vierendeel truss analysis 3

[joistg]

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?

 

[rb1957]

FWIW (which probably ain't much) ...
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 ??

 

[dik]

Your web diagonals should be designed for shear, but the reinforcing should be designed for the moment caused by the unbalanced loading shear. Most design manuals have provision for larger holes through beams and these can be used as a guide.

Dik

 

[joistg]

Thank you for the input. I don't think the change in the bending stiffness is a problem.
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?

 

[MiketheEngineer]

Put the web back in and analyze the truss for balanced uniform loads. If the "added" web is exactly in the middle and the load is balanced - it will have zero axial force and the chords will have opposite but identical axial loads. Therefore it can be removed - right??

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.

 

[joistg]

The truss must be designed for unbalanced load, therefore the axial load in the web will never be zero. Although, the closer it is to the centre of the truss, the less load it will have.
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?

 

[csd72]

joistg,

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.

 

[BAretired]

Your sketch shows nine panels with the middle diagonal missing. Under symmetrical loading, the middle panel feels no moment. Under unsymmetrical loading, the middle panel must resist the shear at the center of the panel. It will be resisted by top and bottom chords in proportion to their stiffness.

BA

 

[joistg]

Thank you all!

 

[ToadJones]

It escapes me right now, but there is a name for this type of truss and there is a design guide out there somewhere.
If I can find it I will let you know.

 

[dhengr]

Joistg:
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.

 

[joistg]

dhengr,
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.

 

[dhengr]

Then design the top chord to do just that. And, it will, once the bottom chord has yielded. And recognize that under this scenario your deflection will be greater and concentrated at the center, but the tension link will still be there, just working btwn. Fy and Fult. If the bottom chord is there it will take its share of the shears, as BA suggested until it yields, despite your protestations, it just doesn’t know any better.

 

[BAretired]

If you load your truss with eight equal concentrated loads, one at each interior panel point, the reactions at each end are equal and the shear in the middle panel is zero, so there are no secondary moments. The primary moment is the simple span moment.

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

 

[dhengr]

BA:
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.

 

[BAretired]

dhengr,

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

 

[ToadJones]

If you spend enough time figuring it out, FEA will have paid for itself.
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.

 

[BAretired]

Toad,

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

 

[ToadJones]

BA-
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.

 

[ToadJones]

Most here are also ignoring the OP's questions about deflections, which is another good reason for FEA....unless you feel like using Crotti-Engessor, or Castigliano or some other tedious hand method.