Question

Problem 7.5 of your textbook (Haldar & Mahadevan): A simply supported beam of span L 360 inches is loaded by a uniformly distributed load w kip/in. and a concentrated kip applied at the midspan. The maximum deflection of the beam at the midspan can be calculated as: mar- 384 EI 48 E A beam with El 63.51 x 106 kip-in.2 Is selected to carry the load. Both w and P are statistically independent RVs with mean values estimated to be 0.2 kip/in. and 25 kip, respectively. The corresponding standard deviations are 0.03 kip/in. and 2.5 kip, respectively. Assume the distributions of w and P are unavailable. The allowable deflection, a, for the beam is a constant of value 1.5 inch. Considering the limit state equation of the form g) - 5a in deflection using the MVFOSM method 0, calculate the reliability index for the beam

Answer 1

PL elg0 given L- 36d ean Value a ho an Vaoiabla w and p, 0.2 K tr) W and deviations; 2

Nao, so calcolate the Valte af (imit "glate-R,n char PL -384 15-ти [2c4.ucu + o ovsp] S-38u 6.812 59 Now calcolating tho value of 시

NCalco tatinq 39 above eaton, e et Sub StHoin Q0u) i man Value iS -ha SAGrㅝard deviation

Cu) 0.82 B- 0.011 B -69,40 Hen Reliability indu, β 64.40 8y using MvEosn masthod,