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A cantilever beam of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?
- a)70 x 103 N-mm
- b)120 x 106 N-mm
- c)80 x 106 N-mm
- d)58.79 x 106 N-mm
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A cantilever beam of 5m length supports a triangularly distributed lo...
Mx = -w/2*x2+w/6L*x3
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maximum bending moment will be at x = L
ML = wL2/3
total load is given which is W = wL/2 (area of triangular distributed load)
So
Bending moment at fixed end = wl2/3
given total load 21 kN
Total load ⇒ wl/2 = 21
wl = 42
= 42 × 5 × 103/3
= 70,000 Nmm
Most Upvoted Answer
A cantilever beam of 5m length supports a triangularly distributed lo...
Calculation of Total Load:
Given that the total load on the cantilever beam is 21 N, which is distributed triangularly over its entire length. The maximum load is at the free end.
The total load can be calculated using the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base is the length of the beam (5m) and the height is the maximum load at the free end. Let's denote the maximum load as P.
Area = (1/2) * 5 * P = 2.5P
According to the problem, the total load is 21 N. So, we can equate the area to the total load and solve for P:
2.5P = 21
P = 21/2.5
P = 8.4 N
Therefore, the maximum load at the free end is 8.4 N.
Calculation of Bending Moment at Fixed End:
To calculate the bending moment at the fixed end of the cantilever beam, we need to consider the load distribution and the moment arm.
Since the load is distributed triangularly, the load at any point along the beam can be calculated using the equation for a straight line:
Load = (maximum load * distance from fixed end) / length of the beam
Let's denote the distance from the fixed end as x. The load at any point along the beam can be calculated as:
Load = (8.4 * x) / 5
The bending moment at any point along the beam is given by the equation:
Bending Moment = Load * Moment Arm
The moment arm is the distance from the point of interest to the fixed end of the beam. In this case, the moment arm is (5 - x).
So, the bending moment at any point along the beam can be calculated as:
Bending Moment = (8.4 * x) / 5 * (5 - x)
To find the bending moment at the fixed end, we substitute x = 5 into the equation:
Bending Moment at Fixed End = (8.4 * 5) / 5 * (5 - 5)
Bending Moment at Fixed End = (8.4 * 5) / 5 * 0
Bending Moment at Fixed End = 0 N-mm
Therefore, the bending moment at the fixed end of the cantilever beam is 0 N-mm.
From the given options, the correct answer is option A) 70 x 10^3 N-mm, which does not match the calculated value. It is possible that there is an error in the options provided.
Given that the total load on the cantilever beam is 21 N, which is distributed triangularly over its entire length. The maximum load is at the free end.
The total load can be calculated using the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, the base is the length of the beam (5m) and the height is the maximum load at the free end. Let's denote the maximum load as P.
Area = (1/2) * 5 * P = 2.5P
According to the problem, the total load is 21 N. So, we can equate the area to the total load and solve for P:
2.5P = 21
P = 21/2.5
P = 8.4 N
Therefore, the maximum load at the free end is 8.4 N.
Calculation of Bending Moment at Fixed End:
To calculate the bending moment at the fixed end of the cantilever beam, we need to consider the load distribution and the moment arm.
Since the load is distributed triangularly, the load at any point along the beam can be calculated using the equation for a straight line:
Load = (maximum load * distance from fixed end) / length of the beam
Let's denote the distance from the fixed end as x. The load at any point along the beam can be calculated as:
Load = (8.4 * x) / 5
The bending moment at any point along the beam is given by the equation:
Bending Moment = Load * Moment Arm
The moment arm is the distance from the point of interest to the fixed end of the beam. In this case, the moment arm is (5 - x).
So, the bending moment at any point along the beam can be calculated as:
Bending Moment = (8.4 * x) / 5 * (5 - x)
To find the bending moment at the fixed end, we substitute x = 5 into the equation:
Bending Moment at Fixed End = (8.4 * 5) / 5 * (5 - 5)
Bending Moment at Fixed End = (8.4 * 5) / 5 * 0
Bending Moment at Fixed End = 0 N-mm
Therefore, the bending moment at the fixed end of the cantilever beam is 0 N-mm.
From the given options, the correct answer is option A) 70 x 10^3 N-mm, which does not match the calculated value. It is possible that there is an error in the options provided.
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A cantilever beam of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. Can you explain this answer?
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A cantilever beam of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. 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 of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. 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 of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. Can you explain this answer?.
A cantilever beam of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. 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 of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. 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 of 5m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 21 N. What is the bending moment at fixed end?a)70 x 103 N-mmb)120 x 106 N-mmc)80 x 106 N-mmd)58.79 x 106 N-mmCorrect answer is option 'A'. Can you explain this answer?.
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