Eccentric Loaded W-Section Beam Design

[pioneer09]

I have a steel w-section that supports bar joist from both directions. The loads are from a concrete deck and mezzanine storage live load that the joists support. The loading is over the length of the beam and is depicted in the attachment. The lengths of the bar joists are however not equal. One span is 18' and the other is 30'. Since the mezzanine loading is applied to the concrete deck, is it correct to assume the load will act like a continuous beam and transmit this through the center of the support beam.

 

[KootK]

is it correct to assume the load will act like a continuous beam and transmit this through the center of the support beam.

I'm afraid not. The lion's share of the loads that make their way to your girder will arrive via the joist seats. Thus, the eccentricity that you're concerned about is real.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[pioneer09]

This is what I had envisioned also. This brings me to the main discussion we are having in our office. The theoretical reaction point on a standard k series bar joist is 2" in from the edge of the supporting material. With this occurring on the support beam, each bar joists theoretical reaction is 3.125" from the beam center line, which would seam to develop a torsional force in the beam due to uneven loading from each side.

In our discussion, some feel if the bar joist seat where extended across the entire beam flange, torsion would be restrained. They feel the beam can not rotate due the extended seat. They also believe the welded seat of the joist opposite the large span joist side helps to restrain torsion if the beam was truly trying to rotate. Any thoughts would be appreciated.

 

[Triangled]

I've usually considered the force distribution under the bearing seat as something more trapezoidal than uniform such that the seat extension across the entire girder flange still wouldn't quite center the reaction over the web. ...Trapezoidal (or, a subset, even triangular) because of the fact that the joist and joist seat is not perfectly rigid and tends to rotate under load. Welded together, I'd think the Girder and Joist would rotate together just as KootK observes and concerns you.
I suppose you could brace back to the joist if the architect allows it or beef up the beam to intrinsically resist the torsion to some extent, or even attach a 1/4" x 2" (or whatever) bearing plate full length centered on top of your girder and require the joists to bear thereupon. This latter concept would tend to transfer the stiffness problem from your girder to the other guy's joists. The joist manufacturer may have to hold back the first web a little bit and increase the stiffness of their joist seat extension. I have found joist manufacturer's readily willing to discuss these details. The magnitude of the joist manufacturer's squawk should be directly proportional to the significance of the issue and indirectly proportional to your peace of mind.

 

[KootK]

I'm pretty sure that this discussion gets had in every design office once every couple of years. My views are similar to Triangled's:

They also believe the welded seat of the joist opposite the large span joist side helps to restrain torsion if the beam was truly trying to rotate.

With a properly designed weld and joist, you can use this method to convert beam torsion in to joist flexure. I don't think it matters which joist (or both) you use for this purpose. I think that this method is more trouble than it's worth as you have to specify the welds for flexure and, more problematically, specify the steel joists to do their part. And really, how stiff is a joist seat in flexure anyhow? Not very.

some feel if the bar joist seat where extended across the entire beam flange, torsion would be restrained. They feel the beam can not rotate due the extended seat.

Yeah, it's really quite glorious if the seats extend past the web of the beam for both joists. If that's the case, the worst case scenario is that the beam just rotates until the load finds the shear center. In reality, most beams won't have competent torsional support at their ends anyhow so, in general, it's good to have some trick up your sleeve other than beam torsion.

One firm that I worked with had a standard detail whereby, if the adjacent spans exceeded a certain amount of imbalance, the joist were to be staggered and made to extend past the beam web. I don't ascribe to that myself. I find it inelegant to have the joists staggered. I also worry that the deck fastener guys might be more prone to messing up with staggered joists. Maybe that's just paranoia. It seems to me that, even if both joists stop, say, 1/2" short of the beam web, you should still be in pretty good shape as your beam would rotate so that the aggregate load would be centered no more than about 1/2" from the beam shear center.

Of course, all of this messing with the point of application of the load also messes with the design assumptions that went into designing the joist seat. Can't have it all, right?

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.