side, was quite brittle. Specimen SP3 to computed capacities have also been observed by others
had slightly larger stirrup spacing than SP1, and the com- (Kuchma et al. 2005) and indicate the challenges of capturing
puted capacities indicated a failure mode bordering flexural shear behavior. The measured and computed capacities sug-
and shear failure. Loading of this specimen was stopped after gest adequate shear strength of A1035 stirrups designed based
excessive flexural cracks began to open at midspan. Specimen on current design equations in which stirrup yield strength is
SP4 was designed after all the other shear specimens had been taken as 100 ksi.
tested. In order to examine shear failure due to A1035 stir-
rups, specimen SP4 was designed such that the capacity pro- Shear Crack Patterns and Widths. One concern for
vided by #4 A615 stirrups would be approximately 15% using high-strength steel for stirrups is whether the high stress
higher than that from #3 A1035 stirrups. This specimen expe- levels induced in the reinforcement may cause excessive crack-
rienced shear failure on the side of the specimen with A1035 ing in the concrete resulting in degradation of the concrete
stirrups. Similar to specimen SR2, the failure was brittle--see component of shear resistance. Figure 19 displays the crack
Figure 18. It should be noted that the failure load was 40% patterns for specimen SR4 corresponding to when the stress
higher than the expected capacity based on a detailed analy- in A1035 stirrups was approximately 100 ksi. Crack patterns
sis using compression-field theory, and 75% larger than the for the regions with A615 and A1035 stirrups were quite sim-
ilar in terms of the load at which they formed and how they
propagated. None of the test specimens exhibited an unusual
behavior of A1035 stirrups in terms of crack formation and
crack patterns.
In addition to marking the diagonal cracks, their widths
were measured at various load increments using a crack
comparometer. Those increments correspond to approxi-
mately 60% to 100% of the "yield strength" of the stirrups
(fy =100 ksi for A1035). Below those increments, diagonal crack-
ing was minimal or nonexistent. The loads at which diagonal
cracks (i.e., shear cracks) could be measured are appreciably
larger than service loads. The largest measured crack widths in
the regions reinforced with #4 A615 and #3 A1035 stirrups are
Figure 18. Failure mode of SP4 (A1035 side). summarized in Table 20. In this table, the load increments are
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Table 19. Measured and computed capacities.
Measured AASHTO Capacity R2K Capacity
Specimen Stirrup Failure
Capacity Computed Measured/ Computed Measured/
ID Type Mode
(kips) (kips) Computed (kips) Computed
A615 Shear, 175 1.51 233 1.14
SR1 26
A1035 A615 side 175 1.51 233 1.14
A615 Shear, 147 1.55 190 1.20
SR2 228
A1035 A615 side 141 1.62 165 1.38
A615 Shear, 121 76 1.59 N/A
SR3
A1035 A615 side 114* 73 1.56 (R2K cannot model
A615 Flexure, 117* 85 1.38 these specimens that
SR4 have overhangs.)
A1035 A1035 side 147 85 1.73
SR5 A1035 N/A 300** 181 1.66 251 1.20
A615 199 1.22 244 0.99
SP1 Flexure 242
A1035 170 1.42 244 0.99
A615 Shear, 139 1.71 157 1.52
SP2 238
A1035 A615 side 130 1.83 149 1.60
A615 175 1.43 243 1.03
SP3 Flexure 250
A1035 154 1.62 239 1.05
A615 Shear, 153 1.51 188 1.23
SP4 231
A1035 A1035 side 132 1.75 164 1.41
Notes:
* Loading was stopped prior to failure so the other side could be tested.
** Loading was stopped after reaching the actuator's capacity, which was 300 kips.
presented in terms of shear stress. The information in Table 20
is presented graphically in Figure 20. As expected, the shear
crack widths exhibit a large scatter; however, the trends of the
data indicate differences between A615 and A1035 stirrups. At
lower levels of shear stress, the crack widths for the regions with
A1035 stirrups are comparable in size to the crack widths for the
regions using A615 stirrups. With an increase in shear stress, the
cracks on the side reinforced with A1035 stirrups widened at a
faster rate than the side with A615 stirrups. This trend should
be anticipated because the A1035 stirrups were smaller than the
A615 stirrups (#3 vs. #4).
