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Calculating the deflection of a wood truss
3

Calculating the deflection of a wood truss

Calculating the deflection of a wood truss

(OP)
I don't have truss or 2D frame software - if I assume the Moment Area of Inertia based on the cross section of the top and bottom chords, as if they were connected with solid web that had no deflection resistance by itself, i.e. solving it as a simple beam, is that ballpark or will give a deflection result too much, or too little?

RE: Calculating the deflection of a wood truss

(OP)
I am concerned about it because it is the girder truss with very heavy loading, 33' long, and only 28" deep. The truss software (from the truss mfr) shows a total load deflection almost to the allowable ratio.

RE: Calculating the deflection of a wood truss

sure you can estimate the MoI as the effective two caps, this is slightly conservative.

Quando Omni Flunkus Moritati

RE: Calculating the deflection of a wood truss

That will under estimate the deflection. In most beams, shear deformation is small, but in trusses it is more significant, but I know of no general method of estimating it, short of performing the calculation.

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

RE: Calculating the deflection of a wood truss

(OP)
Thanks, Mike, that is what I needed.

When I did a hand calculation as described above, I got the exact same value (by coincidence) as their truss software.

Therefore I suspect their software is a bit unconservative, especially because this girder truss is so shallow (span to depth) and is very heavily loaded.

RE: Calculating the deflection of a wood truss

I find it isn't a terrible estimate to use 80-85% of the I of the chords

RE: Calculating the deflection of a wood truss

(OP)
dcarr

Thanks.

RE: Calculating the deflection of a wood truss

MoI of chords < MoI of the full section, yes?
deflection based on MoI of chords > deflection based on full MoI, no?

Quando Omni Flunkus Moritati

RE: Calculating the deflection of a wood truss

If you look at the SJI or Vulcraft catalogs or such, it appears they tend to use a 15% increase in their deflection. Probably to account for shear deformation. This would agree nicely with what "Dcarr" posted.

RE: Calculating the deflection of a wood truss

(OP)
rb,

Yes

Yes

RE: Calculating the deflection of a wood truss

rb1957, You would be correct for a beam but wrong for a truss. The deflection caused by the strain in the interior members of a truss increases the deflection.

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

RE: Calculating the deflection of a wood truss

Heavily loaded or shallow, long span, wood trusses also suffer alot of creep due to nail plate slip. Something the truss companies will deny, but I see all the time.

RE: Calculating the deflection of a wood truss

(OP)
Excel,

Yes that is worrying me a lot about this girder repair that the truss mfr came up with - I recommended they make it deeper but they couldn't, claiming it was impossible because of existing electrical conduit - grrrr.

It is only 28" deep, has a span of 33', and a dead load of about 480 plf

Then to add another layer of anxiety, they stupidly did not originally check how the supported trusses load transfer to each of the 5-plies, so they stupidly had to (in a hurry) used 1/2" dia bolts that further reduced the MoI, and they stupidly made the statement, well...the truss software can't take that into consideration.

Of course, worrying about the huge torsion on that girder would be something they wouldn't be capable of either - they had to use top flange case Simpson THA222-3 hangers, which IMO exacerbate the torsion problem.

All this had to be resolved Friday because they had to fab the girder Friday night and ship it to the jobsite Saturday (yesterday)

RE: Calculating the deflection of a wood truss

(OP)
^^^THA222-2^^^

RE: Calculating the deflection of a wood truss

Can you run some straps from the bottom of the supported trusses, across the bottom of the girder and up the back side to resolve the torsion?

RE: Calculating the deflection of a wood truss

just make a truss stiffness matrix...

RE: Calculating the deflection of a wood truss

(OP)
I think the 2x scab does help resist torsion because it effectively "clamps" the girder against rotation, but this is yet another example of something we can't figure a rational number.

