Explanation Given information: The plane region: Calculations: From the figures shown above, The product of inertia about the centroidal axis: I ¯ x y = 0 ; ( Region is symmetric about the y-coordinate of the centroid ) And, the product of inertia with respect to the x- and y-axis be I x y = ∑ A i x ¯ i y ¯ i = A 1 x ¯ 1 y ¯ 1 + A 2 x ¯ 2 y ¯ 2 − A 3

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN: 9781305501607

Author: Andrew Pytel And Jaan Kiusalaas

Publisher: CENGAGE L

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Question

Chapter 9, Problem 9.46P

To determine

I¯xy and Ixy for the plane region.

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Chapter 9 Solutions

International Edition---engineering Mechanics: Statics, 4th Edition

Ch. 9 - Compute the moment of inertia of the shaded region...Ch. 9 - The properties of the plane region are...Ch. 9 - The moments of inertia of the plane region about...Ch. 9 - The moment of inertia of the plane region about...Ch. 9 - Using integration, find the moment of inertia and...Ch. 9 - Use integration to determine the moment of inertia...Ch. 9 - Determine Ix and Iy for the plane region using...Ch. 9 - Using integration, compute the polar moment of...Ch. 9 - Use integration to compute Ix and Iy for the...Ch. 9 - By integration, determine the moments of inertia...

Ch. 9 - Compute the moment of inertia about the x-axis for...Ch. 9 - By integration, find the moment of inertia about...Ch. 9 - Figure (a) shows the cross section of a column...Ch. 9 - Compute the dimensions of the rectangle shown in...Ch. 9 - Compute Ix and Iy for the W867 shape dimensioned...Ch. 9 - Figure (a) shows the cross-sectional dimensions...Ch. 9 - A W867 section is joined to a C1020 section to...Ch. 9 - Compute Ix and Iy for the region shown.Ch. 9 - Prob. 9.19P Ch. 9 - Calculate Ix for the shaded region, knowing that...Ch. 9 - Compute Iy for the region shown, given that...Ch. 9 - Prob. 9.22P Ch. 9 - Prob. 9.23P Ch. 9 - Determine Ix for the triangular region shown.Ch. 9 - Determine the distance h for which the moment of...Ch. 9 - A circular region of radius R/2 is cut out from...Ch. 9 - Prob. 9.27P Ch. 9 - Determine the ratio a/b for which Ix=Iy for the...Ch. 9 - As a round log passes through a sawmill, two slabs...Ch. 9 - Prob. 9.30P Ch. 9 - By numerical integration, compute the moments of...Ch. 9 - Use numerical integration to compute the moments...Ch. 9 - The plane region A is submerged in a ï¬‚uid of...Ch. 9 - Use integration to verify the formula given in...Ch. 9 - For the quarter circle in Table 9.2, verify the...Ch. 9 - Determine the product of inertia with respect to...Ch. 9 - The product of inertia of triangle (a) with...Ch. 9 - Prob. 9.38P Ch. 9 - For the region shown, Ixy=320103mm4 and Iuv=0....Ch. 9 - Prob. 9.40P Ch. 9 - Calculate the product of inertia with respect to...Ch. 9 - Prob. 9.42P Ch. 9 - Prob. 9.43P Ch. 9 - The figure shows the cross section of a standard...Ch. 9 - Prob. 9.45P Ch. 9 - Prob. 9.46P Ch. 9 - Prob. 9.47P Ch. 9 - Use numerical integration to compute the product...Ch. 9 - Determine the dimension b of the square cutout so...Ch. 9 - For the rectangular region, determine (a) the...Ch. 9 - Prob. 9.51P Ch. 9 - Prob. 9.52P Ch. 9 - Prob. 9.53P Ch. 9 - Prob. 9.54P Ch. 9 - Prob. 9.55P Ch. 9 - The u- and v-axes are the principal axes of the...Ch. 9 - The x- and y-axes are the principal axes for the...Ch. 9 - Prob. 9.58P Ch. 9 - The inertial properties of the region shown with...Ch. 9 - Determine Iu for the inverted T-section shown....Ch. 9 - Using Ix and Iu from Table 9.2, determine the...Ch. 9 - Show that every axis passing through the centroid...Ch. 9 - Prob. 9.63P Ch. 9 - The L806010-mm structural angle has the following...Ch. 9 - Compute the principal centroidal moments of...Ch. 9 - Prob. 9.66P Ch. 9 - Determine the principal axes and the principal...Ch. 9 - Compute the principal centroidal moments of...Ch. 9 - Find the moments and the product of inertia of the...Ch. 9 - Determine the moments and product of inertia of...Ch. 9 - Find the principal moments of inertia and the...Ch. 9 - Determine the moments and product of inertia of...Ch. 9 - Prob. 9.73P Ch. 9 - Prob. 9.74P Ch. 9 - The u- and v-axes are the principal axes of the...Ch. 9 - The x- and y-axes are the principal axes for the...Ch. 9 - Prob. 9.77P Ch. 9 - The L806010-mm structural angle has the following...Ch. 9 - Prob. 9.79RP Ch. 9 - Prob. 9.80RP Ch. 9 - By integration, show that the product of inertia...Ch. 9 - Compute Ix and Iy for the shaded region.Ch. 9 - Using integration, evaluate the moments of inertia...Ch. 9 - The inertial properties at point 0 for a plane...Ch. 9 - Compute Ix and Iy for the shaded region.Ch. 9 - The flanged bolt coupling is fabricated by...Ch. 9 - Prob. 9.87RP Ch. 9 - Compute Ix,Iy, and Ixy for the shaded region.Ch. 9 - Determine Ix and Ixy for the shaded region shown.Ch. 9 - Calculate Ix,Iy, and Ixy for the shaded region...Ch. 9 - For the shaded region shown, determine (a) Ix and...Ch. 9 - Use integration to find Ix,Iy, and Ixy for the...Ch. 9 - Determine the principal moments of inertia and the...Ch. 9 - The properties of the unequal angle section are...

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I ¯ x y a n d I x y for the plane region.

Solution Summary: The author calculates the product of inertia with respect to the x- and y-axis.

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I¯xy and Ixy for the plane region.

Chapter 9 Solutions