Problem # p012

Beam Deflection, Method of Superposition

A beam, supported at each end, is subject to the two loads P1 and P2 at the locations shown. Note that the distance a is less than L/2 and that the distance b is greater than L/2.
Develop the equation for the deflection at the midspan point x=L/2 of the beam in terms of the quantities P1, P2, a, b, and L. To do so, you only have available the equation :

The variables appearing in this equation have the following meaning :

δ = deflection at midspan
L = length of the beam
c = distance of force P from that end of the beam which is closest to P
E = Young's modulus
I = Central moment of Inertia of cross-section of beam