[{"data":1,"prerenderedAt":24},["ShallowReactive",2],{"formula-en-euler-column-critical-load":3},{"formula":4,"related_topics":12,"alternates":21},{"id":5,"code":6,"slug":6,"title":7,"formula":8,"locale":9,"seo_title":10,"seo_description":10,"content_html":11},107,"euler-column-critical-load","Euler Critical Load for a Compressed Column","Ncr = π²EI \u002F leff²","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>For a straight, slender elastic column, Euler's critical load is:\u003C\u002Fp>\u003Cp>$$N_{cr}=\\frac{\\pi^2 E I_{min}}{l_{eff}^2}=\\frac{\\pi^2 E I_{min}}{(\\mu L)^2}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$N_{cr}$\u003C\u002Fstrong> — critical compressive load;\u003C\u002Fli>\u003Cli>\u003Cstrong>$E$\u003C\u002Fstrong> — Young's modulus;\u003C\u002Fli>\u003Cli>\u003Cstrong>$I_{min}$\u003C\u002Fstrong> — minimum centroidal second moment of area;\u003C\u002Fli>\u003Cli>\u003Cstrong>$L$\u003C\u002Fstrong> — actual column length;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\mu$\u003C\u002Fstrong> — effective-length factor;\u003C\u002Fli>\u003Cli>\u003Cstrong>$l_{eff}=\\mu L$\u003C\u002Fstrong> — effective length.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The minimum $I$ identifies the weakest buckling plane. The formula applies to elastic buckling under conditions close to Euler's idealized column model.\u003C\u002Fp>\u003Cp>The calculator does not treat $\\mu$ as an independent unknown; use the already determined effective length $l_{eff}$.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"eyJ0aXRsZSI6IkV1bGVyIENyaXRpY2FsIExvYWQiLCJmb3JtdWxhIjoiTmNyID0gz4DCskVJIC8gbGVmZsKyIiwidmFyaWFibGVzIjpbeyJrZXkiOiJjcml0aWNhbExvYWQiLCJzeW1ib2wiOiJOX2NyIiwibGFiZWwiOiJDcml0aWNhbCBsb2FkIiwicXVhbnRpdHkiOiJmb3JjZSIsImRlZmF1bHRVbml0Ijoia04ifSx7ImtleSI6ImVsYXN0aWNNb2R1bHVzIiwic3ltYm9sIjoiRSIsImxhYmVsIjoiWW91bmcncyBtb2R1bHVzIiwicXVhbnRpdHkiOiJlbGFzdGljTW9kdWx1cyIsImRlZmF1bHRVbml0IjoiR1BhIn0seyJrZXkiOiJzZWNvbmRNb21lbnQiLCJzeW1ib2wiOiJJX21pbiIsImxhYmVsIjoiTWluaW11bSBzZWNvbmQgbW9tZW50IG9mIGFyZWEiLCJxdWFudGl0eSI6InNlY29uZE1vbWVudE9mQXJlYSIsImRlZmF1bHRVbml0IjoiY200In0seyJrZXkiOiJlZmZlY3RpdmVMZW5ndGgiLCJzeW1ib2wiOiJsX2VmZiIsImxhYmVsIjoiRWZmZWN0aXZlIGxlbmd0aCIsInF1YW50aXR5IjoibGVuZ3RoIiwiZGVmYXVsdFVuaXQiOiJtIn1dLCJzb2x2ZSI6eyJjcml0aWNhbExvYWQiOiJNYXRoLlBJICogTWF0aC5QSSAqIGVsYXN0aWNNb2R1bHVzICogc2Vjb25kTW9tZW50IC8gKGVmZmVjdGl2ZUxlbmd0aCAqIGVmZmVjdGl2ZUxlbmd0aCkiLCJlbGFzdGljTW9kdWx1cyI6ImNyaXRpY2FsTG9hZCAqIGVmZmVjdGl2ZUxlbmd0aCAqIGVmZmVjdGl2ZUxlbmd0aCAvIChNYXRoLlBJICogTWF0aC5QSSAqIHNlY29uZE1vbWVudCkiLCJzZWNvbmRNb21lbnQiOiJjcml0aWNhbExvYWQgKiBlZmZlY3RpdmVMZW5ndGggKiBlZmZlY3RpdmVMZW5ndGggLyAoTWF0aC5QSSAqIE1hdGguUEkgKiBlbGFzdGljTW9kdWx1cykiLCJlZmZlY3RpdmVMZW5ndGgiOiJNYXRoLlBJICogTWF0aC5zcXJ0KGVsYXN0aWNNb2R1bHVzICogc2Vjb25kTW9tZW50IC8gY3JpdGljYWxMb2FkKSJ9fQ==\">\u003C\u002Fdiv>\u003C\u002Fdiv>",[13,17],{"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",{"en":22,"uk":23},"https:\u002F\u002Fmechclassroom.com\u002Fen\u002Fformulas\u002Feuler-column-critical-load","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Feuler-column-critical-load",1787712543946]