Explanation Given: The radius of the quadrant ( r ) is 12 ft. The angle of the quadrant ( θ ) is 45 ° . Calculation: Calculate height of triangle OAB ( h ). cos θ = h r cos 45 ° = h 12 h = 12 cos 45 ° Calculate height of the point A from side OD ( h A ) . sin θ = h A r sin ( 45 ) ° = h A 12 h A = 12 sin 45 ° The height of point A from side OD is the height of point B from side OD ( h B ) . h A = h B = 12 sin 45 ° Calculate the height of point B from point A ( h A B ) . h A B = 2 h A h A B = 2 × 12 sin 45 ° m = 24 sin 45 ° m Calculate the intensity of load at point B ( w B ) . w B = γ w h A B b w B = 62.4 lb / ft 3 × ( 24 sin 45 ° ) ft × 6 ft = 6 , 353.778 lb / ft Calculate the horizontal component of resultant force ( F h ) . F h = 1 2 w B h A B F h = 1 2 ( 6 , 353.778 lb / ft ) ( 24 sin 45 ° ) = ( 53 , 913.6 lb ) × 1 kip 1 , 000 lb = 53.9136 k i p Calculate the point of action of horizontal component of resultant force ( y ¯ ) . y ¯ = 1 3 h A B y ¯ = 1 3 ( 24 sin 45 ° ) ft = 5.657 ft Calculate the distance of y ¯ from the side OD ( d ). d = h B − y ¯ d = 12 sin 45 ° ft − 5.657 ft = 2.8284 ft Calculate area of the triangle OAB ( A 1 ) . A 1 = ( 1 2 h A B × h ) A 1 = ( 1 2 × ( 24 sin 45 ° ) ft × ( 12 cos 45 ° ) ft ) = 72 ft 2 Calculate the location of centroid for the triangle OAB ( x ˜ 2 ) . x ˜ 2 = 2 3 h x ˜ 2 = 2 3 × 12 cos 45 ° ft = 5.6569 ft Calculate area of the quadrant OADB ( A 2 ) . A 2 = π 4 r 2 A 2 = π 4 ( 12 ft ) 2 = 113

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2, Problem 111P

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The magnitude and direction of the resultant force of the water on the bearing O and the moment of this force about the bearing.

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Chapter 2, Problem 110P

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