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pyramid roof

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

Are you running a PDelta on it?  

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?

RE: pyramid roof

(OP)
No, im not running p-delta.  I fixed everything at the peak (no releases).  

RE: pyramid roof

(OP)
JAE, this is what I did, I only drew 4 members (each hip).  The bottom connection is all pinned,  I let the peak node free.  Then at each member I fix the connection at the top (no release).  As a result, i get higher thrusts when I fix it.  I dont understand why it went up.

RE: pyramid roof

Try release the rotational restraint on the top node, so you have pin-pin condition, and see the difference in results.

RE: pyramid roof

(OP)
kslee, the top node is FREE.  I am only changing the end release at the top to either fixed or free.  The fixed one yields higher thrust which I dont understand.

RE: pyramid roof

I ran it quickly in Staad & modeled it with the bottom corners fixed, w/ beam releases so no moment transfer. I used a triangular load which started at 0 at the corner, and increased to 250# at the peak on each hip.

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

(OP)
if you model it in 2-D then your L would be 28'.  The height of the peak should be about 3.5 ft.

RE: pyramid roof

Sorry, I should say release the member end moment restraint.

For the fixed model, is there a resulting moment at the fixed end? If so, how it affects the internal forces?

RE: pyramid roof

(OP)
well, there is internal moment at the peak on all 4 members.  There is no reaction at the peak because it is free.

RE: pyramid roof

Ahhh, now I see what you did.  Yes, it makes sense. You made an arch.  Your thrust force is definitely going up

RE: pyramid roof

(OP)
ChipB.. please enlighten me.  My engineering judgement thinks that I should be reducing the thrust but the model thinks otherwise.

RE: pyramid roof

Resolve the moment with a couple, and draw a free body diagram at the pinned end, that shall provide the answer.

RE: pyramid roof

The negative moment at the peak is resolved by extra thrust force.

RE: pyramid roof

I modeled it in RISA as well - same result - higher tie tension with the fixity at the peak.

RE: pyramid roof

(OP)
OK.. I guess I am having one of those days.  After drawing the free body diagram I think I understand it now.  I guess if you make the peak fix, then you can have a roller at the base which is impossible in my situation.  For some reason I thought making it fixed will reduce the thrust but it is actually making it worse.  

RE: pyramid roof

We all have those days.

RE: pyramid roof

COEngineeer

I agree with you. The result surprises me (I had to model it myself).  Makes you question your judgement...  

RE: pyramid roof

COEngineer, I must be having one of those days too.  Both my engineering judgment and an ETABS analysis say the thrust is reduced when the peak is fixed.

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

(OP)
Taro I guess when you fix the top, the thrust is going to be higher but it will only push until it reaches its maximum deflection in the X direction at the base.  I think in real situation you cant really have a true pin pin base on the top framed wall because the pin will slide a little.  Once the base moved a little then the thrust is going to be significantly less.  So I think making the top fixed SHOULD reduce the thrust if there is a movement a little at the base.  I guess I just have to design the tension ring with the highest tension I got (fixed at the peak).  I am planning to use (2)-1 3/4x7 1/4 LVL as tension ring on the top of 2x6 wall w/ single plate.  I then connect each corner with simpson strap (3" wide and about 4' long) 2 at each corner.  Do you think putting (2)-1 3/4x7 1/4 LVL is too much to ask?  Is there any other simpler way?  I calculated it has about 10 kips of thrust.  

RE: pyramid roof

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.

RE: pyramid roof

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.

RE: pyramid roof

(OP)
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.   

RE: pyramid roof

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.

RE: pyramid roof

(OP)
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.  

RE: pyramid roof

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.

RE: pyramid roof

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.

RE: pyramid roof

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.

RE: pyramid roof

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.

RE: pyramid roof

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

RE: pyramid roof

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).

RE: pyramid roof

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.

RE: pyramid roof

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.

RE: pyramid roof

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

RE: pyramid roof

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?

RE: pyramid roof

(OP)
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?

RE: pyramid roof

(OP)
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.  

RE: pyramid roof

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?

RE: pyramid roof

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

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