The change in the length of a rod due to axial force P is given by

L PL AE

=

where L is the length of the rod, P is the applied axial force, A is the cross-sectional area of the rod, and E is the modulus of elasticity. Assume that the change in length of the rod must not exceed 0.15 in. Using 2000 simulation cycles in

(a) the direct MCS method, and

(b) the CE method, determine the failure probability of the rod in meeting this limit. Assume that the noncorrelated random variables have the following probabilistic characteristics:

Random Variable Mean Value COV Distribution Type P 100 kips 0.35 Lognormal L 20 in. 0.05 Normal E 30,000 ksi 0.10 Lognormal A 1 in.2 0.05 Normal