Question

According to Rankine's failure theory, failure occurs when

• A. Maximum shear stress reaches shear yield stress
• B. Distortion energy reaches critical value
• C. Maximum principal stress reaches ultimate strength
• D. Maximum strain energy reaches critical value

Hint:

Common failure theories: \[ \boxed{ \begin{aligned} \text{Rankine} &\rightarrow \text{Maximum Principal Stress} \text{Guest-Tresca} &\rightarrow \text{Maximum Shear Stress} \text{von Mises} &\rightarrow \text{Distortion Energy} \text{Haigh} &\rightarrow \text{Maximum Total Strain Energy} \end{aligned} } \]

Answer 1

The Correct Option is C

Step 1: Recall Rankine's failure theory. Rankine's theory is also known as the \[ \boxed{\text{Maximum Principal Stress Theory}.} \] It states that failure begins when the maximum principal stress reaches the limiting strength of the material.

Step 2: Identify the correct condition. Mathematically, \[ \boxed{ \sigma_{\max} = \sigma_{\text{ultimate}} } \] for brittle materials. Hence, \[ \boxed{ \text{Failure occurs when the maximum principal stress reaches the ultimate strength.} } \] Therefore, \[ \boxed{(C)} \] is the correct answer.