[{"data":1,"prerenderedAt":37},["ShallowReactive",2],{"topic-en-strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Fallowable-stresses-and-factor-of-safety":3},{"topic":4,"trail":18,"children":32,"tasks":33,"alternates":34},{"id":5,"name":6,"locale":7,"path":8,"seo_title":9,"seo_description":10,"seo_text":11,"content_html":12,"content_chunks":13},113,"Allowable Stresses and Factor of Safety","en","strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Fallowable-stresses-and-factor-of-safety","Allowable Stresses and Factor of Safety in Strength Calculations","Allowable stress, selection of a limiting material strength, and the role of the factor of safety in engineering strength calculations.","This topic explains the allowable-stress design approach. It covers selection of the limiting material characteristic, the physical meaning of the factor of safety, and verification of the strength condition. It also explains why the required margin depends on loads, material variability, model accuracy, manufacturing, service conditions, and reliability requirements.","\u003Cp>Real structures are not designed so that working stresses directly reach a limiting material characteristic. An \u003Cstrong>allowable stress\u003C\u002Fstrong> and a \u003Cstrong>factor of safety\u003C\u002Fstrong> provide a margin between normal operation and an unacceptable state.\u003C\u002Fp>\u003Cdiv class=\"formula-chunk\">\u003Cp>In allowable-stress design, a limiting material strength is reduced by a factor of safety:\u003C\u002Fp>\u003Cp>$$[\\sigma]=\\frac{\\sigma_{\\mathrm{lim}}}{n}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>[σ]\u003C\u002Fstrong> — allowable normal stress;\u003C\u002Fli>\u003Cli>\u003Cstrong>σ\u003Csub>lim\u003C\u002Fsub>\u003C\u002Fstrong> — selected limiting material strength;\u003C\u002Fli>\u003Cli>\u003Cstrong>n\u003C\u002Fstrong> — factor of safety, n > 1.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The choice of σ\u003Csub>lim\u003C\u002Fsub> depends on the material and design method: ductile materials are often referenced to yield strength, while brittle materials may be referenced to a fracture strength. The strength condition is $|\\sigma_{\\max}|\\le[\\sigma]$.\u003C\u002Fp>\u003C\u002Fdiv>\u003Ch2>Selecting the limiting characteristic\u003C\u002Fh2>\u003Cp>The limiting characteristic depends on the material, loading type, and adopted calculation method. For ductile materials under static loading, yield strength is often a relevant reference, whereas brittle materials may require fracture-related strength characteristics.\u003C\u002Fp>\u003Ch2>What the safety margin accounts for\u003C\u002Fh2>\u003Cp>The factor of safety accounts for uncertainty in loads, scatter of material properties, simplifications of the mechanical model, geometric deviations, manufacturing conditions, and service environment. Its numerical value is determined by the applicable code or design methodology rather than by one universal rule.\u003C\u002Fp>\u003Ch2>Example\u003C\u002Fh2>\u003Cp>If $\\sigma_{lim}=360$ MPa and $n=1.5$, then $[\\sigma]=360\u002F1.5=240$ MPa. The calculated working stress under the adopted model should not exceed this value.\u003C\u002Fp>",[14],{"id":15,"code":16,"type":17,"locale":7},71,"allowable-normal-stress","formula",[19,23,27,31],{"id":20,"name":21,"path":22},45,"Strength of Materials","strength-of-materials",{"id":24,"name":25,"path":26},46,"Tension and Compression","strength-of-materials\u002Ftension-and-compression",{"id":28,"name":29,"path":30},48,"Mechanical Properties of Materials","strength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials",{"id":5,"name":6,"path":8},[],[],{"en":35,"uk":36},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Ftopics\u002Fstrength-of-materials\u002Ftension-and-compression\u002Fmechanical-properties-of-materials\u002Fallowable-stresses-and-factor-of-safety","https:\u002F\u002Fmechclassroom.com\u002Ftopics\u002Fopir-materialiv\u002Froztyah-i-stysk\u002Fmekhanichni-vlastyvosti-materialiv\u002Fdopustymi-napruzhennia-ta-koefitsiient-zapasu",1787712539097]