Bowstring Truss Analysis

[vmirat]

I need to analyze an existing bowstring truss in a hangar built in 1928. See attached. These trusses are at 20 foot on center.
There's a lot of tension members and not a whole lot of compression members. It seems like it is broken down into three sub-arches on the top chord, which transfer to the two vertical double angles, which then transfer back up to the top chord via tension rods.

Any ideas on how this truss works?

 

[KootK]

Goodness. Are all those members really in the same vertical plane?

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[vmirat]

KootK, yes they are all part of the truss structure.

 

[KootK]

I've never seen anything like this but the attached sketch shows how I think the designer intended things to work:

1) The vertical rods are simply sag rods hanging the bottom chords from the arched top chords.
2) The crossing diagonals in the centre panel are the only rods that are part of the primary truss under gravity loading. They are tension only and only one is active under any given, unsymmetrical load case.
3) The remaining diagonal rods are merely bracing members intended to shorten the buckling lengths of the top chords. The designer has assumed that, due to the curvature of the chords, buckling is only possible in the centrifugal direction (out into space).
4) The two vertical double angle members are part of the primary truss and may be in either tension or compression under asymmetrical loading cases.
5) The horizontal rod at the top of the truss, and the 2-L2x2 angle "bonus top chords" in the first and third panels are the tension chord for the truss when it is exposed to uplift.

The truss is very inelegant in that there are two separate top chord systems: one for gravity loading and one for uplift. If I had to guess, I'd wager that the uplift tension chord is the result of a structural upgrade. Any evidence of that?



The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[msquared48]

I guarantee this was not designed for either uplift or unbalanced line or snow loads.

Mike McCann, PE, SE (WA)

 

[woodman88]

Looks like a Whipple Truss. See Attachment

Garth Dreger PE - AZ Phoenix area
As EOR's we should take the responsibility to design our structures to support the components we allow in our design per that industry standards.

 

[Triangled]

Span to depth seems to be the classic bowstring model/ whipple/ in which the web member forces are minimal. Lots of obvious tension members and few compression capable members.
The secondary top chord puzzled me too, but combined with the tension member diagonals, (why two rods at one panel point?), I'm getting a feeling of a carefully thought out concept addressing uplift and unbalanced loading conditions.

Still standing since 1928.... I'm impressed.

The point loading beacon troubles me the most. I see no support for this other than arching action. I wonder if this was a subsequent addition, not contemplated by the original engineer.

Very interested to follow your thoughts and the thoughts of others on this one.

 

[GregLocock]

I must admit, my first thought was that it had been designed by an airframe designer, the use of tension only members, and excessive economy with material points that way.

How heavy is the beacon compared with wind loads and so on?

Cheers

Greg Locock


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[paddingtongreen]

One thing to remember is that until about WW2, labor was cheap and material was expensive, even in the early fifties we spent extra design time to save material.

I think that we should consider it as a truss supporting a bowstring roof, I don't think that anything there is an afterthought. I wondered about the two, 3/4" rods where one might expect angles, I suspect that the truss is designed pinned-pinned, judging by the "buttresses", reducing the top compression (the curvature of the roof member tends to put those rods in tension).

The bowstring roof looks like three separate pinned-pinned arches.

I would be interested to know if the rods have clevis' and turnbuckles or other means of adjustment for truing up the truss.

Michael.
"Science adjusts its views based on what's observed. Faith is the denial of observation so that belief can be preserved." ~ Tim Minchin

 

[vmirat]

So far, lots of good inputs. Thanks.

The angles are all bolted connections, except at the ends of the truss where the three angle types (two top chord angles and bottom chord angles) are all welded together. All of the rods are welded to connector plates or to the angles.

I'm doing this analysis for two reasons. The first is due to the FAA beacon tower on top, which is the airport beacon for the Colorado Springs Airport, so it's active. We have historic photos of this hangar from the 40's showing a similar tower. Not sure if the building was designed to originally support the tower or not. The second reason is due to missing and damaged truss members. Some of the tension rods are bent, sagging, or even disconnected at the panel points. One truss bottom chord is bent horizontally, like something hit it. The horizontal plane of this roof structure is a network of cross bracing and lateral tie bars to provide lateral support to the truss top and bottom chords and provide lateral stability to the building (I'm thinking the roof was not designed as a diaphragm). Most of these tie bars are gone at the bottom chord level, so there is little to no lateral support for the bottom chord. I've attached a drawing showing the full construction of this building for those of you interested. I don't have any records of the construction of the buttresses and they are covered with a stucco system, so I can't see them to measure. I don't know if the buttresses work independently or if the trusses transfer compression via the bottom chord or diaphragm action to both buttresses (hence the need for lateral support to the bottom chord?).

