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Determining Elastic Equation of Beam with Linearly Distributed Load
I'm trying to solve this question, but I'm not sure where to start. Typically, to solve this type of problem, I would find the vertical support reaction at R (w0.L / 24), then cut the beam (in this case, between L/2 and L, where the load is applied) and determine the equation for the moment (5.w0.L/48 + 5.w0.L.x/24 + x^3 .w0/3L). I would then set the moment equation equal to EI.dy^2 / dx^2 and integrate to get
EIy = 5.w0.L^2 .x^2 /96 + 5.w0.Lx^3 /144 + x^5 .w0/60L + c1x + c2
However, that equation doesn't allow me to solve for point A, as it is only applicable to L/2 to L (and I don't even have boundary conditions to solve both constants). I don't know how to calculate an elastic equation that covers the whole beam in this scenario? Any help would be much appreciated!