Question
Download Solution PDFTwo cantilever beams are of equal length. One carries a uniformly distributed load and other carries same load but concentrated at the free end. The ratio of maximum deflections is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Deflection and slope of various beams are given by:
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\({y_B} = \frac{{P{L^3}}}{{3EI}}\) |
\({\theta _B} = \frac{{P{L^2}}}{{2EI}}\) |
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\({y_B} = \frac{{w{L^4}}}{{8EI}}\) |
\({\theta _B} = \frac{{w{L^3}}}{{6EI}}\) |
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\({y_B} = \frac{{M{L^2}}}{{2EI}}\) |
\({\theta _B} = \frac{{ML}}{{EI}}\) |
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\({y_B} = \frac{{w{L^4}}}{{30EI}}\) |
\({\theta _B} = \frac{{w{L^3}}}{{24EI}}\) |
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\({y_c} = \frac{{P{L^3}}}{{48EI}}\) |
\({\theta _B} = \frac{{P{L^2}}}{{16EI\;}}\) |
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\({y_c} = \frac{5}{{384}}\frac{{w{L^4}}}{{EI}}\) |
\({\theta _B} = \frac{{w{L^3}}}{{24EI}}\) |
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\({y_c} = 0\) |
\({\theta _B} = \frac{{ML}}{{24EI}}\) |
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\({y_c} = \frac{{M{L^2}}}{{8EI}}\) |
\({\theta _B} = \frac{{ML}}{{2EI}}\) |
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\({y_c} = \frac{{P{L^3}}}{{192EI}}\) |
\({\theta _A} = {\theta _B} = {\theta _C} = 0\) |
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\({y_c} = \frac{{w{L^4}}}{{384EI}}\) |
\({\theta _A} = {\theta _B} = {\theta _C} = 0\) |
Where, y = Deflection of the beam, θ = Slope of beam
From the table,
The maximum deflection of a cantilever beam having uniformly distributed load is given as,
\({y_A} = \frac{{w{L^4}}}{{8EI}}=\frac{PL^3}{8EI}\)...................(1)
The maximum deflection of a cantilever beam having point load is given as,
\({y_B} = \frac{{P{L^3}}}{{3EI}}\)...................(2)
From both equation,
\(\frac{y_A}{y_B}=\frac{3}{8}\)
Last updated on Mar 27, 2025
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