Concept explainers
Compute the principal centroidal moments of inertia for the plane area.
Compute the principal centroidal moments of inertia for the plane area.
Answer to Problem 9.65P
The principal centroidal moments of inertia:
Explanation of Solution
Given information:
The plane area shown in figure P9.65.
Calculations:
Conclusion:
The principal centroidal moments of inertia for the plane area shown in figure are:
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Chapter 9 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
- The 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_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_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
- Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.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 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_forward
- For the region shown, Ixy=320103mm4 and Iuv=0. Compute the distance d between the y- and v-axes. (Note: The result is independent of x. )arrow_forwardUsing Ix and Iu from Table 9.2, determine the moment of inertia of the circular sector about the OB-axis. Check your result for =45 with that given for a quarter circle in Table 9.2.arrow_forwardDetermine Iu for the inverted T-section shown. Note that the section is symmetric about the y-axis.arrow_forward
- Find the centroid of the truncated parabolic complement by integration.arrow_forwardUse numerical integration to find the centroid of the volume generated by revolving the area shown about the x-axis.arrow_forwardUsing the method of composite areas, find the centroid of the truncated parabolic complement.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L