Shear Stress
Shear stress is the component of stress that acts parallel (tangential) to a cross-sectional surface, as opposed to normal stress which acts perpendicular to it. It arises when equal and opposite forces act along parallel planes in a material, causing layers to slide relative to one another. Shear stress is critical in the design of bolts, welds, shafts, beams, and adhesive joints, where failure along a plane is the governing mode.
Key Formula
tau = V / A
LaTeX: \tau = \frac{V}{A}
| Symbol | Meaning | Unit |
|---|---|---|
| τ | Shear stress | Pa (N/m²) |
| V | Shear force acting on the surface | N |
| A | Cross-sectional area resisting shear | m² |
Worked Example
Problem
A lap joint uses a single 16 mm diameter bolt to connect two steel plates. The joint carries a shear force of 25 kN. Calculate the average shear stress in the bolt.
Solution
Step 1: Calculate bolt cross-sectional area. A = π × (d/2)² = π × (0.016/2)² = π × (0.008)² = 2.011 × 10⁻⁴ m² Step 2: Apply shear stress formula. τ = V / A = 25 000 N / 2.011 × 10⁻⁴ m² = 1.243 × 10⁸ Pa
Answer
Average shear stress τ ≈ 124.3 MPa
Shear Stress vs Normal Stress — Key Comparisons
| Property | Normal Stress (σ) | Shear Stress (τ) | Example Loading |
|---|---|---|---|
| Direction | Perpendicular to surface | Parallel to surface | — |
| Symbol | σ | τ | — |
| Failure mode | Tensile/compressive fracture | Sliding/shear fracture | — |
| Relevant modulus | Young's modulus E | Shear modulus G | — |
| Steel shear strength | — | ~145–200 MPa | Bolted connections |
Interactive Tools
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Related Terms
Engineering Stress
Engineering stress is defined as the applied force divided by the original cross-sectional area of a specimen, regardless of any deformation that occurs during loading. It is the conventional measure used in materials testing and structural analysis because the original dimensions are easily measured before the test begins. Engineering stress is widely used in design calculations, material data sheets, and stress-strain curves to characterise material behaviour under uniaxial loading.
Torsion (engineering)
Torsion is the twisting of a structural member caused by an applied torque (twisting moment) about its longitudinal axis. In circular shafts, torsion produces a shear stress distribution that varies linearly from zero at the neutral axis to a maximum at the outer surface. Torsion analysis is fundamental for the design of drive shafts, axles, springs, and any component that transmits rotary power.
Young's Modulus
Young's modulus (also called the modulus of elasticity) is the ratio of engineering stress to engineering strain in the linear-elastic region of a material's stress-strain curve. It is a fundamental mechanical property that quantifies the stiffness of a solid material — a higher value means the material resists deformation more effectively. Young's modulus is essential in structural design for calculating deflections, natural frequencies, and load-bearing capacity of components.
The word "shear" is from Old English "scieran" (to cut), reflecting how shear forces cause material planes to slide past each other as if being cut. The Greek letter tau (τ) was adopted by convention to denote shear stress, while sigma (σ) was reserved for normal stress.