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In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is
(A) W1/W2
(B) W2/W1
(C) W2/(W1+ W2)
(D) W1/(W1 + W2)?
(A) W1/W2
(B) W2/W1
(C) W2/(W1+ W2)
(D) W1/(W1 + W2)?
Most Upvoted Answer
In a cantilever beam, 'd2' is the deflection at a distance x from fixe...
Understanding Deflection in a Cantilever Beam
In the given scenario, we have a cantilever beam with two different loads acting on it. The deflections due to these loads can be analyzed using the principles of mechanics.
Deflections Explained
- d1: Deflection at a distance x from the fixed end due to load W1 acting at the tip.
- d2: Deflection at the tip of the beam due to load W2 acting at a distance x from the fixed end.
Key Principles of Deflection
- The deflection of a cantilever beam under a point load can be calculated using the formula:
Deflection (δ) = (Load * Distance^2) / (3 * EI) for a load at the free end, and
Deflection (δ) = (Load * Distance^3) / (3 * EI * Length) for a load not at the free end.
Here, E is the modulus of elasticity, and I is the moment of inertia.
Ratio of Deflections
- When comparing the two deflections:
- For W1: The deflection at distance x will be influenced by the total load acting on the beam.
- For W2: The deflection at the tip also depends on the relative distances and the nature of loading.
Conclusion: Ratio of d1 to d2
- The relationship between these deflections can be expressed as:
d1/d2 = W1/(W1 + W2).
- Therefore, the correct answer is (D) W1/(W1 + W2). This indicates how the deflections relate to each other based on their respective loads.
Understanding these concepts helps in designing safe and efficient structures by accurately predicting deflections in beams under various loading conditions.
In the given scenario, we have a cantilever beam with two different loads acting on it. The deflections due to these loads can be analyzed using the principles of mechanics.
Deflections Explained
- d1: Deflection at a distance x from the fixed end due to load W1 acting at the tip.
- d2: Deflection at the tip of the beam due to load W2 acting at a distance x from the fixed end.
Key Principles of Deflection
- The deflection of a cantilever beam under a point load can be calculated using the formula:
Deflection (δ) = (Load * Distance^2) / (3 * EI) for a load at the free end, and
Deflection (δ) = (Load * Distance^3) / (3 * EI * Length) for a load not at the free end.
Here, E is the modulus of elasticity, and I is the moment of inertia.
Ratio of Deflections
- When comparing the two deflections:
- For W1: The deflection at distance x will be influenced by the total load acting on the beam.
- For W2: The deflection at the tip also depends on the relative distances and the nature of loading.
Conclusion: Ratio of d1 to d2
- The relationship between these deflections can be expressed as:
d1/d2 = W1/(W1 + W2).
- Therefore, the correct answer is (D) W1/(W1 + W2). This indicates how the deflections relate to each other based on their respective loads.
Understanding these concepts helps in designing safe and efficient structures by accurately predicting deflections in beams under various loading conditions.
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In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)?
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In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)? 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 In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)?.
In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)? 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 In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)?.
Solutions for In a cantilever beam, 'd2' is the deflection at a distance x from fixed end support due to a load 'W1' acting at the tip of the beam and 'dl' is the deflection at the tip of the beam due to a load 'W2' acting at a distance x from fixed end support. Then the ratio of d1/d2 is(A) W1/W2(B) W2/W1(C) W2/(W1+ W2)(D) W1/(W1 + W2)? in English & in Hindi are available as part of our courses for Civil Engineering (CE).
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