Problem # p042

Beam Deflection, Method of Superposition

A beam, supported at each end, is subject to the continuous load as shown in the figure to the left.
Determine the equation for the slope (E) at the left end of the beam in terms of the lengths b, c, and L and the weight per unit length, wo, using the method of superposition based on the case given below.

Given is the solution for the following case :

The variables appearing in this equation have the following meaning :

= slope at left end of beam
= slope at right end of beam
L = length of the beam
a = length of continuous load which ends at right end of beam
E = Young's modulus
= Moment of Inertia of cross-section of beam