A cantilever of beam of span l is fixed at one end, the other end resting freely on the middle of a simply supported cross-beam of the same span and section. If the cantilever beam is now loaded with a uniform load of w per unit length, find the reaction at the free end offered by the cross beam.

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  1. \(\frac{3}{8} wl\)
  2. \(\frac{2}{5}wl\)
  3. \(\frac{6}{17}wl\)
  4. \(\frac{3}{17}wl\)

Answer (Detailed Solution Below)

Option 3 : \(\frac{6}{17}wl\)
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Detailed Solution

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Concept:

Deflection of cantilever beam due to point load = \(\frac{Pl^3}{3EI}\)

Deflection of cantilever beam due to udl = \(\frac{wl^4}{8EI}\)

Deflection of SSB due to point load at mid point = \(\frac{Pl^3}{48EI}\)

Solution:

F1 AbhishekM Madhuri 27.11.2021 D2

Deflection at the end of cantilever beam is given by,

\(=\frac{wl^4}{8EI}-\frac{Rl^3}{3EI}\)

Deflection at midpoint of SSB.

=\(\frac{Rl^3}{48EI}\)

Equating both the cases,

\(\frac{wl^4}{8EI} -\frac{Rl^3}{3EI}= \frac{Rl^3}{48EI}\)

\(\frac{wl^4}{8EI} = \frac{Rl^3}{48EI} + \frac{Rl^3}{3EI}\)

\(\frac{wl^4}{8EI}=(\frac{1+16}{48})\frac{Rl^3}{EI}\)

\(R=\frac{6wl}{17}\)

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