Topic: Engineering Mechanics
A travelling crane as shown is used to carry a load of two tonnes at point D. A counter mass CW is to be added as shown to avoid toppling of the crane. Find the limiting value of counter mass and distance, X from F, such that it will not topple the crane even in the absence of load at D. The mass of the crane may be taken as 2 tonnes and is acting 2 meters away from E towards D.
- A. CW = 2 t at X = 8 m
- B. CW = 16 t at X = 10 m
- C. CW = 1.5 t at X = 6 m
- D. CW = 16.67 t at X = 12 m
Answer: A. CW = 2 t at X = 8 m
Explanation: To avoid toppling left (no load at D), overturning moment by CW about the left support must not exceed restoring moment by crane weight: CW * X <= 2 tonnes * 8 m = 16 t-m. To avoid toppling right (load at D), restoring moment by CW must exceed overturning moment: CW * (X + 6) >= 2 * 12 + 2 * 2 = 28 t-m. Testing Option (a): CW=2, X=8 yields CW * X = 16 and CW * (X+6) = 28, perfectly satisfying both limits.