Solution_09

# Solution_09 - CIV-100F Section B/E Solutions Fall 2011...

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CIV-100F Solutions Section B/E Fall 2011 Assignment 9 Due on Monday, November 21 st 2011 Draw a FBD if necessary; Pay attention to significant figures; A ruler is always required. 1- A 0.8m by 0.8m gate AB is located at the bottom of a tank filled with water. The gate is hinged along its top edge A and rests on a frictionless stop at B . The density of the water is 1000 kg/m3. Neglecting the weight of the gate, determine the minimum tension required in cable BCD to open the gate. (Hint: there is no reaction at support B if the gate is opened.) Solution : The free body diagram of the gate AB is drawn as shown (the gate is in the state that it is just opened). ° = = + + = 93 . 61 8461 . 1 64 . 0 48 . 0 45 . 0 27 . 0 tan θ Find the water pressure at point A and B: 2 3 / 5 . 4414 ) 45 . 0 )( / 81 . 9 )( / 1000 ( 1 m N kg p = = 2 3 / 3 . 9123 ) 93 . 0 )( / 81 . 9 )( / 1000 ( 2 = = Calculate the forces caused by water pressure: kN F 8253 . 2 ) 8 . 0 )( 8 . 0 ( 1 1 = = 5068 . 1 ) 8 . 0 )( 8 . 0 )( 1 2 )( 5 . 0 ( 2 = = Take moment about point A: kN T T T F F M A 71 . 5 0 ) 64 . 0 )( sin ( ) 48 . 0 )( cos ( ) 3 / 2 )( 8 . 0 ( 2 ) 4 . 0 ( 1 = = + + = 2- Determine the moments of inertia X I and Y I of the area shown with respect to centroidal axes X and Y as shown. (Hint: you have to find the centroid C first.) Solution : The centroid C (the intersection of X and Y axes) of

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## This note was uploaded on 12/10/2011 for the course CIV 100 taught by Professor Nahrvar during the Spring '08 term at University of Toronto.

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Solution_09 - CIV-100F Section B/E Solutions Fall 2011...

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