Wood bowstring truss - top chord braced?

[DETstru]

I’m having an issue with an 80 year old wood bowstring truss. 100’ span. I had the wood graded as select structural. There are about 20 of these identical trusses in the building. See photo below.

I’m analyzing them for existing and new loads and have a problem with the top chord being partially unbraced. The roof is overbuilt above the arch to create a peak in the center of the building. Thus the rafters/joists do not frame directly into the top chord. I’m wondering if my top chord is truly unbraced for the +/-16 feet between two laterally braced points or if I can rely on the continuous web member for bracing. Note the bottom chord is braced at about 24 feet on center.

I decided to model the web members as they truly are, running through the top chord to the roof diaphragm. I applied a load equal to 2% of the compression in the top flange to that node. This was fine for strength but results in about 0.3” of lateral deflection. With this magnitude of deflection, can I consider the chord braced at that point (it doesn’t work otherwise) or do I need to add “real” bracing?

I’m not sure how to determine what stiffness is sufficient for proper bracing for wood compression members.

 

[KootK]

or if I can rely on the continuous web member for bracing.

I vote yes for sure as long as there's a connection to the diaphragm. I guess it ultimately depends on what kind of sections the continuous webs actually are but it's hard to imagine them not being capable of doing the job given the proportions shown.

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.

 

[KootK]

I think that you're fine either way but I suspect that the critical stability condition would be with the two brace forces facing opposite directions.

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.

 

[DETstru]

Good point about opposing the forces. I'll check it.

My real question is regarding the brace stiffness. When I calculate the required stiffness based on AISC Appendix 6 I fall short of the required stiffness by about a factor of 2 (I know this is not steel but I have no other reference and I'm pretty sure those equations are material independent).

Under those loads the web member laterally deflects 0.3". That puts my brace stiffness at about 4.2 k/in while I'm supposed to be at about 10 k/in.
So the question is, do those bracing equation apply? Are there separate equations for wood members? Or do I just not worry about it?

 

[KootK]

- I do not know of any wood specific brace stiffness assessment algorithms.

- My first stop would have been AISC too although I'm not sure that's the right tool for the job here.

- What kind of member are these continuous webs?

- What kind of member is the bottom chord?

- Is your lateral movement of 0.3" at the location of the applied force?

- Does your lateral deflection come about more from deflection between the ends of the web or from lateral sway at the bottom of the web? I'm guessing the latter.

As I see it, you're "bracing" is really the weight of the truss bottom chord and web acting as ballast over a lever arm to rectify any sway tendency in the web, rotating about the connection to the diaphragm. As such, your effective brace stiffness actually increases as the truss web kicks out at the bottom. The AISC equations don't account for that stiffness increase and neither would a linear truss analysis.

If the web member is a stocky thing, I would treat it as flexurally rigid and do a first principles stability check. You've got:

1) a lever with it's fulcrum at the diaphragm.
2) a destabilizing load that starts at 8'/50 misalignment and increases with further movement.
3) a stabilizing load that starts at zero and increases with further movement.

If you can demonstrate self limiting behavior, you're good to go. And none of that takes into account any lateral catenary action in the bottom chord.

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.

 

[DETstru]

- The webs are 4x6 (full dimension)

- Bottom chord is (2)-4x10's (full dimension)

- 0.3" at the applied load location

- Source of deflection: yes and no
The deflection is very similar to simple span bending. As if the web member is a "beam" that spans from bottom chord to diaphragm with a point load close to the diaphragm end.
Correct, the deflection is not linear. When I first analyzed this I was hoping it would be very self limiting and I could justify a better stiffness that way. It's definitely not linear but not by much. At the point where the web member reaches it's maximum strength (1.0 D/C ratio) the stiffness is about 5.5 k/in. So yes, it does "get stiffer" but not by enough.

I still think this should be fine (it's been there for 80 years...) I was hoping my numbers penciled out to prove it.
My last ditch effort (tomorrow's effort...) will be to try to shave off some of the length of the web that protrudes above the truss by checking the clear distance between the top of truss and the diaphragm connection. I think taking into account the fact that it isn't a real "point" load will help me get close enough.

Thanks Koot.

 

[KootK]

You're welcome. Who doesn't love an old truss problem? Nobody, that's who. If it was compound, I'd do it for you.

The deflection is very similar to simple span bending.

If this and the stiffness determination are simultaneously accurate, I guess it does worry me a bit, particularly with the opposing load consideration. My intuition tells me that this is a non-issue to such a degree that I probably wouldn't even have bothered to check it myself. Live and learn... and try not too get folks killed.



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.

 

[KootK]

Push come to shove, you could strengthen by bolting channels along the sides of those webs between chords to stiffen them up. I'd think that prettier than full on discrete bracing that would have to get triangulated somewhere or tie into the diaphragm.

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.

 

[DETstru]

Good truss problems are hard to find; enjoy them while you can!
I'm sure I could've skipped all this and just braced it but where's the fun in that???

I think the reason the web acts so much like a simple span is because the bottom end is so close to where the bottom chord is braced laterally. I have a lateral brace at the midpoint of the bottom chord (see the red dot on the sketch). The weak axis stiffness of the 2-4x10 bottom chord is pretty sognoficant and doesn't allow much movement. Not to mention the point load applied laterally is so close to the top of the web member anyway so it's reaction into the bottom chord is very small.

If trimming the length gets me reasonably close to that 10 k/in I'm going to call it good enough.

 

[XR250]

DETstru,

Are your webs actually attached to the diaphragm in a manner that would transmit 1.3k +/- ?.

 

[DETstru]

XR250,
I actually don't know but I intend to make the connection work (via retrofit if needed) if I go this route.