Beam Seat Design per Fisher's Joist Design book

[JasonMcCool]

thread507-270827
I found the referenced thread that mentions James Fisher's design method for slotted plate seats for beams bearing opposite steel joists. I've been working through his method to work up a spreadsheet for checking beam connections for either the original slotted plate or for bearing angles each side of web. Our fabricator client prefers the angles over slotting plates, but I'm having some difficulty getting "typical" angle sizes to work. The longitudinal bending moment, weld strength, and beam web shear capacity are all perfectly fine, but the bending on the outstanding leg is necessitating excessively thick angles. Just wondering what other people think of Fisher's assumption of triangular stress distribution longitudinally, but uniform bearing stress perpendicular to the beam, combined with cantilever moment assumption for bending on the outstanding leg. It seems to me like the reaction would be more uniform along the length of the bearing (i.e. stiff web distributes force evenly) and more triangular in the transverse direction (i.e. more flexible OSL of angle causes reaction to be primarily under the beam web). Based on that model, M=wL/3 would be more appropriate than M=wL^2/2. Thoughts?

 

[SteelPE]

I usually specify the plate detail on my drawings. I have had the same problem you are currently having with the thickness of the plates. Never really did anything about it other than just increase the thickness of the plate accordingly. I can see how you would have a problem with a set of angles.

Never had a fabricator try to switch out the angles for the plate. I don't even know how I would weld with angles to the beam in order for the angles and remaining portion of the beam to work together (welding is above the neutral axis while the centroid is below the neutral axis for the angle). I know there is a way to do it, but I really don't want to think about it at this time.

 

[dik]

I'm not sure I understand the problem, but I usually use a rectangular bearing based on the allowable bearing value of the support. This is based on the angle leg and fillet providing much stiffer resistance than the outstanding leg of the angle. The outstanding leg will deflect against load and the bearing value will 'disappear'. I'm not sure what the triangular distribution is... if the greater value is at the upstanding leg and tapers off along the outstanding leg... seems reasonable... if the other way around with the greater value on the outstanding leg, the is very conservative and IMHO, wrong. You can also use bt^2/4 and not bt2/6 for the plastic section.

Dik

 

[SteelPE]

Dik,

Check out the attached for what Jason is talking about in regards to a triangular bearing distribution.

 

[Hokie93]

Cool:
I would consider treating the outstanding angle legs as two upside down unstiffened seats and design them per AISC Steel Construction Manual (13th edition), Chapter 10. In essence the bearing length is that required to prevent web yielding and web crippling and is, usually, significantly less than the full leg length. Thus your moment arm and leg thickness are reduced compared to assuming full bearing across the outstanding leg. Don't forget that the critical section for bending is at the end of the fillet on the outstanding leg. AISC uses 3/8" for the fillet radius for computational purposes.

 

[JasonMcCool]

Since posting, I talked it over with my boss and we came up with an alternate check that seems valid. Curious what other think.
Fisher uses 0.75Fy for the allowable bending stress on the bearing plate in his example, which came from the old SJI criteria for bending on bearing plates (section 4.2(c) in the old 40th edition joist catalog). That has been changed to 0.9Fy in the current joist catalog, I believe to put it in accord with AISC spec section J7 on bearing strength (ASD). But that's based on compressive yielding over a projected area, not bending at extreme fibers. So I'm thinking that the whole cantilever bending model is maybe not the best. What we did was to take the bearing area of the vertical legs of the angles (bearing length over support x angle thickness x 2 angles) x 0.9Fy to get our allowable load. Then simply reaction / allowable for a unity check. That does give a pretty high capacity for bearing, which one would expect. My boss asked if it would really make any difference if the outstanding legs bend, and I don't think it would really. So we're ignoring that limit because the end result is just a load redistribution to bearing on a smaller projected area around the heels of the angles and we're already looking at the most conservative case of only using the vertical legs for bearing. In effect, if it works without any outstanding legs, then it'll work with them even if they're thin. They're basically just for stability and attachment. We're adding a check for flange bending on the support girder since that seems like an area that was neglected in Fisher's example. He did a triangular load at the end of the supported beam to get a worst case moment arm for bending at the cope, which might be realistic if the coped beam were cambered. We're adding a check for bending on the support flange based on the reaction applied at the flange toe to check for the other extreme and its effect on the support flange. The check for weld strength and reinforcement length beyond the cope proceeds similar to Fisher's example using the shear flow with Q and I based on the angles instead of the plate.
Does that sound reasonable? Or even make sense?

 

[Hokie93]

This issue (that using the entire leg length in bearing leads to very conservative leg thicknesses) was resolved long ago by Blodgett for the case of unstiffened bearing seats. Your situation is an upside down unstiffened bearing seat; instead of a beam bearing on an unstiffened seat you have two angles bearing on a beam. So I believe you can utilize the same principles to tackle your situation. As I mentioned in my previous post, the Blodgett/AISC approach uses the bearing length required to prevent web yielding and web crippling of the beam, but not less than the "k" dimension of the beam. This bearing length is typically considerably less than the full angle leg length so you have a reduced moment arm in the cantilever analysis model, which leads to a reasonable leg thickness when you crunch the numbers. This is probably covered in your steel textbook. I know it is covered in Blodgett's "Design of Welded Structures", the Salmon & Johnson steel textbook, and the Gaylord, Gaylord, and Stallmeyer steel textbook.

The 0.9Fy "allowable bending stress" has nothing to do with AISC specification section J7. The value comes from the weak axis bending of a rectangular plate. The 9th edition AISC steel manual (the green book) used an allowable bending stress of 0.75F_y for the weak axis bending of a plate. The value was, effectively, increased to 0.9F_y in the 13th edition manual.

M_n = F_yZ (AISC Eq. F11-1)
Z/S for a rectangle = 1.5, so Z = 1.5*S
M_n = F_y(1.5*S)
Ω = 1.67
M_n/Ω = F_y(1.5*S)/1.67 = 0.9F_yS
F_b = M_n/(Ω*S) = 0.9F_y