10a. Buckling (SSES Ch. 10.110.3) • What is Buckling • Euler Buckling Formula • Radius of Gyration • Slenderness Ratio • Effective Length 
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Radius of Gyration If all of the crosssectional area A were massed a distance r away from the bending axis, the idealized lumpedarea crosssection would have the same moment of inertia I as the actual crosssection if: I = Ar^{2} Distance r is the radius of gyration. There generally two bending axes to consider, and thus two radii of gyration: 
Slenderness ratio is a measure of how long the column is compared to its crosssection's effective width (resistance to bending or buckling). The slenderness ratio is the column's length divided by the radius of gyration. Including the slenderness ratio and the radius of gyration reduces the Buckling Strength to: 
Effective Length
How a column is supported governs its buckling strength. The effective length L_{e} accounts for differences in the end supports. The effective length is the length the column would be if it were to buckle as a pinnedpinned column. The buckling formula for any column is therefore: Common endconditions are given here:

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