How this calculator works
The calculator divides sharp-cornered sections into non-overlapping rectangles, finds the area centroid, then applies the parallel-axis theorem. Elastic modulus uses the farther extreme fibre on each axis, so it is the smaller governing modulus for an asymmetric section. Plastic modulus integrates distance from an equal-area plastic neutral axis, assuming the same yield stress in tension and compression. I, T and channel flanges use thickness t; their web uses tw. The angle has its horizontal leg at the top. Fillets and corner radii are excluded.
Formula
I = sum(I_component + A_component d^2); S = I/c_max; Z = integral |distance from plastic neutral axis| dA.
Worked example
A solid rectangle 100 mm wide and 200 mm deep has Ix = 6.66667 x 10^-5 m4, Sx = 0.000666667 m3 and Zx = 0.001 m3. Its centroid is 50 mm from the left and 100 mm from the bottom.
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Frequently asked questions
Are S and Z interchangeable?
No. S is the elastic section modulus. Z describes a fully plastic idealization and is usually larger.
Are x and y principal axes?
They are centroidal axes parallel to the overall sides. For an angle they need not be principal axes.
Does plastic modulus establish beam capacity?
No. Local and lateral buckling, material behaviour, restraint and design rules can limit the usable moment.