1 Introduction To Statics 2 Basic Operations With Force Systems 3 Resultants Of Force Systems 4 Coplanar Equilibrium Analysis 5 Three-dimensional Equilibrium 6 Beams And Cables 7 Dry Friction 8 Centroids And Distributed Loads 9 Moments And Products Of Inertia Of Areas 10 Virtual Work And Potential Energy Chapter9: Moments And Products Of Inertia Of Areas
Chapter Questions Section: Chapter Questions
Problem 9.1P: Compute the moment of inertia of the shaded region about the y-axis by integration. Problem 9.2P: The properties of the plane region are JC=1000in.4,Ix=7000in.4, and Iy=4000in.4. Calculate A,Ix, and... Problem 9.3P: The moments of inertia of the plane region about the x- and u-axes are Ix=0.4ft4 and Iu=0.6ft4,... Problem 9.4P: The moment of inertia of the plane region about the x-axis and the centroidal x-axis are Ix=0.35ft4... Problem 9.5P: Using integration, find the moment of inertia and the radius of gyration about the x-axis for the... Problem 9.6P: Use integration to determine the moment of inertia of the shaded region about the x-axis. Problem 9.7P: Determine Ix and Iy for the plane region using integration. Problem 9.8P: Using integration, compute the polar moment of inertia about point O for the circular sector. Check... Problem 9.9P: Use integration to compute Ix and Iy for the parabola. Check your answers with the results for the... Problem 9.10P: By integration, determine the moments of inertia about the x-and y-axes for the region shown. Problem 9.11P: Compute the moment of inertia about the x-axis for the region shown using integration. Problem 9.12P: By integration, find the moment of inertia about the y-axis for the region shown. Problem 9.13P: Figure (a) shows the cross section of a column that uses a structural shape known as W867... Problem 9.14P: Compute the dimensions of the rectangle shown in Fig. (b) that has the same kx and ky as the W867... Problem 9.15P: Compute Ix and Iy for the W867 shape dimensioned in the figure. Assume that the section is composed... Problem 9.16P: Figure (a) shows the cross-sectional dimensions for the structural steel section known as C1020... Problem 9.17P: A W867 section is joined to a C1020 section to form a structural member that has the cross section... Problem 9.18P: Compute Ix and Iy for the region shown. Problem 9.19P Problem 9.20P: Calculate Ix for the shaded region, knowing that y=34.27mm. Problem 9.21P: Compute Iy for the region shown, given that x=12.93mm. Problem 9.22P Problem 9.23P Problem 9.24P: Determine Ix for the triangular region shown. Problem 9.25P: Determine the distance h for which the moment of inertia of the region shown about the x-axis will... Problem 9.26P: A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what... Problem 9.27P Problem 9.28P: Determine the ratio a/b for which Ix=Iy for the isosceles triangle. Problem 9.29P: As a round log passes through a sawmill, two slabs are cut off, resulting in the cross section... Problem 9.30P Problem 9.31P: By numerical integration, compute the moments of inertia about the x- and y-axes for the region... Problem 9.32P: Use numerical integration to compute the moments of inertia about the x- and y-axes for the... Problem 9.33P: The plane region A is submerged in a fluid of weight density . The resultant force of the fluid... Problem 9.34P: Use integration to verify the formula given in Table 9.2 for Ixy of a half parabolic complement. Problem 9.35P: For the quarter circle in Table 9.2, verify the following formulas: (a) Ixy by integration; and (b)... Problem 9.36P: Determine the product of inertia with respect to the x- and y-axes for the quarter circular, thin... Problem 9.37P: The product of inertia of triangle (a) with respect to its centroid is Ixy=b2h2/72. What is Ixy for... Problem 9.38P Problem 9.39P: For the region shown, Ixy=320103mm4 and Iuv=0. Compute the distance d between the y- and v-axes.... Problem 9.40P Problem 9.41P: Calculate the product of inertia with respect to the x- and y-axes. Problem 9.42P Problem 9.43P Problem 9.44P: The