A simple beam ACB is constructed with square cross sections and a double taper (see figure).

The depth of the beam at the supports is dA and at the midpoint is dC = 2dA. Each half of the beam has length L. Thus, the depth d and moment of inertia I at distance x from the left-hand end are, respectively,
in which IA is the moment of inertia at end A of the beam. (These equations are valid for x between 0 and L, that is, for the left-hand half of the beam.)
(a) Obtain equations for the slope and deflection of the left-hand half of the beam due to the uniform load.
(b) From those equations obtain formulas for the angle of rotation θA at support A and the deflection δC at the midpoint.

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