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A cantilever of length of span ‘L’ carries a uniformly distributed load of w per unit length over its entire span. If its span is halved, then its slope will become
- a)1/2
- b)1/4
- c)1/8
- d)1/16
Correct answer is option 'C'. Can you explain this answer?
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A cantilever of length of span ‘L’ carries a uniformly distributed lo...
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Solution:
Given, the cantilever of length of span ‘L’ carries a uniformly distributed load of w per unit length over its entire span.
Let us consider a cantilever of length L carrying a uniformly distributed load w per unit length over its entire span.
By using the equation of bending moment, we get,
M = wx^2/2
For finding the slope of the cantilever, we use the equation,
θ = d(y)/dx
where, θ = slope, y = deflection
By integrating the equation of deflection, we get,
y = wx^4/24EI
By differentiating the above equation, we get,
θ = d(y)/dx = wx^3/6EI
Now, let us consider the cantilever of span ‘L/2’ carrying the same load w per unit length over its entire span.
Using the equation of bending moment, we get,
M = wx^2/8
For finding the slope of the cantilever, we use the equation,
θ = d(y)/dx
where, θ = slope, y = deflection
By integrating the equation of deflection, we get,
y = wx^4/384EI
By differentiating the above equation, we get,
θ = d(y)/dx = wx^3/96EI
Comparing the slopes of both cantilevers, we get,
θ1/θ2 = (wx^3/6EI)/(wx^3/96EI)
θ1/θ2 = 16
Therefore, the slope of the cantilever becomes 1/8 when its span is halved. Hence, the correct option is C.
Given, the cantilever of length of span ‘L’ carries a uniformly distributed load of w per unit length over its entire span.
Let us consider a cantilever of length L carrying a uniformly distributed load w per unit length over its entire span.
By using the equation of bending moment, we get,
M = wx^2/2
For finding the slope of the cantilever, we use the equation,
θ = d(y)/dx
where, θ = slope, y = deflection
By integrating the equation of deflection, we get,
y = wx^4/24EI
By differentiating the above equation, we get,
θ = d(y)/dx = wx^3/6EI
Now, let us consider the cantilever of span ‘L/2’ carrying the same load w per unit length over its entire span.
Using the equation of bending moment, we get,
M = wx^2/8
For finding the slope of the cantilever, we use the equation,
θ = d(y)/dx
where, θ = slope, y = deflection
By integrating the equation of deflection, we get,
y = wx^4/384EI
By differentiating the above equation, we get,
θ = d(y)/dx = wx^3/96EI
Comparing the slopes of both cantilevers, we get,
θ1/θ2 = (wx^3/6EI)/(wx^3/96EI)
θ1/θ2 = 16
Therefore, the slope of the cantilever becomes 1/8 when its span is halved. Hence, the correct option is C.
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A cantilever of length of span ‘L’ carries a uniformly distributed load of w per unit length over its entire span. If its span is halved, then its slope will becomea) 1/2b) 1/4c) 1/8d) 1/16Correct answer is option 'C'. Can you explain this answer?
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