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How It Works — Formulas
Warping Constant Cw (I-Beam)
Where Iy is the minor axis moment of inertia and h is the distance between flange centroids (hw + tf). For doubly-symmetric I-sections, warping is resisted by flange bending out-of-plane.
Warping Constant Cw (Channel)
For singly-symmetric channels, Cw depends on the flange width b, the distance h between flange centroids, and the warping factor c. The shear center offset increases warping effects.
Torsion Constant J
For thin-walled open sections, J is approximated as the sum of each segment's (length × thickness³) divided by 3. For closed (box) sections, Bredt's formula applies: J = 4A²m / (∮ds/t).
Shear Center
The shear center is the point where applied shear forces cause no twisting. For channels: Xs = -b²h²tf / (4Ix). It always lies on the axis of symmetry, outside the web for channels.
Box Section (Closed)
Closed box sections have negligible warping (Cw ≈ 0). Their torsional resistance comes from circulating shear flow. Am is the area enclosed by the centerline of the wall.
T-Section
T-sections are singly-symmetric. Cw is calculated using the web height as the effective distance. The shear center is at the web-flange junction for symmetric T-sections.