Question

B5 Consider a steel bridge that deteriorates continuously with time due to corrosion. The initial structure performance of the bridge is 100% with a failure threshold of 25%. Estimate the probability of failure of the bridge when t = 30 years if the progressive deterioration of the bridge can be modelled as a graceful (linear) deterioration with a deterioration rate of 0.75/year during the first 20 years, and an exponential deterioration with a rate of 0.04/year in the following 10 years. Assume the remaining structural capacity is governed by an exponential distribution with an average rate of 0.05

Answer 1

solution

FIRST OF ALL WE NEED TO FIND THE COMPELETE DETERIORATION AND THEN BY LINEA

mitil Rertoimante failue thaeshauld 1-1 ool 2- Probability of fathn affa 20 yeay dedenbrahon 2OX0. aJfer o yeas S+85oo aff 30year L00-1 -O -04x Io rott t.95-S Falue thueshould iNtal Peror mane Pz1 7 "Asi 100 29 0229561 at Peyformane t 26-022 9362-257.)メ D.04030 7100- 4 964 fPEO.95969 # Propeliity o fai lne is 96