26. A tension rod is 2 m long with a yield strength of  . The modulus of elasticity is . If the axial elongation is measured to be , determine the probability of failure using the First Order Second Moment Method. Note that  and  are independent.

Solution

According to Hooke’s law, the tensile stress is

where  is the stain and  is the length of tension rod.

The limit-state function is the actual tensile stress subtracted from the yield strength. Failure occurs when.

where .

Using FOSM, we have

The probability of failure is then given by