International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 9, Problem 9.3P
The moments of inertia of the plane region about the x- and u-axes are
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Determine the shaded area and its moment of inertia with respect to the centroidal axis parallel to AA, knowing that d1 = 25 mm and d2 = 10 mm and that its moments of inertia with respect to AA' and BB' are 2.2 × 106 mm4 and 4x 106 mm4, respectively.
Determine the shaded area and its moment of inertia with respect to the centroidal axis parallel to AA′, knowing that its moments of inertia with respect to AA′ and BB′ are respectively 2.2 × 106 mm4 and 4 × 106 mm4, and that d1 = 25 mm and d2 = 10 mm.
It is known that for a given area Iy = 48 x 106 mm4 and Ixy = -20 x 106 mm4, where the x and y axes are rectangular centroidal axes. If the axis corresponding to the maximum product of inertia is obtained by rotating the x axis 67.5° counterclockwise about C , use Mohr’s circle to determine (a) the moment of inertia Ix of the area, (b) the principal centroidal moments of inertia.
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...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- The 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_forwardKnowing that the shaded area is equal to 6000 mm2 and that its moment of inertia with respect to AA′ is 18 × 106 mm4, determine its moment of inertia with respect to BB′ for d1 = 50 mm and d2 =10 mm.arrow_forwardTwo L4 x 4 x 1/2-in angles are welded to a steel plate as shown. Determine the moments of inertia of the combined section with respect to centroidal axes respectively parallel and perpendicular to the plate.arrow_forward
- For the entire section shown, the moments of inertia with respect to the centroidal x and y axes at point C are Ix = 0.162(106) mm4 and Iy = 0.454(106) mm4, respectively. a. Determine the product of inertia with respect to the centroid at C, in mm4. b. Use a Mohr's Circle to determine the orientation (in degrees) of the principal axes of the section about the centroid C. c. Use the same Mohr's Circle to determine the values of the principal moments of inertia about the centroid C, in mm4.arrow_forwardB-Determine the moment of inertia of the shaded area of the figure below about y axis only. Fig1 Barrow_forwardKnowing that the shaded area is equal to 6000 mm2 and that its moment of inertia with respect to AA, is 18 × 106 mm4, , determine its moment of inertia with respect to BB' for d1=50 mm and d2 = 10mm.arrow_forward
- A channel and a plate are welded together as shown to form a section that is symmetrical with respect to the y axis. Determine the moments of inertia of the combined section with respect to its centroidal x and y axes.arrow_forwarddetermine the centroidal polar moment of inertia of a rectangle 100mm wide by 200 mm higharrow_forwardThe shaded area shown. is bounded by the line y=x m and the curve y2=1.2x m2, where x is in m. Suppose that a = 1.2 m. Determine the moment of inertia for the shaded area about the y axis.arrow_forward
- The shaded area shown is bounded by y axis, line y = 2.42 m and the curve y(x)=(1/(4.4))x3 m, where x is in m. Suppose that a = 2.2 m and h = 2.42 m . Determine the moment of inertia for the shaded area about the y axis. Iy = ?arrow_forwardFor the surface shown in the figure below, determine:a) The xc and yc coordinates of its centroid;b)The moments of inertia and product of inertia in relation to the centroidal axes x' and y' (axes parallel to x and y , which pass through the centroid);c)Using Mohr's circle, the new moments and product of inertia obtained by rotating these centroidal axes by 35° counterclockwise.arrow_forwardThe coordinates of the centroid of the line are = 332 and = 102. Use the first Pappus Guldinus theorem to determine the area, in m2, of the surface of revolution obtained by revolving the line about the x-axis. The coordinates of the centroid of the area between the x-axis and the line in Question 9 are = 357 and = 74.1. Use the second Pappus Guldinus theorem to determine the volume obtained, in m3, by revolving the area about the x-axis.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L
International Edition---engineering Mechanics: St...
Mechanical Engineering
ISBN:9781305501607
Author:Andrew Pytel And Jaan Kiusalaas
Publisher:CENGAGE L
moment of inertia; Author: NCERT OFFICIAL;https://www.youtube.com/watch?v=A4KhJYrt4-s;License: Standard YouTube License, CC-BY