A tapered cantilever beam AB supports a concentrated load P at the free end (see figure). The

Question:

A tapered cantilever beam AB supports a concentrated load P at the free end (see figure).

The cross sections of the beam are rectangular with constant width b, depth dA at support A, and depth dB = 3dA/2 at the support. Thus, the depth d and moment of inertia I at distance x from the free end are, respectively,

in which IA is the moment of inertia at end A of the beam. Determine the equation of the deflection curve and the deflection Î´A at the free end of the beam due to the load P.