COSMOS Chapter 9 Solution 64 - Edubirdie

University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2020
Views:

240

Pages:

1
Author:

Athena Harrison

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 64. xv of the volume is defined by xvV = ∫ xEL dV Selecting the element of volume shown dV = ydA = kxdA V = k ∫ xdA = kx A A Where x A = coordinate of the centroid of area A xvV = ∫ xEL dV = ∫ x ( kx dA ) = k ∫ x 2dA = kI z Where I z = moment of inertia of area with respect to z-axis. Thus xv = kI z I = z which is the same as for center of pressure. kx A A xA A For circular area: I z = I z′ + Aa 2 = 1 4 5 π a + π a2 a2 = π a4 4 4 ( ) xA = a A = π a2 Thus 5 4 πa Iz = 4 2 xv = xA A a π a ( ) xv = 5 a 4

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