Question

1. (20 points) A beam is subject to a load of 500 kip ft (this is the mean load, statistically speaking). The nominal resistance of the member is 700 kip ft (this is the mean resistance). It is estimated that the standard deviation values for the load and resistance are 80 kip ft and 20 kip ft, respectively. Find the approximate probability of failure. Recall that if Rm and Qm are the mean resistance and load, respectively, and V and Vo are the coefficient of variation (standard deviation /mean) for the resistance and load, then the safety index B, can be approximated as:

Answer 1

Mean resistance R_m = 700 kip mean load Q_m = 500 kip coefficient of variation for resistance: V_R = standard deviation for resistance /mean resistance V_R = 20/700 coefficient of variation for load V_R = standard deviation for load/mem load = 80/500 Now safety factor beta = ln(R_m/Q_m)/squareroot V_R^2 + V_Q^2 beta = ln(700/500)/Squareroot(20/700)^2 + (80/500)^2 beta = 2.07