Applied Statics and Strength of Materials (6th Edition)
6th Edition
ISBN: 9780133840544
Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 8.6P
For the area of Problem 8.5 , calculate the exact moment of inertia and then calculate the percent error relative to the results obtained using the approximate method.
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Please show a detailed solution for the computation of moment of inertia.
Problem -05 Moment of InertiaDetermine by direct integration the moment of inertia of the shaded area(Fig -5) with respect to the y axis.
Use the given values in problem to answer the following:
Find the moment of inertia and radius of gyration of the section of this bar about an axis parallel to x-axis going through the center of gravity of the bar.
The bar is symmetrical about the axis parallel to y-axis and going through the center of gravity of the bar and about the axis parallel to z-axis and going through the center of gravity of the bar.
The dimensions of the section are:
l=51 mm, h=29 mm
The triangle: hT=15 mm, lT=18 mm
and the 2 circles: diameter=7.4 mm, hC=8 mm, dC=7 mm.
A is the origin of the referential axis.
Provide an organized table and explain all your steps to find the moment of inertia and radius of gyration about an axis parallel to x-axis and going through the center of gravity of the bar.
Does the radius of gyration make sense?
In the box below enter the y position of the center of gravity of the bar in mm with one decimal.
Chapter 8 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 8 - Calculate the moment of intertia with respect to...Ch. 8 - Calculate the moment of inertia of the triangular...Ch. 8 - A structural steel wide-flange section is...Ch. 8 - The concrete block shown has wall thicknesses of...Ch. 8 - A rectangle has a base of 6 in. and a height of 12...Ch. 8 - For the area of Problem 8.5 , calculate the exact...Ch. 8 - Check the tabulated moment of inertia for a 300610...Ch. 8 - For the cross section of Problem 8.3 , calculate...Ch. 8 - Calculate the moments of intertia with respect to...Ch. 8 - Calculate the moments of intertia with respect to...
Ch. 8 - The rectangular area shown has a square hole cut...Ch. 8 - For the built-up structural steel member shown,...Ch. 8 - Calculate the moments of inertia about both...Ch. 8 - Calculate the moment of inertia with respect to...Ch. 8 - For the two channels shown, calculated the spacing...Ch. 8 - Compute the radii of gyration about both...Ch. 8 - Two C1015.3 channels area welded together at their...Ch. 8 - Compute the radii of gyration with respect to the...Ch. 8 - Compute the radii of gyration with respect to the...Ch. 8 - Compute the radii of gyration with respect to the...Ch. 8 - Compute the radii of gyration with respect to the...Ch. 8 - Calculate the polar moment of inertia for a...Ch. 8 - Calculate the polar moment of inertia for a...Ch. 8 - For the areas (a) aid (b) of Problem 8.9 ,...Ch. 8 - For the following computer problems, any...Ch. 8 - For the following computer problems, any...Ch. 8 - For the following computer problems, any...Ch. 8 - For the cross section shown, calculate the moments...Ch. 8 - Calculate the moments of inertia of the area shown...Ch. 8 - For the cross-sectional areas shown, calculate the...Ch. 8 - For the cross-sectional areas shown, calculate the...Ch. 8 - Calculate the moments of intertia of the built-up...Ch. 8 - Calculate the moments of inertia about both...Ch. 8 - Calculate lx and ly of the built-up steel members...Ch. 8 - Calculate the least radius of gyration for the...Ch. 8 - A structural steel built-up section is fabricated...Ch. 8 - Calculate the polar moment of inertia for the...Ch. 8 - Determine the polar moment of inertia for the...Ch. 8 - Compute the radii of gyration with respect to the...Ch. 8 - Calculate the polar moment of inertia about the...Ch. 8 - The area of the welded member shown is composed of...
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- Gives some 1 Example with solution about the Maximum and Minimum Moments of Inertia Using Mohr's Circle.arrow_forward" POLAR MOMENT OF INERTIA " Please refer to the answer key (book from Engineering Mechanics by SInger) Please include the analyzation of figure so that i could undestand the steps and solution. Thankyou!arrow_forwardProblem 2 Consider a rigid body, whose moments of inertia matrix, calculated with respect to the center of mass and in B-RF coordinates, is: 10 -2 Ig = -2 4 -1 11 8 -1 Find the directions of the principal axes of inertia (i.e., find Rgp) and the principal moments of inertia matrix 19.arrow_forward
- Problem 3 Find the centroidal moment of inertia and radius of gyration of the given cross section below, then determine the moment of inertia and radius of gyration about the z-axis using the translation formulas.arrow_forwardFor the cross section in problem 1 (which is also shown below), you are asked to determine the moment of inertia about x axis or Ix. Show all the necessary steps.arrow_forwardarrow_forwardComplete the following sentence 1- The center of mass of a rigid body in the form of thin wire across y-direction is given by.. 2- The center of mass of a rigid body in the form of thin shell across x-direction is given by. . 3- The moment of inertia of a rigid body rotate about a fixed axis (z- axis ) is given by.. . 4- The rotational kinetic energy of a rigid body rotate about a fixed axis is given by. . 5- The torque about the axis of rotation is given by.... .....................arrow_forwardPlease help. This problem involves moment of inertia of cross-sections. There is only one right choice. Thank you.arrow_forwardMOMENT OF INERTIA Please help me find the correct solution for this problem. Thank you! Asap!arrow_forwardCompute the principal centroidal moments of inertia for the plane area.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_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_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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