Shear Stress Calculator: Direct and Torsional
Calculate direct shear stress (F/A) or torsional shear stress in circular shafts (Tr/J).
Returns results in Pa, kPa, MPa, and psi for engineering.
Shear stress acts parallel to a cross-section, as opposed to normal (tensile/compressive) stress which acts perpendicular. Two cases come up constantly in mechanical design.
Direct shear: tau = F / A
A bolt in single shear, a fillet weld under transverse load, a pin through a clevis: in each case the applied force acts parallel to the shear plane of area A. For an 8 mm diameter bolt (A = pi x 0.004^2 = 5.03 x 10^-5 m^2) carrying 20 kN, the shear stress is 398 MPa. Whether the bolt survives depends on its shear strength, which for structural steel runs about 57 to 65% of tensile strength.
Torsional shear in a solid circular shaft: tau = T * r / J
T is the applied torque in N m, r is the radial distance from the shaft center, and J is the polar moment of inertia. For a solid shaft of diameter d: J = pi * d^4 / 32. Maximum stress occurs at the outer surface where r = d/2. Substituting: tau_max = 16T / (pi * d^3).
Hollow shafts are more efficient, because material near the center contributes almost nothing to torque resistance (stress is proportional to r) while still carrying weight. Removing the inner third of a shaft costs only a few percent of its torsional strength and saves around a tenth of its mass, which is why driveshafts and bicycle axles are hollow.
Shear strength of common materials: structural steel A36 about 200 MPa, stainless steel 316 about 400 MPa, 6061-T6 aluminum about 207 MPa, yellow brass about 200 MPa.
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