---## Plane Stress AnalysisThe state of plane stress at a point can be described by a known tensile stress σx = 80 MPa, an unknown tensile stress σy, and an unknown shear stress τxy, as indicated in the figure. At this point, the maximum shear stress τmax = 80 MPa, and one of the two principal stresses is ±25 MPa. Determine the two unknown stresses (MPa) σy and τxy respectively.### Description of the Figure:A diagram is presented showing a square element subjected to stresses. The element is oriented with its sides parallel to the x and y axes. The following stresses are applied:- Tensile stress σx acts horizontally to the right along the positive x-axis.- Tensile stress σy acts vertically upwards along the positive y-axis.- Shear stress τxy acts in the plane of the element, with both positive and negative directions indicated.### Answer Choices:- a. 100, 78- b. None- c. 178, 130- d. 130, 76- e. 129, 73### Analysis:To solve for the unknown stresses σy and τxy, you can use the derived principal stress conditions and shear stress equations for plane stress conditions:- Maximum shear stress condition equation- Principal stress condition equation### Note:The solution involves solving a system of equations based on the provided conditions and utilizing appropriate mechanical stress transformation equations.---

The state of plane stress at a point can be described by a known tensile stress ox= 80 MPa, an unknown tensile stress ay, and unknown shear stresS Txy, as indicated in the figure. At this point the maximum shear stress tmax=80MPA, and one of the two principal stresses is+25MPA. Solve 9-10.Determine the two unknown stresses (MPa) ay, andtxy respectively. Try a. 100, 78 O b. None O. 178, 130 O d. 130, 76 O e. 129, 73

The state of plane stress at a point can be described by a known tensile stress ox= 80 MPa, an unknown tensile stress ay, and unknown shear stresS Txy, as indicated in the figure. At this point the maximum shear stress tmax=80MPA, and one of the two principal stresses is+25MPA. Solve 9-10.Determine the two unknown stresses (MPa) ay, andtxy respectively. Try a. 100, 78 O b. None O. 178, 130 O d. 130, 76 O e. 129, 73

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Stress transformation

The term stress indicates the measure of internal forces that develop due to an external force's application on an object. When a specific external force is applied to an object, internal stress generates in the material. The value of stress can obtain by taking the ratio of the externally applied force and cross-sectional area of the object. There are different types of stress depending on the type of external force.

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## Plane Stress Analysis

The state of plane stress at a point can be described by a known tensile stress σx = 80 MPa, an unknown tensile stress σy, and an unknown shear stress τxy, as indicated in the figure. At this point, the maximum shear stress τmax = 80 MPa, and one of the two principal stresses is ±25 MPa. Determine the two unknown stresses (MPa) σy and τxy respectively.

### Description of the Figure:

A diagram is presented showing a square element subjected to stresses. The element is oriented with its sides parallel to the x and y axes. The following stresses are applied:

- Tensile stress σx acts horizontally to the right along the positive x-axis.
- Tensile stress σy acts vertically upwards along the positive y-axis.
- Shear stress τxy acts in the plane of the element, with both positive and negative directions indicated.

### Answer Choices:

- a. 100, 78
- b. None
- c. 178, 130
- d. 130, 76
- e. 129, 73

### Analysis:

To solve for the unknown stresses σy and τxy, you can use the derived principal stress conditions and shear stress equations for plane stress conditions:

- Maximum shear stress condition equation
- Principal stress condition equation

### Note:
The solution involves solving a system of equations based on the provided conditions and utilizing appropriate mechanical stress transformation equations.

---

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