Shear Stress Calculator
Calculate shear stress from force and area, or torsional shear on circular shafts using τ = F/A and τ = Tr/J.
What Is Shear Stress?
Shear stress is the tangential force per unit area acting parallel to a surface. It appears when layers of material slide past each other, such as in bolted joints, welded connections, and rotating shafts under torque.
Direct Shear Formula
$$\tau = \frac{F}{A}$$\(F\) is the shear force in newtons and \(A\) is the cross-sectional area in square meters. Example: 500 N across 0.0025 m² gives \(\tau = 200{,}000\) Pa (200 kPa).
Torsional Shear on a Shaft
$$\tau = \frac{T r}{J}, \quad J = \frac{\pi r^4}{2}$$For a solid circular shaft, \(T\) is applied torque, \(r\) is the outer radius, and \(J\) is the polar moment of inertia. Maximum shear stress occurs at the outer surface where \(r\) is largest.
Related tools: Shear Modulus Calculator and Punch Force Calculator.
Frequently Asked Questions
What units does shear stress use?
Shear stress is pressure: pascals (Pa), kilopascals (kPa), or megapascals (MPa). One pascal equals one newton per square meter.
When should I use the torque formula?
Use \(\tau = Tr/J\) for circular shafts in torsion. The direct formula \(\tau = F/A\) applies to flat sections loaded by shear force.
Where is maximum shear stress on a shaft?
On a solid circular shaft, maximum shear stress is at the outer fiber where radius equals the shaft radius. The centerline carries zero shear stress.
How does shear stress relate to material failure?
Compare computed shear stress to the material yield or ultimate shear strength. Exceeding allowable stress leads to permanent deformation or fracture.
Is polar moment J the same as area moment I?
No. Polar moment \(J\) resists torsion about the shaft axis. Area moment \(I\) resists bending. Both depend on cross-section geometry but serve different load types.
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