I need to calculate the strength limit of 2 sticks of 2x2 timber with 2" spacers glued between them every so often, compared to a stick of 2x4" wood. But I'm not sure how to do it.
According to sagulator, with a centre loading of 30lbs per foot:
96" long 2x4 timber deflects 0.16"
96" long 2x2 timber deflects 1.30", 8x as much. AIUI 2x2 is able to bend twice as far before breaking, so it has 1/4 the max load capacity before breakage.
What I don't know how to do is calculate for the bonded spaced 2x2s. (The spacing of the 2x2x2 spacer blocks is undecided.) Anyone know how?
spacers glued between them every so often, compared to a stick of 2x4" wood. But I'm not sure how to do it.
load capacity before breakage.
spacing of the 2x2x2 spacer blocks is undecided.) Anyone know how?
It depends on the strength of the bonding and the spacers (eg how many there are), but you are effectively manufacturing a rather weak 2x6 timber. So, provided the bonding is reasonably strong enough, I'd expect it to perform better than a 2x4 and worse than a 2x6.
" spacers glued between them every so often, compared to a stick of 2x4" wo= od. But I'm not sure how to do it.
e max load capacity before breakage.
he spacing of the 2x2x2 spacer blocks is undecided.) Anyone know how?
I see what you're saying. I'd totally agree if plenty of spacers were used.= I would think though it would have to depend on the spacing of the spacers= - in extremis if we had only 2 spacers, one right at each end, it would be= no stronger than 1 or 2 2x2s, either 1/4 or 1/8th the strangth. I say eith= er because it depends on the length between the spacers, if its short enoug= h only a single 2x2 will break before the rear 2x2 has any effect.
In this case, wide spacing of the 2x2x2 spacers will be used, I'm looking a= t feet between spacers rather than inches. I know this is all a bit counter= intuitive, but its not for house construction, and a large number of spacer= s would be considerable extra work, though not impossible.
spacers glued between them every so often, compared to a stick of 2x4" wood. But I'm not sure how to do it.
load capacity before breakage.
That does not sound right to me. I wouild have said nearly the 1/2 as in half as much wood in there, with some adjustments made. I would actually say that the 2x2 cab bend more than twice as far before breaking
spacing of the 2x2x2 spacer blocks is undecided.) Anyone know how?
yes but its a bitch. It wont be much stronger in ultimate load carrying terms but it will be stiffer than a 2x4
Obviously if the top and bottom can slide over each other its just the direct sum of a pair of 2x2s. But rigidly joining them incerases stiffness a huge amount - its a sort of I beam.
Th easy part to solve is to say that within broad limits, its irrelevant where the spacers go.
The way to look at it is as a bit of 6x2 on edge, with most of the redundant middle section that carries no load, removed.
I COULD put on me thinking cap and throw a load of calculus and two pages of maths in to tell you the exact answer, but if you have tables for a 6x2 beam use those derated by 25% and you will be closer than the natural variation in timber will be.
Last time I did all this shit was calculating the breaking strain and g loading on a couple of model aircraft wing main spars, I designed, it was a bitch then and its sill a bitch now. Took me best part of half a day to remember how to do it from years ago at first year University, and then another three hours to calculate the stresses, and then to look up and try and find the breaking strain of spruce or lime wood. And then get told '+- 50%' etc etc. Great. It might break at 2g, it might hold till 4g!!!
But anyway what you describe is a 6x2 beam with holes drilled in the middle.
" spacers glued between them every so often, compared to a stick of 2x4" wo= od. But I'm not sure how to do it.
e max load capacity before breakage.
he spacing of the 2x2x2 spacer blocks is undecided.) Anyone know how?
I agree that he's got an I-beam, but you can't treat it directly as a
6x2 because the spacers need to be attached to the 2x2s. And I think that's where the problem lies.
The top member is in compression, the bottom member is in tension. The flanges need to transmit the force from the top to the bottom to prevent sliding. The connectors between the spacers and the flanges need therefore to carry this load.
My head is struggling with how to calculate what that load is, but I think it's the likely failure point...
The spacing is not crucial. Again 1st year engineering says that as long as the unsupported length of the strut isnt subject to Euler buckling - which is a yes/no thing, not a 'little bit more or little bit less' thing., then the beam is essentially a 2x6 with a small amount of reduction in stiffness and breaking strain due to the wood removed - but beacuse that is close to the center of bendiing there isn't much stress on the 'removed wood' anyway.
Euler buckling is fun. Basically what the webs need to do is to stop the top part of a loaded beam from crumpling and snapping, and make sure that all the compressive force stays directed at pushing the wood together, not making it go sideways. In the end it boils down to how elastic the wood is and how long the unsupported sections are.
