vierendeel truss analysis
vierendeel truss analysis
(OP)
I have to analyze warren truss with one diagonal missing somewhere in the centre of the truss.I understand that top and bottom chords will have additional moments. The required opening in the truss should quite large, so there is no room for reinforcing both top and bottom chord of the truss. Also, it is a matter of saving (there is lots of trusses like this). How can I analyze this truss? Also, should I be concerned about deflection and how can I calculate it?






RE: vierendeel truss analysis
the load is applied to the beam through the upper chord,
and the diagonals distribute the load to the loawer chord,
and make both chords work together as a beam.
so it seems to me that you have to redistribute the load around the missing diagonal.
reinforcing the upper cap looks reasonable, but i'd add a plate web between the two angles (the original and the reinforcing) to make them work together as a beam.
i'd then apply the load to this reinforced upper chord to see how it redistributes into the surrounding structure.
another consideration is the change in bending stiffness along the truss beam ... something to worry about ??
and what about deflections ??
RE: vierendeel truss analysis
Dik
RE: vierendeel truss analysis
So I can assume that all additional moment from shear is taken by the reinforced top chord and bottom chord is only taking axial load?
Vierendeel trusses deflect more that warren. The fact that one diagonal is missing will contribute to more deflection? How can I approximate it?
RE: vierendeel truss analysis
Sure if everything is perfectly built and the load is balanced. This never happens in real life.
I would pop it into RISA or some such program and check it for unbalanced loads, uplift, etc. Doing it by hand will be tedious.
RE: vierendeel truss analysis
My main question, I suppose, is this: if the top chord is reinforced to withstand combined axial load and moment and if the bottom chord is left unreinforced, will the bottom chord still be subject to the bending moment?
RE: vierendeel truss analysis
You have three components to consider:
1)The axial load in the chords induced by overall bending
2)The local bending in the top chord due to the applied floor load and the greater span between supporting web members
3)the vierendeel type bending from the shear due to unbalanced loads
The basic philosophy will be fundamentally the same as that for penetrations in standard beams.
RE: vierendeel truss analysis
BA
RE: vierendeel truss analysis
RE: vierendeel truss analysis
If I can find it I will let you know.
RE: vierendeel truss analysis
Me thinks BA meant to say that under symmetrical loading the middle panel sees small shears across the panel length, but max. beam moment. And, that moment is taken by the top and bottom chords in compression and tension respectively, with the couple lever arm being the distance btwn. the centroids of the two chords. With unsymmetrical loading on the joist you will still have a significant bending moment near the center panel, but now you will have sizable shear forces acting on the chords as well, and they induce an additional moment in the chords, over and above the couple axial loads. Then there will also be some more complex secondary forces and moments due to the adjacent diags. and the joints in general. When BA and I were still pushing slide rules we designed joints for min. eccentricity and tended to minimize the secondary affects, and then basically pretended they went away. And, it actually worked; over the years I ended up with buckets full of secondary stresses, never did find a market for them.
Draw the moment and shear diagrams for your various loading conditions on that simple beam, both symmetrical and unsymmetrical. Cut the joist, a vert. cut through the t&b chords, at various locations in that center panel and draw your FBD showing the chord axial load for the beam bending moment, and the shears distributed to the two chords as BA suggested and consider the moments these shears induce in the chords, plus the floor loading moment in the top chord. Design accordingly, being a little conservative and call it a day.
Tomorrow, buy a $5000 computer program, input all the variables that we really can't pin down very well anyway, and run that thing for all the different load conditions, to at least 8 significant decimal places. Impress your boss with the .5% savings in steel if you could only get an angle that size, and assuming all of your guesses on the variables are correct.
RE: vierendeel truss analysis
I do not want to distribute any additional moment to the bottom chord of the truss. That is to save on reinforcing bottom chord angles. I would like top chord to take that moment from shear.
RE: vierendeel truss analysis
RE: vierendeel truss analysis
If the panel point loads are unbalanced, the reactions at each end are unequal and the middle panel shear causes secondary moments. If the middle panel shear is V and the panel length is a, dhengr is suggesting that you design the top chord for a secondary moment of V*a/2 and ignore the contribution of the bottom chord. Makes sense to me.
