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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  1. Factor of safety = 2.0
  2. Factor of safety = 4.0
  3. Factor of safety = 2.5
  4. Factor of safety = 3.0

Answer (Detailed Solution Below)

Option 1 : Factor of safety = 2.0
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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, Syt = Yield strength, σ1,2 = Maximum and minimum principal stresses

; Where Sys = Yield shear strength

Principal stresses are given by:  

Calculation:

Given:

σx = 120 MPa, τxy = 60 MPa, Syt = 340 MPa

⇒ 

And 

For the factor of safety,

⇒ N = 2

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