Pick the correct statement(s): A. The bending moment which, acting alone, would produce a maximum stress equal to the major principal stress caused by combined bending and torsion is called the equivalent bending moment. B. The torque which, acting alone, would produce a maximum shear stress equal to the maximum shear stress caused by combined bending and torsion is called the equivalent torque.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 25/01/2018 (Evening)
Detailed Explanation
A shaft under bending M and torque T has bending stress σ = 32M/πD³ and shear stress τ = 16T/πD³ at the surface. Replace the combination by a single equivalent action.
\[ \sigma_1 = \frac{\sigma}{2} + \sqrt{\left(\frac{\sigma}{2}\right)^2+\tau^2} = \frac{32}{\pi D^3}\cdot\frac12\left[M + \sqrt{M^2+T^2}\right] \;\Rightarrow\; M_e = \tfrac12\left[M + \sqrt{M^2+T^2}\right] \]\[ \tau_{max} = \sqrt{\left(\frac{\sigma}{2}\right)^2+\tau^2} = \frac{16}{\pi D^3}\sqrt{M^2+T^2} \;\Rightarrow\; T_e = \sqrt{M^2+T^2} \]
Why “Both A and B” Is Correct
Statement A defines the equivalent bending moment and B the equivalent torque — both are correct.
| Combined bending M and torque T (solid shaft) | Formula |
|---|---|
| Bending stress | σb = 32M/(πD³) |
| Torsional shear stress | τ = 16T/(πD³) |
| Equivalent bending moment (max principal stress) | Me = ½[M + √(M² + T²)] |
| Equivalent torque (max shear stress) | Te = √(M² + T²) |
| Ratio σb/τ | 2M/T |
Why the Other Options Are Wrong
- A. Only A: B is also a correct definition.
- B. Only B: A is also a correct definition.
- D. None of these: Both statements are correct.
Key Point
Me = ½(M + √(M² + T²)) for principal stress; Te = √(M² + T²) for max shear.
Key Concepts for Students
- Rankine's theory uses Me; Guest–Tresca uses Te.
- Me = (M + Te)/2.
- Design D from both and take the larger.
Practice more: this is question 10 in Torsion MCQs – Part 1. Try the whole set and check every answer instantly.