SLOPE AND DEFLECTION FOR A CANTILEVER BEAM SUBJECTED
TO EXTERNAL MOMENT
Fig 1
Fig 2
Consider a cantilever beam PQ of length L subjected to external moment M
on the free end side of the beam.
Fig
2 show the M/EI diagram for the beam subjected to external moment. The effect
of moment remains same throughout the beam; hence there is invariability in
M/EI diagram.
Slope
at the free end = Area of M/EI diagram
ϴQ = (L) (-M/ EI)
ϴQ = (-ML/ EI)
Deflection at Q = (Area of M/EI diagram) (Centroidal distance from Q to
O)
YQ = (L) (-M/ EI) (1/2L)
YQ= -ML2/2EI
YQ= ML2/2EI
(downward direction)
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