The stress state within the lateral wall of a soda can is approximated as shown. p is the internal pressure, r is the radius of the can, t is the wall thickness. Express the stress state shown in a matrix, where the only two non-zero stress components are σxx and σyy, all other stress compoenents are zero. Express the equivalent stress σe associated with the stress state shown in terms of p, r, and t. The image features a square with a coordinate system inside, marked by the axes "x" and "y". The square represents a section of a material subjected to stress analysis, often seen in mechanical or civil engineering.**Diagram Details:**- **Center Square:** Contains axes labeled "x" and "y", indicating directions.- **Stress Directions:** - An upward arrow above the square is labeled $ \frac{pr}{2t} $. - A downward arrow below the square is labeled $ \frac{pr}{2t} $. - A rightward arrow on the right side of the square is labeled $ \frac{pr}{t} $. - A leftward arrow on the left side of the square is also labeled $ \frac{pr}{t} $.**Interpretation:**This diagram visually represents how pressure is distributed across the boundaries of the square section within a material. The variables $ p $, $ r $, and $ t $ are parameters that might represent pressure, a radial dimension, and thickness, respectively. Such diagrams help in understanding how materials will respond to external forces, crucial for ensuring structural integrity under load.

Answered: pr 수 pr 2t 섰 ↓ pr 2t 을

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 stress state within the lateral wall of a soda can is approximated as shown. p is the internal pressure, r is the radius of the can, t is the wall thickness. Express the stress state shown in a matrix, where the only two non-zero stress components are σ_xx and σ_yy, all other stress compoenents are zero. Express the equivalent stress σ_e associated with the stress state shown in terms of p, r, and t.

The image features a square with a coordinate system inside, marked by the axes "x" and "y". The square represents a section of a material subjected to stress analysis, often seen in mechanical or civil engineering.

**Diagram Details:**

- **Center Square:** Contains axes labeled "x" and "y", indicating directions.

- **Stress Directions:**
- An upward arrow above the square is labeled $ \frac{pr}{2t} $.
- A downward arrow below the square is labeled $ \frac{pr}{2t} $.
- A rightward arrow on the right side of the square is labeled $ \frac{pr}{t} $.
- A leftward arrow on the left side of the square is also labeled $ \frac{pr}{t} $.

**Interpretation:**

This diagram visually represents how pressure is distributed across the boundaries of the square section within a material. The variables $ p $, $ r $, and $ t $ are parameters that might represent pressure, a radial dimension, and thickness, respectively. Such diagrams help in understanding how materials will respond to external forces, crucial for ensuring structural integrity under load.

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given;

$i n t e r n a l p r e s s u r e = P t h i c k n e s s = t r a d i u s = r$

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