In the plane element, the state of strain is given by:- \(\epsilon_x = -200 \times 10^{-6}\)- \(\epsilon_y = 100 \times 10^{-6}\)- \(\gamma_{xy} = 75 \times 10^{-6}\)We aim to determine the equivalent state of strain that represents:(a) The principal strains(b) The maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain in relation to the original element.**Diagram Explanation:**The diagram illustrates a deformed differential element in the xy-plane, with the following labels:- The vertical deformation is labeled \(\epsilon_y \, dy\).- A horizontal deformation is labeled \(\epsilon_x \, dx\).- Both shear deformations on the top and side are labeled \(\frac{\gamma_{xy}}{2}\).Axes are oriented with \(x\) horizontally and \(y\) vertically.This visual representation highlights the changes in the shape and orientation of the element due to the specified strains, assisting in understanding how the principal strains and shear strains alter the element.

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The state of strain in a plane element is ex = -200 x 10-6 , Ey = 100 × 10-6 , and Yxy = 75 x 10-6 , as shown below. Determine the equivalent state of strain which represents (a) the principal strains (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element. y Eydy Yxy 2 dy Yxy FExdx 2 dx

The state of strain in a plane element is ex = -200 x 10-6 , Ey = 100 × 10-6 , and Yxy = 75 x 10-6 , as shown below. Determine the equivalent state of strain which represents (a) the principal strains (b) the maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain with respect to the original element. y Eydy Yxy 2 dy Yxy FExdx 2 dx

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

In the plane element, the state of strain is given by:

- \(\epsilon_x = -200 \times 10^{-6}\)
- \(\epsilon_y = 100 \times 10^{-6}\)
- \(\gamma_{xy} = 75 \times 10^{-6}\)

We aim to determine the equivalent state of strain that represents:

(a) The principal strains

(b) The maximum in-plane shear strain and the associated average normal strain. Specify the orientation of the corresponding elements for these states of strain in relation to the original element.

**Diagram Explanation:**

The diagram illustrates a deformed differential element in the xy-plane, with the following labels:

- The vertical deformation is labeled \(\epsilon_y \, dy\).
- A horizontal deformation is labeled \(\epsilon_x \, dx\).
- Both shear deformations on the top and side are labeled \(\frac{\gamma_{xy}}{2}\).

Axes are oriented with \(x\) horizontally and \(y\) vertically.

This visual representation highlights the changes in the shape and orientation of the element due to the specified strains, assisting in understanding how the principal strains and shear strains alter the element.

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