I was wondering how you would derive the moment and elastic curve equations for an incomplete triangular load. Say you have a pin at the left end of the beam and a roller at L/2 from the left, and a triangular load that goes from the pin and ends at the roller. I know you have to do some kind of extension, but how do you come up with the formula.
When you say "triangular load", you mean a distributed load that's zero at the left end and increases linearly to the roller at L/2?
If you know Δ(x) and θ2 for a simply supported beam as a function of L' = L/2 with a triangular load then the deflection would be: Δ = Δ(x) for x=<L/2 = θ2*(x-L/2) for x>=L/2