Shear Strain: Definition & Equation
In this lesson, we’ll learn about shear strain, how it occurs, where it applies, and its relationship to shear stress and the shear modulus. We’ll learn the equation and solve some problems.
Shear Strain Defined
You might already be familiar with Hooke’s law, which states that the force needed to compress or extend a spring is directly proportional to the distance you stretch it. Hooke’s law doesn’t only apply to normal forces. It has many applications, one of which is the shear stress/strain relationship. Shear strain is the ratio of the change in deformation to its original length perpendicular to the axes of the member due to shear stress. Shear stress is stress in parallel to the cross section of the structural member.
From the definition of the shear strain, it is noted that shear strain is dependent on shear stress and the shear modulus (a constant property of the material from which the structural member is cast). Shear stress can occur in different loading conditions, such as lateral loading, axial loading, and bending, and hence, exert strain on the member.
Shear strain is given by the following formula:
shear strain
where
γ = shear strain (which is unit-less)
τ = shear stress (unit of force over unit of area: N/m2, or Pascals in the International System of Units, or pounds per square inch (psi) in the British Imperial System)
G = shear modulus, or modulus of rigidity (defined as the ratio of shear stress over shear strain)
The shear modulus of steel (G) is approximately 80 GPa (11,500,000 psi), the shear modulus of concrete is around 21 GPa (3,000,000 psi), and the shear modulus of aluminum is about 28 GPa (4,000,000 psi).
The difference between shear strain and normal strain is shown in this illustration:
Shear Strain vs Normal Strain
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