[{"data":1,"prerenderedAt":28},["ShallowReactive",2],{"formula-en-euler-applicability-limit":3},{"formula":4,"related_topics":12,"alternates":25},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},110,"euler-applicability-limit","Applicability Limit of Euler's Buckling Formula","λlim = π√(E \u002F σp)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>Euler's critical stress can be written in terms of the slenderness ratio:\u003C\u002Fp>\u003Cp>$$\\sigma_{cr,E}=\\frac{N_{cr}}{A}=\\frac{\\pi^2E}{\\lambda^2}.$$\u003C\u002Fp>\u003Cp>Euler's formula is used in the elastic range when the critical stress does not exceed the proportional limit $\\sigma_p$. The limiting slenderness follows from $\\sigma_{cr,E}=\\sigma_p$:\u003C\u002Fp>\u003Cp>$$\\lambda_{lim}=\\pi\\sqrt{\\frac{E}{\\sigma_p}}.$$\u003C\u002Fp>\u003Cp>Thus, for $\\lambda\\ge\\lambda_{lim}$, the Euler model is consistent with elastic buckling. For lower slenderness, another relation or a code-based buckling curve is required.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17,21],{"id":14,"name":15,"path":16},72,"Stability of Compressed Members","strength-of-materials\u002Fstability-of-compressed-members",{"id":18,"name":19,"path":20},73,"Euler's Formula for Critical Load","strength-of-materials\u002Fstability-of-compressed-members\u002Feulers-formula-critical-load",{"id":22,"name":23,"path":24},74,"Limits of Applicability of Euler's Formula (Yasinsky Formula)","strength-of-materials\u002Fstability-of-compressed-members\u002Flimits-of-applicability-eulers-formula",{"en":26,"uk":27},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Feuler-applicability-limit","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Feuler-applicability-limit",1787712544103]