Table of Contents
What Is Shear Stress?
Shear stress (τ) is the component of stress that acts parallel (tangential) to a cross-section of a material. Unlike normal stress, which acts perpendicular to the cross-section, shear stress tends to cause sliding of one layer over another. It is measured in Pascals (Pa) or pounds per square inch (psi).
Shear stress arises in many engineering situations: bolts and rivets in shear, beams under transverse loading, shafts under torsion, adhesive joints, and fluid flow over surfaces. Understanding shear stress is essential for designing connections, shafts, and structural elements to prevent failure.
Shear Stress Formulas
For direct shear, F is the applied tangential force and A is the area over which it acts. For torsional shear, T is the torque, r is the radial distance from the center (maximum at the outer surface), and J is the polar moment of inertia.
Shear Yield Strengths
| Material | Tensile Yield (MPa) | Shear Yield (MPa) | Ratio |
|---|---|---|---|
| Mild Steel (A36) | 250 | 145 | 0.58 |
| Aluminum 6061-T6 | 276 | 207 | 0.75 |
| Stainless 304 | 215 | 125 | 0.58 |
| Titanium Ti-6Al-4V | 880 | 550 | 0.63 |
| Copper C11000 | 69 | 40 | 0.58 |
Types of Shear Stress
- Direct (transverse) shear: caused by forces applied directly across a section, as in bolts, pins, and rivets.
- Torsional shear: caused by twisting moments in shafts and coupling elements.
- Beam shear: arises from transverse loads on beams, varying parabolically across the cross-section.
- Punching shear: occurs around concentrated loads on slabs, critical in foundation design.
Frequently Asked Questions
What is the relationship between shear stress and tensile yield stress?
According to the von Mises yield criterion (most common for ductile metals), the shear yield stress equals the tensile yield stress divided by the square root of 3, approximately 0.577 times the tensile yield. The Tresca criterion gives 0.5 times the tensile yield. Experimentally, the von Mises criterion better matches observed behavior.
How does shear stress distribute in a beam?
In a rectangular beam under transverse loading, the shear stress varies parabolically across the height. It is zero at the top and bottom surfaces and maximum at the neutral axis. The maximum value is 1.5 times the average shear stress (V/A). For I-beams, the web carries nearly all the shear stress.
What causes shear failure?
Shear failure occurs when the shear stress exceeds the material's shear strength. In ductile materials, this manifests as sliding along planes at approximately 45 degrees to the applied tensile load. In brittle materials, shear failure appears as cracking. Common examples include bolt shear, punch-through in thin materials, and torsional fracture of shafts.