BA
RE: vierendeel truss analysis
Please, splain me the error or my ways.... I would cut the t&b chords (my FBD) just inside the vert. member near the largest shear in my shear diagram, and I would design the top chord for M = (Vmax.)(a), plus its axial loading. I would also question the effectiveness or usefulness of the two vert. members if they don't induce a secondary moment in the bottom chord; that is, akin to a semi-fixed beam btwn. the adjacent bottom diag. panel points, with two point loads (the vert. member forces) on the bottom chord. And, now I think we should at least give a little more thought to the secondary secondary stress in this whole thing, those I said we sometimes allowed to just go away. Joint eccentricities at the middle (open) panel, and issues like welding btwn. t&b chords and diags. being sufficient for any new loading conditions, etc. I'm assuming this is an existing joist design which needs this modification. And, it occurs to me that the bottom chord would be fairly easy to reinforce with a single plate below the angles, or two 2.5x2.5 angles on the existing bot. angles, welded to form two separate square tubes for the bot. chord.
RE: vierendeel truss analysis
I don't think you typed that quite right. You would design the top chord for a secondary moment of V*a/2 plus its axial loading, right?
BA
RE: vierendeel truss analysis
Its hard to knock a program like RISA or STAAD when it comes to this type of situation.
If time is money, buy one and learn how to use it.
Verify with some simple hand checks.
These problems will come up more often than the cut & dry variety.
RE: vierendeel truss analysis
I don't think this "type of situation" warrants a computer analysis. There are problems which do require such powerful tools, but this is not one of them. FEA has its place, but not in this instance.
BA
RE: vierendeel truss analysis
I agree that it doesn't warrant it, but it does make it a hell of a lot less time consuming.
Hell, I love doing this stuff by hand and I usually verify using STAAD or (or the other way around).
Most computer programs will also account for the secondary stresses in the analysis.
Most of these software packages stole the secondary stresses that dhengr had in buckets under his desk to use as prototypes when developing the analysis engines.
RE: vierendeel truss analysis
RE: vierendeel truss analysis
It is simply two propped cantilevers.
My issue with computer analysis is that you always get far more information than you need, and in my experience more information means greater likelihood of mistakes.
I also disagree that it is quicker, particularly in STAAD or an FEM program.
RE: vierendeel truss analysis
it's easy enough to redistribute the shear on the cut away portion of the beam ... the upper chord will beam it into the truss beam. you might consider reinforcing the 1st diagonals either side of the missing one; there'll be some extra shear loading there, but the truss may be able to carry this extra without reinforcing.
deflections, i'd expect they wouldn't be much different from the original beam, except in the cut away portion, and it's easy enough to calc that.
RE: vierendeel truss analysis
I think most trusses are a good case for it. An experienced FEM program user could model this very quickly. I usually model, then code check by hand. So in essence I just using the FEM program to get member forces. Which, will be far more accurate (maybe needlessly so) than hand methods.
Maybe a little bit of pride interfering here?
Still no one has been willing to offer this fella insight on deflections.
RE: vierendeel truss analysis
It is fairly easy and quick to analyse without a computer model. The unbalanced loading is the critical loading for this type of construction.
It is not likely that you can avoid having to design the bottom chord as a flexural member. With an unbalanced loading, the shear will be distributed in proportion to the flexural stiffness of the top and bottom chord.
Dik
RE: vierendeel truss analysis
Material is cheap, manhours are not.
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: vierendeel truss analysis
that you'd need a web splice joining the existing upper angle with the reinforcing angle. this'd imply (to me at least) that the reinforcing angle should be L3.
i'm assuming that he's got these things made and has to rework them.
RE: vierendeel truss analysis
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: vierendeel truss analysis
You say there are lots of these joists, then a thorough analysis is all the more important. I suspect deflection will hurt you if you don't reinf. both the t&b chords, I believe others have mentioned this too. You must check existing diags. and their welded connections to existing 3x3's for the new forces. And, if they don't check, then you have a real mess on your hands. I wonder why you wouldn't just take 4 - 15' long, 2.5x2.5 angles, and place them toe to toe on the existing 3x3 angles, making up 4 tube shaped chord members? A little more mat'l. and labor, but once they are up there to do 2 angles to the top chord, the bot. chords go quickly, all down hand welding. And you end up with a stronger joist with acceptable deflections.
