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60 and 100 ksi for the compression-controlled limit, and 75 to According to current AASHTO specifications, strain in the
100 ksi for the tension-controlled limit. extreme tension reinforcement (t) must exceed 0.0075 in order
to be able to redistribute moments. This strain is 1.5 times the
Tension Controlled: t 0.008
current strain limit of 0.005 that defines tension controlled.
Compression Controlled: t 0.004
The proposed strain limit of 0.012 is also 1.5 times the pro-
Where t is the strain in tensile strain in the extreme longi- posed tension-controlled strain limit of 0.008.
tudinal reinforcement.
These limits are nearly identical to those recommended by
Mast et al. (2008), that is, 0.004 and 0.009. It must be recognized
2.3.4 Experimental Evaluation
that selecting a different value of fy or fs results in different To better understand the behavior and capacity of
calibrations. flexural members reinforced with A1035 bars and evaluate
the aforementioned strain limits for tension-controlled and
2.3.3 Moment Redistribution compression-controlled sections, six specimens were designed,
fabricated, and tested. Appendix D provides detailed informa-
AASHTO §5.7.3.5 allows redistribution of negative moments tion regarding the experimental program as well as a complete
at the internal supports of continuous reinforced-concrete record of the test data.
beams. Redistribution is allowed only when the strain in the
extreme longitudinal reinforcement (t) is equal to, or greater
than, 0.0075. This strain limit of 0.0075 is derived in Mast 2.3.4.1 Test Specimens and Experimental Program
(1992) and can be traced to cases for which the provided area The test specimens, which were 12 in. wide by 16 in. deep
of steel is approximately one-half of that corresponding to bal- flexural members with nominal 10-ksi and 15-ksi concrete
anced failure (see Appendix C). As derived in Appendix C, for and A1035 longitudinal bars, were designed, fabricated, and
such cases the value of t is 0.003 + 2y. For Grade 60 reinforce- tested. To prevent the possibility of shear failure, #4 Grade 60
ment, the yield strain (y) is 0.0021; hence, t becomes 0.0072. A615 stirrups were provided throughout the span. For both
This strain is essentially the same as 0.0075, which is the strain concrete strengths, the specimens were designed based on the
beyond which moment redistribution is permitted. following strain targets: (1) tension-controlled strain limit of
In the case of A1035 reinforcement, the yield strain is 0.008; (2) 0.006, which is in the transition region between
higher than that for Grade 60 reinforcement. As discussed in tension controlled and compression controlled, and (3) above
Appendix C, Mast's Equation provides a very good lower- 0.010 to examine crack widths in beams with low reinforce-
bound estimate of A1035 stress-strain relationship. Mast's ment ratio. The specimen details and material properties of
Equation is as follows: the longitudinal bars are summarized in Tables 11 and 12,
respectively.
if s 0.00241 f s = Es s
The specimens were tested over a 20-ft simple span in a
0.43 four-point loading arrangement having a constant moment
if s > 0.00241 f s = 170 - region of 3.5 ft. The specimens were instrumented to capture
s + 0.00188
the load, deflection, and steel and concrete strains.
Based on Mast's Equation, the strain at 100 ksi is 0.0043.
Using this strain as the yield strain (y), the value of t becomes
2.3.4.2. Results and Discussions
0.0115 (t = 0.003 + 2y = 0.003 + 2(0.0043) = 0.0115) or approx-
imately 0.012. Therefore, 0.012 is proposed as the strain limit Ductility. One of the concerns when using high-strength
for which moment redistribution is allowed for members reinforcing bars such as A1035 is related to the reduced
reinforced with A1035 reinforcement. ductility resulting from the use of larger yield stresses and
Table 11. Flexural specimens.
Reinforcement
Specimen f'c (ksi) Target
(A1035) Comment
ID t
Layer 1 Layer 2 Design Measured
F1 4 #5 2 #5 10 12.9 0.0080 Tension controlled
F2 4 #6 2 #6 10 12.9 0.0060 Transition
F3 4 #5 ---- 10 12.9 0.0115 Tension controlled, small
F4 4 #5 4 #5 15 16.5 0.0080 Tension controlled
F5 4 #6 4 #6 15 16.3 0.0060 Transition
F6 4 #5 2 #5 15 16.9 0.0103 Tension controlled, small

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Table 12. Measured properties of A1035 longitudinal reinforcement.
