Shear strength

A shear force is applied to the top of the rectangle that deform the rectangle into a parallelogram. Having a higher shear modulus of elasticity increases the force needed to deform the rectangle.

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. See tensile strength.

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:

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

For average shear stress

${\displaystyle \tau \scriptstyle (avg)={\frac {V}{A}}}$

where

${\displaystyle \tau \scriptstyle (avg)}$ 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.[1]

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.[2]

As a very rough guide relating tensile, yield, and shear strengths:[3]

USS: Ultimate Shear Strength, UTS: Ultimate Tensile Strength, SYS: Shear Yield Stress, TYS: Tensile Yield Stress

There are no published standard values for shear strength like with tensile and yield strength. Instead, it is common for it to be estimated as 60% of the ultimate tensile strength. Shear strength can be measured by a torsion test where it is equal to their torsional strength.[4][5]

When values measured from physical samples are desired, a number of testing standards are available, covering different material categories and testing conditions. In the US, ASTM standards for measuring shear strength include ASTM B831, D732, D4255, D5379, and D7078. Internationally, ISO testing standards for shear strength include ISO 3597, 12579, and 14130.[7]

• Shear modulus
• Shear stress
• Shear strain
• Shear strength (soil)
• Shear strength (Discontinuity)
• Strength of materials
• Tensile strength