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A beam carries a uniformly distributed load throughout its length. In which of the following configurations will the strain energy be maximum?
- a)Cantilever
- b)Simply supported beam
- c)Propped cantilever
- d)Fixed beam
Correct answer is option 'A'. Can you explain this answer?
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A beam carries a uniformly distributed load throughout its length. In ...
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Introduction:
The strain energy of a beam is the energy stored within the beam due to deformation caused by the applied load. It is a measure of the internal work done on the beam.
Explanation:
The configuration of a beam greatly affects its deflection and deformation under load. Different beam configurations have different levels of strain energy stored within them. Let's analyze each of the given configurations to determine which one will have the maximum strain energy.
a) Cantilever:
A cantilever beam is supported at one end and has a free end. The load is applied at the free end. In this configuration, the beam experiences maximum deflection and deformation due to the applied load. The strain energy is directly proportional to the deflection, so the strain energy will be maximum in a cantilever beam configuration.
b) Simply supported beam:
A simply supported beam is supported at both ends and has no fixed or built-in support. The load is applied at the center of the beam. In this configuration, the beam experiences lesser deflection and deformation compared to a cantilever beam. Therefore, the strain energy will be less than that in a cantilever beam.
c) Propped cantilever:
A propped cantilever beam is supported at one end and has a support at some intermediate point along its length. The load is applied at the free end. This configuration is similar to a cantilever beam, but the presence of the support reduces the deflection and deformation. Therefore, the strain energy will be less than that in a cantilever beam.
d) Fixed beam:
A fixed beam is supported at both ends and has fixed or built-in supports. The load is applied at any point along the beam. This configuration restricts the movement of the beam, resulting in smaller deflection and deformation compared to the other configurations. Therefore, the strain energy will be less than that in a cantilever beam.
Conclusion:
In conclusion, the strain energy will be maximum in a cantilever beam configuration (option A). The cantilever configuration experiences maximum deflection and deformation, resulting in the highest amount of strain energy stored within the beam.
The strain energy of a beam is the energy stored within the beam due to deformation caused by the applied load. It is a measure of the internal work done on the beam.
Explanation:
The configuration of a beam greatly affects its deflection and deformation under load. Different beam configurations have different levels of strain energy stored within them. Let's analyze each of the given configurations to determine which one will have the maximum strain energy.
a) Cantilever:
A cantilever beam is supported at one end and has a free end. The load is applied at the free end. In this configuration, the beam experiences maximum deflection and deformation due to the applied load. The strain energy is directly proportional to the deflection, so the strain energy will be maximum in a cantilever beam configuration.
b) Simply supported beam:
A simply supported beam is supported at both ends and has no fixed or built-in support. The load is applied at the center of the beam. In this configuration, the beam experiences lesser deflection and deformation compared to a cantilever beam. Therefore, the strain energy will be less than that in a cantilever beam.
c) Propped cantilever:
A propped cantilever beam is supported at one end and has a support at some intermediate point along its length. The load is applied at the free end. This configuration is similar to a cantilever beam, but the presence of the support reduces the deflection and deformation. Therefore, the strain energy will be less than that in a cantilever beam.
d) Fixed beam:
A fixed beam is supported at both ends and has fixed or built-in supports. The load is applied at any point along the beam. This configuration restricts the movement of the beam, resulting in smaller deflection and deformation compared to the other configurations. Therefore, the strain energy will be less than that in a cantilever beam.
Conclusion:
In conclusion, the strain energy will be maximum in a cantilever beam configuration (option A). The cantilever configuration experiences maximum deflection and deformation, resulting in the highest amount of strain energy stored within the beam.
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A beam carries a uniformly distributed load throughout its length. In ...
Since energy stored in cantilever loaded with uniformly distributed load is w^2 L^5/40EI
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A beam carries a uniformly distributed load throughout its length. In which of the following configurations will the strain energy be maximum?a)Cantileverb)Simply supported beamc)Propped cantileverd)Fixed beamCorrect answer is option 'A'. Can you explain this answer?
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