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Problem 3.68

Problem 3.68 - Problem 3.68[Difficulty 4 Given Various dam...

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Problem 3.68 [Difficulty: 4] Given: Various dam cross-sections Find: Which requires the least concrete; plot cross-section area A as a function of α Solution: For each case, the dam width b has to be large enough so that the weight of the dam exerts enough moment to balance the moment due to fluid hydrostatic force(s). By doing a moment balance this value of b can be found a) Rectangular dam Straightforward application of the computing equations of Section 3-5 yields b D F H y mg O F H p c A = ρ g D 2 w D = 1 2 ρ g D 2 w = y' y c I xx A y c + = D 2 w D 3 12 w D D 2 + = 2 3 D = so y D y' = D 3 = Also m ρ cement g b D w = SG ρ g b D w = Taking moments about O M 0. 0 = F H y b 2 m g + = so 1 2 ρ g D 2 w D 3 b 2 SG ρ g b D w ( ) = Solving for b b D 3 SG = The minimum rectangular cross-section area is A b D = D 2 3 SG = For concrete, from Table A.1, SG = 2.4, so

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Problem 3.68 - Problem 3.68[Difficulty 4 Given Various dam...

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