Learning topic
Pure Shear and Design of Joints
Calculate shear and bearing stress in bolts, rivets, pins, and welded joints using τ = F/As, shear planes, projected bearing area, and strength checks.
Shear occurs when external forces tend to slide one part of a member relative to another along a separation plane. In simplified engineering calculations for bolts, rivets, pins, and some welded joints, shear stress is often assumed to be uniformly distributed over the calculated shear area.
Average shear stress
For direct shear, the average shear stress is:
$$\tau_{\mathrm{avg}}=\frac{F}{A_s},$$
where $F$ is the force transmitted through the shear plane and $A_s$ is the total calculated shear area. When identical fasteners and shear planes work symmetrically, the total area includes their number.
Pure shear deformation
Pure Shear Deformation
In pure shear, the right angle between material lines changes by γ while opposite faces shift by Δ.
Within the linear-elastic range, shear stress is proportional to shear strain:
$$\tau=G\gamma.$$
- $\tau$ — shear stress, Pa or MPa;
- $G$ — shear modulus, Pa or MPa;
- $\gamma$ — engineering shear strain, rad (dimensionless).
For a linearly elastic isotropic material, $G=E/[2(1+\nu)]$.
In a pure shear state, complementary shear stresses act on mutually perpendicular planes. These paired stresses satisfy moment equilibrium of a small material element.
Shear of fasteners
For a bolt or rivet, the number of shear planes must be identified correctly. A single-shear joint has one resisting cross-sectional area of the shank; a double-shear joint has two. In the average-stress model, the strength condition is $\tau_{\mathrm{avg}}\le[\tau]$.
Bearing stress
Contact between a bolt or rivet and the wall of a hole produces local contact stresses. In a simple design model they are represented by an average bearing stress. For a plate of thickness $t$ and a fastener of diameter $d$, the projected contact area is often taken as $A_b=dt$, giving $\sigma_b=F/A_b$.
Welded joints
In a simplified fillet-weld calculation, the load is related to the effective throat area of the weld. The actual stress distribution may be nonuniform, especially under eccentric loading, so code-based methods and appropriate coefficients are required for responsible design.
Verification procedure
- Identify the load path through the joint.
- Determine the number of active fasteners and shear planes.
- Check fasteners in shear.
- Check bearing of the contacting surfaces.
- If required, check the net section weakened by holes or the effective weld section.
About this topic
Pure shear is a stress state where only shear stresses act on two mutually perpendicular planes. This mathematical model underpins practical design for mechanical fasteners and joints. This page presents strength analysis for riveted, bolted, keyed, and welded connections under shear and bearing loads, with engineering formulas for calculating required rivet counts or weld lengths.