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A point load placed at the mid span of a simply supported beam has been replaced by a uniformly distributed load of same total value. The central deflection in the later case will be
- a)same
- b)less
- c)more
- d)depends upon Z value of beam
Correct answer is option 'B'. Can you explain this answer?
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Introduction:
In this scenario, we are considering a simply supported beam that initially had a point load applied at its mid-span. We are then replacing this point load with a uniformly distributed load of the same total value. The question is asking about the central deflection of the beam in the latter case compared to the former case.
Explanation:
To understand the effect of the load distribution on the central deflection of the beam, let's consider the following points:
1. Distribution of Load:
- In the case of a point load, the load is concentrated at a single point along the beam's span.
- However, in the case of a uniformly distributed load, the load is spread evenly along the entire span of the beam.
2. Load Distribution and Deflection:
- When a point load is applied at the mid-span of a simply supported beam, the beam undergoes deflection, with the maximum deflection occurring at the mid-span.
- However, when a uniformly distributed load is applied, the load is distributed evenly along the span of the beam. This results in a more even distribution of the bending moment and deflection along the beam.
3. Central Deflection:
- In the case of a point load, the maximum deflection occurs at the mid-span of the beam.
- However, when a uniformly distributed load is applied, the load is spread over a larger area, resulting in a more uniform distribution of deflection along the beam. As a result, the central deflection in this case is less than the deflection caused by a point load.
Conclusion:
Based on the above points, we can conclude that when a point load at the mid-span of a simply supported beam is replaced by a uniformly distributed load of the same total value, the central deflection in the latter case will be less. This is because the load distribution is spread over a larger area, resulting in a more uniform distribution of deflection along the beam.
In this scenario, we are considering a simply supported beam that initially had a point load applied at its mid-span. We are then replacing this point load with a uniformly distributed load of the same total value. The question is asking about the central deflection of the beam in the latter case compared to the former case.
Explanation:
To understand the effect of the load distribution on the central deflection of the beam, let's consider the following points:
1. Distribution of Load:
- In the case of a point load, the load is concentrated at a single point along the beam's span.
- However, in the case of a uniformly distributed load, the load is spread evenly along the entire span of the beam.
2. Load Distribution and Deflection:
- When a point load is applied at the mid-span of a simply supported beam, the beam undergoes deflection, with the maximum deflection occurring at the mid-span.
- However, when a uniformly distributed load is applied, the load is distributed evenly along the span of the beam. This results in a more even distribution of the bending moment and deflection along the beam.
3. Central Deflection:
- In the case of a point load, the maximum deflection occurs at the mid-span of the beam.
- However, when a uniformly distributed load is applied, the load is spread over a larger area, resulting in a more uniform distribution of deflection along the beam. As a result, the central deflection in this case is less than the deflection caused by a point load.
Conclusion:
Based on the above points, we can conclude that when a point load at the mid-span of a simply supported beam is replaced by a uniformly distributed load of the same total value, the central deflection in the latter case will be less. This is because the load distribution is spread over a larger area, resulting in a more uniform distribution of deflection along the beam.
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A point load placed at the mid span of a simply supported beam has been replaced by a uniformly distributed load of same total value. The central deflection in the later case will bea)sameb)lessc)mored)depends upon Z value of beamCorrect answer is option 'B'. Can you explain this answer?
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