find shear force x’y’ and derívate the equation for tau x’y’

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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find shear force x’y’ and derívate the equation for tau x’y’
### Polar Coordinate System Diagram

This diagram represents a polar coordinate system, featuring several key angle markers:

- **0, 360 degrees**: Positioned on the positive x-axis.
- **90 degrees**: Located on the positive y-axis.
- **180 degrees**: Found on the negative x-axis.
- **270 degrees**: Situated on the negative y-axis.

The quadrants are labeled:
- **A**
- **S**
- **T**
- **C**

These might correspond to standard trigonometric functions or regions, such as "All, Sine, Tangent, Cosine," indicating where these functions are positive.

### Equation

The equation written is:

\[ T_x y' = -\frac{(\sigma_{xx} - \sigma_{yy})\sin 2\theta + \tau_{xy}\cos 2\theta}{2} \]

This represents a mathematical expression that might relate to stress analysis in materials, involving trigonometric functions to rotate or transform stresses into another coordinate system.
Transcribed Image Text:### Polar Coordinate System Diagram This diagram represents a polar coordinate system, featuring several key angle markers: - **0, 360 degrees**: Positioned on the positive x-axis. - **90 degrees**: Located on the positive y-axis. - **180 degrees**: Found on the negative x-axis. - **270 degrees**: Situated on the negative y-axis. The quadrants are labeled: - **A** - **S** - **T** - **C** These might correspond to standard trigonometric functions or regions, such as "All, Sine, Tangent, Cosine," indicating where these functions are positive. ### Equation The equation written is: \[ T_x y' = -\frac{(\sigma_{xx} - \sigma_{yy})\sin 2\theta + \tau_{xy}\cos 2\theta}{2} \] This represents a mathematical expression that might relate to stress analysis in materials, involving trigonometric functions to rotate or transform stresses into another coordinate system.
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