Joist seat forces in Multiple Span Joist Construction 1

[ingenii]

SJI recommends minimum seat welds which are routinely checked when seats must transfer external loads into the joist chords. But what about internal forces? For a building with multiple bays of joists (assume equal spans and loads) with joists on each side of the supports, the column shortening effect from the compression load in the top chord is restricted by the joist in the adjacent bay. The way I see it, if one end of the joist is not free to "slide" (it could be lateral deflection of a beam or wall), then the chord force is restrained and must be transferred at the joist seat. Has anyone else ever considered this load in determining the weld requirements for the seat? I have attached an example calculation for clarify my question. (Note that I use the full chord force to calculate the column shortening of the top chord. The chord force is really a gradient and so perhaps would be half of what I show.)

 

[KootK]

Has anyone else ever considered this load in determining the weld requirements for the seat?

I haven't. Nor have I seen anyone else check that. Which isn't to say that you're wrong. I do see your point and feel that it's a valid insight.

I imagine that many would justify ignoring that by saying that all of the joists along the line are able to pull inwards a bit and relieve that axial stress. And perhaps that there is some truth to that.

But I feel that the more intellectually honest answer is that structural engineering is a reactive profession and we only react to things that actually cause problems. And these internal forces that you've rightly identified do not seem to cause problems.

In a similar vein, many a diaphragm designer will eventually find it odd that only the framing at the perimeter of the diaphragm is designed for the axial loads. What about all of the interior joist supporting the deck that also have rigid axial connections? I even have a paper somewhere explicitly dealing with that as a "distributed chord phenomenon" or something like that. Yes it's real. No, we don't typically account for it. Meh?

 

[ingenii]

Thanks for your reply. I made a 2D model of an LH joist to convince myself I wasn't crazy. The axial end reaction is there if the top chord is not free to slide. If the joists are all bearing on steel framing, and offset 12", then there will be small in plane moments in the beam flange - but the minimum SJI welds would seem sufficient to transfer the axial tension in the chords, at least for the case I am looking at. However, if the joists are offset at a masonry wall (and not welded to the same embed), then the joist to plate welds may be sufficient, but the headed studs don't come near the capacity required (even if friction force is considered).

I agree that we may not be seeing these issues. For most large joist projects (e.g. warehouses), the interior joist bearings are supported by steel, so the effect of the seat tension on opposite sides of the beam is washed out. Projects with multiple lines of masonry walls supporting joists are typically residential - where the seats are concealed by finishes - so perhaps we don't know we have a problem. For my 30' joist, I am only seeing 1/8" axial shrinkage of the top chord with a roller support. One-half that movement at each end might cause the face of the block to crack and displace, but it would not be a catastrophic failure.

Those residential projects also typically have concrete slabs on deck secured to the joists - which, even without studs, creates a larger compression flange that will affect the results I am seeing. Less deflection means less retrained tension at the ends.

It appears to be a little like trying to restrain thermal growth. Let a little movement occur - and the force goes away.

 

[KootK]

It appears to be a little like trying to restrain thermal growth. Let a little movement occur - and the force goes away.

Yeah, I almost typed the same thing previously.

I made a 2D model of an LH joist to convince myself I wasn't crazy.

More crazy. This should also be true of tensile expansion of the bottom flange of wide flange beams when a line of them are bottom supported.

The nature of structural engineering is that if you think about anything deeply enough, a practical solution becomes impossible.

 

[ingenii]

More crazy. This should also be true of tensile expansion of the bottom flange of wide flange beams when a line of them are bottom supported.

The nature of structural engineering is that if you think about anything deeply enough, a practical solution becomes impossible.

Agreed - on both points.

 

[dold]

I even have a paper somewhere explicitly dealing with that as a "distributed chord phenomenon" or something like that.

Collective chord behavior. https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1044&context=aen_fac

I made a spreadsheet for it ages ago to prove to my boss that our chord sizes were absurd in some of our warehouses, but never really used it. Because, well:

Yes it's real. No, we don't typically account for it.

 

[ingenii]

Collective chord behavior. https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1044&context=aen_fac

I made a spreadsheet for it ages ago to prove to my boss that our chord sizes were absurd in some of our warehouses, but never really used it. Because, well:

Thanks for the reference. Odd that the author states strain compatibility must be met - yet ignores strain compatibility of the joist chords themselves. The connector between the joists on opposite sides of the beams would need to transfer the diaphragm chord force plus the tension force required to prevent axial deflection of the chord that would otherwise occur if the chord were free to slip at one end (they cannot be intermediate chords unless they are continuously connected). The axial deflections we are talking about here are small - 1/8" over a 30 foot span. But given the size of the top chords on LH joists, the force necessary to restrain that small movement is very large, approaching 20 kips in my case. This pretty much forces me to align the joists so the force is transferred via the weld to the bearing plate as the wall is not capable of transferring the load laterally in bending where the joists are not aligned on opposite sides of the wall.

