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?

 

[JAE]

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?

 

[COEngineeer]

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

 

[COEngineeer]

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.

 

[kslee1000]

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

 

[COEngineeer]

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.

 

[ChipB]

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.

 

[COEngineeer]

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

 

[kslee1000]

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?

 

[COEngineeer]

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

 

[ChipB]

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

 

[COEngineeer]

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

 

[kslee1000]

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

 

[Tomfh]

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

 

[JAE]

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

 

[COEngineeer]

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.

 

[ChipB]

We all have those days.

 

[miecz]

COEngineeer

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

 

[Taro]

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.

 

[COEngineeer]

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.