2D Modeling of Trusses

[dsd133]

I am modeling a 2D truss using frame elements. The truss members are built up box members consisting of four plates and 4 connecting angles. The flange plates have 12"x18" perforations spaced at 3'-6" on center. Because of the perforations the area and stiffness vary along the chord members. I don't want to break up each chord into 2ft frames to vary the stiffness so should I compute a weighted area and stiffness. I was originally using the gross area of the section and adjusting the density to account for the perforations but feel this might be over estimating the stiffness of the truss. If I use the net area to define the sections and increase the density to account for the length that isn't perforated then I will be underestimating the stiffness and effect the longitudinal distribution of forces. So what section properties are the most appropriate to use? Has anyone dealt with this issue before?

 

[rb1957]

i'd ratio E by the area ratio, to maintain E*A (axial stiffness).

obviously, you'll have to do a hand calc to clear the cut-out sections.

btw, why not model the truss with 2D elements to get an idea about the signifiance of these factors ?

 

[cntw1953]

This problem can be highly involved, or quite simple.

If you model the chords as continuous member, the stiffness varies along the length. Then you have to account for that.

If modelled as typical truss with all bembers pinned, then the lacing plates will not get into picture, since all members take axial loads only.

Make sense?

 

[EdR]

dsd133:

Maybe I don't understand the structure but if you are modeling with frame (I assume this means truss-axial stiffness only) members then I think you should probably model using the area of the weakest part of the cross section...Both stresses and displacements will be correct if you use the weakest section since most(almost all) of the displacement will occur in these sections.....

rb's suggestion is a good one for some cases but I'm not sure it is necessary in this case.....

Ed.R.

 

[dsd133]

I have all the members modeled as frame elements that have flexural and axial stiffness. The top and bottom chords are modeled as continuos and the verticals and diagonals have moment releases at their ends. The top and bottom chords will have moments but they will be very small in comparison to the axial loads. If I use the weakest section to define the axial stiffness of all members will this not underestimated the global stiffness of the truss? The loads are applied to the truss at panel points from a floorbeam stringer system. The longitudinal distribution of load from the stringers to the floorbeam is a function of the stiffness at the panel points where the floorbeams connect to the truss, so having an accurate overall stiffness of the truss is important.

 

[cntw1953]

If the chords are continuous, I don't see the choice, since the plates and the perforations will have impact over both stress distribution and deflection. Simplification is feasible (as old-timers can testfy) but risky without thorough understanding on behaviors of this type of structure.

 

[paddingtongreen]

The stiffness wouldn't be a factor if your truss were statically determinate, so I assume you are modeling the chords as continuous.

I suggest that you try to model a single length of the section, say 20feet or so, as a beam, changing the section back and forth. From the deflection, calculate the equivalent Moment of Inertia for a constant section beam. Do a similar calculation for compression to find the equivalent area. Use these in your program.

This method is a bit long winded, but it is easily defended because it doesn't look like guesswork.

Michael.
Timing has a lot to do with the outcome of a rain dance.

 

[cntw1953]

I like the idea above, and that's the reason I said this problem could be quite involved, if you desire a more precise result.

 

[rb1957]

i'd ratio E by the area ratio, to maintain E*A (axial stiffness).

obviously, you'll have to do a hand calc to clear the cut-out sections.

btw, why not model the truss with 2D elements to get an idea about the signifiance of these factors ?

 

[rb1957]

dumb a$$ computer ! ...

 

[GBor]

rb? A little turrets syndrome? Or am I missing something in your post to warrant your exclamation?

I, too, would question the use of truss element or beam elements. Looks like plate might actually apply unless your members are quite long, which at that depth, they probably are.

 

[rb1957]

my dear exlorer said that it lost the last session, so i backed up. it took me back to my comment, so i thought it hadn't posted it, so i posted it (again).

i think a simple stick model will give you a good idea as to loadpaths. then you could do a detail model of a truss element and apply the stick model loads, or a hand calc. i appreciate that this thing is about an order of magnitude bigger than what i usually deal with !

 

[Qshake]

First check your thickness for the perforated plates. If these plates are nominal in thickness, you are likely dealing with a cover plate. Depending on the original designer these plates may not have been involved in the original calculations. Generally speaking it's the solid, very thick, side plates that are actually bolted to the gusset plates that transfer load.

That is not to say the cover plates don't transmit load. As others have pointed out, the member will transfer load via the stiffness, L/AE and within the member you can expect the loads in the plates to be proportional to the area of the plates.

If the perforated plates are on the top and bottom of the member, they generally are not connected to the gusset plates and thus should transfer load out through the angles and into the main side plates within a distance of say 2 times the overall dimension of the member away from the gusset plate.

Perhaps it's been noted above, but a simple frame model, neglecting some of the small plates will work fine for overall loads and load paths. Then if you or the client desire a hi fidelity FE model of the joint and gusset plate/member interaction a full blown plate and shell element model can be developed for that. In which case it would limited to partial members framing into the gusset plates and not the full length.

We do this quite a bit in analyzing older truss bridges and some newer ones too.

Regards,
Qshake

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