Are the rafters connected to the crown ring have their moments released at both ends? 1

[T2ioTD]

I modeled a tank roof using the SAP2000 software. The roof plates were modeled as loads (not actual shells) and after running the analysis I found the model would only be stable if the rafters have one of their ends not released (logical) but I am not sure if it is the crown ring side that need to remain fixed.

I remember reading somewhere than rafters are pinned where they meet the shell, and "free to slide by guided" in the center. This is surprising, and I think I have missed something.

I modeled the crown ring as a curved plate of 0.5 mm thickness, height 20 cm with a top plate and a bottom plate of same thickness.

 

[JStephen]

Your modeling needs to match the actual construction or the proposed detailing.
Older grain elevators had steep roofs with compression rings at the center and rafters in compression. Usually, those roofs are fairly steep.
We have built some tank roofs using moment connections to the center hub, which loads the center hub in a "rolling" moment. In that case, the roof can be made fairly flat.
Instability can be:
-Rafters buckling as columns
-Compression ring rotating about the tank axis with rafters "racking" and dropping
-Compression ring flipping sideways
-Snap-through buckling
-Compression ring buckling in compression.
-Rafters buckling as beams
In certain cases, the tank codes allow friction with the roof plate to be considered for lateral stability of a rafter, and that may or may not be adequate in reality.
In the case of the compression ring flipping sideways, that may be resisted by the roof plate, which tends to keep the structure from going up, but not from going down, so complicating any analysis.
Erection considerations may control the design also.

 

[IFRs]

Also watch for unbalanced snow loads...