RE: vierendeel truss analysis
BA and I were trying to offer the OP'er. a fairly clean and simple approx. method for looking at his problem. At one point in time, us older fellows learned, used and only had these methods of analysis. But, through that training and usage I think we developed an intuition and understanding of structures which is missing from the training today. And, these methods are usually our first step in looking at almost any problem. We can always make it more complex later, and more often than not someone else does that for us. As the OP'er's. problem became more complex: i.e. different t&b chords in strength and stiffness; existing diag. members and their welded joints, rather than verts. and Tee joints; useless added verts. and a willingness to let the bot. chord develop plastic hinges and just become a tension link; I was about to write that this problem should ultimately be done with a computer program to actually hone in on member forces and moments, for the deflection, and because there were many joists involved. Many of the secondary issues can probably still be handled by engineering judgement and experience rather than FEA and VonMises stresses. ToadJ beat me to that, and then beat me with it.
I am certainly not against the use of computer software to assist us in doing our structural analysis, in fact they are essential today. What I rail against is turning to them as the very first step in the problem development and solution, and because the designer (engineer? or computer runner?) has so little real understanding of structures that he/she has no other recourse, and then doesn't really understand the output either, for the same reason. If they don't start with some structural intuition, I don't know how they make the proper input decisions, and many of the OP's show this. I think the guys/gals who do some hand calcs., simple FBD's and that sort of study to start using the programs, and then do hand calcs., and various quick checks of the computer output are on the right track.
These may be the final flailings of an old dog unable to learn new tricks. I actually think I understand most of the tricks, I just don't know if I have enough years of engineering left to become proficient at the tricks. Given the use I would put them to, I really can't afford the latest software, I can't keep up with the rate of change, and they have become so complex to use, in trying to do everything under every possible set of conditions, that I have to relearn every time I try to use them, they are no longer intuitive to me, nor are they less time consuming. I was actually a pretty good programmer and computer user for engineering applications from the mid 60's - mid 70's, got away from it for a while and it passed me at the speed of light. I would love to have some of you young people working with me. Gosh, what I could learn from you, maybe teach you a little too.
RE: vierendeel truss analysis
RE: vierendeel truss analysis
To do a deflection calculation, you can use a simple frame program.
BA
RE: vierendeel truss analysis
RE: vierendeel truss analysis
RE: vierendeel truss analysis
RE: vierendeel truss analysis
You didn't dimension it, but it looks like the clear distance between chord angles is 2". Instead of adding angles over 3 panels on the top chord, why not place a HSS 4 x 2 rectangular frame (see attached). The corners can be mitered and stiffened with a plate.
The advantage is that you stiffen both chords without loss of height in the opening.
BA
RE: vierendeel truss analysis
In this day and age, I think you should have a frame program. Having said that, the analysis is pretty straightforward using hand methods. Personally, I would calculate the maximum deflection of the joist assuming full loading on all panels. That is probably the worst case.
BA
RE: vierendeel truss analysis
BAretired, if I reinforce my chords in this manner, HSS web will have to be welded to those reinforcing members. Also, adding two angles as per my sketch improve moment of inertia much better than adding HSS 4x2
RE: vierendeel truss analysis
I see your sketch, but I don't see how you avoid the outside double angle compression diags.(which you didn't show) with your top chord reinf'mt. since some of those top panel points will have a compression diag. You could make those compression diags. an HSS also. Haven't we seen the toes of diag. angles pinched in, to fit btwn. the t&b chord angles? You say you've done these kinds of joist before and reinf'd. both t&b chords, so what's changed to prevent that now? Cheaper (initial mat'l. cost) isn't always better. I'm not suggesting reinf'g. the whole top chord, three panel bays sounds doable on the top chord. But the predominant consideration may be a good stable compression member which takes some bending, not what appears to be a better bending member, but is a less stable compression member. You have to run the numbers to determine which is critical. I'd sure take a look at BA's detail, my guess is you want a good stable compression member, except for the outstanding angle legs at the top. And, making both t&b chords strong enough so they participate equally should improve deflection and make your design problem easier, if you can detail around that cleanly, even with a bit more expensive mat'l. in places. I said I thought allowing the bottom chord to develop plastic hinges and become a tension link would work, I didn't say I thought that would lead to the optimum joist design.
Are you an occasional OWSJ manuf'er., it sounds like you are? If so, how do you analyze your joists now, and doesn't that program spit out deflections at the panel points? Despite my rant about reliance on computers to substitute for structural knowledge, I wouldn't design many trusses with computer software to do it.
RE: vierendeel truss analysis
What is the magnitude of your largest middle panel shear and what is the panel length?
