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If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam is
- a)0.8 m
- b)1.0 m
- c)1.2 m
- d)1.5 m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If the deflection at free end of a uniformly loaded cantilever beam is...
_______1
_______2From (2) ⇒
0.02 × 6 = 0.12substitute in equation (1)
⇒ l = 1.2 m
Most Upvoted Answer
If the deflection at free end of a uniformly loaded cantilever beam is...
Understanding the Problem
In this problem, we are dealing with a cantilever beam subjected to a uniform load. We have two key pieces of information:
- The deflection at the free end of the beam (δ) is 18 mm.
- The slope of the deflection curve at the free end (θ) is 0.02.
The goal is to find the length of the beam (L).
Formulas for Cantilever Beam
For a uniformly loaded cantilever beam, the relationships between deflection, slope, and length can be defined as follows:
- The formula for deflection at the free end:
δ = (w * L^4) / (8 * E * I)
- The formula for slope at the free end:
θ = (w * L^3) / (3 * E * I)
Where:
- w = uniform load per unit length
- E = modulus of elasticity
- I = moment of inertia
Relating Deflection and Slope
From the two equations, we can derive a relationship between deflection and slope. By eliminating w, we can express L in terms of δ and θ.
By manipulating the equations, we arrive at a simplified relation:
L = (3 * δ / θ)^(1/3)
Calculating Length of the Beam
Substituting the given values:
- δ = 18 mm = 0.018 m
- θ = 0.02
L = (3 * 0.018 / 0.02)^(1/3)
Calculating this gives us:
L = (2.7)^(1/3) ≈ 1.2 m
Conclusion
Thus, the length of the cantilever beam is approximately 1.2 m, confirming that the correct answer is option 'C'.
In this problem, we are dealing with a cantilever beam subjected to a uniform load. We have two key pieces of information:
- The deflection at the free end of the beam (δ) is 18 mm.
- The slope of the deflection curve at the free end (θ) is 0.02.
The goal is to find the length of the beam (L).
Formulas for Cantilever Beam
For a uniformly loaded cantilever beam, the relationships between deflection, slope, and length can be defined as follows:
- The formula for deflection at the free end:
δ = (w * L^4) / (8 * E * I)
- The formula for slope at the free end:
θ = (w * L^3) / (3 * E * I)
Where:
- w = uniform load per unit length
- E = modulus of elasticity
- I = moment of inertia
Relating Deflection and Slope
From the two equations, we can derive a relationship between deflection and slope. By eliminating w, we can express L in terms of δ and θ.
By manipulating the equations, we arrive at a simplified relation:
L = (3 * δ / θ)^(1/3)
Calculating Length of the Beam
Substituting the given values:
- δ = 18 mm = 0.018 m
- θ = 0.02
L = (3 * 0.018 / 0.02)^(1/3)
Calculating this gives us:
L = (2.7)^(1/3) ≈ 1.2 m
Conclusion
Thus, the length of the cantilever beam is approximately 1.2 m, confirming that the correct answer is option 'C'.
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If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer?.
If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer? for Civil Engineering (CE) 2025 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer?.
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If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of If the deflection at free end of a uniformly loaded cantilever beam is 18 mm and the slope of the deflection curve at the free end is 0.02 then the length of the beam isa)0.8 mb)1.0 mc)1.2 md)1.5 mCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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