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A thin rectangular plate is uniformly, deformed, as shown. Determine the shear strain Yxy at P. Assume a = 20 in., b = 27 in., c = 0.13 in, and d = 0.14 in. R S

A thin rectangular plate is uniformly, deformed, as shown. Determine the shear strain Yxy at P. Assume a = 20 in., b = 27 in., c = 0.13 in, and d = 0.14 in. R S

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**Shear Strain Calculation in a Uniformly Deformed Rectangular Plate** **Problem Statement:** A thin rectangular plate is uniformly deformed, as shown in the diagram. Determine the shear strain \( \gamma_{xy} \) at point P. Assume: - \( a = 20 \text{ in.} \) - \( b = 27 \text{ in.} \) - \( c = 0.13 \text{ in.} \) - \( d = 0.14 \text{ in.} \) **Diagram Description:** The diagram illustrates a rectangular plate deformed into a parallelogram: - The undistorted plate is represented by a light-colored rectangle with vertices labeled P, Q, R, and S. - The deformed plate is shown as a darker parallelogram with dashed edges parallel to the original rectangle. - The dimensions of the plate are as follows: - \( a \) is the horizontal distance from P to Q, measured along the x-axis (20 inches). - \( b \) is the vertical distance from P to R, measured along the y-axis (27 inches). - \( c \) is the horizontal displacement at the top-right corner S from its original position (0.13 inches). - \( d \) is the vertical displacement at point R from its original position (0.14 inches). - Axes: - The x-axis is horizontal. - The y-axis is vertical. **Calculated Solution:** \[ \gamma_{xy} = 11.7 \; \mu\text{rad} \] This problem demonstrates the calculation of shear strain for a uniformly deformed plate by using specified displacements to establish strain at a given point. The final result provides the shear strain at point P in micro-radians (\( \mu\text{rad} \)).
Transcribed Image Text:**Shear Strain Calculation in a Uniformly Deformed Rectangular Plate** **Problem Statement:** A thin rectangular plate is uniformly deformed, as shown in the diagram. Determine the shear strain \( \gamma_{xy} \) at point P. Assume: - \( a = 20 \text{ in.} \) - \( b = 27 \text{ in.} \) - \( c = 0.13 \text{ in.} \) - \( d = 0.14 \text{ in.} \) **Diagram Description:** The diagram illustrates a rectangular plate deformed into a parallelogram: - The undistorted plate is represented by a light-colored rectangle with vertices labeled P, Q, R, and S. - The deformed plate is shown as a darker parallelogram with dashed edges parallel to the original rectangle. - The dimensions of the plate are as follows: - \( a \) is the horizontal distance from P to Q, measured along the x-axis (20 inches). - \( b \) is the vertical distance from P to R, measured along the y-axis (27 inches). - \( c \) is the horizontal displacement at the top-right corner S from its original position (0.13 inches). - \( d \) is the vertical displacement at point R from its original position (0.14 inches). - Axes: - The x-axis is horizontal. - The y-axis is vertical. **Calculated Solution:** \[ \gamma_{xy} = 11.7 \; \mu\text{rad} \] This problem demonstrates the calculation of shear strain for a uniformly deformed plate by using specified displacements to establish strain at a given point. The final result provides the shear strain at point P in micro-radians (\( \mu\text{rad} \)).
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