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A masonry dam of trapezoidal cross section, with one face vertical, has a thickness of 1m at the top and 3m at the bottom. It is 7m high and has horizontal base. The vertical face is subjected to water pressure, the water standing 4.5m above the base. The weight of the masonry is 23.5kN/cu.m. Assuming no hydrostatic uplift, where will the resultant pressure intersect the base, and what will be the intensity of pressure at the heel and toe.?
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A masonry dam of trapezoidal cross section, with one face vertical, ha...
Analysis of a Trapezoidal Cross Section Masonry Dam Subjected to Water Pressure

Given:

  • Trapezoidal cross section masonry dam

  • Thickness of 1m at the top and 3m at the bottom

  • Height of 7m

  • Vertical face subjected to water pressure

  • Water standing at 4.5m above the base

  • Weight of the masonry is 23.5kN/cu.m

  • No hydrostatic uplift



To Find:

  • Where the resultant pressure intersects the base

  • The intensity of pressure at the heel and toe



Solution:

  1. Calculate the volume and weight of the masonry dam:


    • Volume = [(1+3)/2] x 7 x 1 = 14 cu.m

    • Weight = 14 x 23.5 = 329 kN


  2. Calculate the water pressure:


    • Pressure = 9.81 x 4.5 x 1 = 44.145 kN/cu.m


  3. Calculate the horizontal force due to water pressure:


    • Force = Pressure x [(1+3)/2] x 7 = 44.145 x 14 = 617.23 kN


  4. Calculate the vertical force due to weight of the masonry:


    • Force = Weight x (7/2) = 329 x 3.5 = 1151.5 kN


  5. Calculate the resultant force:


    • Resultant Force = sqrt[(Horizontal Force)^2 + (Vertical Force)^2] = sqrt[(617.23)^2 + (1151.5)^2] = 1298.2 kN


  6. Calculate the position of the resultant force:


    • Position = (Horizontal Force/Resultant Force) x (1+3)/2 = (617.23/1298.2) x 2 = 0.93m from the toe


  7. Calculate the intensity of pressure at the heel and toe:


    • Pressure at the heel = (Horizontal Force + Vertical Force)/(1 x 4) = (617.23 + 1151.5)/4 = 442.68 kN/cu.m

    • Pressure at the toe = (Horizontal Force - Vertical Force)/(3 x 4) = (617.23 - 1151.5)/12 = -34.61 kN/cu.m (negative sign indicates tension)




Conclusion:
The resultant pressure intersects the base at a distance of 0.93m from the toe. The intensity of pressure at the heel is 442.68 kN/cu.m and at the toe is -34.61 kN/cu.m (tension).
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A masonry dam of trapezoidal cross section, with one face vertical, has a thickness of 1m at the top and 3m at the bottom. It is 7m high and has horizontal base. The vertical face is subjected to water pressure, the water standing 4.5m above the base. The weight of the masonry is 23.5kN/cu.m. Assuming no hydrostatic uplift, where will the resultant pressure intersect the base, and what will be the intensity of pressure at the heel and toe.?
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A masonry dam of trapezoidal cross section, with one face vertical, has a thickness of 1m at the top and 3m at the bottom. It is 7m high and has horizontal base. The vertical face is subjected to water pressure, the water standing 4.5m above the base. The weight of the masonry is 23.5kN/cu.m. Assuming no hydrostatic uplift, where will the resultant pressure intersect the base, and what will be the intensity of pressure at the heel and toe.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A masonry dam of trapezoidal cross section, with one face vertical, has a thickness of 1m at the top and 3m at the bottom. It is 7m high and has horizontal base. The vertical face is subjected to water pressure, the water standing 4.5m above the base. The weight of the masonry is 23.5kN/cu.m. Assuming no hydrostatic uplift, where will the resultant pressure intersect the base, and what will be the intensity of pressure at the heel and toe.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A masonry dam of trapezoidal cross section, with one face vertical, has a thickness of 1m at the top and 3m at the bottom. It is 7m high and has horizontal base. The vertical face is subjected to water pressure, the water standing 4.5m above the base. The weight of the masonry is 23.5kN/cu.m. Assuming no hydrostatic uplift, where will the resultant pressure intersect the base, and what will be the intensity of pressure at the heel and toe.?.
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