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If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain?
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If a simply supported beam of span L, carries a uniformly distributed ...
To find the deflection at the centre of a simply supported beam with a uniformly distributed load, we can use the formula for the deflection of a beam under a uniformly distributed load:
δ = 5wL^4 / (384EI)
Where:
δ = deflection at the centre of the beam
w = uniformly distributed load
L = span of the beam
I = moment of inertia of the beam
E = modulus of elasticity of the beam
Now, let's break down the calculation step-by-step:
1. Moment of Inertia (I):
The moment of inertia depends on the shape of the beam. For example, for a rectangular beam, the moment of inertia (I) is given by the formula:
I = (b * h^3) / 12
Where:
b = width of the beam
h = height of the beam
2. Substituting the moment of inertia (I) in the deflection formula:
Now, we substitute the moment of inertia (I) into the deflection formula:
δ = 5wL^4 / (384E * [(b * h^3) / 12])
Simplifying the equation further:
δ = 5wL^4 * (12 / 384E * bh^3)
δ = 5wL^4 * (1 / 32E * bh^3)
3. Final Simplification:
Finally, we can simplify the equation by combining the constants:
δ = 5wL^4 / (32Ebh^3)
In the given answer, the constant 192 is used instead of 32. This might be a typographical error, as using 32 as the constant is more common and accurate.
So, the correct formula for the deflection at the centre of the beam under a uniformly distributed load is:
δ = 5wL^4 / (32Ebh^3)
Note: Make sure to check the units of all variables and ensure they are consistent throughout the calculation.
δ = 5wL^4 / (384EI)
Where:
δ = deflection at the centre of the beam
w = uniformly distributed load
L = span of the beam
I = moment of inertia of the beam
E = modulus of elasticity of the beam
Now, let's break down the calculation step-by-step:
1. Moment of Inertia (I):
The moment of inertia depends on the shape of the beam. For example, for a rectangular beam, the moment of inertia (I) is given by the formula:
I = (b * h^3) / 12
Where:
b = width of the beam
h = height of the beam
2. Substituting the moment of inertia (I) in the deflection formula:
Now, we substitute the moment of inertia (I) into the deflection formula:
δ = 5wL^4 / (384E * [(b * h^3) / 12])
Simplifying the equation further:
δ = 5wL^4 * (12 / 384E * bh^3)
δ = 5wL^4 * (1 / 32E * bh^3)
3. Final Simplification:
Finally, we can simplify the equation by combining the constants:
δ = 5wL^4 / (32Ebh^3)
In the given answer, the constant 192 is used instead of 32. This might be a typographical error, as using 32 as the constant is more common and accurate.
So, the correct formula for the deflection at the centre of the beam under a uniformly distributed load is:
δ = 5wL^4 / (32Ebh^3)
Note: Make sure to check the units of all variables and ensure they are consistent throughout the calculation.
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If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain?
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If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain?.
If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a simply supported beam of span L, carries a uniformly distributed load of 2w/m and the moment of inertia is I, the deflection at the centre of the beam is : Ans - 5wl⁴/192EI . Can any one explain?.
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