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How do you calculate the load capacity of a roof truss, like the ones commonly sold for house construction - made of 2x4 wood, fastened with metal plates, triangle shape with webbing?

I know enough physics to see that it would depend on:

  • The size of the truss
  • The exact configuration of the webbing
  • The type and thickness of wood (but let's say it's a standard construction lumber)
  • The fasteners (but let's say they are strong enough)
  • The exact location of the load - I would want to know a few critical points, so I can interpolate the rest
  • The direction of load (but let's assume it's down)

However, I can't really translate this into a lbs number of how much the truss can handle.

Is there some easy way to estimate it, without writing a whole physics simulation in Matlab, or getting a civil engineering degree?

Also, ideally I would like an answer other than "ask the manufacturer" - I want to estimate it even when the original designer/manufacturer is not available.

Also, I'm asking about the freestanding truss only. So no need to factor in weight of roof etc.

gomennathan
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  • OK it's not technically a duplicate but really, really close. Also, what's a "freestanding truss". One that's sitting on the ground and leaned up against the wall? A truss that's not part of a roof (or floor) system isn't really supporting much of anything. – FreeMan Oct 27 '23 at 16:14
  • A single truss will probably only hold enough weight that a single span of 2x4 can, if you are talking about applying weight straight down from the top. – crip659 Oct 27 '23 at 17:17
  • @freeman If it's not a duplicate, shouldn't it remain open? I asked because this seemed like a much better question that's relevant to many people in general: People who are trying to add storage to an attic, people who are traversing an attic, people who are building houses, people worried about a lot of snow... I don't see how this question is making the site a worse store of knowledge and I'm baffled at the decision to close. – gomennathan Oct 28 '23 at 22:15
  • If you read carefully, it was not closed as a duplicate. – FreeMan Oct 28 '23 at 23:53

1 Answers1

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There's so much complexity in trusses that engineers want nothing to do with the analysis. That's why specialized manufacturers exist. Vulcraft comes to mind as the steel analogue to wooden truss manufacturers.

A 2x4 has a tensile strength, a compressive strength (predicated on the 2x4's length), and a strong axis bending strength. You have to transform your structure's loading into truss member demands for comparison against the 2x4 strengths. A truss connection plate and its fasteners into the wood have strengths aligned with the line of pull from each truss member. The truss member demands also get compared to these strengths.

How do you transform your structure's loading into truss member demands? Get a textbook on statics and work your way through the "method of sections." Alternatively there are structural analysis computer programs. If you don't know statics, then you have no business using such a program.

How do you compute the truss member strengths? You would look up the material properties for your lumber species and grade in the "Reference Design Values" chapter of the National Design Specification Supplement. From there, you would use the National Design Specification (NDS) to compute the truss member strengths for comparison against your computed demands.

How do you compute the connection strengths? Well that depends on your connection plates. Are they plywood? Steel? And the fasteners. Are they 10d nails arranged symmetrically? Then the NDS's "Dowel-Type Fasteners" chapter would be the place to go.

popham
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    Basically, you're saying that the only way to do this is by "writing a whole physics simulation in Matlab, or getting a civil engineering degree" or "ask the manufacturer", all are things the OP doesn't want to do. I'd agree with you 100%, just pointing out that an answer within the OPs criteria is basically, "You can't". – FreeMan Oct 27 '23 at 18:26
  • @FreeMan, the complexity is in managing the massive amount of information that piles up. Statics was a sophomore level class at my university. Technically if he wants to consider loads between the truss panel points, then he should know Bernoulli beam theory from another sophomore level class. Even the electrical engineers took statics at my university. Links to those AWC documents, statics, and some rigorous information management are almost sufficient. The connection plates would require some pointers into another AWC document or the AISC's Steel Construction Manual. – popham Oct 27 '23 at 19:49
  • @FreeMan, structure movement under ground motion, nonlinear stuff like corotational beam elements, etc. require "whole physics simulations" in environments like MatLab. That kind of stuff requires the civil engineering degree. Anybody who's taking the corresponding classes as an undergraduate probably goes on to get a masters. At my university, anyway. – popham Oct 27 '23 at 19:54
  • All that just reinforces my point, within the constraints of the OP's criteria (without Matlab and/or a civil engineering degree), it really can't be effectively done. OP is asking for a unicorn - can't be done. – FreeMan Oct 27 '23 at 21:02
  • I agree with the first comment from @FreeMan. This amount to saying "it can't be done easily". That's a valid answer - maybe it is truly too complex for a simple estimate, and that's that. However, I am skeptical it's true and I think this answer is not really well supported for a negative answer for me to accept. But then again, clearly the mods think this is not worth discussing on this community and not worth for users here to learn, so I guess... – gomennathan Oct 28 '23 at 22:18
  • That said, it can't be that hard. Trusses have been widespread even in the 19th century before computerized simulations. Medieval craftsmen could figure them out. Certainly a precise calculation with 1% margin of error is going to take work, but a rough estimate seems very possible, especially for simpler configurations. – gomennathan Oct 28 '23 at 22:20
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    Yeah, 10# per board foot of chord should do you just fine. (Oh, but you have to offset that with your climate zone * pi firkins. Use 3 if you live in Texas.) But in seriousness to the OP, if you knew the answer, you wouldn’t have had to ask. @popham gave you the answer. End of. Your only alternative is to progressively load it until it breaks, then rebuild. – Aloysius Defenestrate Oct 28 '23 at 23:01
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    4th para tells you where to go to get reference data, @gomennathan. Find the grading stamps on your truss lumber, look it up at those sites and start working out the math. YOU are the one who asked "Is there some easy way to estimate it", and the answer is, in all likelihood, NO. That's why people spend 4 years getting an engineering degree or use software developed by people how have said degree. It's not easy. That doesn't mean you can't do it, just that it won't be easy. This is, without a doubt, the answer to the question you asked. – FreeMan Oct 28 '23 at 23:56
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    @gomennathan, there's a wide gulf between medieval trusses and modern ones. There are many truss manufacturers. The ones producing cheap, light trusses get to stay in business. "Why put 9 nails in a connection when 8 is sufficient?" That reasoning has been extrapolated across your whole truss. You'll find some wasted 2x4 material in there, but little else wasted. If your trusses are uninsulated and spaced on 24" centers, then maybe there's an extra 10 psf of live load capacity in the bottom chords. That would only be because of a hard constraint from the code, though. – popham Oct 29 '23 at 00:36
  • You guys sure are angry that someone is trying to learn a simple thing... – gomennathan Oct 29 '23 at 15:33
  • @gomennathan, by not "pinging" somebody with an @, I'm the only person who will see your last remark. I like answering specific engineering questions. I do it around here all the time, e.g. https://diy.stackexchange.com/questions/285344/how-do-i-calculate-the-weight-tolerance-for-a-steel-gate-post. If you have a specific question, then you should ask it. My instinct with design is to develop the full strength of materials unless I want a fuse in a specific location. This is not the attitude of large scale truss manufacturers. Extra strength is "waste" in that business. – popham Oct 29 '23 at 16:31
  • Angry? No. Underwhelmed when you come back and call something simple that patently isn’t? Yes. – Aloysius Defenestrate Oct 29 '23 at 17:50