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I am creating a torsional testing rig for a Formula Sae car, the front of the car will be pivoted about the center on a beam with the loading off to one side. In the design I need to calculate the deflection of the beam in order to determine which material and what profile of metal will be most cost effective however my deflection equations appear to be statically indeterminate. Below is a free body diagram

My problem is when I arrive at the equation for deflection I have two integration constants but only one initial condition saying that the deflection is 0 at the pivot. Is there a way to solve this or is there a conservative approximate that will yield satisfactory results?

image url: http://imgur.com/n45Wyhw