Does anyone know how the deflection formula for beam delfection was derived? Was it through integration? Any ideas would really help! :)

Most of these formulae are derived using the Unit-Load method, which also use integration.

The basic equation in beam theory is:


\frac {d^2} {dx^2} ( EI \frac {d^2 u} {dx^2} ) = w(x)


where u is displacement, E is Young's modulus ( a measure of how stiff the beam material is), I is the moment of inertia of the beam cross-section, and w(x) is the load applied to the beam. So yes, integration is definitely involved. For a simple point load P at the end of a cantilevered beam of length L (like a person standing on the end of a diving board), this collapses to


EI ( \frac {d^2 u} {dx^2} ) = PL


And the deflection out at the end of the diving board is:


u(L) = \frac {PL^3} {2 EI}


See Euler-Bernoulli beam equation - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation) for a primer on beam theory.