#### Beam Deflection, Method of Superposition

A beam, supported at each end, is subject to the two loads P_{1}
and P_{2} 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
*P*_{1}, P_{2}, 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