BA
RE: vierendeel truss analysis
RE: vierendeel truss analysis
BA
RE: vierendeel truss analysis
Your responses are coming too slowly. I asked you what your maximum shear in the middle panel is and also the panel length. You will find that you get a lot more out of these sessions if you respond immediately, not wait until we have all gone to sleep. So, get with it!!!
BA
RE: vierendeel truss analysis
Dik
RE: vierendeel truss analysis
I would think you could possibly design one based on shear only with a pinned connection to the truss in each corner.
Just a thought.
RE: vierendeel truss analysis
RE: vierendeel truss analysis
I agree with you, but we have to cool our jets
Remember the first time we faced many of these types of problems, the trips to the Univ. library because our own ref. books weren't enough, the head scratching and late evenings because we thought we owed it to our job, the project or our boss, the discussions with older engineers, maybe from other offices, or our old profs., the digging through old plans and calcs. to see how it was done, our friendly fabricator, etc. etc.? Now, ya just click on the internet, some wise guy like you gives good advice, maybe ya take the advice, maybe ya don't, maybe ya know which is the good advice, or not, and ya don't know how to check this out either, so ya run it through a FEA program, with bad input assumptions, and call it a day. Ya certainly don't waste your own free time checking on Eng-Tips for the latest on your questions. Some new structures make me nervous, and I am the nervouser because I'm not sure which ones.
RE: vierendeel truss analysis
Tired and cranky...sounds about right.
BA
RE: vierendeel truss analysis
Quit being a smart A$$, as I seem to recall, your not too many years away from tired and cranky.
RE: vierendeel truss analysis
missed that one!
RE: vierendeel truss analysis
Thanks, I think I'll "cool my jets".
BA
RE: vierendeel truss analysis
Dik
RE: vierendeel truss analysis
I'll admit I am irritated by the older engineers who reject FEM (seemingly out-of-hand) or make sneeky remarks to cut on it.
I'd venture to say that you are as much irritated with your lacking in ability to use FEM as you are with "younger engineers" using it.
I use FEM almost every day. I also teach guys younger than myself how to properly use FEM and when they are barking up the wrong tree. I have learned a lot about load paths in structures by studying classical methods (on my own time) and then comparing them to my FE models.
You get to the point where you can review the results of your FE models and right away see "hmmm somethings not right".
You guys shouldn't be so quick to assume that "younger engineers" just build pretty models and accept the results as if they were Bible.
I'm also not so proud as to deny I have been shown a thing or two by guys with a lot less experience than I. I tell those guys "thank you, good job". It also goes a long way when the table is turned and I have to tell them that they did something wrong.
Because you fellas learned over the course of generous break-in period on the drafting board how to do things by hand doesn't make using FEM wrong in any way at all. The same guys using FEM might be the guys who should you how to send an email back in the 90's. These guys are expected to learn quickly as they come out of school how to use these software programs. I don't think it is right, but, I know for a fact this is the case. I deal with it everyday. Hell, none of us youngsters ever even had the chance to make our hand writing look exactly like stencils used to make general notes on drawings before CAD, which was probably equally rejected.
Call me what you want, but this isn't as much conjecture as you might think. I am a third generation engineer with 6 siblings working in the engineering community. I have literally heard it all and I have been hearing it since I can even remember.
dhengr....lets hear it!
RE: vierendeel truss analysis
I believe, as you do, that there are many problems which may be solved more quickly and more precisely using FEM than by using hand methods. I started using computers in 1959 when my boss decided that it was time somebody in the office had some idea about their potential. I attended lessons offered in Edmonton, Alberta by a company called Royal McBee. The computer was called LGP-30. I was fascinated by it because it appeared to have lots of potential in solving engineering problems, but I never became very proficient at doing anything very useful on it because it had to be addressed in machine language...even more laborious than Assembly language.
I studied Fortran and wrote a few very simple programs on specially prepared sheets which were subsequently transcribed by a technician on a sort of a typewriter. That output was fed into another machine which punched cards with little rectangular holes. These were read by the computer which converted the punch cards into instructions. One little hole in the wrong place meant your program failed.
I neglected my programming pursuits for about twenty years, but in the early eighties, I decided to revisit the world of computing. I settled on Borland's version of Pascal. I thoroughly enjoyed studying that language and I wrote a Cad system and a 2D Frame Program, both of which I used on real engineering projects, although I must admit, they were not particularly user friendly. I wrote lots of quick and dirty routines to solve specific problems.
