Question

Given a shear stress of tau_xy = 35 MPa and a shear modulus of G = 75 GPa, the shear strain is most nearly

A. 2.5 Times 10⁻⁵ rad
B. 4.7 Times 10⁻⁴ rad
C. 5.5 Times 10⁻⁴ rad
D. 8.3 Times 10⁻⁴ rad

Answer 1

The shear strain given a shear stress of 35 MPa and a shear modulus of 75 GPa is calculated using the formula γ = τ_xy / G, which yields an answer of approximately 4.7 x 10⁴ radians.

Step-by-step explanation:

The student is asking a question related to the field of solid mechanics, specifically the calculation of shear strain given the shear stress and the shear modulus. The subject of the question is Engineering, and it is typically at a College level. To calculate the shear strain, we use the relationship between shear stress (τ_xy), shear strain (γ), and the shear modulus (G), which is defined as τ_xy = Gγ. Rearranging the equation to solve for shear strain gives us γ = τ_xy / G. Substituting the given values τ_xy = 35 MPa and G = 75 GPa into the equation results in γ = 35 MPa / 75 GPa = (35 x 10^6 Pa) / (75 x 10^9 Pa) = 0.467 x 10^-3 radians. Therefore, the shear strain is most nearly B. 4.7 Times 10⁴ rad.