Learning topic
Shear and Direct Shear
Pure shear, Hooke’s law in shear, average direct shear stress, single and double shear, and basic connection checks.
Shear and direct shear cover material distortion caused by relative sliding of adjacent layers and the practical design of connectors that may be sheared by a transverse force. The principal quantities are shear stress \(\tau\), shear strain \(\gamma\), and shear modulus \(G\).
Pure shear
In pure shear, complementary shear stresses act on mutually perpendicular planes. Initially right angles change while the first-order linear dimensions of the element remain unchanged.
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, $G=E/[2(1+\nu)]$.
Direct shear
For a bolt, rivet, pin, or another short connector, the introductory design model assumes a uniform average shear stress over the shear plane:
\[\tau_{avg}=\frac{V}{A_s}.\]
For \(n\) identical active shear planes, the total resisting area is \(nA_s\). Single and double shear must therefore be distinguished.
Connection checks
- shear resistance of the bolt, rivet, or pin;
- bearing of the connected parts;
- resistance of the weakened net section;
- edge shear-out or tear-out;
- weld resistance where applicable.
Limits of the model
The average-stress formula is a direct-shear model and does not describe the detailed nonuniform stress field. Transverse shear in beams belongs to the bending section.
Further study
The next topic treats pure shear, single and double shear, and the design of bolted, riveted, pinned, and welded joints. Torsion is organized as a separate section at the same hierarchy level.
About this topic
Shear and direct shear introduce shear stress, shear strain, and Hooke’s law in shear. The section covers pure shear, single and double direct shear, and basic checks for bolts, rivets, pins, and welds.