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If the deflection at the free end of a uniformly loaded cantilever beam is 15 mm and the slope of the deflection curve at the free end is 0.02 radian. then the length of the beam is
- a)0.8 m
- b)1 m
- c)1.2 m
- d)1.5 m
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If the deflection at the free end of a uniformly loaded cantilever be...
Deflection at free end, δ = 
= 15 mm
= 15 mmSlope at free end, θ = 
= 0.02
= 0.02∴ From the two
L = 1 m
Most Upvoted Answer
If the deflection at the free end of a uniformly loaded cantilever be...
Given data:
Deflection at free end, y = 15 mm
Slope of deflection curve at free end, θ = 0.02 radian
To find: Length of the beam
Formula used:
The deflection at the free end of a cantilever beam under a uniformly distributed load is given by:
y = (wL^3)/(3EI)
The slope of the deflection curve at the free end of a cantilever beam under a uniformly distributed load is given by:
θ = (wL^2)/(2EI)
where,
w = uniformly distributed load
L = length of the beam
E = Young's modulus of the material of the beam
I = moment of inertia of the beam cross-section
Calculation:
Let's assume the Young's modulus and moment of inertia are the same throughout the beam. Therefore, we can equate the above two formulas to get the value of wL.
y = (wL^3)/(3EI)
θ = (wL^2)/(2EI)
Combining the above two equations, we get:
θ = (2y/L) * (1/L)
Solving for L, we get:
L = (2y/θ)^0.5
Substituting the given values, we get:
L = (2*15/0.02)^0.5
L = 1224.74 mm or 1.2247 m
Therefore, the length of the beam is 1 m (approx).
Hence, option (b) is the correct answer.
Deflection at free end, y = 15 mm
Slope of deflection curve at free end, θ = 0.02 radian
To find: Length of the beam
Formula used:
The deflection at the free end of a cantilever beam under a uniformly distributed load is given by:
y = (wL^3)/(3EI)
The slope of the deflection curve at the free end of a cantilever beam under a uniformly distributed load is given by:
θ = (wL^2)/(2EI)
where,
w = uniformly distributed load
L = length of the beam
E = Young's modulus of the material of the beam
I = moment of inertia of the beam cross-section
Calculation:
Let's assume the Young's modulus and moment of inertia are the same throughout the beam. Therefore, we can equate the above two formulas to get the value of wL.
y = (wL^3)/(3EI)
θ = (wL^2)/(2EI)
Combining the above two equations, we get:
θ = (2y/L) * (1/L)
Solving for L, we get:
L = (2y/θ)^0.5
Substituting the given values, we get:
L = (2*15/0.02)^0.5
L = 1224.74 mm or 1.2247 m
Therefore, the length of the beam is 1 m (approx).
Hence, option (b) is the correct answer.
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If the deflection at the free end of a uniformly loaded cantilever beam is 15 mm and the slope of the deflection curve at the free end is 0.02 radian. then the length of the beam isa) 0.8 mb) 1 mc) 1.2 md) 1.5 mCorrect answer is option 'B'. Can you explain this answer?
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