Bolt Tensile and Shear Stress Calculator

How are tensile and shear stress in a bolt calculated?

Force along the bolt axis causes tensile stress, force across it causes shear stress. In tension the weakest place is the threaded section, so the force is divided by the tensile stress area: σ = F_t / (n × A_s). For metric threads A_s = π / 4 × (d − 0.9382 × P)². For an M12 coarse thread that is 84.3 mm², whereas a plain 12 mm bar would have 113 mm².

In shear the force is shared between the shear planes: τ = F_v / (n × m × A_v), where m is the number of shear planes per bolt. Use the tensile stress area if the shear plane passes through the threads and the nominal diameter area if it passes through the plain shank.

When both act together

With tension and shear acting together, the von Mises equivalent stress is σ_eq = √(σ² + 3 × τ²). It is compared with the yield strength to give the safety factor S = R_e / σ_eq.

Example

Four M12 bolts of class 8.8 carry 40 kN in tension and 20 kN in shear in total, with the shear plane through the threads. Each bolt takes 10 kN tension and 5 kN shear. Then σ = 10 000 / 84.27 = 118.7 MPa, τ = 5000 / 84.27 = 59.3 MPa and σ_eq = 157 MPa. With a yield strength of 640 MPa the safety factor is 4.08.

Limits

This calculation gives only the mean stress from external load. A tightened bolt also carries preload, so the real tension is higher. Load may not be shared equally, and under fluctuating load fatigue governs. Structural, lifting and pressure vessel connections use the resistance equations of their own standards.