a) Using the expressions for the linear strain tensor, compute the value of the shear strain €12- b) From €12, calculate the engineering shear strain 7/12- c) Compute the average engineering shear strain 12 using the definition of engineer- ing shear strain and compare it with the 12 calculated in (b).

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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The problem involves a rectangular piece of jello subjected to simple shear, as illustrated in the accompanying diagram (Figure 2).

---

**Task:**

(a) Using the expressions for the linear strain tensor, compute the value of the shear strain \( \varepsilon_{12} \).

(b) From \( \varepsilon_{12} \), calculate the engineering shear strain \( \gamma_{12} \).

(c) Compute the average engineering shear strain \( \bar{\gamma}_{12} \) using the definition of engineering shear strain and compare it with the \( \gamma_{12} \) calculated in (b).

---

**Diagram Explanation (Figure 2):**

- The diagram shows a rectangular piece of jello being sheared.
- The rectangle has dimensions of 150 mm in length along the \( X_2 \) axis.
- The piece is 200 mm tall along the \( X_1 \) axis.
- The top and bottom of the rectangle are displaced by 3 mm to the right.
- Points \( A \) and \( B \) show original and sheared positions.

Figure 2 visually demonstrates the deformation experienced by the jello, emphasizing the effects of shear displacement.
Transcribed Image Text:The problem involves a rectangular piece of jello subjected to simple shear, as illustrated in the accompanying diagram (Figure 2). --- **Task:** (a) Using the expressions for the linear strain tensor, compute the value of the shear strain \( \varepsilon_{12} \). (b) From \( \varepsilon_{12} \), calculate the engineering shear strain \( \gamma_{12} \). (c) Compute the average engineering shear strain \( \bar{\gamma}_{12} \) using the definition of engineering shear strain and compare it with the \( \gamma_{12} \) calculated in (b). --- **Diagram Explanation (Figure 2):** - The diagram shows a rectangular piece of jello being sheared. - The rectangle has dimensions of 150 mm in length along the \( X_2 \) axis. - The piece is 200 mm tall along the \( X_1 \) axis. - The top and bottom of the rectangle are displaced by 3 mm to the right. - Points \( A \) and \( B \) show original and sheared positions. Figure 2 visually demonstrates the deformation experienced by the jello, emphasizing the effects of shear displacement.
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