Shear Stress Calculator: Direct Shear (F/A), Beam Shear (VQ/It) and Shaft Torsion (Tr/J)
Shear stress for pins and bolts in single or double shear, beams (rectangle, tube, I-beam or VQ/It) and shafts in torsion, with shear strain and safety factor.
How it works
Direct shear: τ = F ÷ (n × A), n = 1 (single) or 2 (double shear), A = πd²/4 for a pin · Beam (transverse) shear: τ = VQ ÷ (I·t); rectangle τmax = 3V/(2A); solid circle τmax = 4V/(3A); round tube τmax = 4V/(3A) × (R² + Rr + r²)/(R² + r²) · Torsion: τmax = T·r ÷ J, J = π(D⁴ − d⁴)/32 · Shear strain γ = τ ÷ G · Angle of twist θ = TL ÷ (JG)
Shear stress is force per unit area acting along a surface, the stress that slides one layer of material past the next. This calculator covers the three cases engineers meet most. Direct shear is the average stress in a pin, bolt, rivet, key or glued lap: the force divided by the area of each shear plane, halved when the part is in double shear. Transverse shear in a beam is not uniform: Jourawski’s formula τ = VQ/(It) gives it at any height, where Q is the first moment of the area beyond that point, I the moment of inertia and t the width at the point. It peaks at the neutral axis, at 1.5 × the average V/A for a rectangle and 4/3 × for a solid circle. In an I-beam the web carries almost all of it. Torsion of a round shaft gives shear stress that grows linearly from the centre to a maximum T·r/J at the surface. Enter any unit; work is done in newtons and millimetres, so 1 N/mm² = 1 MPa, and every result is also given in psi. Under More options you can pick a material to get the shear strain γ = τ/G and, for shafts, the angle of twist, and enter an allowable shear stress for a safety factor. Results assume linear-elastic, homogeneous material and ignore stress concentrations at holes, keyways and fillets. For the full capacity of bolts (tension plus shear tables) see the bolt shear and tension calculator, and for bending stress use the beam section modulus calculator; combine shear with normal stresses in the von Mises stress calculator.
Worked example
A 12 mm pin carries 20 kN in single shear. The shear area is π × 12² ÷ 4 = 113.10 mm², so the average shear stress is 20,000 N ÷ 113.10 mm² = 176.8 MPa (25,648 psi). If the pin were in double shear, each plane would carry 10 kN and the stress would halve to 88.42 MPa. With an allowable shear stress of 320 MPa (half the 640 MPa yield of a class 8.8 pin), the factor of safety is 320 ÷ 176.8 = 1.81.
Sources: Jönköping University, Solid Mechanics: 8.4 Shear stress (pin in double shear; 20 kN, 12 mm pin example) · EngineerExcel: Average shear stress formula (5,000 N pin in double shear example) · Omni Calculator: Shear stress (VQ/It, rectangle, hollow circle, I-beam and torsion formulas)
Frequently asked questions
What is the formula for shear stress?
The average shear stress is τ = F/A, the force parallel to a surface divided by the area resisting it. In a beam the stress varies with height and τ = VQ/(It); in a round shaft under torque τ = T·r/J. The SI unit is the pascal; engineers usually work in MPa (N/mm²) or psi.
What is the difference between single and double shear?
In single shear the load crosses one plane, as in a lap joint with one bolt. In double shear a pin passes through a clevis or between two outer plates, so two cross-sections share the load and the stress is F/(2A), half the single-shear value.
Where is shear stress highest in a beam?
At the neutral axis, where bending stress is zero. For a rectangular section the maximum is 1.5 times the average V/A; for a solid circle it is 4/3 times; for an I-beam it is roughly V divided by the web area, because the web carries almost all of the shear.
How do I find the shear stress in a shaft from torque?
Divide torque by the polar section modulus: τ = T·r/J, which for a solid shaft is 16T/(πD³). A 50 mm shaft carrying 1 kN·m sees 16 × 1,000,000 ÷ (π × 50³) = 40.74 MPa at its surface.
How is shear stress related to shear strain?
In the elastic range, shear strain γ = τ/G, where G is the shear modulus: about 79 GPa for steel and 26 GPa for aluminium. γ is the change in angle of an originally square element, in radians.
What allowable shear stress should I use?
Many design methods take the shear yield strength as about 0.5 to 0.577 times the tensile yield strength (Tresca and von Mises), then apply a safety factor. Codes such as AISC, Eurocode 3 or the bolt grade standard give the exact values for each part.
Related calculators
For learning and preliminary sizing only. Structural and safety-critical parts must be designed and checked by a qualified engineer to the applicable code.