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A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given point, an element with its sides parallel to x and y axes is found to have a shear strain of 1x10, while an element at 45° to the first has a shear strain of 4x10 (Fig. 2). a) Calçulate the maximum shear strain at this point. b) If the shear modulus 100 MPa, find the difference between the two principal stresses. y y =4x104 ソ=104 \ 45 °

A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given point, an element with its sides parallel to x and y axes is found to have a shear strain of 1x10, while an element at 45° to the first has a shear strain of 4x10 (Fig. 2). a) Calçulate the maximum shear strain at this point. b) If the shear modulus 100 MPa, find the difference between the two principal stresses. y y =4x104 ソ=104 \ 45 °

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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**2. Analysis of Shear Strain in a Two-Dimensional Stress System** A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given point, an element with its sides parallel to the x and y axes is found to have a shear strain of \(1 \times 10^{-4}\), while an element at 45° to the first has a shear strain of \(4 \times 10^{-4}\) (Fig. 2). **Questions:** a) Calculate the maximum shear strain at this point. b) If the shear modulus is \(100 \, \text{MPa}\), find the difference between the two principal stresses. **Explanation of Figures:** - The first graph illustrates a rectangular element aligned with the x and y axes, showing a shear strain \(\gamma = 10^{-4}\). - The second graph depicts a rhombus-shaped element oriented at a 45° angle to the original element, showing an increased shear strain \(\gamma ' = 4 \times 10^{-4}\). The diagrams illustrate the changes in shear strain experienced by the material when oriented differently relative to the primary axis. This visual representation is essential for understanding stress transformations in materials subject to multidirectional forces.
Transcribed Image Text:**2. Analysis of Shear Strain in a Two-Dimensional Stress System** A sheet of material is subjected to a two-dimensional stress system in the x-y plane. At a given point, an element with its sides parallel to the x and y axes is found to have a shear strain of \(1 \times 10^{-4}\), while an element at 45° to the first has a shear strain of \(4 \times 10^{-4}\) (Fig. 2). **Questions:** a) Calculate the maximum shear strain at this point. b) If the shear modulus is \(100 \, \text{MPa}\), find the difference between the two principal stresses. **Explanation of Figures:** - The first graph illustrates a rectangular element aligned with the x and y axes, showing a shear strain \(\gamma = 10^{-4}\). - The second graph depicts a rhombus-shaped element oriented at a 45° angle to the original element, showing an increased shear strain \(\gamma ' = 4 \times 10^{-4}\). The diagrams illustrate the changes in shear strain experienced by the material when oriented differently relative to the primary axis. This visual representation is essential for understanding stress transformations in materials subject to multidirectional forces.
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