SLOPE AND DEFLECTION FOR A CANTILEVER BEAM SUBJECTED TO EXTERNAL MOMENT

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

ϴ_Q = (L) (-M/ EI)

ϴ_Q = (-ML/ EI)

Deflection at Q = (Area of M/EI diagram) (Centroidal distance from Q to O)

Y_{Q =} (L) (-M/ EI) (1/2L)

Y_Q= -ML²/2EI

Y_Q= ML²/2EI (downward direction)