According to the maximum principal stress theory, what is the ratio between normal stress to yield stress of a material such that yielding of material takes place?
- A1/2
- B1Correct
- C√2
- D2
Solution
Concept
Maximum Principal Stress Theory
Formula
σ1 = σy (or σ1 / σy = 1)
Step-by-step solution
1. State the condition for yielding according to Maximum Principal Stress Theory: σ1 = σy. 2. Divide maximum normal stress (σ1) by yield stress (σy) to calculate the ratio: σ1 / σy = 1.
Explanation
According to the maximum principal stress theory (Rankine's theory), yielding or failure occurs when the maximum normal stress in a material reaches its yield stress. Since both values are equal at the onset of yielding, their ratio (normal stress ÷ yield stress) equals 1.
Shortcut
Remember the key rule for Maximum Principal Stress Theory (Rankine's Theory): Yielding occurs when Normal Stress = Yield Stress, so their ratio is always 1:1 (Ratio = 1).
Common mistake
Students often confuse Maximum Principal Stress Theory (Rankine's theory) with Maximum Shear Stress Theory (Tresca's theory), leading them to incorrectly select 1/2 by assuming a shear stress relationship rather than equating maximum normal stress directly to yield stress.
Correct answer: B) 1