Question

An engineer wants to estimate the reliability of a structure. The distributions of the dead load, the live load and the resistance of the structure are Gaussian and independent. The dead load is normally distributed with a mean of 18 MPa and a standard deviation of 5 MPa. The mean and standard deviation of the live load are 22 and 12 MPa, respectively. The structure is made of high performance concrete with a mean resistance of 60 MPa and a standard deviation of 5 MPa. Knowing that failure is the event in which the total loads exceed the resistance,

Determine: 1) The probability of failure of the structure.

2)The engineer would like to explore the effect of multiplying the loads and resistance by safety factors. Recalculate the probability of failure after applying the following factors of safety: 0.8 for the resistance and 1 .1 for the loads.

Answer 1

The total load has distribution .

The resistance has distribution

a) The probability of failure of the structure,

b) After applying the following factors of safety: 0.8 for the resistance and 1 .1 for the load,

and

b) The probability of failure of the structure,