Q.51 A BG track is laid with a sleeper density of N + 3. The width of the sleeper is 20.25 cm. Find the minimum depth of the ballast cushion.
- A10.125 cm
- B30.5 cmCorrect
- C61 cm
- D20.375 cm
Solution
Concept
Load from each sleeper spreads at 45° through the ballast. The pressure bulbs of two nearby sleepers should just meet at the formation level.
Formula
S = W + 2Db, so Db = (S - W)/2; S = L/(N + x)
Step-by-step solution
1. For a BG track, take rail length L = 13 m. So N = 13. 2. Sleeper density = N + 3 = 13 + 3 = 16 sleepers per rail length. 3. Sleeper spacing S = 1300/16 = 81.25 cm. 4. Use S = W + 2Db, so Db = (S - W)/2. 5. Db = (81.25 - 20.25)/2 = 61/2 = 30.5 cm.
Explanation
Load spreads at 45° below each sleeper, so the spread width is W + 2D. For a minimum depth, the spread zones of two nearby sleepers just touch, which means sleeper spacing = W + 2D. This gives a minimum ballast depth of 30.5 cm.
Why the other options are wrong
A: 10.125 cm is only half the sleeper width. C: 61 cm is the clear gap between sleepers (S - W), not the depth. D: 20.375 cm does not come from the correct formula.
Shortcut
Depth = (spacing - sleeper width)/2 = (1300/16 - 20.25)/2 = 30.5 cm
Common mistake
Forgetting to divide (S - W) by 2, which gives 61 cm.
Correct answer: B) 30.5 cm