Nowadays, there are so many programs available to engineers that it does not pay to attempt to write them from scratch. The problem is that today, the software people don't want to spend the time and money to prepare documentation adequate for the normal person to understand how to use their product. In consequence, young engineers are struggling with how to input data and how to interpret the output.
You said: I do not reject FEM. I believe it is a wonderful tool and eliminates drudgery in calculations. I also believe it should be used only by those who understand the principles of the problem they are trying to solve and who can do a rough check by hand to ensure their answer is in the ballpark. Otherwise, they have no business using FEM or any other computer program.
BA
RE: vierendeel truss analysis
RE: vierendeel truss analysis
Can't disagree with anything you said.
I do disagree with comments like:
"Tomorrow, buy a $5000 computer program, input all the variables that we really can't pin down very well anyway, and run that thing for all the different load conditions, to at least 8 significant decimal places. Impress your boss with the .5% savings in steel if you could only get an angle that size, and assuming all of your guesses on the variables are correct"
It's snide comments like these of the strawman nature that get old.
I know some of it is in good fun, I do it too.
I just think the savings that one might impress his boss with will come in improved productivity once he learns the software.
I think you'll agree that in this day, its a necessity if for no other reason than staying competitive.
RE: vierendeel truss analysis
Dik
RE: vierendeel truss analysis
Let's have a race....and accuracy counts
RE: vierendeel truss analysis
dhangr:
I'm a young engineer and probably can't teach you much about computer programs but I'd pay to have a few of your "courses". You are one smart dude.
Not to discredit any of the other elders on this site.
Makes me feel like theres an infinite amount of information that I don't do.
EIT
RE: vierendeel truss analysis
The conservative assumption for manual analysis, is that you have have two, four bay trusses, connected by a beam, bridging the central gap, the beam connected to the first two node points on either side of the gap. In this case, the bottom chord is ignored in the gap, the reactions at the node points distribute through the diagonals. The change of slope of the beam through the gap can be used to estimate the additional deflection.
If this result is not satisfactory, the next thing is to calculate the effect of the bending of the beam on the bottom chord. This is just possible by hand but it is a longish iterative process finding a balance between the effect of the bending of the beam and the force couple of the chords. Unless you have spent good time using and understanding these archaic methods, this really needs an FEA program. (Any reduction in the bending of the beam by the force couple changes the forces many of the other members).
p.s. I would welcome a clear argument as to why and how I'm wrong.
Michael.
Timing has a lot to do with the outcome of a rain dance.
RE: vierendeel truss analysis
I have to agree with much of what TJ says. I strongly believe that using TODAY's programs - which are much more user friendly than those of the 70's - help the engineer get a much MORE intuitive sense of design than using moment distribution or other energy methods by hand.
I can alter a member size, loading, etc at the drop of a hat and immediately see the effects of any of my input or assumptions. I know this is true because I've experienced it doing both ways (by hand vs. computer). The drudgery of hand calcs doesn't always lead to a good intuitive view of the analysis, rather, I feel that hand calcs can actually interfere with it as you spend more time with the math and less with the engineering design.
The analysis program I use today is very user friendly, has a great manual, I've tested it against hand calcs, I trust it, and it is easy to teach engineering design principles (not just simple bookkeeping analysis methods) to younger engineers. Most of they younger engineer interns "get it" at a vastly quicker pace than my own peers took so many ears ago.
Enjoyed the discussion above - thanks all.
RE: vierendeel truss analysis
I do not understand this:
"two, four bay trusses, connected by a beam, bridging the central gap, the beam connected to the first two node points on either side of the gap". Can you explain?
RE: vierendeel truss analysis
By anti-symmetry, the beam has an inflection point at the middle of the opening, so you are dealing with two propped cantilevers with a load applied at the inflection point. If you want to consider the bottom chord contribution, you have another pair of propped cantilevers of different stiffness.
BA
RE: vierendeel truss analysis
BA
RE: vierendeel truss analysis
RE: vierendeel truss analysis
RE: vierendeel truss analysis
RE: vierendeel truss analysis
RE: vierendeel truss analysis
Regarding an abacus... I worked with a Chinese engineer about 40 years back that used an abacus... really a fast calculator if you know how to use it...
Dik
RE: vierendeel truss analysis
RE: vierendeel truss analysis
take my post with a grain of salt...I wasn't seriously issuing a challenge.
FEM would produce, instantly, more numbers.
Several of these would be very accurate deflection numbers. Deflections that might control the design. Ponding comes to mind.