![Reliability](https://upload.wikimedia.org/wikipedia/commons/9/9c/Reliability.png)
Structural reliability is about applying
reliability engineering theories to
building
A building, or edifice, is an enclosed structure with a roof and walls standing more or less permanently in one place, such as a house or factory (although there's also portable buildings). Buildings come in a variety of sizes, shapes, and fu ...
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
A complement is something that completes something else.
Complement may refer specifically to:
The arts
* Complement (music), an interval that, when added to another, spans an octave
** Aggregate complementation, the separation of pitch-clas ...
of failure
. 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 a plan or specification for the construction of an object or system or for the implementation of an activity or process or the result of that plan or specification in the form of a prototype, product, or process. The verb ''to design' ...
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
is the probability of failure,
is the cumulative distribution function of resistance (R), and
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 Normal(s) or The Normal(s) may refer to:
Film and television
* ''Normal'' (2003 film), starring Jessica Lange and Tom Wilkinson
* ''Normal'' (2007 film), starring Carrie-Anne Moss, Kevin Zegers, Callum Keith Rennie, and Andrew Airlie
* ''Norma ...
, 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 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