How this calculator works
Direct shear returns an average F/A. Beam modes use the elementary transverse-shear law VQ/(It), which estimates a cross-section stress distribution away from concentrated loads and supports. For I sections, the local width changes at the flange-web junction. Shaft modes use the circular torsion solution and evaluate a point in the solid or annular material. All inputs are magnitudes, so the results omit load-direction signs. Inverse mode recovers the applied shear force or torque from a measured stress at the chosen point; a zero-stress point cannot identify the load.
Formula
Average tau = F/A; beam tau = VQ/(I t); rectangle tau(y) = 3V[1-4y^2/h^2]/(2 b h); circular torsion tau(r) = T r/J.
Worked example
A 1 kN shear force on a 100 mm by 200 mm rectangle gives average shear 0.05 MPa and maximum shear 0.075 MPa. At one-quarter of the full depth from the neutral axis, shear is 0.05625 MPa.
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Frequently asked questions
Why is maximum rectangular shear 1.5 times average?
The elementary beam solution is parabolic through the depth, with zero shear at the top and bottom surfaces.
Can I use VQ/(It) in a short deep beam?
It is an elementary beam approximation. Deep beams and local load regions may require a more detailed model.
Does circular-shaft stress use the polar moment?
Yes. For solid and hollow circular shafts, the polar second moment is also the Saint-Venant torsion constant.