A solid circular shaft is subjected to a bending moment of 120 Nm and a torque of 160 Nm. Using the Tresca criterion, what is the equivalent bending moment?
- A160 Nm
- B180 Nm
- C200 NmCorrect
- D220 Nm
Solution
Concept
Equivalent moment under maximum shear stress theory
Formula
Te = √(M2 + T2)
Step-by-step solution
1. Under the Tresca maximum shear stress theory, maximum shear stress is given by τmax = (16 / (π × d3)) × √(M2 + T2). 2. The equivalent moment representing this maximum shear stress state is Me = √(M2 + T2). 3. Given bending moment M = 120 Nm and torque T = 160 Nm. 4. Me = √(1202 + 1602) = √(14400 + 25600) = √(40000) = 200 Nm. Answer: C
Explanation
According to the Tresca (maximum shear stress) criterion, the combined action of bending moment M and twisting moment T is expressed through an equivalent moment equal to √(M2 + T2). Evaluating this for M = 120 Nm and T = 160 Nm gives 200 Nm.
Why the other options are wrong
A) 160 Nm corresponds to Rankine's equivalent bending moment theory. B) 180 Nm is an arithmetic average. D) 220 Nm is an incorrect calculation.
Shortcut
Standard 3-4-5 right triangle: 120, 160, 200 Nm.
Common mistake
Applying Rankine's maximum principal stress formula 0.5·(M + √(M2 + T2)) which yields 160 Nm instead of Tresca's criterion.
Correct answer: C) 200 Nm