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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 the length of portion AB is equal to?
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A simply supported beam ABC of length l carries a concentrated load P ...
Solution:
Understanding the problem
A simply supported beam ABC of length l carries a concentrated load P at an intermediate point B. The slope at A is 0.75 times the slope at C. We have to find the length of portion AB.
Assumptions
We assume that the beam is uniform and the cross-section of the beam is constant.
Free Body Diagram
We draw the free body diagram of the beam.
We take moments about A.
∑MA = 0
P(l/2 - AB) - RA * AB = 0
RA = P(l/2 - AB) / AB
Now, we take moments about C.
∑MC = 0
P(l/2 - BC) - RC * BC = 0
RC = P(l/2 - BC) / BC
Slope
The slope at A is given by:
θA = RA * AB2 / (2EI)
The slope at C is given by:
θC = RC * BC2 / (2EI)
We know that θA = 0.75 * θC
Substituting the values of RA and RC, we get:
AB3 / BC3 = 3 * 0.75 * (l - BC) / (2 * BC * (l - AB))
Solving for AB
We simplify the above equation to get:
AB3 = 2.25 * BC3 - 3 * BC2 * AB + 1.5 * l * BC2 - 2.25 * l * BC * AB
We solve this equation to get the value of AB.
Final Answer
The length of portion AB is equal to the value of AB obtained from the above equation.
Community Answer
A simply supported beam ABC of length l carries a concentrated load P ...
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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 the length of portion AB is equal to?
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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 the length of portion AB is equal to? 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 the length of portion AB is equal to? 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 the length of portion AB is equal to?.
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 the length of portion AB is equal to? 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 the length of portion AB is equal to? 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 the length of portion AB is equal to?.
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