Shear strength

In structural and mechanical engineering, the shear strength of a component is important for designing the dimensions and materials to be used for the manufacture or construction of the component (e.g. beams, plates, or bolts). In a reinforced concrete beam, the main purpose of reinforcing bar (rebar) stirrups is to increase the shear strength.

Equations

For shear stress ${\displaystyle \tau }$ applies

${\displaystyle \tau =\frac{{\sigma }_1-{\sigma }_3}{2},}$

where

${\displaystyle {\sigma }_1}$ is major principal stress and

${\displaystyle {\sigma }_3}$ is minor principal stress.

In general: ductile materials (e.g. aluminum) fail in shear, whereas brittle materials (e.g. cast iron) fail in tension .

To calculate:

Given total force at failure (F) and the force-resisting area (e.g. the cross-section of a bolt loaded in shear), ultimate shear strength (${\displaystyle \tau }$) is:

${\displaystyle \tau =\frac{F}{A}=\frac{F}{\pi r_{\text{bolt}}^2}=\frac{4F}{\pi d_{\text{bolt}}^2}}$

For average shear stress

${\displaystyle {\tau }_{\text{avg}}=\frac{V}{A}}$

where

${\displaystyle {\tau }_{\text{avg}}}$ is the average shear stress,

${\displaystyle V}$ is the shear force applied to each section of the part, and

${\displaystyle A}$ is the area of the section.

Average shear stress can also be defined as the total force of ${\displaystyle V}$ as

${\displaystyle V=\int \tau dA}$

This is only the average stress, actual stress distribution is not uniform. In real world applications, this equation only gives an approximation and the maximum shear stress would be higher. Stress is not often equally distributed across a part so the shear strength would need to be higher to account for the estimate.