(a) A615 Side Despite these differences, it should be noted that the diag-
onal cracks became measurable at shear stresses exceeding
2 fc which is commonly used as concrete shear strength. At
such stress levels, the magnitude of crack width is less of a
concern because ensuing adequate load-carrying capacity is
the main design objective. Moreover, the differences between
the crack widths for regions with A615 and A1035 are rela-
tively small.
Strain Levels and Stirrup Forces. Even though the lon-
gitudinal bars are all A1035 steel, the strains recorded on the
two sides with A615 and A1035 stirrups should be equivalent if
the stirrups are performing equally according to compression-
field theory. A representative load-longitudinal strain rela-
(b) A0135 Side tionship is shown in Figure 21; this figure is for specimen SR1.
Figure 19. Crack patterns of SR4. The longitudinal strains (measured by strain gages SG6 and
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Table 20. Maximum shear crack width. SG7) near the mid-span are exceptionally similar, and those
measured near the quarter points are also good with a differ-
Maximum Crack Width in a Given ence of only a few hundred microstrain. The sudden jump
Specimen Shear Stress Region (in.)
ID ( f c') in the strain readings around 145 kips on the A1035 side is
A615 Side A1035 Side
attributed to formation of a crack near the strain gage, which
3.21 0.0098 0.0098 led to continued differences between the strain values. All
3.56 0.0118 0.0138
SR1
3.93 0.0157 0.0157
things considered, the longitudinal strain data again point
4.37 0.0217 0.0236 toward similar behavior between the two types of steel used
2.45 0.0157 0.0118 for the stirrups.
SR2 2.88 0.0256 0.0157 In addition to placing strain gages on the longitudinal bars,
3.09 0.0276 0.0177 strain gages also were bonded to the stirrups at the mid-
2.53 0.0118 0.0236
SR3
depth. Using the measured stress-strain relationships of the
2.99 0.0157 0.0295
3.42 0.0236 0.0335 #4 A615 and #3 A1035 steel (Appendix A), the strain readings
2.57 0.0138 0.0098 A fd
can be converted into stirrup forces using Vs = v s v which
2.99 0.0197 0.0157 S
SR4 3.45 0.0217 0.0197 can then be used to analyze the performance of the stirrups.
3.87 0.0236 0.0276
Figure 22 illustrates the variation of stirrup force as a func-
4.30 0.0315 0.0354
2.26 0.0098
tion of applied shear for specimen SR2. The two mirrored
2.69 N/A 0.0118 strain gage locations (refer to the inset) show nearly identi-
SR5 (This specimen only
3.00 had A1035 stirrups.) 0.0157 cal results. The similarities of the stirrup forces suggest that
3.28 0.0177 the stirrups performed in accordance with the design objec-
SP1 **Cracks were too small to measure. tive of developing nearly equal forces in #4 A615 and #3
6.38 0.0118 0.0157
SP2 7.27 0.0157 0.0177
A1035 stirrups. Yielding of A615 stirrups is evident from
7.95 0.0256 0.0276 SG1 that was outside of the region influenced by the con-
6.93 0.0079 0.0079 centrated load applied at the midspan and reactions. Between
SP3 7.88 0.0098 0.0118 approximately 70 and 85 kips, the stirrup force remained
8.79 0.0118 0.0138 essentially unchanged even though the applied shear force
7.01 0.0059 0.0138
SP4
was increased by nearly 15 kips. In contrast, A1035 stirrups
8.03 0.0098 0.0177
8.99 0.0118 0.0276 could continue to provide shear resistance after A615 stir-
Shear stress = Shear force divided by bvdv.
rups had yielded. The trend of data was generally similar
for the other specimens, although formation of cracks near
the strain gages occasionally affected the computed stirrup
forces.
Figure 20. Maximum shear crack width--shear stress.
