The state of stress at a point with respect to a \( O x_1 x_2 x_3 \) coordinate system is given by:\[[\sigma_{ij}] = \begin{bmatrix}1 & 3 & 2 \\3 & 1 & 0 \\2 & 0 & -2\end{bmatrix}\]What are the stress components with respect to axes \( O x_1' x_2' x_3' \), which are obtained from the first by a \(45^\circ\) rotation (positive counterclockwise) about the \( x_3 \) axis?

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The state of stress at a point with respect to a Ox₁x₂x3 coordinate system is given by 10.1= 3 2 31 0 20 -21 What are the stress components with respect to axes Oxxx, which are obtained from the first by a 45° rotation (positive counterclockwise) about the x3 axis

The state of stress at a point with respect to a Ox₁x₂x3 coordinate system is given by 10.1= 3 2 31 0 20 -21 What are the stress components with respect to axes Oxxx, which are obtained from the first by a 45° rotation (positive counterclockwise) about the x3 axis

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Solid Mechanics

Engineering mechanics is a branch of science that deals with forces causing bulk motion in bodies and the effect that these forces cause on the bodies. Engineering mechanics does not deal with the internal changes that occur on account of these external forces. The internal effects in a body or a material under the action of external forces are studied in a new branch of science called solid mechanics, the strength of materials, or the mechanical behavior of engineering materials.

Question

The state of stress at a point with respect to a \( O x_1 x_2 x_3 \) coordinate system is given by:

\[
[\sigma_{ij}] =
\begin{bmatrix}
1 & 3 & 2 \\
3 & 1 & 0 \\
2 & 0 & -2
\end{bmatrix}
\]

What are the stress components with respect to axes \( O x_1' x_2' x_3' \), which are obtained from the first by a \(45^\circ\) rotation (positive counterclockwise) about the \( x_3 \) axis?

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