 

[ANE91]

Your computed axial shortening is at midspan, at the point of maximum moment, right? Maybe I’m just tired from work, but I feel that the axial chord force would be zero at the ends, as the moment is zero. Apologies if I’ve missed something obvious; I should do as you did and convince myself with a model.

 

[ingenii]

Your computed axial shortening is at midspan, at the point of maximum moment, right? Maybe I’m just tired from work, but I feel that the axial chord force would be zero at the ends, as the moment is zero. Apologies if I’ve missed something obvious; I should do as you did and convince myself with a model.

The chord force determined from M/d is zero at the end of the span and maximum at the center. Since a joist is a truss - each segment between diagonals has a different axial load depending on the moment at that segment of the joist. The axial shortening (delta) of each chord segment can be found from PL/AE. If you add the shortening from each segment of the top chord - that is the total length the top chord shortens over the total span. If that axial shortening is not allowed to occur because the ends of the joist are restrained - the retaining force can be found from P=(sum of delta)AE/L. This force is constant and so causes negative values of compression (i.e. tension) at the supports and reduces the original maximum compressive chord force found from M/d at midspan.

If you make a 2D truss model of the joist and pin both ends (instead of pin and roller) - you will find you have equal and opposite axial forces at each end of the joist, even though there are no horizontal loads applied. Let one support roll and the axial force disappears. It is analogous to fixing both ends of a beam. The moment diagram, once all positive for a simple span is now a smaller magnitude of positive at midspan with negative moments at the supports. For the retained joist chord, the neutral axis moves up so you have smaller compressive force in the top chord at midpsan because you develop negative (tension) chord forces at the supports.

 

[bones206]

Along with axial shortening, the actual behavior could include subtle out of plane buckling of the top chords between brace points.

It would be interesting to model an entire bay of joists with axial restraint and bridging explicitly modeled to see how the axial reactions compare to a fully retrained, plane frame joist model.

 

[ingenii]

I thought I would post an update. I could not get my head around the magnitude of lateral force I was seeing in my model at the end of the joist versus our collective experience regarding the lack of historical issues related to lateral forces at the joist seats. I felt there must be something I was missing. There was. The one thing that was not in my joist model was the seat. I threw in a 4" square rigid offset element and voila, the horizontal reaction dropped from 18.4 k to 3.4 k. So the joists do not have true pinned connections, but there is sufficient flexibility in the seat to allow enough lateral translation of the top chord to eliminate most (but not all) of the lateral reaction.

A was said numerous times - it is real, but we don't account for it.

I appreciate everyone that took the time to weigh in on this.

 

[ingenii]

One more follow-up: I sent my question to SJI and they responded - here is how they explain it:

"Now, you describe a model in which the open web steel joist is not simply supported, but instead, is supported at both ends by pinned supports which are fully restrained from translating in any direction. Yes, using that structural model, we will see large horizontal support reactions develop at the supports. Those horizontal axial forces due to translational constraint induce top chord axial tensile forces which counteract the top chord compressive forces due to simply supported behavior and greatly reduce the top chord axial compressive force at mid-span

So, the fundamental question becomes, which of these two structural models is the closest to actual joist behavior, in an actual building, under normal gravity loading, using standard detailing practices?

As it turns out, standard detailing is generally geared toward statically determinate simply supported conditions. To achieve full constraint at supports requires a lot of special detailing that is not included in standard detailing. While, it is true that the supports are partially restrained, they behave much closer to simply supported than to fully restrained.

To understand why, we can look at the relative magnitudes of forces and displacement in the two idealized models.

For the simply supported model, the horizontal displacement of the roller support is quite small, usually on the range of about 1/16 inch or less (1/32 inch each end since both seats have the same level of partial restraint). For the fully translationally restrained model, the horizontal forces are quite large, usually on the range of 10 kips or more. However, the detailing of our standard joist bearing seats, the connection of the seats to the top chord, and the connection of the seats to the supporting structure, and the stiffness of all the component parts and connections is such that a force of substantially less than 10 kips can move the top of the seat substantially more than 1/32 inch.

Thus, the joist and support conditions behave very close to a simply supported condition, and not all like a fully constrained condition."

Which is essentially what I discovered when I added the seat to my model.