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How to solve Euler-Bernoulli beam for point load?
I am student and learning beam theory. I am trying to solve Euler-Bernoulli 4th order differential equation to find the deflection of a beam. The equation is
EI v''''(x) = w
where v is the transverse deflection and w is the distributed uniform load on the beam.
But how would you solve the above if the beam is fixed on both ends, and instead of w, I have a point load P at say distance 'a' from the left end? For a beam fixed on both ends, I use the following boundary conditions
v'(0)=0; v(0)=0; v'(L)=0; v(L)=0; assuming the beam has length L.
But the problem for me, is that the above equation is meant to be used when the load is distributed over the beam. So, when the load is only a point load, what should I do? The wiki page http://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory here seems to talk a little about this, but I could not understand it. I am only a first year student.
Any one can explain in simple terms what I need to do for point load? (assuming there is no w, just a point load somewhere on the beam, both ends fixed). Sorry that my question is very basic for this advanced forum, but I did not know where else to ask this.