The principal stresses at a point in an elastic material are 2σ tensile and σ tensile. If an elastic limit in simple tension is 200 N/mm², according to the maximum principal stress theory, the value of σ at failure will be
- A108 N/mm²
- B100 N/mm²Correct
- C90 N/mm²
- D80 N/mm²
Solution
Concept
Rankine theory
Formula
σ₁ ≤ σyt
Step-by-step solution
1. Maximum principal stress = 2σ. 2. At failure 2σ = 200 N/mm², so σ = 100 N/mm².
Explanation
The maximum principal stress theory says that failure occurs when the largest principal stress reaches the elastic limit in simple tension.
Why the other options are wrong
108, 90 and 80 N/mm² would result from using other theories (strain energy, shear energy or shear stress).
Shortcut
σ₁ = σy.
Common mistake
Using the shear stress theory (which would give σ = 200).
Correct answer: B) 100 N/mm²