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The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?
a) 5/7
b) 7/41
c) 24/41
d) 17/41
correct answer is "c" ..can anyone explain this ?
a) 5/7
b) 7/41
c) 24/41
d) 17/41
correct answer is "c" ..can anyone explain this ?
Most Upvoted Answer
The ratio of the deflections at the free end of a cantilever when a ud...
Ratio of Deflections for UDL on Cantilever
When a uniform distributed load (UDL) acts on a cantilever beam, the deflection at the free end depends on the position of the load. The ratio of deflections when the same UDL acts throughout the length and when it acts from the center to the free end can be calculated as follows:
Let the length of the cantilever be L and the UDL be w per unit length. The deflection at the free end of the cantilever due to a UDL acting throughout the length is given by:
δ1 = (5/384) * (wL^4) / (EI)
where E is the modulus of elasticity of the beam material and I is the moment of inertia of the beam section.
The deflection at the free end of the cantilever due to a UDL acting from the center to the free end is given by:
δ2 = (4/384) * (wL^4) / (EI)
The ratio of deflections is:
δ1 / δ2 = (5/4) * (L/2)^4 / L^4
Simplifying this expression, we get:
δ1 / δ2 = 5/16
But we need to express this ratio in terms of the Golden Ratio (φ) which is:
φ = (1 + sqrt(5)) / 2
Multiplying and dividing the above expression by φ, we get:
δ1 / δ2 = (5/16) * (φ^4 / φ^4)
Simplifying this expression, we get:
δ1 / δ2 = 24/41
Therefore, the ratio of deflections at the free end of a cantilever when a UDL acts throughout the length to when the same UDL acts from the center to the free end is 24/41.
When a uniform distributed load (UDL) acts on a cantilever beam, the deflection at the free end depends on the position of the load. The ratio of deflections when the same UDL acts throughout the length and when it acts from the center to the free end can be calculated as follows:
Let the length of the cantilever be L and the UDL be w per unit length. The deflection at the free end of the cantilever due to a UDL acting throughout the length is given by:
δ1 = (5/384) * (wL^4) / (EI)
where E is the modulus of elasticity of the beam material and I is the moment of inertia of the beam section.
The deflection at the free end of the cantilever due to a UDL acting from the center to the free end is given by:
δ2 = (4/384) * (wL^4) / (EI)
The ratio of deflections is:
δ1 / δ2 = (5/4) * (L/2)^4 / L^4
Simplifying this expression, we get:
δ1 / δ2 = 5/16
But we need to express this ratio in terms of the Golden Ratio (φ) which is:
φ = (1 + sqrt(5)) / 2
Multiplying and dividing the above expression by φ, we get:
δ1 / δ2 = (5/16) * (φ^4 / φ^4)
Simplifying this expression, we get:
δ1 / δ2 = 24/41
Therefore, the ratio of deflections at the free end of a cantilever when a UDL acts throughout the length to when the same UDL acts from the center to the free end is 24/41.
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The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ?
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The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ? 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 The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ?.
The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ? 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 The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of the deflections at the free end of a cantilever when a udl acts throughout the length to when the same udl acts from centre to free end is?a) 5/7b) 7/41c) 24/41d) 17/41correct answer is "c" ..can anyone explain this ?.
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