figure shows the cross section of a standard L806010-mm structural steel, unequal angle section.... Problem 9.45P Problem 9.46P Problem 9.47P Problem 9.48P: Use numerical integration to compute the product of inertia of the region show with respect to the... Problem 9.49P: Determine the dimension b of the square cutout so that Ixy=0 for the region shown. Problem 9.50P: For the rectangular region, determine (a) the principal moments of inertia and the principal... Problem 9.51P Problem 9.52P Problem 9.53P Problem 9.54P Problem 9.55P Problem 9.56P: The u- and v-axes are the principal axes of the region shown. Given that Iu=7600in.4,Iv=5000in.4,... Problem 9.57P: The x- and y-axes are the principal axes for the region shown with Ix=6106mm4 and Iy=2106mm4. (a)... Problem 9.58P Problem 9.59P: The inertial properties of the region shown with respect to the x- and y-axes are Ix=Iy=16.023106mm4... Problem 9.60P: Determine Iu for the inverted T-section shown. Note that the section is symmetric about the y-axis. Problem 9.61P: Using Ix and Iu from Table 9.2, determine the moment of inertia of the circular sector about the... Problem 9.62P: Show that every axis passing through the centroid of the equilateral triangle is a principal axis. Problem 9.63P Problem 9.64P: The L806010-mm structural angle has the following cross-sectional properties:... Problem 9.65P: Compute the principal centroidal moments of inertia for the plane area. Problem 9.66P Problem 9.67P: Determine the principal axes and the principal moments of inertia for the plane region. Problem 9.68P: Compute the principal centroidal moments of inertia and the corresponding principal directions for... Problem 9.69P: Find the moments and the product of inertia of the rectangle about the u-v axes at the centroid C. Problem 9.70P: Determine the moments and product of inertia of the half-parabola about the u-v axes that pass... Problem 9.71P: Find the principal moments of inertia and the principal directions at the centroid C of the... Problem 9.72P: Determine the moments and product of inertia of the elliptical area with respect to the u-v axes.... Problem 9.73P Problem 9.74P Problem 9.75P: The u- and v-axes are the principal axes of the region shown. Given that Iu=8400in.4,Iv=5000in.4,... Problem 9.76P: The x- and y-axes are the principal axes for the region shown, with Ix=8106mm4 and Iy=2106mm4. (a)... Problem 9.77P Problem 9.78P: The L806010-mm structural angle has the following cross-sectional properties:... Problem 9.79RP Problem 9.80RP Problem 9.81RP: By integration, show that the product of inertia with respect to the x- and y-axes for the quarter... Problem 9.82RP: Compute Ix and Iy for the shaded region. Problem 9.83RP: Using integration, evaluate the moments of inertia about the x- and y-axes for the parallelogram. Problem 9.84RP: The inertial properties at point 0 for a plane region are Ix=200106mm4,Iy=300106mm4, and... Problem 9.85RP: Compute Ix and Iy for the shaded region. Problem 9.86RP: The flanged bolt coupling is fabricated by drilling 10 evenly spaced 0.5-in. diameter bolt holes in... Problem 9.87RP Problem 9.88RP: Compute Ix,Iy, and Ixy for the shaded region. Problem 9.89RP: Determine Ix and Ixy for the shaded region shown. Problem 9.90RP: Calculate Ix,Iy, and Ixy for the shaded region shown. Problem 9.91RP: For the shaded region shown, determine (a) Ix and Iy; and (b) Ix and Iy using the parallel axis... Problem 9.92RP: Use integration to find Ix,Iy, and Ixy for the shaded region shown. Problem 9.93RP: Determine the principal moments of inertia and the principal directions at the centroid of the... Problem 9.94RP: The properties of the unequal angle section are Ix=80.9in.4,Iy=38.8in.4, and Iu=21.3in.4. Determine... Problem 9.46P
An elastic, isotropic, homogeneous, circular cylinder of height L and radius R isvector , strain (epsilon ) and stress (σ) matrices.
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Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
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