Test: Theories of Failure - Civil Engineering (CE) MCQ

Proportionality limit shear stress
= 300/2 = 150N/mm²
Maximum shear stress

∴ Factor of safety = 150/75 = 2.0

When one of the principal stresses at a point is large in comparison to the other, the situation resembles uniaxial tension test. Therefore all theories give nearly the same results.

For ductile material the most suitable theory is maximum shear stress theory.
Other theories for ductile material, Maximum Strain Energy Theory and Maximum Shear Stress Theory (Most Conservative Theory)
For brittle material the most suitable theory is Maximum Principal Stress Theory.
Other theories for brittle material, Maximum Principal Stress Theory.

Maximum principal stress theory (Rankine theory) is suitable for brittle materials.

Equivalent stress
= σ₁ - μσ₂
= 100 - 0.25 x 50 = 87.5 N/mm²

According to maximum principal stress theory, 
σ₁ = σ_y
According to maximum shear stress theory,
σ₁ - σ₂ = σ_y
Under pure bending, 
Therefore, in both the cases, permissible bending moment is M,

It is clear from the relation T/J = (Shear Stress)/ (Radial Distance) that a shaft subjected to pure torsion is to be designed for maximum shear stress theory.

Shear strain energy

Yielding may occur either in tension or compression.
For yielding in tension,
According to normal strain theory, 

For yielding in compression,