To determine The horizontal and vertical components of reaction at A , and the tension in the cable due to the water pressure. Explanation Given: The height of point A from base ( h A ) is 6 ft. The height between point O and B ( h O B ) is 6 ft. The unit weight of water ( γ w ) is 62.4 lb / ft 3 . The width of the tank ( b ) is 4ft. Calculation: Draw the cross section of the gate and mark the dimensions as shown in Figure (1). Calculate area of the square AOBD ( A 1 ) . A 1 = h A × h O B A 1 = 6 ft × 6 ft = 36 ft 2 Calculate the location of centroid of the square AOBD from the top ( x 1 ) . x 1 = 1 2 h A x 1 = 1 2 × 6 ft = 3 ft Calculate the area of the quadrant OAB ( A 2 ) . A 2 = π 4 ( r ) 2 A 2 = π 4 ( 6 ft ) 2 = 28.274 ft 2 Calculate the location of centroid of the quadrant OAB ( x 2 ) . x 2 = r − 4 r 3 π x 2 = 6 ft − 4 3 π ( 6 ft ) = 3.454 ft Calculate the area of the segment ADBA ( A ). A = A 1 − A 2 A = 36 ft 2 − 28.274 ft 2 = 7.726 ft 2 Draw the cross section of segments and show the area of segment ACBA as shown in Figure (2). Calculate centroid of the segment ADBA ( x ¯ ) . x ¯ = A 1 x 1 − A 2 x 2 A x ¯ = 36 ft 2 × 3 ft − 28.274 ft 2 × 3.454 ft 7.726 ft 2 = 1.3402 ft Calculate the intensity of load at point A ( w A ) . w A = γ w h A b w A = 62.4 lb/ft 3 × 6 ft × 4 ft = 1 , 497.6 lb / ft The horizontal component of the resultant force acting on the shell is equal to the pressure force on the vertically projected area of the shell. Calculate the horizontal component of the resultant force ( F h ) . F h = 1 2 w A h A F h = 1 2 × 1 , 497

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2, Problem 104P

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The horizontal and vertical components of reaction at A, and the tension in the cable due to the water pressure.

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Chapter 2, Problem 103P

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