The stresses at a point on the circumference of a circular rod in tension and shear are 120 MPa and 60 MPa respectively. If the yield strength of the rod material is 340 MPa, the factor of safety in the rod material using maximum shear stress theory is nearly equal to

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This question was previously asked in

MPPSC AE Mechanical 2021 Official Paper

Answer 1

Concept:

The Maximum Shear Stress Theory was given by Guest and Tresca,

i.e. Maximum shear stress τmax = larger of

Where N = Factor of safety, S_yt = Yield strength, σ_1,2 = Maximum and minimum principal stresses

; Where S_ys = Yield shear strength

Principal stresses are given by:

Calculation:

Given:

σ_x = 120 MPa, τ_xy = 60 MPa, S_yt = 340 MPa

⇒

And

For the factor of safety,

⇒ N = 2

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