Question
Download Solution PDFA 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
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:
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,
\(\frac{wl^4}{8EI} -\frac{Rl^3}{3EI}= \frac{Rl^3}{48EI}\)
\(\frac{wl^4}{8EI} = \frac{Rl^3}{48EI} + \frac{Rl^3}{3EI}\)
\(\frac{wl^4}{8EI}=(\frac{1+16}{48})\frac{Rl^3}{EI}\)
\(R=\frac{6wl}{17}\)
Last updated on May 28, 2025
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