Calculated Ultimate Yield Strength (ksi)
Bar Rupture
Specimens Modulus of Strength @ Strain @ Strain 0.2%
Size Strain
Elasticity (ksi) (ksi) = 0.0035 = 0.0050 Offset
#5 F1, F2, F3 0.103 26074 164.1 89.2 112.5 130.2
#5 F4, F5, F6 0.137 27280 164.9 92.9 115.0 129.2
#6 F1, F2, F3 0.103 29001 161.3 91.1 111.7 121.8
#6 F4, F5, F5 0.145 27711 165.3 94.1 117.9 134.4
the subsequent greater utilization of the concrete capacity. states, which can conveniently be accomplished by evaluating
The midspan deflection (expressed in terms of span length, the load-deflection response. The analytical load-deflections
L = 20 ft) corresponding to the maximum is tabulated in were obtained by using a computer program called Response
Table 13. The deflections at ultimate are clearly large. All of 2000 (Bentz 2000). Modeling of the specimens is discussed in
the specimens exhibited a well-distributed crack pattern. Well Appendix D. The measured and predicted load-deflection
before failure, noticeable crack opening and curvature of the responses for specimens F1 and F4, which are deemed to rep-
beams were noticed (Figure 7). Prior to failure, the beams resent members that will likely be encountered in practice,
exhibited visual warning signs of distress (see Figure 8). The are compared in Figure 10. For specimen F1, which was cast
large deflections and visual warning signs of distress before fail- with nominal 10-ksi concrete, the analytical load-deflection
ure attest to the ductility of the specimens. response is remarkably close to its experimental counterpart.
In contrast, the computed load-deflection for the specimen
Overall Response and Capacity. The measured load- cast with nominal 15-ksi concrete (i.e., specimen F4) exhibits
deflection relationships are plotted in Figure 9. As discussed a higher stiffness than the experimental data. This difference
above, the specimens exhibit large deflections prior to failure. is attributed to overestimation of aggregate interlock in the
The expected capacities were computed based on standard matrix of 15-ksi concrete. Considering the challenges of
strain compatibility analyses in which the stress-strain rela- modeling high-strength concrete, the shown load-deflection
tionship of A1035 longitudinal bars was modeled (1) as being response for specimen F4 is adequate. The results shown in
elastic-perfectly plastic having a yield strength (fy) equal to Figure 10 suggest that well-established techniques are appli-
100 ksi, which approximately corresponds to the stress at cable to members reinforced with A1035 high-strength lon-
strain of 0.004; (2) by an equation proposed by Mast (1992); gitudinal bars, and stiffness of such members can adequately
and (3) by the Ramberg-Osgood function describing the be computed.
measured stress-strain behavior. The ratios of observed-to-
predicted behavior are given in Table 14. All of the specimens Strain Level. The average strain from strain gages bonded
reached and exceeded their predicted capacities. Reflective of to the longitudinal bars at midspan is plotted versus the
the previously described analytical work, the predictions applied load in Figure 11. For each specimen, the target design
made using the Ramberg-Osgood representation of the steel strain (t in Table 11) is also plotted. The measured strains
behavior are remarkably close to the experimentally observed
behavior while those made using the fy = 100 ksi assumption
are quite conservative. The capacities based on Mast's Equa-
tion are reasonably close to the measured values.
In addition to being able to accurately predict the capacity
of members reinforced with high-strength A1035 reinforcing
bars, it is equally important to examine whether established
modeling procedures can capture the stiffness at various limit
Table 13. Maximum
midspan deflection.
Specimen Deflection
F1 L/44
F2 L/48
F3 L/39
F4 L/38
F5 L/47 Figure 7. Cracking patterns in Specimen F4 prior to
F6 L/29 failure.