Structural reliability is about applying

reliability engineering Reliability engineering is a sub-discipline of systems engineering that emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended functi ...

theories to

building A building or edifice is an enclosed Structure#Load-bearing, structure with a roof, walls and window, windows, usually standing permanently in one place, such as a house or factory. Buildings come in a variety of sizes, shapes, and functions, a ...

s and, more generally, structural analysis. Reliability is also used as a probabilistic measure of structural safety. The reliability of a structure is defined as the probability of

complement Complement may refer to: The arts * Complement (music), an interval that, when added to another, spans an octave ** Aggregate complementation, the separation of pitch-class collections into complementary sets * Complementary color, in the visu ...

of failure

(\text = 1 - \text)

. The failure occurs when the total applied load is larger than the total resistance of the structure. Structural reliability has become known as a design philosophy in the twenty-first century, and it might replace traditional deterministic ways of

design A design is the concept or proposal for an object, process, or system. The word ''design'' refers to something that is or has been intentionally created by a thinking agent, and is sometimes used to refer to the inherent nature of something ...

and maintenance.

Theory

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

P_f

is the probability of failure,

F_R(s)

is the cumulative distribution function of resistance (R), and

f_s(s)

is the probability density of load (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 𝑋 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.

Solution approaches

Analytical solutions

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.

Simulation

In most cases load and resistance are not normally distributed. Therefore, solving the integrals of equations () and () analytically is impossible. Using

Monte Carlo simulation Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be det ...

is an approach that could be used in such cases.{{Cite book, title=Okasha, N. M., & Frangopol, D. M. (2009). Lifetime-oriented multi-objective optimization of structural maintenance considering system reliability, redundancy and life-cycle cost using GA. Structural Safety, 31(6), 460-474.

References

Reliability analysis Reliability engineering Structural engineering