The square deforms into the position shown by the dashed lines in. The dimensions are S=49 mm, S′=54 mm, Δx1=5 mm, and Δx2=9 mm. Side D'B' remains horizontal.A)Determine the shear strain at A relative to the x, y axes.B) Determine the shear strain at B relative to the x, y axes.C) Determine the shear strain at C relative to the x, y axes. The image depicts a deformed square, illustrating shear deformation. The original square, labeled as ABCD, transforms into a parallelogram with dashed lines indicating the deformation.Key Elements:1. **Original Shape (Square ABCD):** - Side AB is parallel to side DC and both have a length denoted as \( S \). - Side AD is parallel to side BC and also has a length of \( S \).2. **Deformation:** - The square tilts to the right, forming a parallelogram. - The angle \(\angle DAB\) increases slightly to 91.5°, indicating shear strain.3. **Displacement:** - Point B moves to \( B' \), introducing a horizontal shift \(\Delta x_1\). - Point C moves to \( C' \), with a horizontal shift of \(\Delta x_2\).4. **Measurements:** - Vertical displacement remains constant at \( S \) for points D and D', as well as A and C. - The horizontal displacement between initial and deformed positions is shown as \(\Delta x_1\) and \(\Delta x_2\). This diagram serves as a visual explanation for shear deformation, where the internal angle change and horizontal displacements show how forces might act on a material to distort its shape while retaining the same vertical dimension.

Answered: The square deforms into the position…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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The square deforms into the position shown by the dashed lines in. The dimensions are S=49 mm, S′=54 mm, Δx1=5 mm, and Δx2=9 mm. Side D'B' remains horizontal.

A)Determine the shear strain at A relative to the x, y axes.

B) Determine the shear strain at B relative to the x, y axes.

C) Determine the shear strain at C relative to the x, y axes.

The image depicts a deformed square, illustrating shear deformation. The original square, labeled as ABCD, transforms into a parallelogram with dashed lines indicating the deformation.

Key Elements:

1. **Original Shape (Square ABCD):**
- Side AB is parallel to side DC and both have a length denoted as \( S \).
- Side AD is parallel to side BC and also has a length of \( S \).

2. **Deformation:**
- The square tilts to the right, forming a parallelogram.
- The angle \(\angle DAB\) increases slightly to 91.5°, indicating shear strain.

3. **Displacement:**
- Point B moves to \( B' \), introducing a horizontal shift \(\Delta x_1\).
- Point C moves to \( C' \), with a horizontal shift of \(\Delta x_2\).

4. **Measurements:**
- Vertical displacement remains constant at \( S \) for points D and D', as well as A and C.
- The horizontal displacement between initial and deformed positions is shown as \(\Delta x_1\) and \(\Delta x_2\).

This diagram serves as a visual explanation for shear deformation, where the internal angle change and horizontal displacements show how forces might act on a material to distort its shape while retaining the same vertical dimension.

Expert Solution

Step 1: all given data, figures and determining parts are written here.

Given data- S=49 mm, S′=54 mm, Δx1=5 mm, and Δx2=9 mm

Determine-

A) the shear strain at A relative to the x, y axes.

B) the shear strain at B relative to the x, y axes.

C) the shear strain at C relative to the x, y axes.

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