International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
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Chapter 9, Problem 9.48P
Use numerical integration to compute the product of inertia of the region show with respect to the x- and y-axes.
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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. 9.19PCh. 9 - Calculate Ix for the shaded region, knowing that...Ch. 9 - Compute Iy for the region shown, given that...Ch. 9 - Prob. 9.22PCh. 9 - Prob. 9.23PCh. 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. 9.27PCh. 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. 9.30PCh. 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 fluid 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. 9.38PCh. 9 - For the region shown, Ixy=320103mm4 and Iuv=0....Ch. 9 - Prob. 9.40PCh. 9 - Calculate the product of inertia with respect to...Ch. 9 - Prob. 9.42PCh. 9 - Prob. 9.43PCh. 9 - The figure shows the cross section of a standard...Ch. 9 - Prob. 9.45PCh. 9 - Prob. 9.46PCh. 9 - Prob. 9.47PCh. 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. 9.51PCh. 9 - Prob. 9.52PCh. 9 - Prob. 9.53PCh. 9 - Prob. 9.54PCh. 9 - Prob. 9.55PCh. 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. 9.58PCh. 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. 9.63PCh. 9 - The L806010-mm structural angle has the following...Ch. 9 - Compute the principal centroidal moments of...Ch. 9 - Prob. 9.66PCh. 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. 9.73PCh. 9 - Prob. 9.74PCh. 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. 9.77PCh. 9 - The L806010-mm structural angle has the following...Ch. 9 - Prob. 9.79RPCh. 9 - Prob. 9.80RPCh. 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. 9.87RPCh. 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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- Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.arrow_forwardCompute Ix and Iy for the region shown.arrow_forwardThe moment of inertia of the plane region about the x-axis and the centroidal x-axis are Ix=0.35ft4 and Ix=0.08in.4, respectively. Determine the coordinate y of the centroid and the moment of inertia of the region about the u-axis.arrow_forward
- The moments of inertia of the plane region about the x- and u-axes are Ix=0.4ft4 and Iu=0.6ft4, respectively. Determine y (the y-coordinate of the centroid C) and Ix (the moment of inertia about the centroidal x-axis).arrow_forwardDetermine the product of inertia with respect to the x- and y-axes for the quarter circular, thin ring (tR) by integration.arrow_forwardThe L806010-mm structural angle has the following cross-sectional properties: Ix=0.808106mm4,Iy=0.388106mm4, and I2=0.213106mm4, where I2 is a centroidal principal moment of inertia. Assuming that Ixy is negative, compute (a) I1 (the other centroidal principal moment of inertia); and (b) the principal directions at the centroid.arrow_forward
- Determine Ix and Iy for the plane region using integration.arrow_forwardThe product of inertia of triangle (a) with respect to its centroid is Ixy=b2h2/72. What is Ixy for triangles (b)-(d)? (Hint: Investigate the signs in the expression Ixy=IxyAxy.)arrow_forwardThe L806010-mm structural angle has the following cross-sectional properties: Ix=0.808106mm4,Iy=0.388106mm4, and I2=0.213106mm4, where I2 is a principal centroidal moment of inertia. Assuming Ixy is negative, compute (a) I1 (the other principal centroidal moment of inertia); and (b) the principal directions.arrow_forward
- 2. Locate the X-X and Y-Y centroidal axes, and calculate the moments of inertia with respect to both centroidal axes for the areas shown below. 1 Inswer: (1) X: (2) y: (3) With respect to the X-X centroidal axis: With respect to the Y-Y centroidal axis: in in.arrow_forwardDetermine the moment of inertia about x and y axes for the area bounded by the curves as shown in figure by direct integration method.arrow_forwardComplete solutionsarrow_forward
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