To determine Find the centroid of the plane area. Explanation Calculation: Sketch the cross-section of plane area as shown in Figure 1. Refer to Figure 1. Consider the section (1) as parabolic and section (2) as triangle. For section (1), The breadth of the parabolic segment is a = 8 in . and height is b = 4 in . . The section (2), The base of the triangle is a = 8 in . and height is b = 4 in . . Calculate the area using the relation as shown below. For parabolic segment, A = 2 3 a b For triangle, A = 1 2 a b Calculate the sum of the plane area using the relation as shown below. Reduce the area and centroid of the triangle from the area and centroid of the parabolic segment. Sum = ( 1 ) − ( 2 ) . Calculate the area and the centroid of each section as shown in table below. Section Area A ( in . 2 ) x ¯ ( in . ) y ¯ ( in . ) x ¯ A ( in . 3 ) y ¯ A ( in . 3 ) (1) 2 3 × 8 × 4 = 21.333 3 5 × 8 = 4.8 3 8 × 4 = 1.5 102.398 32 (2) 1 2 × 8 × 4 = 16 2 3 × 8 = 5.3333 1 3 × 4 = 1.3333 85.333 21.333 Sum 5.333 17.065 10.667 Calculate the centroid along x axis ( X ¯ ) as shown below

Vector Mechanics for Engineers: Statics, 11th Edition

11th Edition

ISBN: 9780077687304

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek

Publisher: McGraw-Hill Education

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Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related t…

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Chapter 5.1, Problem 5.13P

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Find the centroid of the plane area.

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Vector Mechanics for Engineers: Statics, 11th Edition

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