A rectangular log of wood is floating in water with a load of 100 N at its centre. The maximum shear force in the log is:
Try it first: pick an option, then read the explanation.
Asked in SSC JE 2012
Detailed Explanation
The extra load is carried by the water. If the log stays level, the extra buoyancy is spread uniformly along its length: an upward UDL of 100/l per metre balancing the 100 N downward at the centre. It is like a simply supported beam turned upside down.
Upward intensity \( q = \dfrac{100}{l} \). At distance x from an end: \( V = qx \).
Just left of the centre: \( V = \dfrac{100}{l}\cdot\dfrac{l}{2} = 50\ \text{N} \); just right: \( -50\ \text{N} \). At the ends: 0.
Why “50 N at the centre” Is Correct
The largest shear, 50 N, occurs at the centre (changing sign there) — option (b). The ends are free, so the shear there is zero. Bending moment peaks at the centre too: 100l/8 = 12.5l N·m.
Why the Other Options Are Wrong
- A. 50 N at each end: The ends of the log are free, so the shear there is zero.
- C. 100 N at the centre: 100 N is the total jump in shear at the centre, not the shear on either side.
- D. zero shear all through: The upward buoyancy and the central load do produce shear.
Key Point
Floating beam with central load = inverted SS beam with UDL reaction: V_max = W/2 at the centre.
Key Concepts for Students
- Foundations on soil can be treated the same way (uniform soil pressure).
- The sign of the shear flips at the point load.
- Max BM = Wl/8, half that of a SS beam with the same central load.
Practice more: this is question 57 in Bending Moment and Shear Force MCQs – Part 4. Try the whole set and check every answer instantly.