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I have the scenario where I wish to model the movement of a simply supported beam under a central point load. I've done some stuff in R Studio to come up with deflection plots and that's fine. In reality though, I have a pair of parallel beams (similarly supported and loaded) but when they deflect, I want to investigate the behaviour of some points which are referenced to one of the beams' surface by an angular offset to perpendicular.

Imagine the setup in the diagram. The parallel straight beams have two lines (x, y) which leave the top beam at angles A & B. I am interested in the lengths x and y after the beams have deflected (as I have poorly shown) - x', y' are going to be different to x,y - this I appreciate, but I would like to model it somehow.

I believe that something like Solidworks will do this for me, but it's expensive. I can also start from scratch and do something in python or R, but I was wondering what open source or low cost modelling software might exist which would allow me to do this (in the same way that Solidworks might - but without all the other stuff that Solidworks does!)

Any ideas?very poor beam bending depiction

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  • $\begingroup$ You should still be able to calculate this using basic beam theory and underlying assumptions. $\endgroup$ Jul 9, 2023 at 8:32

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If the beams are simply supported and being acted upon by a central point load, you don't need any software, the deflection of the beams will be $$ \delta(x)=\frac{P_i}{12E_iI_i}\left(\frac{3}{4}xL_i^2-x^3 \right) $$ for any coordinate in the range $0\leq x\leq\frac{L_i}{2}$ (the deflection for the right part of the beam will be symmetric).

In the previous expression $P_i, E_i, I_i$ and $L_i$ are the applied load, the modulus of elasticity, the moment of inertia (second moment of area) and the length of the $i-$th beam, respectively. I suspect both beams are identical, but it was not stated.

With this you can calculate the deflected coordinates of any pair of points and get the length of your $x^\prime$ and $y^\prime$.

This assumes small deformation theory, which should be a reasonable assumption in most real-life cases, unless your beams are made of rubber or something like that.

As a side note, what you are considering is exactly why trusses work, in case you are interested.

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