[{"data":1,"prerenderedAt":24},["ShallowReactive",2],{"formula-en-column-radius-slenderness":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},109,"column-radius-slenderness","Radius of Gyration and Column Slenderness","i = √(I \u002F A)","en",null,"\u003Cdiv class=\"formula-chunk\">\u003Cp>The radius of gyration of a cross-sectional area about a selected centroidal axis is:\u003C\u002Fp>\u003Cp>$$i=\\sqrt{\\frac{I}{A}}.$$\u003C\u002Fp>\u003Cp>The column slenderness ratio is:\u003C\u002Fp>\u003Cp>$$\\lambda=\\frac{l_{eff}}{i}=\\frac{\\mu L}{i}.$$\u003C\u002Fp>\u003Cp>For buckling assessment, use the minimum radius of gyration:\u003C\u002Fp>\u003Cp>$$i_{min}=\\sqrt{\\frac{I_{min}}{A}},\\qquad \\lambda_{max}=\\frac{\\mu L}{i_{min}}.$$\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>$i$\u003C\u002Fstrong> — radius of gyration;\u003C\u002Fli>\u003Cli>\u003Cstrong>$I$\u003C\u002Fstrong> — centroidal second moment of area;\u003C\u002Fli>\u003Cli>\u003Cstrong>$A$\u003C\u002Fstrong> — cross-sectional area;\u003C\u002Fli>\u003Cli>\u003Cstrong>$\\lambda$\u003C\u002Fstrong> — slenderness ratio;\u003C\u002Fli>\u003Cli>\u003Cstrong>$l_{eff}=\\mu L$\u003C\u002Fstrong> — effective length;\u003C\u002Fli>\u003Cli>\u003Cstrong>$i_{min}$, $I_{min}$\u003C\u002Fstrong> — minimum radius of gyration and minimum centroidal second moment of area.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>The larger $\\lambda$ is, the more slender the member and the more likely its load capacity is to be governed by buckling rather than material strength alone.\u003C\u002Fp>\u003Cp>The calculator below evaluates radius of gyration, second moment of area, or cross-sectional area. Slenderness $\\lambda$ is not included because the calculator registry has no separate dimensionless quantity for this parameter.\u003C\u002Fp>\u003Cdiv data-formula-calculator-config=\"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\">\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\u002Fcolumn-radius-slenderness","https:\u002F\u002Fmechclassroom.com\u002Fformulas\u002Fcolumn-radius-slenderness",1787712544052]