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Concentric support of thin plate

Concentric support of thin plate

(OP)
I am looking for a reference (starting point) for calculating ring forces in concentric girders supporting thin plates with large deflection. I have a 40m circle with 4 concentric rings (10m, 20m, 30m and 36m)supporting 5mm aluminum plate with uniform pressure applied (1.5kn/m2). Each ring has evenly spaced hangers that provide the vertical support suspending the entire floor. I have found roarke cases that provide reasonable membrane stress values for the plate but I am having difficulties analyzing the stiffeners for the lateral loads induced by the plate? The stiffeners are welded to the top of the plate. I have assumed the outer stiffener resists all lateral loadings and the inner stiffeners are designed for vertical load only. We will use FEA models to evaluate results. I would like to develop a spreadsheet to use in addition to the FEA model. Thank you for any assistance.

RE: Concentric support of thin plate

maybe it's me but I don't have a clear picture of this.

is there load in the hangers ?

is the pressure load on the plate or the floor ?

if you've got concentric girders, can you add radial girders to support the plate (and avoid large displacements) ?

if you've got large displacements in the plate, then you have large displacements in the floor (connected to the plate) ??

another day in paradise, or is paradise one day closer ?

RE: Concentric support of thin plate

Roark has load cases for circular rings under various in-plane loading that should suffice for that.
One thing to watch, is that your evaluation of the plate may hAVE assumed that rings are "fixed" in the radial direction, when in fact they are not. So solving a set of several plate spans and several rings may turn into an X-unknowns and X-equations type of problem.

The edition of Roark that I have does NOT have equations for circular rings loaded normal to the ring. You can use the solution for curved beams, but they are very cumbersome. For a circular ring with uniform load and equally spaced supports normal to the plane of the ring, you can derive your own expressions for moment and torsion. For an even number of supports, simplest method is sum moments about a centerline of half the ring to find moment at support or at midspan, then sum moments about each axis on a small segment to get moment and torsion distribution. (Note that in a plane of symmetry, shear and torsion should be zero unless there is a load point at that location.) For an odd number of supports, you can isolate one support and a segment of ring from mid-span to mid-span and proceed similarly.

RE: Concentric support of thin plate

You should better describe your structure and provide sketches: from your description one would assume that a 5 mm thick alu plate is spanning between two girders over a 10 m span?!

prex
http://www.xcalcs.com : Online engineering calculations
https://www.megamag.it : Magnetic brakes and launchers for fun rides
https://www.levitans.com : Air bearing pads

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