pyramid roof
pyramid roof
(OP)
I have a pyramid roof for a tower about 20'x20'. The roof is 4:12. The client wants to express the ceiling so I cant put trusses. So I decided to use the double plates (2x6) as tension ring. So I model it risa 3d and assume that each hip will be pinned on both sides. I got about 8 kips of thrust on each direction. So I decided to fix the top connections to try to reduce the thrust (create a moment connection). This is the part I dont understand, as soon I fixed the top, my thrust went up to 11+ kips!! Can someone explain it to me why? I dont undestand why. I rechecked my model like 10X and I cant figure out why it doesnt go down. Am I missing something here? It is suppose to go down right?






RE: pyramid roof
I would think that with the fixity, it would reduce since the reliance on the tension ring.
Did you just fix the straight bending moments going through to the opposite ridge member, or also torsional fixity as well?
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I got 3.5k of thrust in each direction (X & Z)
Looking at the forces, they cancel out with the adjacent member, which is what one would expect.
A lot of this is going to go into your plywood before it ever makes it to your top plate.
RE: pyramid roof
RE: pyramid roof
For the fixed model, is there a resulting moment at the fixed end? If so, how it affects the internal forces?
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I agree with you. The result surprises me (I had to model it myself). Makes you question your judgement...
RE: pyramid roof
If you built the pyramid out of "rigidium" (an infinitely rigid material that many architects believe exist when they draw structures) then there would be no thrust at all when the peak was fixed. Check the model for the 11th time. There must be something else going on.
RE: pyramid roof
RE: pyramid roof
As for the detailing, double LVLs with Simpson straps at the corners seems quite reasonable.
RE: pyramid roof
Try modelling it with the 4 top plate members as well and pinned supports. This will give you lower reactions from the top fixed case as the top plates will deflect.
I imagine this is the source of the discrepancies between different peoples results.
RE: pyramid roof
csd, I did that also and got the same results.
RE: pyramid roof
Computer modeling is not needed to demonstrate this. You can make a simple physical model at your desk to prove it to yourself. Grab a book from your shelf and place it on your desk with the bound side up at the peak. When you let go, the sides kick out and the top flattens. Now use some cardboard and tape make a "moment connection" to fix the angle at the peak. When you let go, nothing happens. The sides don't kick out and the peak doesn't flatten because of the internal moment.
RE: pyramid roof
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RE: pyramid roof
If you relax the supports the thrust starts reducing, all the way down to zero once you reach a roller support.
RE: pyramid roof
If a very flexible member is used in the computer analysis, the member curvature effects dominate the results and you end up with the counterintuitive results. Try modeling the hip members with a stiffer element and you will find that the thrust goes down (and approaches the hand calc result as the rigidity approaches infinity).
So in terms of COEngineer's design... Yes, it is possible to reduce the thrust by fixing the beams at the peak as long as the hip beams have sufficient stiffness. But the practical question is whether it is economical to go this route rather than just designing the top plates for the original thrust. I doubt it.
RE: pyramid roof
Look at it as a FBD.
Cut the structure at the peak. You'll have moment there because it's rigid. Therefore you also have an additional horizontal reaction at the support to equate with that moment, i.e. more thrust.
RE: pyramid roof
You are throwing me off with your tension ring. If the hips are @ 45 degrees to the corners, your components will cancel each other out as you go around your structure. I, personally, would block and nail the first four foot section of plywood at the boundary edge, and panel joint, and try to take the forces through tension in the plywood. Also, if you through bolted the top plates in the corners, it would assist in disbursing the load. You could also place tension strapping on the top of the plywood along the hip. Kind of like ridge strapping. It will be under the felt and shingles.
Does this make sense or am I totally missing the point?
Chip
RE: pyramid roof
RE: pyramid roof
Why do you guys think there is a huge Haunch in a pre-engineered metal building at this location?
And then, the thrust is transferred down the column into the footing.
RE: pyramid roof
RE: pyramid roof
Yes, you are right, Metal bldgs are sometimes pinned at the ridge. Thanks for correcting.
Yes, you are also correct in that if you assume an infinitely rigid member, as in one that remains flat along the bottom, you would have no thrust. That's b/c the forces are taken internally in the member, i.e. tension along the bottom section. In this case, you have no bottom section. Therefore the tension is "thrust".
Think about the typical scissors truss. The moment at the top is resolved into a force couple, however, you still have to either figure one support as a roller, or take up the thrust in your top plates.
If you have Gaylord & Gaylord's Structural Engineering Handbook, you can look it up in there. It's a pretty tedious calculation.
Chip
RE: pyramid roof
Or would you check how much horizontal deflection the thrust will cause and determine if it is acceptable?
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Sructural EIT, I ended up calculating deflection at the peak with pin and roller at the base. I just devided my span with 360 and make sure my peak sags less than that. According to risa, the roller will only move .4" horizontally, I guess in real situation then each base will move .2". Do you guys think I need to modify how I connect this bent beam to the LVL columns? I have a pretty big thrust force but it will only deflect a little. Do I need to put some kind of roller connection (slotted hole) like structEIT mentioned?
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