Shear Stress Calculator — Direct, Fluid & Beam
Compute shear stress for three common scenarios: direct shear (force divided by area), fluid viscous shear using Newton's law of viscosity, or maximum shear stress in a rectangular beam cross-section.
Shear type
N
m²
τ = F / A
- 1
Shear force F and area A
F = 1,000 N, A = 0.005 m² - 2
Shear stress τ = F ÷ A
1,000 ÷ 0.005 = 200,000
How does this calculator work?
Shear stress τ = F/A for direct loading; τ = μ × (Δv/Δy) for viscous fluids (Newton's law); τ_max = 1.5 × V/(b × h) for the neutral-axis peak in a rectangular beam. Select the mode, enter the relevant dimensions and forces, and read the shear stress in pascals (Pa).
Formula
How this is calculated
Shear stress (τ, Pa) is a tangential force per unit area — it acts parallel to a surface rather than perpendicular to it like normal stress. Three common situations call for different formulas.
Direct shear applies when a force F acts parallel to a cross-sectional area A: τ = F/A. This describes bolts, pins, rivets, and adhesive lap joints resisting a transverse load. The area A is the cross-section that would fail in shear.
Fluid viscous shear follows Newton's law of viscosity: τ = μ × (dv/dy), where μ is the dynamic (absolute) viscosity of the fluid, and dv/dy is the velocity gradient perpendicular to the flow direction. A steeper velocity profile (faster change in velocity over a shorter distance) produces higher shear stress; a more viscous fluid (larger μ) also amplifies the stress. This underpins lubrication, pipe-flow analysis (Hagen–Poiseuille), and rheology.
For a beam with a rectangular cross-section (width b, height h) carrying a transverse shear force V, the shear stress is not uniform: it is zero at the top and bottom surfaces and reaches a maximum at the neutral axis. The maximum value is τ_max = 1.5 × V/(b × h) = 1.5 × (V/A). This formula follows from the general beam shear formula τ = VQ/(Ib) after evaluating the first moment of area Q and second moment I for a rectangle at the mid-height. The factor 1.5 is specific to rectangular sections; other shapes (I-beams, circular sections) have different distributions.
Frequently asked questions
Normal stress (σ) acts perpendicular to a surface — it either stretches (tension) or compresses a material. Shear stress (τ) acts parallel (tangential) to a surface, tending to cause sliding between layers. In structural analysis, both types often act simultaneously; the Von Mises criterion combines them to predict yielding in ductile materials.
In a beam, the shear stress distribution follows a parabolic profile from zero at the top and bottom fibres to a peak at the neutral axis. For a rectangle, integrating the parabolic distribution gives a peak that is exactly 1.5 times the average value V/A. For I-beams the factor is higher (approaching 1.0 for the web alone if flanges carry most of the moment); for solid circular sections the factor is 4/3.
Use SI units throughout for consistent results: viscosity in Pa·s (also called N·s/m²), velocity in m/s, and layer separation in metres. Water at 20 °C has μ ≈ 0.001 Pa·s; engine oil is typically 0.1–0.3 Pa·s; honey is around 10 Pa·s. The result is in pascals (Pa).
Also known as
TG we-Calculate Editorial Team. (2026). Shear Stress Calculator — Direct, Fluid & Beam [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/shear-stress-calculator
TG we-Calculate Editorial Team. "Shear Stress Calculator — Direct, Fluid & Beam." TG we-Calculate. 2026. https://we-calculate.com/calculator/shear-stress-calculator.
TG we-Calculate Editorial Team, "Shear Stress Calculator — Direct, Fluid & Beam," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/shear-stress-calculator
@misc{wecalculate_shear_stress_calculator, title = {Shear Stress Calculator — Direct, Fluid & Beam}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/shear-stress-calculator}}, year = {2026}, note = {TG we-Calculate} }
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