plot heaviside functions with a linspace

Plotting the deflection of a beam using castigliano's second theorum. I already plotted it for at the application of load and it does match my FEA model so I believe it to be accurate. I am now trying to plot the deflctection everywhere and I am having trouble with integrating heaviside functions and letting the location of my dummy load go from 0 to the end of the beam. Don't know where to even start to d-bug this.

Thanks everyone

[Derek Reitnouer]

I think I need to loop at determined values of s where the dummy load is applied. I think this code is closer.