The moment required to rotate the near end of a prismatic beam through a unit angle, without translation, with the far end fixed, is:
Try it first: pick an option, then read the explanation.
Correct answer: D. 4EI/L
Asked in SSC JE 2013
Detailed Explanation
The book places this beam-stiffness question (used in moment distribution and slope deflection) in the torsion chapter.
\[ M_{AB} = \frac{2EI}{L}(2\theta_A + \theta_B),\quad \theta_B = 0,\ \theta_A = 1 \;\Rightarrow\; M_{AB} = \frac{4EI}{L},\quad M_{BA} = \frac{2EI}{L} \]
Why “4EI/L” Is Correct
The stiffness is 4EI/L; half of it (2EI/L) is carried over to the fixed far end.
| Far end | Stiffness (moment for unit rotation) | Carry-over factor |
|---|---|---|
| Fixed | 4EI/L | 1/2 |
| Hinged | 3EI/L | 0 |
| Symmetric span (both rotate equally) | 2EI/L | — |
| Antisymmetric | 6EI/L | — |
Why the Other Options Are Wrong
- A. EI/L: EI/L is not a standard beam stiffness.
- B. 2EI/L: 2EI/L is the carry-over moment at the fixed far end, or the stiffness for symmetric rotation.
- C. 3EI/L: 3EI/L applies when the far end is hinged.
Key Point
Far end fixed: k = 4EI/L (carry-over ½). Far end hinged: k = 3EI/L.
Key Concepts for Students
- Used to compute distribution factors.
- Compare torsional stiffness GJ/L for shafts.
- Translation of one end would add 6EIΔ/L² moments.
Practice more: this is question 13 in Torsion MCQs – Part 1. Try the whole set and check every answer instantly.