Analyze as Thin shell, Plate or membrane 2

[dgkhan]

I have a 0.06 inch thick plate 44 inch x 24 inch. It is supported at perimeter with HSS 2x2. I have to check how much UDL this plate can take. I am using older version of SAP. Shall I assign it as thin shell, plate or membrane or shall I analyze it manually as a thin strip (beam)

 

[hokie66]

It is too thin to act in bending, so you only have tension to depend on. I suppose you would call it a membrane. Will be like a 2 way catenary. You also have to check the perimeter members to take the bending.

 

[rb1957]

roark would have the solution as well.

as a membrane, i'd avoid any linear FEM, due to large displacements. alternatively, model the flat panel as a spherical surface. it's easy to see deformed shape for the included circle (the circle tangent to the side) ... tricky to picture the shape near the corners (outside of the circle) ... but you can fudge something.

alternatively, as you say, you can analyze the central strips ... i expect this'll be conservative since there is some support at the sides that you're aren't accounting for.

best is a non-linear FEM ... all depends on how accurate you want to be.

 

[dik]

The plate is too thin to act as anything other than a membrane and it's capacity will be governed by deflection and capacity of the HSS perimeter tubing.

Dik

 

[rb1957]

good point ... how is the perimeter tuding connected to "the rest of the world" ... discretely (at the corners?), or continuously (unlikely?)?

if discretely, they'll behave as beams loaded obliquely by the membrane loading ( or in two directions (from the applied pressure) and from the membrane tension (the in-plane component).

 

[dgkhan]

rb1957
I do not know so let's take worse case and assume connection to perimeter HSS random.

 

[rb1957]

sorry, but you got to know ... you're looking at the problem, what's stopping it from flying off into space ?

if the problem is (how do we say) alittle less real ... i'd assume it's supported on the corners, that'd be more conservative than say at 8 points on the perimeter (say the 1/3 and 2/3 points on each side).

 

[dgkhan]

rb1957
I have looked at the as-built dwg. Looks like it is welded at four corners only.

 

[rb1957]

is this the connection between the sheet and the perimeter tubes, or the tubes and "the rest of the world" ?

 

[dik]

The sheet should be welded all around to the HSS... if not, then if it is welded only at the corners, then this can also be modelled. You have to analyze it by FE Methods. Also what is keeping the thin sheet from lifting along the 44" length? The HSS tubing should be supported either continuously along opposite sides or possibly at the corners and mid span of the long dimension.

What sort of loading? a few psi?

Dik

 

[dgkhan]

rb1957
I have a 0.06 inch thick plate 44 inch x 24 inch. It is supported at perimeter with HSS 2x2.There are four wheel at four corners welded to u/s HSS

 

[rb1957]

i understand from your post that the sheet is welded to the perimeter tube only at the four corners (not the greatest design). are the welds in tension (i hope not) ?

i think these welds will be the limiting feature of your design (0.06" sheet can handle a bunch of pressure).

how will you maintain a pressure seal around the perimeter of the sheet (0.06" really isn't plate) ? as the pressure is applied the sheet will deflect and open up gaps to the perimeter tube and vent the pressure.

again, what is stopping the tubes from flying off into space ? the pressure is applied to the sheet, the sheet is welded to the tubes, the tubes are attached to "the rest of the world" by ...

 

[dgkhan]

rb1957
There are four wheels at four corners welded to u/s HSS.
It is just a kind of trolley. All I need to see how much weight we can place on this trolley?

 

[rb1957]

i apologise ... i thought "wheels" was a typo !

so you've got a distributed load on the sheet, the sheet is tack welded in the corners to a tube frame, and the tube frame is supported by 4 wheels, also in the corners.

will the load in sheet put the welds (between the sheet and the tube frame) into tension (like is the sheet attached to the lower face of the tube frame) or into shear (the sheet has flanges onto the sides of the tube frame and the welds are running up/down ... i guess that's the clue about the loading on the welds ... if they're up/down they'll be in shear and pretty effective, if they're side-to-side then they'll be in tension and pretty inefficient.

what's the load capability of the wheels (and their axles) ?

 

[dgkhan]

rb1957.
I can take care of weld and HSS and Wheels. Pleaee guide me on plate only. It is tack welded on top of HSS at all corners. I just need the UDL whcih this plate can bear safely. Rest I can do thru welds, HSS and wheels and to ground. Thanks.

 

[rb1957]

from roark 4th ed pg239 (flat plate solution 81), a square plate a (= sqrt(b*d)?) loaded by pressure (uniformly distributed weight) = W/bd, supported in the corners ...
y(center) = 0.308*(1-v^2)* (p*a^4) / (E*t^3)
s(max) = 0.9152*(p*a^2)/t^2.

max stress is near enough W/t^2 (!) ... this is at the edge of the sheet. to understand the loading onto the welds, i'd draw an arc with y deflection in the middle (and zero deflection at the corners) ... you're looking at a section through the diagonal of the sheet. this'll show you the slope at the corners. this'll show you how much tension is being applied to your welds (as well as their shear, =W/4)

i'd start with W = 2*shear strength of a weld (i know there are 4, but you need to leave some capability for the tension loads). if that works out well, you can increase it (but you won't exceed 4*weld shear).

 

[dgkhan]

Last question rb1957
What are the criteria to define whether it is a thin shell, membrane or plate?

 

[csd72]

If you take membrane action into account, then your edge tubes need to be able to resist the tension of the plate as well as the perpendicular reaction.

No such thing as a free lunch I am afraid.

 

[rb1957]

pretty much everything (membrane, thin shell, plates)starts to react out-of-plane loads by bending. plates are stiff enough (have enough thickness) so that they can react these loads in bending and produce small out-of-plane deflections. membranes are very thin and can't support out-of-plane loads without deflecting significantly ( > 2* thickness); these guys react out-of-plane loads with in-plane tension (draw part of a balloon, spherical, the pressure load is balanced by tangential loads in the balloon skin). thin shells are somewhere inbetween !

 

[dik]

csd72:
I think you have to consider it as a membrane only... the spans are too great l/d = 400... There will be negligible flexural component.