Direct stress due to self-weight and extreme bending stress at the base of a masonry dam is given as 22 N/mm² and 14 N/mm² respectively. Determine the value of extreme resultant stresses.
- AMax stress = 66 N/mm², Min stress = 22 N/mm²
- BMax stress = 44 N/mm², Min stress = -66 N/mm²
- CMax stress = 66 N/mm², Min stress = -22 N/mm²Correct
- DMax stress = 44 N/mm², Min stress = 22 N/mm²
Solution
Concept
Resultant stress at the dam base = direct stress ± bending stress.
Formula
σmax = σd + σb ; σmin = σd - σb
Step-by-step solution
1. Direct stress σd = 22 N/mm². 2. As printed, bending stress σb = 14 N/mm². Then σmax = 22 + 14 = 36 N/mm² and σmin = 22 - 14 = 8 N/mm². No option matches. 3. If σb = 44 N/mm² (14 is likely a typo for 44), then σmax = 22 + 44 = 66 N/mm². 4. σmin = 22 - 44 = -22 N/mm² (tension). 5. This matches option C.
Explanation
At the dam base, direct stress acts all over the base, and bending stress adds on one face and subtracts on the other. Maximum stress is the sum and minimum stress is the difference. With bending stress 44 N/mm², the result is 66 N/mm² and -22 N/mm².
Shortcut
Max = sum, Min = difference. Check which option has (Max + Min)/2 = 22.
Common mistake
Adding the stresses for both faces, or forgetting that the minimum stress can become negative (tension).
Correct answer: C) Max stress = 66 N/mm², Min stress = -22 N/mm²