Meriam, Kraige & Bolton — Distributed Forces: Centroids and Centers of Gravity: Problem 5_198

⚡ Mecademy AIENG정역학 · ch5  Problem Statement A 5-m-wide vertical gate is rigidly connected to a 3-m-wide panel which provides a seal for an underground drain passage during severe storms. For the situation shown, determine the depth of fresh water which will cause the gate to begin to open and drain water into the underground passage. A 1.5-m cube of concrete is used to hold the horizontal 3-m-wide panel flush with the ground during normal operating conditions. Problem 5/198 (a) Determination of the depth of fresh water 1. Formula: To find the depth at which the gate begins to open, we must consider the moment equilibrium about the hinge at point . The gate assembly will begin to open when the clockwise moment due to the hydrostatic pressure on the vertical gate equals the sum of the counter-clockwise moments due to the hydrostatic pressure on the horizontal panel and the weight of the concrete block. where: 2. Substitution: Given values: Width of vertical gate, Width of horizontal panel, Length of horizontal panel, Concrete cube side, Distance of concrete block from hinge , Density of water, Density of concrete, (assumed standard value) h h h A M = ∑ A 0⟹M = gate M + panel M concrete M = gate (h− ∫ 0 h y)P(y)w dy= g ρ gw h 6 1 wg 3 M = panel F ⋅ panel d = p (ρ gh⋅ w L ⋅ p w )⋅ p 2 L p M = concrete W ⋅ c d = c (ρ gs)⋅ c 3 d c w = g 5 m w = p 3 m L = p 2 m+2 m=4 m s=1.5 m Ad = c 2 m ρ = w 1000 kg/m 3 ρ = c 2400 kg/m 3 Substituting into the moment equation: 3. Calculation: Div