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32 250 200 Force (kips) 150 100 50 w i thout softening w i th softening Experiment 0 0 1 2 3 4 5 6 7 8 9 10 Displacement (in.) (a) PC girders 250 200 Force (kips) 150 100 Case 4-1_FE Case 4-2_FE 50 12in-S90-NoMA 0 0 1 2 3 4 5 Displacement (in.) (b) RC girders Figure 2.15. Representative shear force-displacement relationship. (COV) are calculated as 0.01, 0.07, and 0.07, respectively. For ing FRP strengthening for shear. Figure 2.16 illustrates the RC girders, the average shear strength ratio was 0.98 with a strain distribution determined from FE analysis along the maximum ratio of 1.11 and a minimum ratio of 0.90, and principal direction of a critical FRP sheet for a series of VAR, STDEV, and COV are calculated as 0.00, 0.07, and 0.07, increasing load stages. As shown in the figure, when the test respectively. The FE analyses showed a good agreement with beam reached the ultimate state (i.e., a loading state of 250 kips), test results for the ultimate strength suggesting that the devel- the maximum strain in the FRP was only 0.0091 which is 54% oped FE models appropriately predict the ultimate strength of the rupture strain (0.017). of both PC and RC girders. The FE analysis allowed investigation of local behaviors 2.7 Performance Evaluation of that could not be examined through experiments such as the Existing Design Methods interface behavior between concrete and FRP sheets. The FE analysis also provides the stress and strain variations for con- This section presents a summary of the performance eval- crete, steel, FRP, and interface regions that were used to uation conducted for existing models and relationships for investigate each component contribution to the shear trans- Vf. Table 2.10 presents a summary of the performance of 21 fer mechanism. In particular, strain variations along the prin- different relationships (i.e., 17 models presented in research cipal direction of FRP sheets are valuable inputs for design- papers and four models included in code and guideline docu-