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Which failure theory would be appropriate to solve the following problem: A rotating shaft is supported by bearings at each end. The shaft supports a single load in the center.

Which failure theory would be appropriate to solve the following problem: A rotating shaft is supported by bearings at each end. The shaft supports a single load in the center.

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
Problem 1.1MA
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### Problem Statement: **Which failure theory would be appropriate to solve the following problem:** A rotating shaft is supported by bearings at each end. The shaft supports a single load in the center. ### Possible Answers: - Endurance Limit - Modified Mohr Theory - Coulomb-Mohr Theory - Maximum Normal Stress Theory - Goodman Criterion - von Mises - Maximum Shear Stress Theory - Distortion Energy Theory ### Explanation of Theories: 1. **Endurance Limit**: Refers to the maximum stress a material can withstand for an infinite number of cycles without breaking. 2. **Modified Mohr Theory**: An extension of Mohr's theory that considers both normal and shear stress to predict failure in ductile materials. 3. **Coulomb-Mohr Theory**: Combines Coulomb's frictional failure theory with Mohr's theory to predict failure in brittle materials. 4. **Maximum Normal Stress Theory** (Rankine Theory): Predicts failure when the maximum normal stress in a material reaches a critical value. 5. **Goodman Criterion**: Used to predict the fatigue life of a material by considering mean and alternating stresses. 6. **von Mises** (Distortion Energy Theory): Predicts failure when the distortion energy in a material reaches a certain value, particularly useful for ductile materials. 7. **Maximum Shear Stress Theory** (Tresca Theory): Predicts failure when the maximum shear stress in a material reaches or exceeds the shear stress at yielding. 8. **Distortion Energy Theory** (von Mises Theory): Often used interchangeably with the von Mises theory, focusing on the energy distortion in predicting failure. This educational material helps students understand different failure theories and apply them to a practical problem involving a rotating shaft supported by bearings, subject to a central load. Each theory provides insight into when and why materials might fail under different types of stress and loading conditions.
Transcribed Image Text:### Problem Statement: **Which failure theory would be appropriate to solve the following problem:** A rotating shaft is supported by bearings at each end. The shaft supports a single load in the center. ### Possible Answers: - Endurance Limit - Modified Mohr Theory - Coulomb-Mohr Theory - Maximum Normal Stress Theory - Goodman Criterion - von Mises - Maximum Shear Stress Theory - Distortion Energy Theory ### Explanation of Theories: 1. **Endurance Limit**: Refers to the maximum stress a material can withstand for an infinite number of cycles without breaking. 2. **Modified Mohr Theory**: An extension of Mohr's theory that considers both normal and shear stress to predict failure in ductile materials. 3. **Coulomb-Mohr Theory**: Combines Coulomb's frictional failure theory with Mohr's theory to predict failure in brittle materials. 4. **Maximum Normal Stress Theory** (Rankine Theory): Predicts failure when the maximum normal stress in a material reaches a critical value. 5. **Goodman Criterion**: Used to predict the fatigue life of a material by considering mean and alternating stresses. 6. **von Mises** (Distortion Energy Theory): Predicts failure when the distortion energy in a material reaches a certain value, particularly useful for ductile materials. 7. **Maximum Shear Stress Theory** (Tresca Theory): Predicts failure when the maximum shear stress in a material reaches or exceeds the shear stress at yielding. 8. **Distortion Energy Theory** (von Mises Theory): Often used interchangeably with the von Mises theory, focusing on the energy distortion in predicting failure. This educational material helps students understand different failure theories and apply them to a practical problem involving a rotating shaft supported by bearings, subject to a central load. Each theory provides insight into when and why materials might fail under different types of stress and loading conditions.
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