Problem 3.84 - Problem 3.84 Given: [Difficulty: 3] Curved...

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Problem 3.84 [Difficulty: 3] Given: Curved surface, in shape of quarter cylinder, with given radius R and width w; liquid concrete stands to depth H. R1 f t = w4 f t = F vmax 350 lbf = SG 2.50 = From Table A.1, App A Find: (a) Maximum depth of concrete to avoid cracking (b) Line of action on the form. (c) Plot the vertical force and line of action over H ranging from 0 to R. Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards from free surface) F v A y p d = (Vertical Hydrostatic Force) d h θ 1 F V x x’ y θ x' F v F v x d = (Moment of vertical force) Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts on free surface of the concrete Integrating the hydrostatic pressure equation: p ρ g h = From the geometry: y R sin θ () = x R cos θ = hyd = dRH = dA w R d θ = Therefore the vertical component of the hydrostatic force is: F v A y p
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Problem 3.84 - Problem 3.84 Given: [Difficulty: 3] Curved...

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