# Fatigue Testing of Shear Reinforcement in Prestressed Concrete T-Beams of Bridges
## 3 Test Results
The behavior exemplarily described for beam T-33-2 was typical for all test beams. After the concrete tensile strength had been degraded by the cyclic loading, existing cracks widened and elongated and new cracks developed. Due to shear cracking, the stirrups exhibited cyclic stress ranges. Once the fatigue strength of the reinforcing steel was reached, a fatigue failure of a stirrup leg occurred, which led to a redistribution of the shear forces within the shear span. Adjacent stirrups obtained higher stress levels and stress ranges, which either accelerated their fatigue failure or caused a rupture by exceeding the residual tensile strength. Because of the shear crack pattern, which developed successively and randomly, the stirrups did not exhibit the same stress range and same stress level over the whole test period despite the applied constant shear loads. The stress ranges of the stirrups increased stepwise with each failure of a stirrup leg. After reaching pronounced shear cracks and several stirrup ruptures, the original truss model changed to a direct compression strut system between load application and support. Figure 6 shows the final crack patterns of all T-beams. Figure 4: Development of (**a**) deflection and (**b**) indication of crack width with increasing load cycles for test T-33-2a. In Figure 7 the resisted load cycles of all tests are summarized, considering the shear reinforcement ratio \(\rho_{\rm w}\) (0.22%; 0.33%; 0.67%), calculated stress range of stirrups \(\Delta\sigma_{\rm calc}\) (200 N/mm\({}^{2}\), 250 N/mm\({}^{2}\)) and the upper shear force related to the shear cracking force \(V_{\rm max}\)/\(V_{\rm cr}\). Based on the cyclic shear force range in the tests \(\Delta V_{test}\), the stress ranges \(\Delta\sigma_{\rm calc}\) were calculated according to Equation (1), assuming a strut inclination of \(\theta_{\rm fat}\) according to Equation (3). In general, the stirrups failed earlier with increasing stress range and/or increasing upper load. The load cycles listed in Table 2 and the maximum values in Figure 7 represent the point of final shear fatigue failure of the beam after several stirrups had failed already in advance. Based on the evaluation of the measured stirrup legs, the resisted number of load cycles of each stirrup and its strain during the test can be determined in more detail. The boxplot in Figure 7 shows the range between minimum and maximum number of load cycles until the failure of a single stirrup leg (thin line) and the mean value of all stirrup leg failures (box). The top line in the diagram indicates that the upper shear forces \(V_{\rm max}\) during cyclic testing varied between 110% and 195% of the shear cracking load \(V_{\rm cr}\). In test T-33-2, with a calculated stress range of \(\Delta\sigma_{\rm calc}\) = 250 N/mm\({}^{2}\), the first fatigue failure of stirrup occurred after 375,000 load cycles, the last one after 1,370,000 loads, leading to the final shear fatigue failure of the beam. The mean resisted load cycles of all stirrups was 1,040,800 cycles. In total, 6 of 8 stirrups had to fail over a period of 1.07 million load cycles, before the final shear failure of one shear span occurred. In the other shear span, 5 of 8 stirrups had to fail for final shear failure after 1.37 million load cycles. In other words, the loss of some stirrups does not cause the shear failure of a prestressed beam. The development of a crack pattern and growth of crack widths announces the final failure in an acceptable way. In test T-22-1 with a pronounced shear crack pattern under static preloading, the first stirrup did not fail after more than seven million load cycles. For this reason, the test was stopped and the number of load cycles at that time was used for the mean value \(N_{\rm test}\).