1. The problem statement, all variables and given/known data Well this is the second time I have been given a problem that I just don't know what to do at work. Simply put you have a beam that has 3 supports. A,B,C. With a weight at point w. The goal I am told is to find all 3 points with just the the known of w (weight), L(length of beam), x (distance of point B from point A) and y (distance of weight from point A) l-------L----------l l---y---w _______l_________ l------x---l--------l A---------B-------C 2. Relevant equations You got me. He said this would be easier than finding the weight of the support points on a piece of machinery. 3. The attempt at a solution I tried using moments around point A and C but yeah that didn't work at all.
The problem is statically indeterminate and you need to do a deflection analysis with one of the supports removed, calculate the deflection at that removed support, and reactions, then determine the force required at the removed support to give the negative of that deflection at the removed support such that the sum total of the deflection at that support is zero. Then use superposition to determine all reactions. Is this a Homework problem?
Oh no Jay this is my New boss giving me a problem to figure out and then derive a formula or solution that I can put into excel so that when we get an inquiry about load points for our Isolators that we could if need be tell them which product would best suit their needs out of our product line. This requires one to either know the weight at each of the supports which will have isolators attached or that we determine it for them if they don't know. This is just driving me batty. I got Roark's formula and a MIT guys paper that discusses this but I am in way over my head. I still got 2 and a half years of my ME degree plan to finish. PS the little diagram is what he has drawn for me on papaer as well. so you have as much information as I have.
I'm surprised that Roark does not include a table for this application. Did you look under "Continuous Beam - Two Unequal Spans - Concentrated Load At Any Point" ?