The state of stress at a point in a member is shown on the rectangular stress element where the magnitudes of the stresses are |σx|=11 ksi, |σy|=31 ksi, and |τxy|=17 ksi. Determine the state of stress on an element rotated 50∘ counterclockwise from the element shown.
The state of stress at a point in a member is shown on the rectangular stress element where the magnitudes of the stresses are |σx|=11 ksi, |σy|=31 ksi, and |τxy|=17 ksi. Determine the state of stress on an element rotated 50∘ counterclockwise from the element shown.
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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The state of stress at a point in a member is shown on the rectangular stress element where the magnitudes of the stresses are |σx|=11 ksi, |σy|=31 ksi, and |τxy|=17 ksi.
Determine the state of stress on an element rotated 50∘ counterclockwise from the element shown.
Transcribed Image Text:The image depicts a two-dimensional stress element, which is a representation used in mechanics to illustrate the different types of stresses acting on a material.
### Detailed Explanation:
- **Normal Stresses (\(\sigma_x\) and \(\sigma_y\))**:
- \(\sigma_x\) is the normal stress acting on the element in the horizontal direction. It is represented by two arrows pointing towards and away from the right side of the square.
- \(\sigma_y\) is the normal stress acting in the vertical direction. It is shown by two arrows pointing towards and away from the top of the square.
- **Shear Stress (\(\tau_{xy}\))**:
- \(\tau_{xy}\) is the shear stress acting parallel to the surface of the element. It is depicted by arrows on the sides of the square. These arrows indicate that there is a tangential force causing a shearing effect across the element.
Understanding this diagram is crucial for analyzing stress distributions in materials to predict failure and design structures accordingly. The depiction is typical in studying material mechanics, stress analysis, and engineering applications.
The background of the element is shaded in a beige color to distinguish it from the surrounding arrows, which represent the stresses acting on it.
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