Part B - Normal strain, cross-sectional area, load, and Poisson's ratio Four axially loaded members are shown below. All members have the same value for E (Young's modulus). Rank the members from largest to smallest absolute value of the average normal strain perpendicular to the applied load at cross section a-a shown in the figure.

Elements Of Electromagnetics
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**Part B - Normal Strain, Cross-Sectional Area, Load, and Poisson’s Ratio**

Four axially loaded members are shown below. All members have the same value for \( E \) (Young’s modulus).

**Task:** Rank the members from largest to smallest absolute value of the average normal strain perpendicular to the applied load at cross section a-a shown in the figure.

*Note: Refer to the accompanying diagram for a visual representation of the axially loaded members to complete the ranking task.*
Transcribed Image Text:**Part B - Normal Strain, Cross-Sectional Area, Load, and Poisson’s Ratio** Four axially loaded members are shown below. All members have the same value for \( E \) (Young’s modulus). **Task:** Rank the members from largest to smallest absolute value of the average normal strain perpendicular to the applied load at cross section a-a shown in the figure. *Note: Refer to the accompanying diagram for a visual representation of the axially loaded members to complete the ranking task.*
The diagram illustrates four horizontal cylinders subjected to axial forces. The cylinders vary in area and are labeled with their respective Poisson's ratios.

1. **First Cylinder**:
   - **Forces**: \( \frac{P}{2} \) applied on both sides.
   - **Area**: \( \frac{A}{2} \)
   - **Poisson's Ratio**: \( \frac{\nu}{3} \)

2. **Second Cylinder**:
   - **Forces**: \( P \) applied on both sides.
   - **Area**: \( A \)
   - **Poisson's Ratio**: \( \nu \)

3. **Third Cylinder**:
   - **Forces**: \( 2P \) applied on both sides.
   - **Area**: \( 2A \)
   - **Poisson's Ratio**: \( 2\nu \)

4. **Fourth Cylinder**:
   - **Forces**: \( 3P \) applied on both sides.
   - **Area**: \( 3A \)
   - **Poisson's Ratio**: \( \frac{\nu}{2} \)

Below the cylinders, there is a row labeled from "Largest" to "Smallest", pointing towards a possible task or activity, possibly organizing or comparing these properties in order of magnitude.
Transcribed Image Text:The diagram illustrates four horizontal cylinders subjected to axial forces. The cylinders vary in area and are labeled with their respective Poisson's ratios. 1. **First Cylinder**: - **Forces**: \( \frac{P}{2} \) applied on both sides. - **Area**: \( \frac{A}{2} \) - **Poisson's Ratio**: \( \frac{\nu}{3} \) 2. **Second Cylinder**: - **Forces**: \( P \) applied on both sides. - **Area**: \( A \) - **Poisson's Ratio**: \( \nu \) 3. **Third Cylinder**: - **Forces**: \( 2P \) applied on both sides. - **Area**: \( 2A \) - **Poisson's Ratio**: \( 2\nu \) 4. **Fourth Cylinder**: - **Forces**: \( 3P \) applied on both sides. - **Area**: \( 3A \) - **Poisson's Ratio**: \( \frac{\nu}{2} \) Below the cylinders, there is a row labeled from "Largest" to "Smallest", pointing towards a possible task or activity, possibly organizing or comparing these properties in order of magnitude.
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