If a material has a shear modulus of 80 GPa and a shear stress of 40 MPa is appl

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Question: If a material has a shear modulus of 80 GPa and a shear stress of 40 MPa is applied, what is the shear strain? (2023)

Options:

Correct Answer: 0.0005

Exam Year: 2023

Solution:

Shear strain (γ) = Shear stress (τ) / Shear modulus (G) = 40 MPa / 80 GPa = 0.0005.

If a material has a shear modulus of 80 GPa and a shear stress of 40 MPa is applied, what is the shear strain? (2023)

If a material has a shear modulus of 80 GPa and a shear stress of 40 MPa is applied, what is the shear strain? (2023)

Step 1: Understand the terms. Shear modulus (G) is a measure of how much a material deforms under shear stress. Shear stress (τ) is the force applied per unit area.
Step 2: Convert the units if necessary. Here, shear stress is given in MPa (megapascals) and shear modulus in GPa (gigapascals). 1 GPa = 1000 MPa.
Step 3: Write down the formula for shear strain (γ): γ = τ / G.
Step 4: Substitute the values into the formula. τ = 40 MPa and G = 80 GPa = 80,000 MPa.
Step 5: Calculate the shear strain: γ = 40 MPa / 80,000 MPa.
Step 6: Perform the division: γ = 0.0005.

Shear Modulus – The ratio of shear stress to shear strain, indicating how a material deforms under shear forces.
Shear Stress – The force per unit area applied parallel to the surface of a material.
Shear Strain – The measure of deformation representing the displacement between particles in a material.