Issue 50

M. Godio et alii, Frattura ed Integrità Strutturale, 50 (2019) 194-208; DOI: 10.3221/IGF-ESIS.50.17 202 Configuration w t  (mm) w w H /t  ( - ) b r  w (%t ) w,eff w t /t  ( - ) m E  (MPa) O/W ( - ) I f  (Hz) C0* 200 14 2 0.96 500 0.09 6.91 C1 200 14 2 0.96 125 0.09 9.77 C2 200 14 2 0.96 250 0.09 19.54 C3 200 14 2 0.96 1000 0.09 27.64 C4 200 14 2 0.96 2000 0.09 6.91 C5 100 28 2 0.96 500 0.18 13.82 C6 150 19 2 0.96 500 0.12 17.28 C7 250 11 2 0.96 500 0.07 20.73 C8 300 9 2 0.96 500 0.06 13.82 C9 200 14 0.5 0.99 500 0.09 13.82 C10 200 14 1 0.98 500 0.09 13.82 C11 200 14 1.5 0.97 500 0.09 13.82 C12 200 14 3 0.94 500 0.09 13.82 C13 200 14 2 0.96 500 1.40 13.82 C14 200 14 2 0.96 500 2.06 13.82 C15 200 14 2 0.96 500 4.03 13.82 C16 200 14 2 0.96 500 6.01 13.82 *Reference configuration Table 2 : Walls analysed in the parametric study. Properties in bold are varied with respect to the reference configuration. R ESULTS OF THE STUDY Results for support motions with phase shift Fig. 5 shows the fragility curves for each of the configurations analysed in the parametric study and for support motions with different phase-shift, i.e. generated by Eqn. (8) for β equal to 0, 0.5 and 1. The fragility curves are built from the results of the IDA, as cumulative distributions of the limit PGA, denoted here as PGA lim . This latter corresponds to the PGA of the time history in which the wall attains failure for the first time along the IDA and it is defined from Eqn. (9), as the average acceleration of the top and bottom supports:     T B lim β t t u t u t PGA max max u 2       (14) The condition used for wall failure is that the wall undergoes a mid-height displacement d equal or larger than the limit displacement d 0 . The probability of wall failure is therefore P (|d|≥d 0 ). This displacement is calculated as the maximum displacement that the wall attains under a uniformly distributed lateral load, assuming a failure mechanism similar to the one depicted in Fig. 2, but with fixed wall supports. The expression for d 0 is obtained in [41] and, for clarity, is reported here: w,ef 0 f t 2(1 ξ) d   (15) where ξ denotes the position of the middle masonry cracked joint, which can be calculated as: