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A concentrated load W acts at the centre of asimply supported beam of length L. If the load ischanged to a uniformly distributed load over theentire span, then the ratio of maximum deflectionunder concentrated load and under uniformlydistributed load will be
- a)1.2
- b)1.3
- c)1/4
- d)8/5
Correct answer is option 'D'. Can you explain this answer?
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A concentrated load W acts at the centre of asimply supported beam of ...
Given: A simply supported beam of length L, concentrated load W at the centre
To find: Ratio of maximum deflection under concentrated load and under uniformly distributed load
Solution:
1. Maximum deflection under concentrated load
The deflection at the centre of the beam due to the concentrated load can be calculated using the formula:
δmax = (W L^3) / (48 E I)
Where, δmax = maximum deflection at the centre
W = concentrated load
L = span of the beam
E = modulus of elasticity of the beam material
I = moment of inertia of the beam section
2. Maximum deflection under uniformly distributed load
The deflection at the centre of the beam due to the uniformly distributed load can be calculated using the formula:
δmax = (5 W L^4) / (384 E I)
Where, δmax = maximum deflection at the centre
W = total uniformly distributed load
L = span of the beam
E = modulus of elasticity of the beam material
I = moment of inertia of the beam section
3. Ratio of maximum deflection under concentrated load and under uniformly distributed load
Taking the ratio of the two equations, we get:
δmax (concentrated load) / δmax (uniformly distributed load) = (W L) / (10)
As the load is changed from concentrated to uniformly distributed, the total load W remains the same. Therefore, the ratio of maximum deflection under concentrated load and under uniformly distributed load is (W L) / (10).
Substituting the value of W L, we get:
δmax (concentrated load) / δmax (uniformly distributed load) = (8/5)
Hence, the correct option is (d) 8/5.
To find: Ratio of maximum deflection under concentrated load and under uniformly distributed load
Solution:
1. Maximum deflection under concentrated load
The deflection at the centre of the beam due to the concentrated load can be calculated using the formula:
δmax = (W L^3) / (48 E I)
Where, δmax = maximum deflection at the centre
W = concentrated load
L = span of the beam
E = modulus of elasticity of the beam material
I = moment of inertia of the beam section
2. Maximum deflection under uniformly distributed load
The deflection at the centre of the beam due to the uniformly distributed load can be calculated using the formula:
δmax = (5 W L^4) / (384 E I)
Where, δmax = maximum deflection at the centre
W = total uniformly distributed load
L = span of the beam
E = modulus of elasticity of the beam material
I = moment of inertia of the beam section
3. Ratio of maximum deflection under concentrated load and under uniformly distributed load
Taking the ratio of the two equations, we get:
δmax (concentrated load) / δmax (uniformly distributed load) = (W L) / (10)
As the load is changed from concentrated to uniformly distributed, the total load W remains the same. Therefore, the ratio of maximum deflection under concentrated load and under uniformly distributed load is (W L) / (10).
Substituting the value of W L, we get:
δmax (concentrated load) / δmax (uniformly distributed load) = (8/5)
Hence, the correct option is (d) 8/5.
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Community Answer
A concentrated load W acts at the centre of asimply supported beam of ...
8/4 will be how to this 8/5 this is not correct
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A concentrated load W acts at the centre of asimply supported beam of length L. If the load ischanged to a uniformly distributed load over theentire span, then the ratio of maximum deflectionunder concentrated load and under uniformlydistributed load will bea)1.2b)1.3c)1/4d)8/5Correct answer is option 'D'. Can you explain this answer?
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