3b. Shear Stress and Strain (SSES Ch. 3.2) • Shear Strain • Shear Deformation • General Shear Strain • Shear Stress • Complementary Shear Stress • Shear Modulus • Elastic Shear Strain Energy Density 
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Shear Deformation

General Shear Strain 

Shear strain g is measured in radians, which is a nonunit (shear strain is dimensionless). 
Shear Stress Shear stress has units of force per unit area (ksi, MPa, etc.). 
The crosssectional area of a 


Complementary Shear Stress
Now consider an element with shear stresses acting on the left and right faces (these faces are on the crosssections of the last cylinder). To prevent rotation of element, there must be an equal and opposite resisting couple caused by shear stresses at the top and bottom faces of the stress element. These shear stresses are the complementary shear stresses.

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Shear Modulus
For isotropic, homogeneous materials only, i.e., steel, aluminum, etc. This is NOT true for composites and other nonisotropic or nonhomogeneous materials such as fiberglass, steelreinforced concrete, etc. For most metals, n ~ 1/3, which means the G can be approximated:

Elastic Shear Strain Energy Density
The maximum value of the elastic strain energy is the shear resilience. It occurs when the stress in the stress reaches the shear yield strength:

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