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The deformation of a bar under its own weight as compared to that when subjected to a direct axial load equal to its own weight will be
- a)The same
- b)One-fourth
- c)Half
- d)Double
Correct answer is option 'C'. Can you explain this answer?
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The deformation of a bar under its own weight as compared to that when...
Understanding Deformation Under Different Loads
When comparing the deformation of a bar under its own weight to that under a direct axial load equal to its own weight, the results differ due to the nature of the loading conditions.
1. Deformation Under Own Weight
- When a bar is subjected to its own weight, the deformation occurs due to a uniformly distributed load along its length.
- The deflection can be calculated using the formula for a cantilever beam under uniform load, leading to a certain deformation value.
2. Deformation Under Direct Axial Load
- When the same bar is subjected to a direct axial load equal to its weight, the load is concentrated at the ends, creating a different stress distribution.
- This scenario results in a linear deformation that can be calculated using the formula for axial loading, which typically yields a larger deformation value compared to the distributed load case.
3. Comparison of Deformations
- The key difference lies in how the weight is applied. A uniformly distributed load causes less deformation than a concentrated load.
- The specific ratio of deformation under these two conditions is that the deformation under direct axial load is twice that of the deformation due to its own weight.
Conclusion
Thus, the deformation of a bar under its own weight is half that of the deformation when subjected to a direct axial load equal to its own weight, confirming option 'C' as the correct answer.
Understanding these principles is crucial for structural analysis and design in civil engineering.
When comparing the deformation of a bar under its own weight to that under a direct axial load equal to its own weight, the results differ due to the nature of the loading conditions.
1. Deformation Under Own Weight
- When a bar is subjected to its own weight, the deformation occurs due to a uniformly distributed load along its length.
- The deflection can be calculated using the formula for a cantilever beam under uniform load, leading to a certain deformation value.
2. Deformation Under Direct Axial Load
- When the same bar is subjected to a direct axial load equal to its weight, the load is concentrated at the ends, creating a different stress distribution.
- This scenario results in a linear deformation that can be calculated using the formula for axial loading, which typically yields a larger deformation value compared to the distributed load case.
3. Comparison of Deformations
- The key difference lies in how the weight is applied. A uniformly distributed load causes less deformation than a concentrated load.
- The specific ratio of deformation under these two conditions is that the deformation under direct axial load is twice that of the deformation due to its own weight.
Conclusion
Thus, the deformation of a bar under its own weight is half that of the deformation when subjected to a direct axial load equal to its own weight, confirming option 'C' as the correct answer.
Understanding these principles is crucial for structural analysis and design in civil engineering.
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