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I'm trying to validate an FE model that I'm using by comparing to a simplified analytical solution to the problem.

The part I'm analyzing is a lug that is constrained on one end and has a point load on the other end. My idea is to model it as a stepped cantilever beam with either two or three steps then find the deflection using castigliano's second theorem.

What would be the most accurate way of modelling the deflection at the tip? What cross section sizes should I use for the different steps of the beam?

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First step is just a cantilever a long by 2c deep. Hopefully that is somewhat stiffer than your FEA and you can easily check that by fixing the cantilever at the left hand end in the FEA.

The other bit is much more complex, but I suspect a moment of (a+60)x your force applied to the centre of a fixed ended beam length 80 depth 45 will give you the rotation of the base of the cantilever, call it theta. Then the deflection at the hole is theta*a+the tip deflection from the first step. That's probably a bit stiffer than the FEA but not by much.

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