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A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is?
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A simply supported beam ABC of length l carries a concentrated load P ...
Solution:
Given data:
Length of beam = l
Load on beam = P
Slope at point A = 0.75 times slope at point C
To find: Length of portion AN
Assumptions:
Beam is homogeneous and isotropic.
The deflection of the beam is negligible.
Beam is simply supported.
The beam is subjected to a concentrated load at point B.
The beam has negligible self-weight.
The bending moment at point B is zero.
Analysis:
Let us consider the beam ABC as shown in the figure below.
The beam is simply supported at points A and C.
The beam carries a concentrated load P at point B.
The bending moment at points A and C is zero.
Therefore, the bending moment at point B can be calculated as follows:
M_B = P * l / 2
The slope at point A is given as:
θ_A = 0.75 * θ_C
The slope of the beam at point A can be calculated as follows:
θ_A = M_B * l / (2 * EI)
where E is the modulus of elasticity of the beam material and I is the moment of inertia of the beam cross-section.
The slope of the beam at point C can be calculated as follows:
θ_C = M_B * l / (2 * EI)
Therefore, we have:
θ_A / θ_C = 0.75
(M_B * l / (2 * EI)) / (M_B * l / (2 * EI)) = 0.75
1 = 0.75
This is not possible.
Therefore, the given data is not consistent.
Hence, the length of portion AN cannot be determined.
Conclusion:
The given data is not consistent. Therefore, the length of portion AN cannot be determined.
Given data:
Length of beam = l
Load on beam = P
Slope at point A = 0.75 times slope at point C
To find: Length of portion AN
Assumptions:
Beam is homogeneous and isotropic.
The deflection of the beam is negligible.
Beam is simply supported.
The beam is subjected to a concentrated load at point B.
The beam has negligible self-weight.
The bending moment at point B is zero.
Analysis:
Let us consider the beam ABC as shown in the figure below.
The beam is simply supported at points A and C.
The beam carries a concentrated load P at point B.
The bending moment at points A and C is zero.
Therefore, the bending moment at point B can be calculated as follows:
M_B = P * l / 2
The slope at point A is given as:
θ_A = 0.75 * θ_C
The slope of the beam at point A can be calculated as follows:
θ_A = M_B * l / (2 * EI)
where E is the modulus of elasticity of the beam material and I is the moment of inertia of the beam cross-section.
The slope of the beam at point C can be calculated as follows:
θ_C = M_B * l / (2 * EI)
Therefore, we have:
θ_A / θ_C = 0.75
(M_B * l / (2 * EI)) / (M_B * l / (2 * EI)) = 0.75
1 = 0.75
This is not possible.
Therefore, the given data is not consistent.
Hence, the length of portion AN cannot be determined.
Conclusion:
The given data is not consistent. Therefore, the length of portion AN cannot be determined.
Community Answer
A simply supported beam ABC of length l carries a concentrated load P ...
5l/7
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A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is?
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A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is? 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 simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is?.
A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is? 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 simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B if the slope at A is 0.75 times the slope at C then length of portion AN is?.
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