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A beam carrying a uniformly distribute load rests on two supports ‘b’ apart with equal overhangs ‘a’ at each end. The ratio b/a for zero bending moment at midspan is.
- a)1/2
- b)1
- c)3/2
- d)2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A beam carrying a uniformly distribute load rests on two supports ‘b’ ...
(a + b / 2)= b
a = b/2
b/a = 2
Correct option = D
Most Upvoted Answer
A beam carrying a uniformly distribute load rests on two supports ‘b’ ...
Ratio for Zero Bending Moment at Midspan
To determine the ratio b/a for zero bending moment at midspan, we need to consider the equilibrium of forces and moments acting on the beam.
Equilibrium of Forces
- For zero bending moment at midspan, the beam should be in equilibrium.
- The reactions at the supports will be equal and opposite to the load acting on the beam.
- The reactions will create a couple to balance the distributed load.
Equilibrium of Moments
- The bending moment at midspan will be zero when the sum of moments about that point is zero.
- The overhangs 'a' at each end will create a moment that counteracts the moment due to the distributed load.
Ratio Calculation
- Let's assume the reactions at the supports are R.
- The total length of the beam is 2a + b.
- The total load on the beam is w(2a + b).
- To balance the moments about the midspan, the moment due to the reactions at the supports should be equal and opposite to the moment due to the distributed load.
- This leads to the equation: Rb = w(2a + b)(a + b/2).
- By solving this equation, we get b/a = 2.
Therefore, the correct answer is option 'D' (2).
To determine the ratio b/a for zero bending moment at midspan, we need to consider the equilibrium of forces and moments acting on the beam.
Equilibrium of Forces
- For zero bending moment at midspan, the beam should be in equilibrium.
- The reactions at the supports will be equal and opposite to the load acting on the beam.
- The reactions will create a couple to balance the distributed load.
Equilibrium of Moments
- The bending moment at midspan will be zero when the sum of moments about that point is zero.
- The overhangs 'a' at each end will create a moment that counteracts the moment due to the distributed load.
Ratio Calculation
- Let's assume the reactions at the supports are R.
- The total length of the beam is 2a + b.
- The total load on the beam is w(2a + b).
- To balance the moments about the midspan, the moment due to the reactions at the supports should be equal and opposite to the moment due to the distributed load.
- This leads to the equation: Rb = w(2a + b)(a + b/2).
- By solving this equation, we get b/a = 2.
Therefore, the correct answer is option 'D' (2).
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A beam carrying a uniformly distribute load rests on two supports ‘b’ apart with equal overhangs ‘a’ at each end. The ratio b/a for zero bending moment at midspan is.a)1/2b)1c)3/2d)2Correct answer is option 'D'. Can you explain this answer?
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