How this calculator works
Rectangular components are combined using signed areas and the parallel-axis theorem. Circular sections use annulus formulas. Symmetric sections reduce to M y/Ixx. For an angle with non-zero product of inertia, the coupled elastic stress field is evaluated at all section corners. The applied moment is about the horizontal centroidal axis with zero vertical-axis moment. Fillets, holes and residual stress are omitted.
Formula
Ixx = sum(Ixx_local + A dy^2); Iyy = sum(Iyy_local + A dx^2); Ixy = sum(A dx dy). sigma = Mx[Iyy(y-yc)-Ixy(x-xc)]/(Ixx Iyy-Ixy^2). For Ixy=0, Sx=Ixx/c and sigma_max=|M|/Sx.
Worked example
A 100 mm wide by 200 mm deep rectangle has Ixx = 66666666.67 mm^4 and Sx = 666666.67 mm^3. A 1 kN m moment gives 1.5 MPa maximum elastic stress.
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Frequently asked questions
Which way does the section face?
Depth is vertical. Tee flanges are at the top; a channel web is at the left; angle legs extend right and upward from the bottom-left corner.
Why treat angle sections differently?
Their horizontal and vertical centroidal axes are generally not principal axes, so the product of inertia couples the bending response.
Is this a code capacity check?
No. Results are estimates and are not a substitute for a licensed engineer. Bearing, connections, stability, local code requirements and all applicable load combinations need separate checks.