# The x - and y -axes are the principal axes for the region shown, with I x = 8 × 10 6 mm 4 and I y = 2 × 10 6 mm 4 . (a) Calculate the angle θ for which I u v is maximum. (b) Determine I u , I v , and I u v for the angle θ found in part (a).

### International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
ISBN: 9781305501607

### International Edition---engineerin...

4th Edition
Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
ISBN: 9781305501607

#### Solutions

Chapter
Section
Chapter 9, Problem 9.76P
Textbook Problem

## The x- and y-axes are the principal axes for the region shown, with I x = 8 × 10 6   mm 4 and I y = 2 × 10 6   mm 4 . (a) Calculate the angle θ for which I u v is maximum. (b) Determine I u , I v , and I u v for the angle θ found in part (a).

Expert Solution
To determine

(a)

The angle θ for which Iuv is maximum.

### Explanation of Solution

Given information:

The region:

The x- and y-axes are the principal axes. And,

Ix=8×106 mm4Iy=2×106 mm4

Calculations:

Using Mohr's circle analysis:

The figure shows the Mohr's circle. Here the horizontal axis represents the moment of inertia (M.I) and the vertical axis represents product of inertia (P.I).

Take point x with coordinates (Ix,I xy) and point y with coordinates (Iy,I xy).Join the points x and y, and draw the circle with the diameter of length xy

Expert Solution
To determine

(b)

To find:

Iu, Iv and Iuv for the angle θ found in part (a).

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