What is the maximum normal stress theory (Rankine’s theory) of failure?
- AFailure occurs when the maximum shear stress reaches a critical value
- BFailure occurs when the maximum normal stress reaches the critical strengthCorrect
- CFailure occurs when the von Mises stress reaches the critical strength
- DFailure occurs when the hydrostatic stress reaches a critical value
Solution
Concept
Maximum normal stress theory of failure
Formula
NONE
Step-by-step solution
1. Rankine's failure criterion states that yielding occurs when maximum principal stress reaches ultimate strength. 2. Structural failure theories evaluate multi-axial stress states against uniaxial material strength. Answer: B
Explanation
Rankine's theory predicts that a material yields or fractures when the maximum principal stress in a multi-axial state reaches the yield or ultimate strength observed in simple tension. It assumes that failure is governed purely by the magnitude of the largest normal stress. Therefore, option B is the correct statement of this theory.
Why the other options are wrong
A) Failure governed by maximum shear stress corresponds to Tresca's failure criterion. D) Hydrostatic stress changes volume without inducing yield under classical failure theories.
Shortcut
Rankine's theory = Maximum Normal Stress theory, suitable for brittle materials.
Common mistake
Confusing Rankine's maximum normal stress theory with Tresca's maximum shear stress theory and selecting option A.
Correct answer: B) Failure occurs when the maximum normal stress reaches the critical strength