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A cantilever of length L, moment of inertia I,Young's modulus E carries a concentrated load W at the middle of its length. The slope ofcantilever at the free end is
- a)WL.2/2EI
- b)WL2/4EI
- c)WL2/8EI
- d)WL2/16EI
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cantilever of length L, moment of inertia I,Youngs modulus E carries...
The slope of cantilever at the free end is WL^2 / 2EI
When a concentrated load W is applied at the middle of the cantilever, the cantilever will bend and produce a slope at the free end. The amount of slope is determined by the amount of load, the length of the cantilever, the moment of inertia of the cantilever, and the Young's modulus of the material.
The slope at the free end can be determined using the slope-deflection equation which relates the load, the length, the moment of inertia and the Young's modulus of the cantilever. The slope at the free end of the cantilever is given by:
θ = WL^2 / 2EI
Where
θ = slope at the free end
W = concentrated load at the middle of the cantilever
L = length of the cantilever
E = Young's modulus of the material
I = moment of inertia of the cantilever
Hence the answer is WL^2 / 2EI which corresponds to option A.
Most Upvoted Answer
A cantilever of length L, moment of inertia I,Youngs modulus E carries...
Given:
Length of Cantilever, L
Moment of Inertia, I
Young's Modulus, E
Concentrated Load, W at the middle of its length
To Find: The slope of the cantilever at the free end
Solution:
The slope of the cantilever at the free end can be determined by taking the moment of the concentrated load W about the fixed end of the cantilever and then using it to calculate the deflection at the free end.
1. Moment of the concentrated load about the fixed end:
The moment of the concentrated load W about the fixed end of the cantilever is given by:
M = W(L/2)
2. Deflection at the free end:
The deflection at the free end of the cantilever due to the moment M can be calculated using the following equation:
θ = M*L/(2*EI)
Where θ is the slope of the cantilever at the free end.
3. Substituting the value of M in the above equation, we get:
θ = W(L/2)*L/(2*EI)
Simplifying the above equation, we get:
θ = WL^2/(4EI)
Therefore, the slope of the cantilever at the free end is given by option 'A': WL.2/2EI
Length of Cantilever, L
Moment of Inertia, I
Young's Modulus, E
Concentrated Load, W at the middle of its length
To Find: The slope of the cantilever at the free end
Solution:
The slope of the cantilever at the free end can be determined by taking the moment of the concentrated load W about the fixed end of the cantilever and then using it to calculate the deflection at the free end.
1. Moment of the concentrated load about the fixed end:
The moment of the concentrated load W about the fixed end of the cantilever is given by:
M = W(L/2)
2. Deflection at the free end:
The deflection at the free end of the cantilever due to the moment M can be calculated using the following equation:
θ = M*L/(2*EI)
Where θ is the slope of the cantilever at the free end.
3. Substituting the value of M in the above equation, we get:
θ = W(L/2)*L/(2*EI)
Simplifying the above equation, we get:
θ = WL^2/(4EI)
Therefore, the slope of the cantilever at the free end is given by option 'A': WL.2/2EI
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Community Answer
A cantilever of length L, moment of inertia I,Youngs modulus E carries...
C option is correct
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A cantilever of length L, moment of inertia I,Youngs modulus E carries a concentrated load W at the middle of its length. The slope ofcantilever at the free end isa)WL.2/2EIb)WL2/4EIc)WL2/8EId)WL2/16EICorrect answer is option 'A'. Can you explain this answer?
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A cantilever of length L, moment of inertia I,Youngs modulus E carries a concentrated load W at the middle of its length. The slope ofcantilever at the free end isa)WL.2/2EIb)WL2/4EIc)WL2/8EId)WL2/16EICorrect answer is option 'A'. Can you explain this answer? 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 A cantilever of length L, moment of inertia I,Youngs modulus E carries a concentrated load W at the middle of its length. The slope ofcantilever at the free end isa)WL.2/2EIb)WL2/4EIc)WL2/8EId)WL2/16EICorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever of length L, moment of inertia I,Youngs modulus E carries a concentrated load W at the middle of its length. The slope ofcantilever at the free end isa)WL.2/2EIb)WL2/4EIc)WL2/8EId)WL2/16EICorrect answer is option 'A'. Can you explain this answer?.
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