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Crack progression in the beams began with the appearance of flexural cracks in the maximum moment region, followed by additional flexural cracks forming between the load and support regions as the load was increased. Upon further increasing the applied load, the majority of the flexural cracks developed vertically and, after that, inclined flexure-shear cracks began to appear. As the load increased further, the inclined cracks progressed both upward toward the applied load plate and horizontally along the longitudinal reinforcement toward the support (see Fig. 3). Figure 3 offers a direct visual comparison of the crack shape and distribution at failure for both the SCC beams.
Unlike the parametric tests, nonparametric tests are referred to as distribution-free tests. These tests have the advantage of requiring no assumption of normality, and they usually compare medians rather than means. The Wilcoxon signed-rank test is usually identified as a nonparametric alternative to the paired t test. The hypothesis for this test is the same as those for the paired t test. The Wilcoxon signed rank test assumes that the distribution of the difference of pairs is symmetrical. This assumption can be checked; if the distribution is normal, it is also symmetrical. As mentioned earlier, the data follows normal distribution and the Wilcoxon signed ranks test can be used. The p value for the Wilcoxon signed rank was 0.363 (>0.05), that confirmed the null hypothesis at the 0.05 significance level. Interestingly, the p values for both the paired t tests (parametric test) and the Wilcoxon signed rank test (nonparametric test) are very close to each other.
Table 7 presents the tensile strain in the longitudinal tension reinforcement at the quarter-point of the span (middle of the shear test region) obtained from both the experiments (strain gauges) and also the AASHTO LRFD-10 equation. This AASHTO LRFD-10 equation underestimates the strain for the SCC beams. The measured strains are based on the installed strain gages. Even with the potential for slight inaccuracies in the strain gage readings due to localized cracking and the slight reduction in cross section required for mounting the gages, the measured readings offer a valuable basis of comparison with the AASHTO LRFD-10 equation. The concrete component of shear (V c ) is the sum of the resistance due to three shear mechanisms: uncracked concrete, aggregate interlock, and dowel action. Higher strain in the tension reinforcement means more dowel action and since no significant difference was observed in the shear crack patterns compared with CC beams, it may be concluded that the SCC beams have lower aggregate interlock. Authors suggest push-off specimen tests for future research to evaluate aggregate interlock between the CC and SCC mix designs.
The angle of the critical shear crack is an important design parameter in the AASHTO LRFD-10 sectional design method. Although it is difficult to determine precisely as it is open to interpretation. The procedure used to determine this angle consisted of measuring the angle of a portion of the critical shear crack between two reference points, with the points corresponding to right after crossing the alignment of the longitudinal reinforcement and before entering the compression zone (Fig. 6). The diagonal shear crack angle is calculated in AASHTO LRFD-10 by Eq. (3).
Table 7 compares measured diagonal shear crack angle from the test specimens with the calculated angle from the AASHTO LRFD-10 equation. As it can be seen from Table 7, the AASHTO LRFD-10 equation accurately predicted the diagonal shear crack angle for the SCC beams with stirrup, but it underestimated for the beams without stirrup.
The AASHTO LRFD estimation of the longitudinal tensile strain of the reinforcements is less than the actual strain for the SCC beams. This higher strain in the reinforcements can be attributed to higher dowel action. Since both the SCC and the CC beams had the same crack patterns, it may be inferred that the SCC beams have lower aggregate interlock compared with the CC beams.
The AASHTO LRFD equation predicts the diagonal shear crack angle of both the CC and SCC beams very well for beams with shear reinforcement, but it underestimates for the beams without shear reinforcement. 2ff7e9595c
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