Structural reliability is about applying reliability engineering theories to buildings and, more generally, structural analysis.[1] [2] Reliability is also used as a probabilistic measure of structural safety. The reliability of a structure is defined as the probability of complement of failure
(Reliability=1-ProbabilityofFailure)
In structural reliability studies, both loads and resistances are modeled as probabilistic variables. Using this approach the probability of failure of a structure is calculated. When loads and resistances are explicit and have their own independent function, the probability of failure could be formulated as follows.
where
Pf
FR(s)
fs(s)
However, in most cases, the distribution of loads and resistances are not independent and the probability of failure is defined via the following more general formula.
where is the vector of the basic variables, and G(X) that is called is the limit state function could be a line, surface or volume that the integral is taken on its surface.
In some cases when load and resistance are explicitly expressed (such as equation above), and their distributions are normal, the integral of equation has a closed-form solution as follows.
In most cases load and resistance are not normally distributed. Therefore, solving the integrals of equations and analytically is impossible. Using Monte Carlo simulation is an approach that could be used in such cases.[4]