pyramid roof

[COEngineeer]

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?

 

[Taro]

COEngineer, it doesn't matter if the supports are allowed to deflect to relieve the thrust. If the peak is fixed, the thrust will be less. If the beams are very rigid, the thrust will be nearly zero. There is a problem with either the model you are using for analysis or with the software's solution. I tend to believe it is something in the modeling, because I tried it with both ETABS and Risa and got the same answer (reduced thrust).

As for the detailing, double LVLs with Simpson straps at the corners seems quite reasonable.

 

[csd72]

COEngineer,

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.

 

[COEngineeer]

Taro, the thrust will be higher if you fix it. I think you modeled your wrong. I think you need to analyze the horizontal deflection at the supports if you fix the peak instead of reactions(make the base pinned and roller). If you have the peak fix with pinned pinned base, then your thrust will be higher than the pinned peak. The only reason fixed at the peak is more benneficial is because you can have a roller at one of the support so that you have no thrust at all, but if you pinned both supports, you actually have more thrust than pinned peak. I hope I am making sense.

csd, I did that also and got the same results.

 

[Taro]

No, I don't think you are making sense. It doesn't matter whether the supports are fixed, pinned, roller or springs. The only reason that there is thrust is that the bottom nodes have to kick out sideways as the peak tries to flatten. For the pinned case, the only means of resisting this flattening is the thrust reaction. With the peak fixed, however, the flattening can be resisted by the internal moments so the supports are not needed to hold the peak up and there is less thrust. In fact, with a theoretical infinitely rigid material there is no thrust at all.

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.

 

[COEngineeer]

TARO, what you said were my same initial thoughts. But if you do a free body diagram, the thrust is higher if you fix the top. 3 other members agreed that the thrusts do go up when you fix it.

 

[Taro]

Not true. If you draw a free body diagram (which assumes rigid body behavior) of the fixed peak case, there is NO thrust. Of course in the real world (where members are not infinitely rigid) there is some thrust because of the deformations of the members, but it is certainly less than the pinned case.

 

[Tomfh]

A fixed peak does increase the thrust. By fixing the peak you superimpose a negative moment onto the structure. The negative moment adds hogging curvature which increases the outwards push at the supports.

If you relax the supports the thrust starts reducing, all the way down to zero once you reach a roller support.

 

[Taro]

Ahh, Tomfh's comment has shed some light on where the confusion lies. It is a case of hand analysis versus computer analysis, old-school versus new-school. The traditional hand analysis methods assume rigid body behavior and neglect member curvature (P-small delta) effects.

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.

 

[Tomfh]

You still get the extra thrust with small displacement.

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.

 

[ChipB]

COEngineer,
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

 

[Lion06]

I think I agree with Taro on this. If you assume an infinitely rigid member, there will be zero thrust. If you have a moment connection at the peak and vertical loads, the reactions MUST be vertical (there will be no horizontal reaction or thrust).

 

[ChipB]

Ummm.....
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.

 

[Lion06]

I believe the pre-engineered buildings beams are tapered smaller toward the center (where we are considering fixed) and much, much larger at the ends (where we are considering pinned). I don't think the comparison can be made.

 

[ChipB]

StructuralEIT,
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

 

[Lion06]

I guess the question I have now is do you assume pinned-pinned (not pinned-roller) and design for this thrust (regardless of fixing at top or not) since it will be difficult to detail a "roller" at one end unless you have some sort of horizontal slotted hole in your hold down mechanism?
Or would you check how much horizontal deflection the thrust will cause and determine if it is acceptable?

 

[COEngineeer]

I didnt go for a tension ring because I could not figure out how to connect the hips onto the tension ring (7.5 kips of compression). So I went for a bent steel beam from one corner to other corner and used double LVL on other hips.

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?

 

[COEngineeer]

the reason I could not figure out the hip connection because the roof cantilever 3 more feet so I can only noth the hip so much.

 

[Lion06]

I ran into a similar problem recently. I would like to get some opinions. We had some scissor trusses that failed. While modelling and analyzing them, we tried having the supports as pinned-pinned, and as pinned-roller. If you design as pinned-pinned, not only does this create thrust at the walls, but if you assume the walls rigid (so that there is no horizontal translation at the supports, it changes the stresses in the members drastically. Obviously, the wall isn't infinitely rigid and will deflect, allowing the truss support to translate. It will not, however allow it to translate the full amount because it does have some amount of stiffness. The bottom chord actually went from tension to compression because of it. How would you guys model it and how would you detail the support connections it to get to behave the way you model it?

 

[COEngineeer]

I think truss manuf. design it as pin roller and limit the horizontal deflection. How much horizontal deflection? I dont know they varies.