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The state of plane stress shown occurs in a machine component made of a steel with oy = 36 ksi. Using the maximum-distortion-energy criterion, determine whether yield will occur when (a) ty = 15 ksi, (b) Ty = 18 ksi, (c) try = 21 ksi. If yield does not occur, determine the corresponding factor of safety.

The state of plane stress shown occurs in a machine component made of a steel with oy = 36 ksi. Using the maximum-distortion-energy criterion, determine whether yield will occur when (a) ty = 15 ksi, (b) Ty = 18 ksi, (c) try = 21 ksi. If yield does not occur, determine the corresponding factor of safety.

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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**Problem 7.83** The state of plane stress shown occurs in a machine component made of a steel with \( \sigma_y = 36 \text{ ksi} \). Using the maximum-distortion-energy criterion, determine whether yield will occur when (a) \( \tau_{xy} = 15 \text{ ksi} \), (b) \( \tau_{xy} = 18 \text{ ksi} \), (c) \( \tau_{xy} = 21 \text{ ksi} \). If yield does not occur, determine the corresponding factor of safety.
Transcribed Image Text:**Problem 7.83** The state of plane stress shown occurs in a machine component made of a steel with \( \sigma_y = 36 \text{ ksi} \). Using the maximum-distortion-energy criterion, determine whether yield will occur when (a) \( \tau_{xy} = 15 \text{ ksi} \), (b) \( \tau_{xy} = 18 \text{ ksi} \), (c) \( \tau_{xy} = 21 \text{ ksi} \). If yield does not occur, determine the corresponding factor of safety.
### Stress Analysis: Figure P7.83 In Figure P7.83, we observe a diagram illustrating a two-dimensional stress state on a square element. The stresses are represented by vectors indicating both magnitude and direction. #### Key Elements: 1. **Normal Stresses:** - **Vertical Stress:** A downward normal stress of 12 ksi (kips per square inch) is applied on the top side of the square. This is countered by an upward stress of 12 ksi at the bottom side, maintaining equilibrium. - **Horizontal Stress:** The left side of the square features a leftward normal stress of 3 ksi. Similarly, the right side shows an equal rightward stress of 3 ksi. 2. **Shear Stress:** - **Shear Stress (τ_xy):** The square is subjected to a shear stress, denoted as \( \tau_{xy} \), operating diagonally across the element, demonstrating forces that might cause distortion of the shape. #### Understanding the Diagram: These components collectively depict the stress state at a given point on a structural element. The normal stresses are responsible for dimensional changes along their respective axes, while shear stresses are critical in understanding potential angular distortions. This diagram serves as a fundamental concept in mechanical and structural engineering, assisting in the assessment of material performance under various loading conditions. Understanding these stress interactions is vital for ensuring the structural integrity and safety of engineering designs.
Transcribed Image Text:### Stress Analysis: Figure P7.83 In Figure P7.83, we observe a diagram illustrating a two-dimensional stress state on a square element. The stresses are represented by vectors indicating both magnitude and direction. #### Key Elements: 1. **Normal Stresses:** - **Vertical Stress:** A downward normal stress of 12 ksi (kips per square inch) is applied on the top side of the square. This is countered by an upward stress of 12 ksi at the bottom side, maintaining equilibrium. - **Horizontal Stress:** The left side of the square features a leftward normal stress of 3 ksi. Similarly, the right side shows an equal rightward stress of 3 ksi. 2. **Shear Stress:** - **Shear Stress (τ_xy):** The square is subjected to a shear stress, denoted as \( \tau_{xy} \), operating diagonally across the element, demonstrating forces that might cause distortion of the shape. #### Understanding the Diagram: These components collectively depict the stress state at a given point on a structural element. The normal stresses are responsible for dimensional changes along their respective axes, while shear stresses are critical in understanding potential angular distortions. This diagram serves as a fundamental concept in mechanical and structural engineering, assisting in the assessment of material performance under various loading conditions. Understanding these stress interactions is vital for ensuring the structural integrity and safety of engineering designs.
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