A 6 m high masonry dam (density = 20,000 N/m3) has a top width of one meter, a base width of 4 m, and a vertical water face. When the reservoir is full, the minimum stress at the base will be_______________________?
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Answer: C. 7500 N/m 2
Explanation
Calculations for a masonry dam's base pressure distribution under full reservoir conditions result in a minimum compressive base stress of 7500 N/m². Summing vertical loads and overturning moments determines the resultant force location and resultant eccentricity at the dam base. Applying the trapezoidal stress distribution formula for retaining structures confirms the minimum compressive stress value at the heel. Gravity dams resist water pressure through their own massive weight, transferring loads safely downward into supporting foundation rock strata. Hydrostatic pressure acts horizontally against the dam face, creating an overturning moment that shifts the resultant force toward the downstream toe. Base stress analysis ensures that masonry dams remain under compression across their entire base without developing tensile stress cracks.
Option A underestimates the base pressure by orders of magnitude, ignoring the massive hydrostatic and dead load forces acting on the dam. Option B represents a lower stress magnitude that fails to satisfy the equilibrium equations for a 6-meter high masonry gravity dam. Option D overestimates the minimum compressive base stress, resulting from an error in calculating the resultant eccentricity or section modulus.
- Subject
- Engineering
- Category
- Civil Engineering
- Topic
- —
- Difficulty
- medium
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