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Which of the following is not an assumption in the Theory of Simple Bending?
- a)The material of the beam is homogenous and isotropic.
- b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.
- c)The radius of curvature is small as compared to the dimensions of the beam.
- d)The beam is subjected to pure bending and the effect of shear is neglected.
Correct answer is option 'C'. Can you explain this answer?
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Which of the following is not an assumption in the Theory of Simple B...
Following are the assumptions made in the theory of Simple Bending
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1. The material of the beam is homogenous and isotropic.
2. The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.
3. Members have symmetric cross-sections and are subjected to bending in the plane of symmetry.
4. The beam is subjected to pure bending and the effect of shear is neglected.
5. Plane sections through a beam taken normal to the axis of the beam remain plane after the beam is subjected to bending.
6. The radius of curvature is large as compared to the dimensions of the beam.
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Which of the following is not an assumption in the Theory of Simple B...
In the Theory of Simple Bending, the assumption that is not valid is option 'C', which states that the radius of curvature is small as compared to the dimensions of the beam.
Explanation:
The Theory of Simple Bending is a fundamental concept in structural mechanics that is used to analyze the behavior of beams under bending loads. It is based on several assumptions that simplify the analysis and allow for the derivation of equations that describe the bending behavior of beams.
1. Material of the beam is homogenous and isotropic:
This assumption implies that the material of the beam has uniform properties throughout its cross-section and that it behaves the same in all directions. It allows for the use of simple mathematical models to describe the stress and strain distribution in the beam.
2. The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature:
This assumption simplifies the analysis by assuming that the beam undergoes pure bending, where the longitudinal fibers of the beam bend in circular arcs. This simplification allows for the derivation of equations that relate the bending moment, curvature, and stress in the beam.
3. The radius of curvature is small as compared to the dimensions of the beam:
This assumption is not valid in the Theory of Simple Bending. In reality, beams can have large radii of curvature, especially in cases where the beam is subjected to high bending moments or has large dimensions. Ignoring this assumption can lead to significant errors in the analysis of the beam's behavior.
4. The beam is subjected to pure bending, and the effect of shear is neglected:
This assumption simplifies the analysis by considering only the bending moment in the beam and neglecting the shear forces. It is valid when the beam is significantly stiffer in bending than in shear. In cases where shear is important, more advanced theories such as the Theory of Elasticity or the Theory of Timoshenko Beam should be used.
In conclusion, the assumption that is not valid in the Theory of Simple Bending is option 'C', which states that the radius of curvature is small as compared to the dimensions of the beam. This assumption is often not valid in real-world applications and should be carefully considered when analyzing the behavior of beams under bending loads.
Explanation:
The Theory of Simple Bending is a fundamental concept in structural mechanics that is used to analyze the behavior of beams under bending loads. It is based on several assumptions that simplify the analysis and allow for the derivation of equations that describe the bending behavior of beams.
1. Material of the beam is homogenous and isotropic:
This assumption implies that the material of the beam has uniform properties throughout its cross-section and that it behaves the same in all directions. It allows for the use of simple mathematical models to describe the stress and strain distribution in the beam.
2. The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature:
This assumption simplifies the analysis by assuming that the beam undergoes pure bending, where the longitudinal fibers of the beam bend in circular arcs. This simplification allows for the derivation of equations that relate the bending moment, curvature, and stress in the beam.
3. The radius of curvature is small as compared to the dimensions of the beam:
This assumption is not valid in the Theory of Simple Bending. In reality, beams can have large radii of curvature, especially in cases where the beam is subjected to high bending moments or has large dimensions. Ignoring this assumption can lead to significant errors in the analysis of the beam's behavior.
4. The beam is subjected to pure bending, and the effect of shear is neglected:
This assumption simplifies the analysis by considering only the bending moment in the beam and neglecting the shear forces. It is valid when the beam is significantly stiffer in bending than in shear. In cases where shear is important, more advanced theories such as the Theory of Elasticity or the Theory of Timoshenko Beam should be used.
In conclusion, the assumption that is not valid in the Theory of Simple Bending is option 'C', which states that the radius of curvature is small as compared to the dimensions of the beam. This assumption is often not valid in real-world applications and should be carefully considered when analyzing the behavior of beams under bending loads.
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Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer?
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Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer?.
Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following is not an assumption in the Theory of Simple Bending?a)The material of the beam is homogenous and isotropic.b)The beam is initially straight, and all the longitudinal fibers bend in circular arcs with a common center of curvature.c)The radius of curvature is small as compared to the dimensions of the beam.d)The beam is subjected to pure bending and the effect of shear is neglected.Correct answer is option 'C'. Can you explain this answer?.
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