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A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?
- a)50 x 106 N mm
- b)12.5 x 106 N mm
- c)100 x 106 N mm
- d)25 x 106 N mm
Correct answer is option 'A'. Can you explain this answer?
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A cantilever beam of 2m length supports a triangularly distributed loa...
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Given:
Length of cantilever beam = 2 m
Total load = 37.5 kN
To find: Bending moment at the fixed end of the beam
Approach:
1. Calculate the maximum load at the free end of the beam
2. Calculate the area of the triangular load distribution
3. Calculate the centroid of the triangular load distribution
4. Use the principle of moments to calculate the bending moment at the fixed end of the beam
Calculation:
1. The maximum load at the free end of the beam can be calculated as follows:
Maximum load = Total load x (1/2)
= 37.5 kN x (1/2)
= 18.75 kN
2. The area of the triangular load distribution can be calculated as follows:
Area of triangle = (base x height) / 2
= (2 m x 18.75 kN) / 2
= 18.75 kN-m
3. The centroid of the triangular load distribution can be calculated as follows:
Centroid = (2/3) x height from the fixed end of the beam
= (2/3) x (2 m)
= 1.33 m
4. The bending moment at the fixed end of the beam can be calculated using the principle of moments:
Bending moment at fixed end = Total load x distance to centroid
= 37.5 kN x 1.33 m
= 50 x 10^6 N-mm
Therefore, the correct answer is option A, 50 x 10^6 N-mm.
Length of cantilever beam = 2 m
Total load = 37.5 kN
To find: Bending moment at the fixed end of the beam
Approach:
1. Calculate the maximum load at the free end of the beam
2. Calculate the area of the triangular load distribution
3. Calculate the centroid of the triangular load distribution
4. Use the principle of moments to calculate the bending moment at the fixed end of the beam
Calculation:
1. The maximum load at the free end of the beam can be calculated as follows:
Maximum load = Total load x (1/2)
= 37.5 kN x (1/2)
= 18.75 kN
2. The area of the triangular load distribution can be calculated as follows:
Area of triangle = (base x height) / 2
= (2 m x 18.75 kN) / 2
= 18.75 kN-m
3. The centroid of the triangular load distribution can be calculated as follows:
Centroid = (2/3) x height from the fixed end of the beam
= (2/3) x (2 m)
= 1.33 m
4. The bending moment at the fixed end of the beam can be calculated using the principle of moments:
Bending moment at fixed end = Total load x distance to centroid
= 37.5 kN x 1.33 m
= 50 x 10^6 N-mm
Therefore, the correct answer is option A, 50 x 10^6 N-mm.
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A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer?
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A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer?.
A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever beam of 2m length supports a triangularly distributed load over its entire length, the maximum of which is at the free end. The total load is 37.5 kN.What is the bending moment at the fixed end?a)50 x106 N mmb)12.5 x106 N mmc)100 x106 N mmd)25 x106 N mmCorrect answer is option 'A'. Can you explain this answer?.
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