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Problem 3.58 - Problem 3.58 Given[Difficulty 4 Window in...

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Problem 3.58 [Difficulty: 4] Given: Window, in shape of isosceles triangle and hinged at the top is located in the vertical wall of a form that contains concrete. a 0.4 m = b 0.3 m = c 0.25 m = SG c 2.5 = (From Table A.1, App. A) Find: The minimum force applied at D needed to keep the window closed. Plot the results over the range of concrete depth between 0 and a. Solution: We will apply the hydrostatics equations to this system. Governing Equations: dp dh ρ g = (Hydrostatic Pressure - h is positive downwards) F R A p d = (Hydrostatic Force on door) y' F R A y p d = (First moment of force) Σ M 0 = (Rotational equilibrium) d dA h a w b D Assumptions: (1) Static fluid (2) Incompressible fluid (3) Atmospheric pressure acts at free surface and on the outside of the window. Integrating the pressure equation yields: p ρ g h d ( ) = for h > d p 0 = for h < d where d a c = d 0.15 m = Summing moments around the hinge: F D a A h p d + 0 = F D dF = pdA h a F D 1 a A h p
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