2015-08-13
384
If the probability density functions for strength and stress of a structure are described by normal functions with known means mi and standard deviation Di the probability density function for difference in strength and stress is also a normal distribution.
The reliability is equal to 0.5 if the means of the distributions coincide. It is larger than 0.5 if the mean for stress is smaller than for strength.
The summed area under a density function is equal to 1.
The probability of failure is equal to the integral over the range where both functions f(s) and F'(s) are nonzero.
The summation is over three intervals. The probability of failure of a structure is 0.09 and its reliability is 0.91.
Engineering changes can alter the positions of the probability density functions.
A. Cross section area increase results in a stress decrease.
B. Stress concentration results in a stress increase.
C. Service in low temperatures results in brittle fracture (strength decrease).
D. Heat treatment of welded joints results in residual stress decrease (strength increase).
The reliability index is a measure of the reliability of a structure. The minimum reliability index of structural components corresponds to the reliability index of the whole structure. The smaller the reliability index bi, the more probable the failure.
