Boarder290:
You said.... “Currently tie bars are determined by a long history of what has worked and what has not. We are looking to create an excel sheet for new designs along with updating old, where we fill in all of the variables and it spits out size, location of a tie bar or two or three if necessary, instead of guess and check with fea.” Do you know what works and what doesn’t, and why? Screwing around with more than a couple different tie bar sizes doesn’t seem to make much practical sense, to save a couple pounds of mat’l. Of course the top and bot. pls. and those needing special clearance cut-outs are exceptions to this thinking.
Boy, that’s a really tall order, and a lot different than your OP. You’re a real dreamer, you’ll be an old man before you get that ‘excel sheet’ working in a meaningful way. Who suggested this approach, or is this your idea? Why shoot so low, why not a program which designs the entire fork lift? Input as follows; mast length, 3 sections or 2, max. load, operator weight, girth and hair style, and operating cross slope; press ‘enter’ and out pops a complete fork lift design, CAD included.

These real world problems just do not lend themselves well to the std. classroom/textbook approach of packing 63 variables into one half page long formula, for a perfect solution.
You really have to break that problem down into a number of independent spread sheets and smaller problems. To start, you would do well to really pick the brains of the older engineers at the company, who developed that history, for their experience and judgement on these problems. Is that photo your machine, or just an example? Your last set of sketches finally shows what you are really dealing with, and that’s good. But, I still wish we had some rail dimensions, sizes and properties, and real approx. dimensions for L, e, r, & x, and loads, for some sense of proportion. What worked and what didn’t, and why in both cases? If you don’t know these answers, how can you build your programs? Those tie plates are a fairly common solution, in one form or another, because they are about the only alternative, the only thing that will fit in the telescoping space available. They are not a particularly good solution because they don’t offer much torsional fixity. The tie pls. are loaded about their weak axis in bending to resist the rail twisting and spreading. And then, they connect to the guide rails in the worst location, at only one flange, sorta as a spring loaded hinge point and their resistance is dependent on prying action at the roots of the fillet welds to the rails. They are the least of all of the evils, so to speak. I’d want to see all of the arrangement drawings for a typical (one of the larger) masts, along with the part details, and the design calcs. to start picking that apart and see what was possible.
Look instead, at analyzing the problem in pieces so you can start to get a handle on how changes in different variables affect the results. You’ve got to start picking at this problem a piece at a time, so you start to gain some intuition of what causes what, or what improves a particular situation when another variable changes; and add this to the history and judgement you get from the experienced engineers. This is truly an example of where having an older mentor right there who can be pointing at the same detail on some drawings would really be helpful. He will have the intuition and judgement that you don’t have, and you will have the computer savvy to do the modeling with his guidance. While this may seem horribly unsophisticated in comparison to a big spread sheet, I would look at a given rail size and ask how far from the base pl. (your ‘g’ dim.) I can go with the carriage rollers at some load (1k?) before the rails spread or roll to an unacceptable limit. What dictates that unacceptable limit? Combine this with some simple testing.
The problem is essentially the same whether the two pairs of rollers are for the fork carriage (your ‘r’ & ‘g’) on a single mast section, or if they are for the lower support rollers (your ‘x’ and a new ‘g’) acting on its next lower support rails, right? Study those as they relate to height location in the supporting mast section. At what height location do they cause the most rail twist per 1k load? Your guide rail sections are a specially rolled section for this purpose, aren’t they? So, you have a limited selection, with known section props. right? You’ll run out of variables such as b triple prime, before you run out of unknowns. You are not going to be changing k, h, m & n, they’re unneeded variables, not well named/defined either. k is a flange width, m & n are flange and web thicknesses respectively. e should be center to center of the rails, and equals t for analysis purposes.
I would really enjoy being involved in a project like this, but I would really rein in what you are trying to do at the outset. Study the upper stage of the mast and move the fork carriage up and down on it. This might well be a FEA model and analysis. Fix the ends torsionally in one case (my cap and base pls.), and free these up in another. If your design is like the photo, it looks like you could put a base pl. on each section. How and how much does a typical rail section twist. Keep these models fairly clean and simple. Except for major axis bending of the rails, and the spreading action caused by the roller loadings. Most of the torsional action takes place btwn. any pair of rollers on a given rail, doesn’t it? But, they cause spreading too. And, the rails above and below the pair of loading rollers, must resist any spreading action or any remaining twisting action.
I would look for a way, btwn. the carriage rollers in height, to prevent its supporting rails from spreading or twisting too much. As a first suggestion, cam rollers or stop bars from the back of the carriage to the outer tips of the flanges of the rails. These restraining devices would control lateral movement of the rails right around the load rollers, and that’s really what counts as long as that movement isn’t too great elsewhere. I suspect the upper two sections have a bit more spreading and torsional action because there are two sets of rollers acting on them. One loading each section and the other being its support rollers.