Explanation Given: The base of the rectangle ( b r ) is 2 ft. The height of the rectangle ( h r ) is 3 ft. The unit weight of butyl alcohol ( γ b a ) is 50.1 lb / ft 3 Calculation: Calculate the area of the rectangular portion of the trapezoid ( A 1 ) . A 1 = b r h r A 1 = 2 ft × 3 ft = 6 ft 2 Draw the cross section of the trapezoid and mark the dimensions as shown in Figure (1). Calculate the location of centroid of the rectangle from top of the tank ( x 1 ) . x 1 = 1 2 ( h r ) x 1 = 1 2 ( 3 ) = 1.5 ft Calculate the area of the triangular portion of the trapezoid ( A 2 ) . A 2 = 1 2 ( b t + b t ) h t A 2 = 1 2 ( 2 + 2 ) 3 = 6 ft 2 Calculate the location of centroid of the triangle from top of the tank ( x 2 ) . x 2 = 1 3 ( h t ) x 2 = 1 3 ( 3 ft ) = 1 ft Calculate area of the trapezoid ( A ). A = A 1 + A 2 A = 6 ft 2 + 6 ft 2 = 12 ft 2 Calculate the location of centroid ( y ¯ ) . y ¯ = x 1 A 1 + x 2 A 2 A y ¯ = ( 1.5 × 6 ) + ( 1 × 6 ) 12 = 1.25 ft Calculate the area moment of inertia of trapezoid passing through the centroidal axis ( I ¯ x )

2nd Edition

ISBN: 9780134649290

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 2, Problem 79P

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The resultant force and its locations where the force acting on the trapezoidal plate.

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Chapter 2, Problem 78P

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