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A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also at
- a)mid point of the cantilever
- b)fixed point of the cantilever
- c)1/4th length from free end
- d)3/4th length from free end
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A cantilever carrying uniformly distributed load W over its full lengt...
Explanation:
When a cantilever is propped at its free end, the reaction force at the prop is equal and opposite to the load W. This means that the cantilever is in equilibrium and the bending moment at any point along the length of the cantilever must be zero.
However, the distribution of the bending moment is not uniform along the length of the cantilever. It is maximum at the fixed end and decreases towards the free end. The location of zero bending moment can be determined by equating the bending moment equation to zero.
The bending moment equation for a uniformly distributed load over the full length of a cantilever is given by:
M(x) = (Wx^2)/2 - Wl^2x/2
Where,
M(x) is the bending moment at a distance x from the fixed end
W is the uniformly distributed load
l is the length of the cantilever
To find the location of zero bending moment, we need to solve the above equation for M(x) = 0.
(Wx^2)/2 - Wl^2x/2 = 0
x^2 - l^2x = 0
x(x - l^2) = 0
x = 0 or x = l^2
Since the bending moment is zero at the fixed end, the only valid solution is x = l^2. This means that the bending moment is zero at a distance of 3/4th length from the free end of the cantilever.
When a cantilever is propped at its free end, the reaction force at the prop is equal and opposite to the load W. This means that the cantilever is in equilibrium and the bending moment at any point along the length of the cantilever must be zero.
However, the distribution of the bending moment is not uniform along the length of the cantilever. It is maximum at the fixed end and decreases towards the free end. The location of zero bending moment can be determined by equating the bending moment equation to zero.
The bending moment equation for a uniformly distributed load over the full length of a cantilever is given by:
M(x) = (Wx^2)/2 - Wl^2x/2
Where,
M(x) is the bending moment at a distance x from the fixed end
W is the uniformly distributed load
l is the length of the cantilever
To find the location of zero bending moment, we need to solve the above equation for M(x) = 0.
(Wx^2)/2 - Wl^2x/2 = 0
x^2 - l^2x = 0
x(x - l^2) = 0
x = 0 or x = l^2
Since the bending moment is zero at the fixed end, the only valid solution is x = l^2. This means that the bending moment is zero at a distance of 3/4th length from the free end of the cantilever.
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Community Answer
A cantilever carrying uniformly distributed load W over its full lengt...
Deflection for cantilever udl = wl^4/8EI.
Deflection for point load = pl^3/3EI.
Equating both deflections.
Wl^4/8EI=pl^3/3EI.
Here p=3wl/8.
Let a section xx at the distance x from the free end.
Then, Mx = p*x-w*x*x/2.
Mx= 3wlx/8 -wxx/2.
For Mx = 0.
So, x=(3/4)l, so at 3/4 distance from the free end where BM=0.
Deflection for point load = pl^3/3EI.
Equating both deflections.
Wl^4/8EI=pl^3/3EI.
Here p=3wl/8.
Let a section xx at the distance x from the free end.
Then, Mx = p*x-w*x*x/2.
Mx= 3wlx/8 -wxx/2.
For Mx = 0.
So, x=(3/4)l, so at 3/4 distance from the free end where BM=0.
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A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer?
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A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer?.
A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A cantilever carrying uniformly distributed load W over its full length is propped at its free end such that it is at the level of the fixed end. The bending moment will be zero at its free end and also ata)mid point of the cantileverb)fixed point of the cantileverc)1/4th length from free endd)3/4th length from free endCorrect answer is option 'D'. Can you explain this answer?.
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