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A simply supported beam has equal over-hanging lengths and carries equal concentrated loads P at ends. Bending moment over the length between the supports
- a)Is zero
- b)Is a non-zero constant
- c)Varies uniformly from one support to the other
- d)Is maximum at mid-span
Correct answer is option 'B'. Can you explain this answer?
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A simply supported beam has equal over-hanging lengths and carries equ...
**Answer:**
To analyze the bending moment over the length between the supports, we need to consider the equilibrium of forces and moments acting on the beam.
**1. Equilibrium of Forces:**
Since the beam is simply supported, it can only exert vertical reactions at the supports. The vertical reactions at each support will balance the weight of the beam and the concentrated loads P at the ends.
Therefore, the vertical reactions at the supports will be equal to P/2 each, as they need to balance the load P at the ends.
**2. Equilibrium of Moments:**
To calculate the bending moment at any point on the beam, we need to consider the moments acting on the beam.
Since the beam is symmetrical and the loads are concentrated at the ends, the beam will experience equal and opposite moments at the supports.
At each support, the moment will be equal to P multiplied by the distance between the load and the support (equal to the overhanging length).
**3. Bending Moment Diagram:**
The bending moment diagram for the beam will consist of two equal and opposite moments, each acting at the supports. Between the supports, the bending moment will be constant and equal to the magnitude of the applied moments at the supports.
Therefore, the bending moment over the length between the supports will be a non-zero constant, which is equal to P times the overhanging length.
**Conclusion:**
Based on the above analysis, we can conclude that the correct answer is option 'B': The bending moment over the length between the supports is a non-zero constant.
To analyze the bending moment over the length between the supports, we need to consider the equilibrium of forces and moments acting on the beam.
**1. Equilibrium of Forces:**
Since the beam is simply supported, it can only exert vertical reactions at the supports. The vertical reactions at each support will balance the weight of the beam and the concentrated loads P at the ends.
Therefore, the vertical reactions at the supports will be equal to P/2 each, as they need to balance the load P at the ends.
**2. Equilibrium of Moments:**
To calculate the bending moment at any point on the beam, we need to consider the moments acting on the beam.
Since the beam is symmetrical and the loads are concentrated at the ends, the beam will experience equal and opposite moments at the supports.
At each support, the moment will be equal to P multiplied by the distance between the load and the support (equal to the overhanging length).
**3. Bending Moment Diagram:**
The bending moment diagram for the beam will consist of two equal and opposite moments, each acting at the supports. Between the supports, the bending moment will be constant and equal to the magnitude of the applied moments at the supports.
Therefore, the bending moment over the length between the supports will be a non-zero constant, which is equal to P times the overhanging length.
**Conclusion:**
Based on the above analysis, we can conclude that the correct answer is option 'B': The bending moment over the length between the supports is a non-zero constant.
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