Explanation Given information: The plane region: Calculations: Outer rectangle: A 1 = 120 ( 140 ) = 16800 m m 2 x 1 ¯ = 60 m m y 1 ¯ = 60 m m Inner rectangle: A 2 = − 60 ( 80 ) = − 4800 m m 2 x 2 ¯ = 70 m m y 2 ¯ = 80 m m ∴ T h e c e n t r o i d o f t h e p l a n e r e g i o n : A = ∑ A i = 16800 − 4800 = 12000 m m 2 x ¯ = ∑ A i x i ¯ A = 16800 ( 60 ) − 4800 ( 70 ) 12000 = 56.0 m m y ¯ = ∑ A i y i ¯ A = 16800 ( 70 ) − 4800 ( 80 ) 12000 = 66

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN: 9781305501607

Author: Andrew Pytel And Jaan Kiusalaas

Publisher: CENGAGE L

See similar textbooks

Concept explainers

The Space Lattice and Unit Cells

Every matter consists of atoms, molecules, and ions. If these atoms, molecules, and ions (micro-particles) are represented in a three-dimensional space-occupying certain specific points in space, then these arrangements are termed as space lattices and t…

Question

Chapter 9, Problem 9.40P

To determine

I¯xy for the plane region.

Expert Solution & Answer

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. 9.19P Ch. 9 - Calculate Ix for the shaded region, knowing that...Ch. 9 - Compute Iy for the region shown, given that...Ch. 9 - Prob. 9.22P Ch. 9 - Prob. 9.23P Ch. 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. 9.27P Ch. 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. 9.30P Ch. 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 ï¬‚uid 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. 9.38P Ch. 9 - For the region shown, Ixy=320103mm4 and Iuv=0....Ch. 9 - Prob. 9.40P Ch. 9 - Calculate the product of inertia with respect to...Ch. 9 - Prob. 9.42P Ch. 9 - Prob. 9.43P Ch. 9 - The figure shows the cross section of a standard...Ch. 9 - Prob. 9.45P Ch. 9 - Prob. 9.46P Ch. 9 - Prob. 9.47P Ch. 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. 9.51P Ch. 9 - Prob. 9.52P Ch. 9 - Prob. 9.53P Ch. 9 - Prob. 9.54P Ch. 9 - Prob. 9.55P Ch. 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. 9.58P Ch. 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. 9.63P Ch. 9 - The L806010-mm structural angle has the following...Ch. 9 - Compute the principal centroidal moments of...Ch. 9 - Prob. 9.66P Ch. 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. 9.73P Ch. 9 - Prob. 9.74P Ch. 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. 9.77P Ch. 9 - The L806010-mm structural angle has the following...Ch. 9 - Prob. 9.79RP Ch. 9 - Prob. 9.80RP Ch. 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. 9.87RP Ch. 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.

I ¯ x y for the plane region.

Solution Summary: The author calculates the plane region using a stackrel 'I_xy'.

Concept explainers

I¯xy for the plane region.

Chapter 9 Solutions