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A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will be
- a)2 δ
- b)δ
- c)δ /4
- d)δ /2
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A cantilever beam AB, fixed at the end A and carrying a load W at the ...
Using Maxwell Reciprocal theorem
Virtual Work Done = Constant
Virtual Work Done = Constant
(Load at Mid Point) (Deflection at Mid-Point due to load at B) = (Load at B) (Deflection at B due to load at Mid Point)
(0.5 W) (δ) = ( W) (Deflection at B)
Deflection at B = (δ)/2
Deflection at B = (δ)/2
Most Upvoted Answer
A cantilever beam AB, fixed at the end A and carrying a load W at the ...
An amount δ under the load. The deflection δ can be calculated using the following formula:
δ = (W*L^3)/(3*E*I)
where W is the load applied at the free end B, L is the length of the beam, E is the elastic modulus of the material of the beam, and I is the moment of inertia of the beam's cross-section.
The moment of inertia I can be calculated using the formula:
I = (b*d^3)/12
where b is the width of the beam and d is the depth of the beam.
Once the deflection δ is calculated, the stress and strain in the beam can be determined using the following equations:
σ = M*y/I
ε = δ/y
where M is the bending moment at a point y on the beam, calculated using the formula:
M = W*(L-y)
Overall, the deflection of a cantilever beam under a load can be calculated using several formulas and equations, taking into account the material properties and dimensions of the beam.
δ = (W*L^3)/(3*E*I)
where W is the load applied at the free end B, L is the length of the beam, E is the elastic modulus of the material of the beam, and I is the moment of inertia of the beam's cross-section.
The moment of inertia I can be calculated using the formula:
I = (b*d^3)/12
where b is the width of the beam and d is the depth of the beam.
Once the deflection δ is calculated, the stress and strain in the beam can be determined using the following equations:
σ = M*y/I
ε = δ/y
where M is the bending moment at a point y on the beam, calculated using the formula:
M = W*(L-y)
Overall, the deflection of a cantilever beam under a load can be calculated using several formulas and equations, taking into account the material properties and dimensions of the beam.
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A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer?
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A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer?.
A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam AB, fixed at the end A and carrying a load W at the force end B, is found to deflect by δ at the midpoint of AB. The deflection of B due to load W/2 at the midpoint will bea)2 δb)δc)δ /4d)δ /2Correct answer is option 'D'. Can you explain this answer?.
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