A pile of length L is lifted at two points. For the hogging moment at the two points of suspension to equal the sagging moment at the centre, the distance of each suspension point from its nearer end is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 23/01/2018 (Evening)
Detailed Explanation
The pile's self-weight is a UDL w. Lifted at two symmetric points a from each end, it acts like a beam with two overhangs: hogging over the lifting points, sagging at the centre. Equal moments give the smallest peak moment.
Hogging at a support: \( M_h = \frac{wa^2}{2} \)
Sagging at centre: \( M_s = \frac{wL}{2}\left(\frac{L}{2}-a\right) - \frac{w}{2}\left(\frac{L}{2}\right)^2 = \frac{wL^2}{8} - \frac{wLa}{2} \)
\[ \frac{a^2}{2} = \frac{L^2}{8} - \frac{La}{2} \Rightarrow a = \frac{(\sqrt2-1)L}{2} = 0.207L \]
Why “0.207 L” Is Correct
Lifting at 0.207L from each end makes both moments equal to about 0.0214wL² — the minimum possible design moment for two-point lifting.
Why the Other Options Are Wrong
- A. 0.107 L: 0.107L leaves the sagging moment larger than the hogging moment.
- C. 0.307 L: 0.307L makes the hogging moment larger.
- D. 0.407 L: 0.407L puts the points too close to the centre; hogging dominates.
Key Point
Two-point lifting of a pile: a = 0.207L from each end; M = 0.0214wL².
Key Concepts for Students
- Single-point lifting (one end on the ground): lift at 0.293L from the top end.
- Precast pile reinforcement is designed for handling moments.
- Same logic as equal overhangs with UDL.
Practice more: this is question 64 in Bending and Shear Stress MCQs – Part 5. Try the whole set and check every answer instantly.