3. When the point O is the origin of the coordinate axis (x-y axes) in Fig. 3-1, (1) I determine the centroid (location of the point C) of the given area. (2) with respect to the x' and y' axes (Iry). (Note that x'-y' axes pass through the centroid of the given area) determine moment of inertia with respect to the x' axis (I) and y' axis (I), and product of inertia (3) determine the principal axes about C and the values of the principal moments about C. 250 mm 1 ly = hb³ 12 I 30 mm 300 mm h 30 mm 1 30 mm 150 mm

3. When the point O is the origin of the coordinate axis (x-y axes) in Fig. 3-1, (1) I determine the centroid (location of the point C) of the given area. (2) with respect to the x' and y' axes (Iry). (Note that x'-y' axes pass through the centroid of the given area) determine moment of inertia with respect to the x' axis (I) and y' axis (I), and product of inertia (3) determine the principal axes about C and the values of the principal moments about C. 250 mm 1 ly = hb³ 12 I 30 mm 300 mm h 30 mm 1 30 mm 150 mm

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

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.78P: The L806010-mm structural angle has the following cross-sectional properties:...

See similar textbooks

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.
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.
Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.
Verify the centroidal z-coordinate of the pyramid shown in Table 8.3 by integration.
The 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.)
Determine Ix for the triangular region shown.
Find the centroid of the truncated parabolic complement by integration.
The 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).
Compute Ix and Iy for the region shown.
Figure (a) shows the cross section of a column that uses a structural shape known as W867 (wide-flange beam, nominally 8 in. deep, weighing 67 lb/ft). The American Institute of Steel Construction Structural Steel Handbook lists the following cross-sectional properties: A=19.7in.2,Ix=272in.4, and Iy=88.6in.4. Determine the dimensions of the rectangle in Fig. (b) that has the same Ix and Iy as a W867 section.
Compute the principal centroidal moments of inertia for the plane area.
The equation of the catenary shown is y = 100 cosh (x/100) where x and y are measured in feet (the catenary is the shape of a cable suspended between two points). Locate the y-coordinate 0f the centroid of the catenary by numerical integration using x=25ft.