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structural reliability wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 theory 2 solution approaches toggle solution approaches subsection 2 1 analytical solutions 2 2 simulation 3 references toggle the table of contents structural reliability 5 languages العربية کوردی español فارسی français edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia ensuring structures safety through probabilistic analysis 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 probability of failure displaystyle text reliability 1 text probability 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 3 and maintenance 2 theory edit 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 1 2 p f 0 f r s f s s d s displaystyle p_ f int _ 0 infty f_ r s f_ s s ds 1 where p f displaystyle p_ f is the probability of failure f r s displaystyle f_ r s is the cumulative distribution function of resistance r and f s s displaystyle 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 p f g x f x x d x displaystyle p_ f iiint _ g x f_ x x dx 2 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 edit analytical solutions edit in some cases when load and resistance are explicitly expressed such as equation 1 above and their distributions are normal the integral of equation 1 has a closed form solution as follows p f 1 φ β displaystyle p_ f 1 phi beta β μ r μ s σ r 2 σ s 2 displaystyle beta frac mu _ r mu _ s sqrt sigma _ r 2 sigma _ s 2 3 simulation edit in most cases load and resistance are not normally distributed therefore solving the integrals of equations 1 and 2 analytically is impossible using monte carlo simulation is an approach that could be used in such cases 1 4 references edit 1 2 3 melchers r e 2002 structural reliability analysis and prediction 2nd ed john wiley chichester uk 1 2 3 piryonesi sayed madeh tavakolan mehdi 9 january 2017 a mathematical programming model for solving cost safety optimization cso problems in the maintenance of structures ksce journal of civil engineering 21 6 2226 2234 bibcode 2017ksjce 21 2226p doi 10 1007 s12205 017 0531 z s2cid 255532962 choi s k grandhi r canfield r a 2006 reliability based structural design springer science business media 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 retrieved from https en wikipedia org w index php title structural_reliability oldid 1314826682 categories reliability analysis reliability engineering structural engineering hidden categories articles with short description short description matches wikidata this page was last edited on 3 october 2025 at 11 44 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents structural reliability 5 languages add topic