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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?
Most Upvoted 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
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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? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
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? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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?.
Solutions for 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? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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