Max Stress & Deformation of flat plate under TRIANGULAR pressure load 1

• Jun 21, 2007

1
• #2

prex

Structural

Jul 4, 2000

1,917

Look in the first site below.
If you are dealing with a circular plate and a linearly increasing load over a diameter, then Roark has it, as well as many other loading conditions and plate shapes.

prex

http://www.xcalcs.com

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• Jun 21, 2007

• #3

miecz

Structural

Sep 30, 2004

1,400

Rourk's Formulas for Stress and Strain, Table 26.
Blodgett's Design of Welded Structures.
PCA's Rectangular Concrete Tanks.
Moody's Moments and Reactions for Rectangular Plates

 

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• Jun 21, 2007

• #4

JoeTank

Structural

Oct 28, 1999

1,133

A reasonable estimate is to use the average pressure as a uniform load. Then add an extra 5% and that will get you pretty close. I've compared the results to accurate solutions and it works fairly well if you have no other resources to work with.

Joe Tank

 

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• Jun 22, 2007

• Thread starter
• #5

drscottuk

Structural

Jun 21, 2007

23

Thanks for the tips guys The xcalcs software managed to give a reasonable deflection profile, I'll order Roark's book today for the stress calc & see if that helps.

 

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• Jun 25, 2007

• #6

rtmote

Structural

Nov 10, 2005

102

I swear by Roark, this should be compulsory purchase for structural engineers.

 

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• Jun 25, 2007

• #7

csd72

Structural

May 4, 2006

4,574

I second rtmotes comments, Roarks is one of those handfull of texts that no structural office should be without.

csd

 

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• Jun 25, 2007

• #8

miecz

Structural

Sep 30, 2004

1,400

While the Roark Book is excellent for general engineering usage, some of the other references may be better for your application. Blodgett has an example of a stiffened steel tank. The PCA book tabulates moments and shears for various tank geometries. Moody's tables are hard to find, but also very useful.

 

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• Jun 25, 2007

• #9

rb1957

Aerospace

Apr 15, 2005

15,720

i suspect that this problem is not so readily solved by Roark. I'm thinking about the panel supported on three sides. Sure the top (and the bulk of the panel) could reasonably be represented as a simply supported beam, possibly a beam with intermediate elastic supports (representing the angles) but the lower portion is well supported by the lower edge support which would be a complex geometry for Roark. What makes this more significant is the loading is increasing towards the lower edge.

it would seem that the top edge is undeflected, that the out-of-plane deflection increases with depth, untill the effect of the lower edge is felt by the panel 'cause the bottom edge is also undeflected ... this is probably where the maximum bending happens in the angle stiffeners

 

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• Jun 26, 2007

• Thread starter
• #10

drscottuk

Structural

Jun 21, 2007

23

Interesting comments, I got round the problem in the end by a thin plate bending formula from prex's suggestion. Luckily the membrane and bending stresses weren't too huge on the bottom edge lip so the weld should hold.

I'm resurrecting a FE thin plate analysis code (from PhD) at the moment for any future unusual plate bending problems. Roark and Moody's books will hopefully enlighten the triangular pressure input load for it.

 

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• Jul 4, 2007

• #11

joe73

Mechanical

Jul 4, 2007

3

Interesting topic, just today I worked on a similar problem.
My load is an triangular pressure on a circular plate which is highest on the inner radius and 0 at outer radius.

I tried Roark to find a formula but there isn't one for the case I had. My workaround: I figured out an average pressure and verified that via FEA.
The Roark formula gave a slightly higher value, so I am on the safe side in this case.

 

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• Jul 4, 2007

• #12

prex

Structural

Jul 4, 2000

1,917

Well Roark has it, and even a parabolically increasing load, if I understand correctly your setup: annular plate with some kind of support and axisymmetric load?

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

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• Jul 4, 2007

• #13

joe73

Mechanical

Jul 4, 2007

3

Prex, I am talking about the flange of a winch (quite a common application and I am surprised it's very hard to get information about calculating force on these flange), highest pressure on the drum (inner radius), 0 at the outer radius. Pressure is caused by the cables.

 

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• Jul 5, 2007

• #14

prex

Structural

Jul 4, 2000

1,917

OK, so you have an annular plate with a built-in (or fixed) support at inner radius, a free outer radius and pressure increasing from inner to outer radius. You can calculate this with Xcalcs going to Plates -> Simple bending -> Annular pl. -> Free-fixed -> Distr.load : you can specify there a linearly varying load along radius, starting with a given value at inner radius, and going to zero at outer radius (or elsewhere) (and I didn't recall that the parabolically varying load is also there ).

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

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• Jul 5, 2007

• #15

joe73

Mechanical

Jul 4, 2007

3

Thanks, found it, one more source to verify my calculations.

 

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