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For thin walled beams subjected to axial forces, buckling can occur as the result of bending instability as shown in table bellow, or because of torsional instability. The torsional buckling loads Pcr for uniform shaft with axial forces passing through the shear center are

given by (Pilkey 1987):







I0c: moment of inertia about centroid (Ixc+ Iyc).


ex, ey:  distance in x,y direction between centroid and shear center..



Stability formulas are implemented in this version of ShapeDesigner and user can used theme in the efficient custom design solver component.