Finding Shear Strain: Step-by-Step Guide

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SUMMARY

The discussion focuses on calculating shear strain using the formula \( S = \frac{F}{A} \frac{h}{x} \) and highlights a common error in applying shear stress. The user incorrectly assumes that applying a force to two sides doubles the shear stress, leading to discrepancies in their calculations. The correct interpretation of shear stress and strain is crucial for accurate results, particularly in materials science and engineering applications.

PREREQUISITES
  • Understanding of shear strain and shear stress concepts
  • Familiarity with the formula \( S = \frac{F}{A} \frac{h}{x} \)
  • Basic knowledge of material properties and mechanics
  • Ability to perform unit conversions in scientific calculations
NEXT STEPS
  • Review the principles of shear stress and strain in materials science
  • Study the derivation and application of the shear strain formula
  • Learn about the effects of force application on material behavior
  • Explore common mistakes in mechanical calculations and how to avoid them
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Students in engineering and materials science, professionals involved in mechanical design, and anyone interested in understanding the principles of shear strain and stress in practical applications.

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Homework Statement
A square steel plate is 10.0 cm on a side and 0.500 cm thick.
Find the shear strain that results if a force of magnitude ##9.0\times10^5N## is applied to each of the four sides, parallel to the side. Plate is in equilibrium.
Find the displacement x in centimeters.
Relevant Equations
Shear stress ##=\frac FA##, shear strain ##=\frac xh##, ##S_\text{steel}=7.5\times10^{10}##
$$S=\frac FA\frac hx\Leftrightarrow\frac{F}{SA}=\frac xh=\text{shear strain}\\
\frac xh=\frac{9.0\times10^5}{10.0\times0.500\times10^{-4}\times7.5\times10^{10}}=1.2\times10^{-3}\\
x=1.2\times10^{-3}\times0.500=6.0\times10^{-4}\,cm$$
I'm doing something wrong, any help?
 
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Both my answers are off by a factor of 2. Applying a force to two sides is equivalent to ##\text{Sheer stress}=2\frac FA##? I think that I have been mislead by this:
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