### Stress Analysis in Materials#### Figure (e)This diagram illustrates the multi-axial stress components acting on a material denoted by "E". The following stress components are present:- \( \sigma_y = 30 \) MPa: This is the normal stress acting in the vertical direction.- \( \sigma_x = 120 \) MPa: This is the normal stress acting in the horizontal direction.- \( \tau_{xy} = 85 \) MPa: This is the shear stress acting on the material.The diagram shows these stresses as follows:- The vertical arrow pointing upwards represents the normal stress \( \sigma_y \).- The horizontal arrow pointing leftwards represents the normal stress \( \sigma_x \).- The arrow tangential to the vertical face of the block represents the shear stress \( \tau_{xy} \).#### Figure (f)This diagram shows a different set of multi-axial stress components acting on the same material "E". The stress components are:- \( \sigma_y = 80 \) MPa: This is the normal stress acting in the vertical direction.- \( \sigma_x = 30 \) MPa: This is the normal stress acting in the horizontal direction.- \( \tau_{xy} = 15 \) MPa: This is the shear stress acting on the material.The diagram shows these stresses as follows:- The vertical arrow pointing downwards represents the normal stress \( \sigma_y \).- The horizontal arrow pointing leftwards represents the normal stress \( \sigma_x \).- The arrow tangential to the vertical face of the block represents the shear stress \( \tau_{xy} \).These diagrams are crucial in understanding how different stress components interact and influence the behavior of a material under various load conditions. For each of the elements shown below, draw Mohr’s circle and determine the principal stresses (\(\sigma_1, \sigma_2, \sigma_3\)). In addition, determine the maximum shear stress (\(\tau_{max}\)).

GivenPart eσx=-120MPaσy=30MPaτxy=85Mpa part fσx=30MPaσy=-80MPaτxy=15Mpa

Answered: (e) E = бу 30 MPa Txy 85 MPa Ox 120 MPa…

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(e) E = бу 30 MPa Txy 85 MPa Ox 120 MPa = =

Elements Of Electromagnetics

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ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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### Stress Analysis in Materials

#### Figure (e)

This diagram illustrates the multi-axial stress components acting on a material denoted by "E". The following stress components are present:

- \( \sigma_y = 30 \) MPa: This is the normal stress acting in the vertical direction.
- \( \sigma_x = 120 \) MPa: This is the normal stress acting in the horizontal direction.
- \( \tau_{xy} = 85 \) MPa: This is the shear stress acting on the material.

The diagram shows these stresses as follows:
- The vertical arrow pointing upwards represents the normal stress \( \sigma_y \).
- The horizontal arrow pointing leftwards represents the normal stress \( \sigma_x \).
- The arrow tangential to the vertical face of the block represents the shear stress \( \tau_{xy} \).

#### Figure (f)

This diagram shows a different set of multi-axial stress components acting on the same material "E". The stress components are:

- \( \sigma_y = 80 \) MPa: This is the normal stress acting in the vertical direction.
- \( \sigma_x = 30 \) MPa: This is the normal stress acting in the horizontal direction.
- \( \tau_{xy} = 15 \) MPa: This is the shear stress acting on the material.

The diagram shows these stresses as follows:
- The vertical arrow pointing downwards represents the normal stress \( \sigma_y \).
- The horizontal arrow pointing leftwards represents the normal stress \( \sigma_x \).
- The arrow tangential to the vertical face of the block represents the shear stress \( \tau_{xy} \).

These diagrams are crucial in understanding how different stress components interact and influence the behavior of a material under various load conditions.

For each of the elements shown below, draw Mohr’s circle and determine the principal stresses (\(\sigma_1, \sigma_2, \sigma_3\)). In addition, determine the maximum shear stress (\(\tau_{max}\)).

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