Wooden Bowstring Truss - Chord Effective Lengths

[trustthemodel]

Hello all,

I have a couple of questions pertaining to the design of an old bowstring truss, particularly the chords of the truss.

Background:
- 50's era wooden bowstring truss with approximately 60' span
- Truss web members are 3x4 members at the centerline of the truss with chord members to each side of the web members (top and bottom chords are (2) members with web member connections in gap between those members)
- Roof structure comprised of wood decking supported by purlins (8 purlins total) bearing on the top of the top chord
- Truss bottom chord previously reinforced with steel rods
- Truss top chord has failed, to be replaced with glulam member

Questions:

1 - For the compression design of the top chord we are considering the top chord braced in-plane at the web panel points and braced out of plane at the purlin locations. I had initially looked at the effective length factors (in- and out-of-plane) of the top chord as K=1.0. However, because of the continuity of the top chord, I am considering adjusting the effective length factor for in-plane buckling to K=1.2 (fixed-fixed supports, translation allowed at one end) and for out-of-plane buckling to K=0.65 (Fixed-fixed supports, no translation allowed out-of-plane). Does this seem like a reasonable change?

2 - For the flexural design of the wood members NDS specifies an effective length, Le, be used to calculate the slenderness of the beam, in order to evaluate a critical buckling value, in order to get beam a stability factor. Now NDS Table 3.3.3 only gives effective beam lengths for single span beams and for cantilever beams. How would one go about defining the effective length for the top and bottom chords (which somewhat act like a multiple span beams) using the NDS? Is there some conservative assumption we can make similar to defining Cb=1.0 for steel or would one have to go member by member and define the effective length based on how the moment diagrams compare to the single span conditions given in by NDS Table 3.3.3?

Thanks in advance to anyone who read through that block of text. Any advice would be greatly appreciated!

 

[KootK]

1) For in plane and out of plane buckling, I'd go K=1.0. I'd find it hard to justify anything less for this situation. I don't get your fixed-fixed-translation proposal so you might have to elaborate on that one if you'd like further consideration of it. Particularly given that you're replacing the chords instead of justifying them as they are, I think that it makes sense to keep things simple and conventionally conservative. There's little to be gained here by going hog wild with complex theory.

2) Similarly to above, I'd go with le = distance between truss panel points. This is appropriate for members with only rotational restraint at the ends. Given that chord continuity will result in bottom side compression stresses, I think this is the way to go.

 

[Agent666]

If your structure doesn't fit the classic cases (and assumptions on which these are based) as outlined in codes (there's a good list of these assumptions in the AISC manual form memory). The best and only real route available is actually to do a rational buckling analysis.

Guessing isn't really an option, how do you know you are correct, you don't. Your assumptions are guesses.

Especially with curved members, or chords with varying axial loads along the length the rational buckling analysis is the only way really.

Its 2019, most software these days have features for working out buckling analyses and buckling loads. These work out the critical buckling load directly, you'll need to still apply any factors relating to accounting for initial imperfections.

Refer to AISC for example/comparison for steel design using a rational buckling analysis. Because it's important to recognise that the critical buckling value from a rational buckling analysis is for a analytically perfectly straight member, real members have imperfections which further reduce capacity. I've posted a few answers in the past relating to this, so have a search through my past posts if you want to know more about this procedure.

 

[trustthemodel]

KootK,

Thanks for the reply!

1) The idea was that the compressive capacity of the top chord along its length could be checked using segments of the truss treated as columns which would have unbraced lengths in- and out-of-plane as defined above. The unbraced length in either direction would define the end nodes of the "column" section which I am considering to have some fixity due to the continuity of the member. Purlins seem to me to restrain out-of-plane movement giving me the "Fixed-Fixed with no translation" case, while In-plane the end nodes would see some translation due to deflection of the truss giving me the "Fixed-Fixed with translation" case.

On a side note, running the numbers with the adjusted effective lengths increased my compressive capacity by 3%. As you said, this leaves little to be gained by making the argument, however we are looking to squeeze any capacity we can out of this member and avoid having to size a deeper chord member than we have to.

