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Ch 11: Equilibrium & Elasticity
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 11: Equilibrium & ElasticityProblem 37
Chapter 11, Problem 37

A square steel plate is 10.0 cm on a side and 0.500 cm thick. (a) Find the shear strain that results if a force of magnitude 9.0×105 N is applied to each of the four sides, parallel to the side. (b) Find the displacement x (in centimeters).

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1
Understand the problem: We need to find the shear strain and the displacement of a square steel plate when a force is applied parallel to its sides.
Recall the formula for shear strain (γ), which is the ratio of the displacement (x) to the original length (L): γ = x / L.
Use the formula for shear stress (τ), which is the force (F) applied divided by the area (A) it is applied to: τ = F / A. Here, A is the area of one side of the square plate.
The shear modulus (G) relates shear stress and shear strain: τ = G * γ. Rearrange this to find the shear strain: γ = τ / G.
To find the displacement (x), use the relationship γ = x / L, where L is the side length of the plate. Rearrange to find x: x = γ * L.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Shear Stress

Shear stress is the force per unit area acting parallel to the surface of a material. It is calculated by dividing the applied force by the area over which the force is distributed. In this problem, the shear stress is crucial for determining the shear strain, as it directly influences how the material deforms under the applied force.
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Shear Strain

Shear strain is a measure of how much a material deforms in response to shear stress. It is defined as the displacement of a layer of the material divided by its original length. Understanding shear strain is essential for calculating the deformation of the steel plate when subjected to the given force, as it quantifies the angular distortion experienced by the material.

Shear Modulus

The shear modulus, also known as the modulus of rigidity, is a material property that describes its response to shear stress. It is the ratio of shear stress to shear strain and provides insight into the material's stiffness. For this problem, knowing the shear modulus of steel allows us to relate the applied force to the resulting shear strain and displacement, enabling the calculation of the plate's deformation.
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Example 1
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