I asked them how they came up with that number of nails but got no response - see attached

RE: Calculating the deflection of a wood truss

I clearly remember from college my structural analysis professor telling us that for parallel chord trusses you could get a rough initial estimate of the deflection as:

Twice the deflection calculated for a beam, with the beam moment of inertia calculated only from the chord areas (excluding the bh^3/12 of the individual chord elements)

as AELLC referred to in his original post.

See the attached reference from Andrew Orton's, "The Way We Build Now: Form, Scale and Technique" that seems to agree.

RE: Calculating the deflection of a wood truss

(OP)
I checked the truss software deflection, and it exactly matched the method of using only MoI of chord areas - to 3 significant digits.

However I am doing a study in my spare time, saying that is moderately inadequate.

Quote (Twice the deflection calculated for a beam,)


Where did he get that? Sounds over-conservative.

RE: Calculating the deflection of a wood truss

(OP)

Quote (See the attached reference from Andrew Orton's, "The Way We Build Now: Form, Scale and Technique" that seems to agree. )


It doesn't say twice the delta, it just says delta is higher. See above posts by others, they are estimating 15-20% higher, not 100% higher.

RE: Calculating the deflection of a wood truss

(OP)
Shoot me and put me out of my misery, now I am getting emails saying the truss repair wasn't done Saturday as planned, they are still tweaking their method.

The posts above and elsewhere are saying additional, hard-to calculate delta from:

1) Axial deformation of web members under their axial loads

2) Elastic (spring) deformation of the splice plates, especially at chords

3) Long-term creep of truss plates (not the plate itself, its grip into the wood)

RE: Calculating the deflection of a wood truss

Quote:

It doesn't say twice the delta, it just says delta is higher. See above posts by others, they are estimating 15-20% higher, not 100% higher.

The reference says the equation for delta is 10WL^3/384EI. That is twice the classical beam theory equation 5WL^3/384EI.

It all depends on span/depth ratio and the fixity of the web connections. With a SJI steel joist you have very high span/depth ratio, and the web members have high axial and rotational fixity to the chord members. It is approaching the behavior of a solid beam. So, SJI has empirically found their factor. The last long span, parallel chord timber truss I designed had a span/depth ratio of 7, and approaching truly pinned web member connections. The deflection using GTStrudl was ~1.8 times the beam analogy I referenced, and actual measurements showed ~1.9 (for dead load).

I spent three minutes running a quick truss through GTStrudl and got the following:
Span = 70'
Depth (c-c of chords) = 10'
Chords: W8x21
Load: 3 kips @ each of 7 top chord joints ==> .30 k/ft = .025 k/in
Beam-analogy moment of inertia = 2 x (6.16 x (60^2)) = 44352 in4
Deflection using beam-analogy = (5wL^4)/(384EI) = .126"
Deflection using GTStrudl = .2164"

Ratio of Theory/Beam-Analogy = .2164/.126 = 1.71

I've used this technique for years and have gotten a "feel" for what factor to use depending on joint type and span/depth ratio. Again, I only use this as a starting point with a spreadsheet to begin the design of a truss. That usually gives a good estimate for selecting your initial chord size.

RE: Calculating the deflection of a wood truss

(OP)
theonly,

OK I missed that.

What you are saying, is all those expensive truss softwares such as Alpine Truss and Mitek are completely wrong for the deflection calculation.

RE: Calculating the deflection of a wood truss

AELLC,

I have no clue with respect to truss-specific software. Never used them. However, those packages should be using virtual work or another "true" analysis approach rather than a beam-analogy approximation. I just didn't want someone in the future coming to this thread and using 1.2 x beam-analogy deflection numbers when its not appropriate.

RE: Calculating the deflection of a wood truss

(OP)
theonly,

I don't have access to the truss mfr software. My only ax to grind is the resolution of a serious mistake made by the truss designer.

Also in the future I would like to have a wood truss "rough estimate" design capability in my design Excels so I can put more stringent notes on my framing plans, directing the truss mfr to take extra care.

Right now they totally ignore what I indicate anyway, ugh.

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