2) It seems to me that defining the effective length for flexure as the length between panel points would be unconservative considering that we are only braced laterally between purlins at the top chord (with spacing greater than panel points) and braced laterally by cross bracing (near center span) and the end seat of the truss at the bottom chord. Am I missing something here?

 

[trustthemodel]

Agent666,

Thanks for the reply!

I agree, conservative guesses are really the only guesses we should be making.

I will follow your advice and look what the office has available for a buckling analysis for these truss members.

 

[Agent666]

Regarding your point 2, if the purlins are providing effective restraint, then yes that defines the segment length you should be looking at for bending. Might be easier to provide an actual drawing so everyones talking the same language and people get a chance to see if there is anything else that perhaps has not been mentioned.

 

[trustthemodel]

Agent666/All,

Here is an elevation of the truss we're looking at.

[URL unfurl="true"]https://res.cloudinary.com/engineering-com/image/upload/v1561639439/tips/Bowstring_Truss_cwwwpa.pdf[/url]

 

[BAretired]

If the elevation is accurate, there appears to be a missing diagonal near each end of the truss.

BA

 

[trustthemodel]

BA,

The ends of the truss had (2) 3x8 blocks near the saddle which I included in the elevation/truss model as the diagonal closest to the truss ends. To your point, I am not too familiar with bowstring truss construction practices and will look into whether a diagonal might have been missed here.

Following up the Top Chord Design:
Looking at provisions for spaced columns (2015 NDS - 15.1) it seems that some fixity can be accounted for due to the web members acting as end blocks for a composite top chord section.
The section 15.2.1.2 has me confused seeing that it mentions this fixity is only effective for out-of-plane buckling but refers the reader to 15.2.3 (which includes the beam stability factor calculation with a fixity factor) for in-plane buckling condition.

 

[BAretired]

Bowstring trusses designed and built in the 1950's may not meet current building codes because codes have changed significantly since then. The following article discusses this in some detail:

https://www.westernwoodstructures.com/index.php/white-papers/bowstring-trusses/

Perhaps the most significant code change is the provision for unbalanced snow, potentially causing stress reversal in some web members.

The truss elevation above indicates a deviation from normal practice; load is applied in concentrations by purlins rather than by more closely spaced joists resulting in eccentricities in a parabolic top chord.

BA

 

[Agent666]

I'd also make sure you account for the eccentricities where the diagonals node in your analysis.

Whether the diagonals/vertical members provide any meaningful continuity to enhance the rotational restraint of the chord is dependant on the connections. I'd hazard a guess with timber and the sloppiness of connections that they are more pinned than fixed. It might not matter if you show by a buckling analysis that there is another global buckling mode that governs.

 

[trustthemodel]

Agent666,

The truss was modeled with pin-pin web members with end nodes at the points where web centroids intersected with the chord centroids so that the chords take those eccentric connection forces.

On NDS 15.1:

If I am interpreting 15.1 correctly it looks like the code would not consider the top chord to act as a composite section for the compression. The code checks the capacity of the individual chord members (accounting for some out-of-plane fixity) and the sum of the individual capacities are meant to be the capacity of that section.

I understand the connections for web members to top chord may be a bit sloppy but shouldn't we be able to consider a composite section as long as (i) blocking is provided to keep individual member slenderness less than the composite slenderness and (ii) connections get checked for the shear for out-of-plane buckling? (Something along the lines of a steel double angle column)

 

[Agent666]

My gut feeling is they will act as two separate members. An appropriate model considering the two members, blocking, etc and a rational buckling analysis would tell you if there is any global buckling that might be the two chords acting compositely or whether they just do their own thing.

 

[KootK]

but shouldn't we be able to consider a composite section as long as (i) blocking is provided to keep individual member slenderness less than the composite slenderness and (ii) connections get checked for the shear for out-of-plane buckling? (Something along the lines of a steel double angle column

I would think so as long as an appropriate reduction is taken to account for connection slip at the blocking, reducing the efficacy of the composite behavior. This link contains some excellent discussion on the issue: Link.