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A simply supported beam carries a total load W which is uniformly distributed on the entire span. The center of beam is propped so that it is brought to the level of end supports. The prop reaction would be
- a)W/3
- b)W/2
- c)3W/8
- d)5W/8
Correct answer is option 'D'. Can you explain this answer?
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A simply supported beam carries a total load W which is uniformly dist...
After equating central deflection for both the cases, we have
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A simply supported beam carries a total load W which is uniformly dist...
Given information:
- Simply supported beam
- Total load W uniformly distributed on the entire span
- Center of the beam is propped to the level of end supports
To find:
- Prop reaction
Analysis:
- Since the beam is simply supported, it means that it is supported on both ends and is free to rotate at these points.
- The load W is uniformly distributed on the entire span, which means that the load is the same at every point along the beam.
- The center of the beam is propped, which means that there is an additional support at the center of the beam.
- The prop reaction is the force exerted by the prop to support the beam.
Solution:
To find the prop reaction, we can use the concept of equilibrium. Since the beam is in equilibrium, the sum of all the forces acting on it must be zero.
Step 1: Calculate the reaction at each end support
- Since the beam is simply supported, the reactions at both end supports will be equal.
- Let's assume the reaction at each end support is R.
- According to the principle of equilibrium, the sum of the vertical forces must be zero.
- The load W is uniformly distributed, so the load per unit length will be W/L, where L is the length of the beam.
- The load on each half of the beam will be (W/L)*(L/2) = W/2.
- There are two reactions at the end supports and one reaction at the prop, so the sum of the vertical forces is R + R - W/2 = 0.
- Solving this equation, we get R = W/4.
Step 2: Calculate the prop reaction
- The prop reaction is the force exerted by the prop to support the beam.
- According to the principle of equilibrium, the sum of the vertical forces must be zero.
- The load on each half of the beam is W/2.
- The reaction at each end support is W/4.
- The reaction at the prop is W/2 - W/4 - W/4 = W/8.
- Therefore, the prop reaction is W/8.
Conclusion:
The prop reaction is W/8, which matches with option D.
- Simply supported beam
- Total load W uniformly distributed on the entire span
- Center of the beam is propped to the level of end supports
To find:
- Prop reaction
Analysis:
- Since the beam is simply supported, it means that it is supported on both ends and is free to rotate at these points.
- The load W is uniformly distributed on the entire span, which means that the load is the same at every point along the beam.
- The center of the beam is propped, which means that there is an additional support at the center of the beam.
- The prop reaction is the force exerted by the prop to support the beam.
Solution:
To find the prop reaction, we can use the concept of equilibrium. Since the beam is in equilibrium, the sum of all the forces acting on it must be zero.
Step 1: Calculate the reaction at each end support
- Since the beam is simply supported, the reactions at both end supports will be equal.
- Let's assume the reaction at each end support is R.
- According to the principle of equilibrium, the sum of the vertical forces must be zero.
- The load W is uniformly distributed, so the load per unit length will be W/L, where L is the length of the beam.
- The load on each half of the beam will be (W/L)*(L/2) = W/2.
- There are two reactions at the end supports and one reaction at the prop, so the sum of the vertical forces is R + R - W/2 = 0.
- Solving this equation, we get R = W/4.
Step 2: Calculate the prop reaction
- The prop reaction is the force exerted by the prop to support the beam.
- According to the principle of equilibrium, the sum of the vertical forces must be zero.
- The load on each half of the beam is W/2.
- The reaction at each end support is W/4.
- The reaction at the prop is W/2 - W/4 - W/4 = W/8.
- Therefore, the prop reaction is W/8.
Conclusion:
The prop reaction is W/8, which matches with option D.
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A simply supported beam carries a total load W which is uniformly distributed on the entire span. The center of beam is propped so that it is brought to the level of end supports. The prop reaction would bea)W/3b)W/2c)3W/8d)5W/8Correct answer is option 'D'. Can you explain this answer?
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