If you like the longer a bit of wood - say a vertical column is - then the more likely it is to break by bowing and snapping, than crushing. The point at which its equally likely to do either, is the Euler limit, and that is the maximum length of wood that you should leave unsupported in compression without it being weakened. In practice you err on the side of safety.
Note also that very thin tall beans are also subject to euler effects by twisting sideways and also from actual bowing in the vertical direction. So a ceiling/floor of all thin joists is weaker without the floor being nailed down hard - that stops that - and is made stiffer by herringbone bracing between the joists.
If you u cant be arsed to do the calcs on the Euler effects, buy some balsa wood and make up a model. Use scale spacings and glue it with PVA or superglue, then suspend and hang weights off. That will show you whether for similar elasticity you are in the Euler zone or not. Balsa is good as its still wood, so the relationship between strength and stiffness is similar - its all cellulose fibres at the end of the day!
I tested my main spars by sticking the wings in place and propping the tips and hanging weighs on the center: twice model weight is 4g because the bending moment of a tip supported wing is about twice that of a evenly distributed lift across the wing. A bit better with an elliptical wing because more lift is near the center in fact.
spacers glued between them every so often, compared to a stick of 2x4" wood. But I'm not sure how to do it.
load capacity before breakage.
spacing of the 2x2x2 spacer blocks is undecided.) Anyone know how?
Thats what glue is for.
"shear webs" in model aircraft parlance Though actually they carry a lot of vertical load in a true I beam with thin webs - the top wanst to buckle downwards and they have to resist that. We used vertical grain normally.
The connectors between the spacers and the flanges
No. Its very small really. you now that because wood doesn't normally shear along the grain in beam failure, it snaps by failure of the tensile fibres at the bottom. Or if there is a bit of reinforcing along there like glass fibre, by compression in the beam top (when you smash and crash as many model aircraft as I have done, you get to know what breaks, and where.
So I would simply - if its par wood - cut blocks and glue and nail the thing - or screw - it together. The screws really being too clamp up the joint as much as anything else. Id say 18" spacing would be fine,.
I think that's the sort of thing where I'd just test it - easy and cheap to make, so long as waiting for the glue to dry on something you're going to destroy isn't an issue. Load up with concrete blocks / bricks / whatever and see how it behaves. It might not be as accurate as running the calculations, but if you're looking for something that you know is not going to fail under known conditions then you can engineer it to take whatever loads are going to be found "in the wild" with a hefty margin for error.
I'd be worried about spacers failing at the glued joints as the upper* and lower 2x2s deflect - I assume there's some reason (possibly aesthetics!) that a 2x8" can't be used instead?
I think that's the sort of thing where I'd just test it - easy and cheap to make, so long as waiting for the glue to dry on something you're going to destroy isn't an issue. Load up with concrete blocks / bricks / whatever and see how it behaves. It might not be as accurate as running the calculations, but if you're looking for something that you know is not going to fail under known conditions then you can engineer it to take whatever loads are going to be found "in the wild" with a hefty margin for error.
I'd be worried about spacers failing at the glued joints as the upper* and lower 2x2s deflect - I assume there's some reason (possibly aesthetics!) that a 2x8" can't be used instead?
Oh 20:1? no way. Ive built planes with that sort of bracing and you light as well not bother.
If you are not to shy to say what the application is and what you are trying to do, there may well be a solution that someone knows that you haven't even considered.
Yes, I wouldnt be surprised, but I'm hesitant to go into detail at the mome= nt. Its similar to a floor structure in that there will be loads of these l= ight composite beams supporting one large load. And different in that placi= ng the spacers is something of an issue, hence the desire to minimise such = work as far as possible.
One idea that might perhaps work is randomly spaced spacers just glue coate= d and thrown in, literally. It won't matter if a minority of the beams are = weak.
Its similar to a floor structure in that there will be loads of these light composite beams supporting one large load. And different in that placing the spacers is something of an issue, hence the desire to minimise such work as far as possible.
and thrown in, literally. It won't matter if a minority of the beams are weak.
You haven't really explained your criteria for this project. Saving weight? Saving cost? Least work?
Least work would be to use 2x6 timber. To lighten that, the classic method is to drill holes though.
For the same cost and weight as your 2 pieces of 2 x 2, I would have thought that you would be best to make up a T-shaped girder using two pieces of 4 x 1.
And so on .... Unless you give more info, this is a classic case of GIGO.
oment. Its similar to a floor structure in that there will be loads of thes= e light composite beams supporting one large load. And different in that pl= acing the spacers is something of an issue, hence the desire to minimise su= ch work as far as possible.
ted and thrown in, literally. It won't matter if a minority of the beams ar= e weak.
A joist needs most of its strength at the centre, the shoulders at the supports could be a lot smaller were it not for practicalities such as using the floor or ceiling to put boards on etc.
So your spacers need to be more numerous where the load is greatest. If weight is a deciding factor, have you considered drilling holes in the spacers?
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