For No tension to develop in the gravity dam the eccentricity ‘e’ of the resultant force should be
- ALess than b / 3
- BLess than b / 6Correct
- CLess than b / 4
- DLess than b / 12
Solution
Concept
No tension condition in gravity dam
Formula
NONE
Step-by-step solution
1. Tensile stresses at the base of a gravity dam are avoided to prevent joint opening and cracking. 2. According to the middle-third rule, the resultant force must fall within the middle third of the base width b. 3. Hence, the eccentricity 'e' measured from the center line must satisfy e ≤ b / 6. Answer: B
Explanation
To prevent tensile stresses from developing at the base of a gravity dam, the resultant force must act within the middle-third of the base width b. This condition implies that the eccentricity e of the resultant force measured from the center line must be less than or equal to b / 6. Keeping eccentricity within this limit ensures that the entire dam base remains under compressive stress.
Why the other options are wrong
A) An eccentricity of b / 3 allows the resultant to fall outside the middle third, causing tension at the heel. C) An eccentricity of b / 4 exceeds the middle-third limit of b / 6 required to eliminate tensile stress. D) Although b / 12 prevents tension, the maximum allowable limit to strictly avoid tension is b / 6.
Shortcut
Middle third rule: eccentricity e ≤ b / 6 to prevent tension.
Common mistake
Confusing the eccentricity limit of b/6 with the middle-third total width requirement of b/3.
Correct answer: B) Less than b / 6