Large Disk Supported in Center - Deflection 2

[CarbonCAD]

I have a 43" dia x 1.5" thick disk sitting on top of an 8" dia shaft. I need to figure out how much the disk is going to flex downwards like an umbrella. Specifically the deflection amount on the OD edge. The only calculations I can find are for rupture disks and discs with the OD supported and how much deflection there is in the center. It can't be totally uncommon.

 

[SnTMan]

Deflection under what? Its own weight? Roarks Formulas for Stress and Strain surely has a relevant case.

Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[JStephen]

You'll find the formulas in Roark's. Note that you may have to superimpose one or more load cases. Specifically, if you use the load cases where the outside edge is simply supported, and superimpose load cases such that the outside reaction is zero, you then have a "free" edge condition.

 

[CarbonCAD]

Deflection under it's own weight.
I'm thinking I may be able to use this from Roark's:

2. An annular aluminum plate with an outer radius of 20 in and an inner
radius of 5 in is to be loaded with an annular line load of 40 lb=in at a radius of
10 in. Both the inner and outer edges are simply supported, and it is required
to determine the maximum deflection and maximum stress as a function of the
plate thickness.

Once my plate starts to deflect it should act similar to a ring simply supported on the inner radius.

 

[CarbonCAD]

This one specifically:

 

[SnTMan]

Yeah, if your plate is annular. How accurate you need to be?

The problem with sloppy work is that the supply FAR EXCEEDS the demand

 

[robyengIT]

according to your description (2. An annular aluminum plate with an outer radius of 20 in and an inner
radius of 5 in is to be loaded with an annular line load of 40 lb=in at a radius of
10 in. Both the inner and outer edges are simply supported, and it is required
to determine the maximum deflection and maximum stress as a function of the
plate thickness) should be Table 11.2 case no. 1k.

case no. 2k is for its own weight with "ro" equal to the inner radius

 

[rb1957]

OP says "outer edge deflection" ... surely this means the outer edge is not SS ? (hence 2k, not 1k)

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

 

[robyengIT]

Roark's 7th ed - table 11.2 - case 1k outer edge free, inner edge simply supported : the difference is the load. OP says annular line load of 40 lb=in at a radius of 10 in (exactly the case 1k)

In case 2k (as per OP) the load is not annular line load but uniformly distributed (own weight)

 

[rb1957]

ok, just you wrote "inner and outer edges supported" ... so I assumed ...

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

 

[LiftDivergence]

How is the plate attached to the 8" dia. shaft?

If you have a copy of Theory of Plates and Shells by Timoshenko, Chapter 3, Symmetrical Bending of Circular Plates, Case 3 on Page 62 might do well for you. That is for a case where a central column of material passes through the plate, but the boundary conditions may approximate your scenario better than the Roark Case above. Timoshenko's case basically assumes there is no deflection in the center where the disk is common to the shaft. That could be pretty close to what you have, depending on the attachment.

Keep em' Flying
//Fight Corrosion!

 

[robyengIT]

Liftdivergence : this Timoshenko is similar to Roark's table 11.2 case 2l

 

[CarbonCAD]

Timoshenko was simpler and the solution I got was very close to what the average of the physical measurements. The problem with the physical measurements is that, in my case, it does not make a perfect "umbrella" but becomes wavy like a boonie hat brim. Very small and not visible by the naked eye but seen on the probe measurements.

 

[rb1957]

because the circumference of the deflected perimeter is less than the undeflected, and so the "extra" material has to go somewhere (waving the perimeter).

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

 

[rb1957]

@robyengIT ... I think the OP is mis-using Roark's description in the(his?) second post. The original post is not like this.


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