Tie bars between I-beams

[boarder290]

I'm looking to figure out a way to determine how often a welded tie bar is needed within a given length of I-beam. There will be a tie bar at each end and a force will be pushing on the flange of the beam (blue arrows) at the blue plane. This will cause the beam to want to peel out relative to each other an angle of theta, thus causing the tie bar to bend as well. I'm looking for a way to have an equation in which you input the desired angle, length and thickness of the tie bars, and height of the top and bottom tie bar, and it will output a location and height of the required intermediate tie bar. Any thoughts or a point in the right direction is appreciated.

 

[paddingtongreen]

Where is/are the reaction(s)? This will take off into the great beyond, as shown.

The answer you get will be theoretical because bar sizes are subject to tolerances.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[boarder290]

The beams will be fixed at one end and all I am trying for is theoretical, there will be a factor of safety implemented.

I am thinking of cutting the section in half at the blue plan and treating it with a torsional load on a cantilever beam. The part I am unsure of is how to include the tie bar into the calculations for the torsional rigidity of the beams.

 

[paddingtongreen]

If the beams are truly fixed at one end, why the tie bar at that end? If the end is truly fixed, most of the torsion will go to that end along with major axis bending.

Think again about how to ask this question with all of the parameters before dhengr gets here, he is less patient than I.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[boarder290]

Assume the beams are sitting on the ground for the vertical constraint.
The green arrows in the picture below depict the horizontal constraint in both directions.

The forces are shown in blue are also applied on the hidden side of the other beam. They are equal per couple however are not necessarily equal per rail (the 2 blue arrows in the first picture are unequal). The forces are free to slide the length of the beam.

 

[dhengr]

Boarder290:
Let’s quit assuming.... If you can’t describe your problem so an experienced engineer can start to understand it, it will be a tough haul to ever solve it. Put some loads, some real dimensions, member sizes, etc. on that CAD sketch, and tell us what it is. It looks like the vertical guide rails (mast?) on a fork lift to me, with the forks points in the Y direction. Ask yourself what info. you need to start to solve this problem, and get it on your sketch. You would be surprised how this type of info. influences an experienced engineer in his first impressions and judgements on the problem. Your tie bars are only spacers, at that back flange, they will not help you much/any with the torsional problem. Put top and bottom (horiz.) plates at least as deep as the I-bms. are, as if a single cap pl. and single base pl. all the way across the mast. This will tie the two rails together torsionally and limit their rotation, at the ends. What? Me impatient? We both just want him to put his thinking cap on, and quit keeping secrets. This isn’t a game of 20 questions.

 

[paddingtongreen]

Boarder290
Consider where the columns are connected to a "foundation", the ends have six degrees of freedom, one in the line of each orthogonal axis and one rotating around each of them. Clearly, they are restrained in the line of the vertical axis and in the line of and around the common horizontal axis, unless restrained at the top. Are they free to rotate about the vertical? Is the top restrained in any way? These are all questions, for which, we have no information but which we need to help answer your question

If this is similar to a fork lift, the loads getting to your tie bars varies with the height of the loads.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[boarder290]

Alright, going to basically start over at this point.

Application-Forklift mast
Problem- When all stages extended, carriage or one section of mast pulling roller out of the mast by twisting the beam. The carriage twists when there is unequal loading on the forks or the fork truck is on an uneven surface, or a combination of both. Tie bars are then used between rail sections to stiffen rails from bending or twisting thus allowing the carriage to work its way out.

The carriage applies the load through load rollers and force on the rail is shown in blue.
The mast is constrained at the green arrows.

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.

All the variables are as follows:

a-bottom tie bar distance from bottom
b-middle tie bar distance from bottom
c-top and bottom tie bar height
d-middle tie bar height
e-rail spread-edge of k to edge of k
g-load roller height from bottom
h-rail depth
k-rail width
L-rail length
n-web width
m-flange width
r-carriage retention-distance between load rollers
t-tie bar length
x-mast retention-distance between roller of one stage and the next

There is no problem specifically, I would like to solve the equations with the use of variables.

 

[boarder290]

I found a picture of a situation in which testing if the the carriage could pop out or rails would fail.

 

[boarder290]

Anyone?

 

[trainguy]

My gut tells me it would make sense to test various arrangements, and use the test data in a spreadsheet. Probably cheaper than doing all that analysis.

tg

 

[dhengr]

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.

 

[boarder290]

The biggest problem in talking with the experienced engineers who developed the original designers is that they don’t exist, at least not at our company. We started out as simply a manufacturing facility, building oem products and slowly over the years have acquired designs from companies we purchased them from. Recently we have found a niche in custom masts and carriages. Over time we have figured out every main aspect of the mast and carriage design except tie bar location and size. We have a fairly young design team, majority under 30, everyone under 35, so the experience is lacking some.

I know an excel sheet is a bit of a dream but ones allowed to dram right? Our boss wants us to try to figure out something using hand calculations and verifying them with fea, to exercise our brains, even if the hand calculations are crude at best.

That gets me back to my original post, trying to keep it simple enough to do by hand, but complicated enough to be useful. I went with two cantilever beams fixed at one end, tie bar at the other, and using torsional equations for a beam. I am stuck with trying to figure out how to work the tie bars into the equations.

The mast in the picture is ours I believe; however we don’t do anything with truck design. I will try to dig up some larger masts to show how they are attached, and get some dimensions and loads for perspective.
As far as adding in retaining devices ,that is something that we do on our heavier, more expensive masts, but it’s hard to justify another $1000 on something that costs $8000 when is seems like everything today is sadly cost driven, not quality driven.

If you have any input or anymore guidance that would be greatly appreciated.

 

[ThomasH]

Hi

I have not read all the previous replying posts so I may repeat something already suggested.

You have two I-sections and the question is regarding the spacing for the tie bars between the flanges, correct?

I would suggest that you study the problem one section at a time. Calculate the section properties for bending and torsion. Set up equations for equilibrium and stability with the proper boundary conditions. Unfortunately the boundary conditions will probably be springs but that is reality. You may or may not find some possible simplification along the way.

You can compare it to a finite element approach but you do it "by hand" or by Excel sheet. Do one element, then the next, the assemble.

As for the tie bars, I think they will primarily contribute to the torsion of the single beam. As I understand it the forces does not have to be equal between the beams. Unfortunate, because symmetry would help.

A different approach would be to set up a parametric model in some kind of software. But that was not the question as I understood it.

Maybe this can help you a bit in your work.

Good Luck

Thomas