By the way, this building is on the National Historic Register.

 

[Triangled]

So, to confirm, is he 3 angle type connection at third span top chord all bolted too?
Vertical to arch to diagonal?

 

[vmirat]

Yes. The top chord angles are not continuous. See attached photo.

 

[KootK]

Super cool project. The trusses are insanely skimpy yet likely to make it to 2x the anticipated building service life. Inspiring. Some more thoughts:

1) X2 for Triangled's question. If it's bolted, that suggests that everything is original construction.

2) I, for one, would love to see photos of some of the connections if you've got 'em.

3) Is it your impression that all of the truss members are original construction?

4) Are the L2x2 top chords connected to the rod diagonals that they cross in any way?

5) While I understand the temptation to see this as three tied arches over a macro-truss, I'm pretty sceptical of that. I don't think that the proportions of the mini arches make sense. You'd generate monster member and connection forces just resisting minor transverse loads. You might even get snap through buckling of the arch. Additionally, I think that the more favourable proportions of the big tied arch make it a more likely load path. The only big advantage that I see with the mini-arches would potentially be for unbalanced load conditions. As MSsquared mentioned, I doubt that would have been considered in 1928.

6) I would assume that the trusses are pinned at one end and roller-pinned at the other. Don't count on the buttresses to resist arch compression. The tension ties will be a much stiffer load path for the arch thrusts.

7) Take the replacement of the bottom chord bracing seriously (as I'm sure you intend to). It does at least three important jobs. It's a secondary diaphragm; It braces the bottom chord against compression buckling during uplift; it provides tension chord bracing (Link).



The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[KootK]

We must have been typing at the same vmirat. You've already answered some of my questions. The trusses are gorgeous. Somehow they look more elegant in real life. One more observation:

Regardless of the designer's intent with the double top chords, I suspect that when the truss responds to load, the two top chords will share the top chord compression load. They'll share in a ratio that it is close to the ratio of their areas. That will be a little off because the curvature of the top chord reduces its axial stiffness some. Other than for very localized / partial loading, I don't see the L2x2 in tension at all. In part, that's why I'm doubtful about the three-arch theory. Hopefully you'll get a chance to FEM model these trusses and find out how they really behave.



The greatest trick that bond stress ever pulled was convincing the world it didn't exist.

 

[vmirat]

I attached a photo of the end of the truss. I tried to attach more than one photo but the attachment utility won't let me.

As far as I can tell, everything is original.
The tension rods run through the 2-L2x2 angles and are welded to the L5x3-1/2 top chord angles. They are not connected to the 2-L2x2's.
The trusses are bolted to a wall top plate at both ends.

One other thing. I am assuming that the grade of steel of everything is ASTM A7, which has an FY=30,000 psi.

 

[vmirat]

I've decided that this is not a bowstring truss but is a tied arch. All of the tie bars are there to maintain its shape under lateral loading. I figure the 2x4 top plate bolted to the top of the top chord at 4' O.C. provides lateral stability in compression. The D+S (balanced) load combination results in a compression of 67005#. The capacity of the two top chord angles is 114640#.

 

[Triangled]

Yup, been thinking tied arch too

 

[BAretired]

There has always been some consideration of unbalanced snow loads in the design of curved roofs, but modern codes provide for the possibility of a much larger unbalance than was formerly the case. Observations of curved arena roofs have shown that, in some cases, almost all of the snow on the windward side is blown over to the leeward side.

A tied arch is not suitable to resisting large unbalanced loads and it may be necessary to convert the arch into a bowstring truss with the addition of a few web members in order to bring it into compliance with current standards.

BA

 

[KootK]

Bowstring trusses are tied arches too. They just typically have more -- and more competent -- webbing so that the proportion of the shear transmitted through trussing is proportionately higher than what you've got. Whether it was intended or not, that central panel is pretty well trussed.

One of the unique features of the arch that we're discussing here, as opposed to a stone arch, is that the arch thickness is very thin relative to the arch span. There's really no opportunity for the line of thrust to wiggle around within the thickness of the arch and respond to varying loading conditions. As a consequence, I think that the system should be thought of like this:

1) The portion of the applied load that would produce a funicular curve matching the shape of the arch goes to the arch.
2) The remainder of the applied load will be resisted through a combination of truss action and flexure in the top chord / arch. For the sake of the design, hopefully it's mostly the former.

Another complication that I hadn't considered before is that the L2x2 "chords" will likely need to be treated as tension only members due to their very long un-braced length.

The greatest trick that bond stress ever pulled was convincing the world it didn't exist.