Roark's - possible error in tabulated values 2

[nuche1973]

I am looking at Table 11.4 "Fomulas for flat plates with straight boundries and constant thickness", case 7a, tabulated values for Beta 2, of Roark's Formulas for Stress and Strain, 7 edition, 2002:
The values seem to be parabolic and not linear, whereas, the values for similar tables appear to be linear. So:

Q1: Does anyone else see this, Perhaps in a differnt edition?
Q2: or have I been looking at this book for too long and I'm "stressed".

Any suggestions would be appreciated. Thanks.

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[rb1957]

you can find the original reference online, goggle "Moody Rectangular Plates" ... seriously.

I've looked into this stuff before and thought it was ok ... and Moody's report includes a lot more data.

 

[IRstuff]

If anyone's interested in the what some of the other BLM Engineering Monographs are, they're located here:

http://www.usbr.gov/pmts/hydraulics_lab/pubs/manuals_monographs.html#monographs

TTFN

FAQ731-376
Chinese prisoner wins Nobel Peace Prize

 

[Sparweb]

How's that for circular references: some of their reports list Roark's Formulas for Stress and Strain in their bibliographies.


Steven Fahey, CET

 

[ESPcomposites]

You may have to be more specific about the condition/case if you want to check against other editions. I have the sixth and table 11 is for beams.

Brian

http://www.espcomposites.com

 

[nuche1973]

ESPcomposites: the specifics are:
Table 11.4:Formulas for flat plates with straight boundries and constant thickness
Case 7a:Rectangular plate, one edge fixed, opposite edge free, remaining edges simply supported. Uniform load over entire plate.
Table for Beta values (Beta2): my book reads (from left to right).048 .190 .386 .565 .730 .688 .434

This is for stresses at the free edge in relationship to the a/b ratio.

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[rb1957]

i think ESP was asking for your edition of Roark, or at least to reference it. did you find the reference (Moody) ? is there still a question ??

 

[ESPcomposites]

He did mention it was 7th edition, but there wasn't enough info to check against other editions since the tables changed.

In the sixth edition, it is table 26. The beta2 values are the same in the sixth as well.

The results do seem a little odd, I agree. Perhaps you can run a quick FEM to check it out?

Brian

http://www.espcomposites.com

 

[nuche1973]

ESPcomposites:
Thanks. I was wondering what was in another edition. I downloaded the Moody document. Now I have to decide which is faster: a FEM analysis or a numerical review of the data in Moody? (since they are not identical)

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[rb1957]

do you mean Moody isn't the same as Roark ? i thought it was ... Roark was more limited (ie few cases).

using Raork/Moody will always be a compromise, as you'll have to conservatively model your loading to suit their cases (I expect).

FEA Should/Might be pretty quick, and should reasonably confrm Moody (who worked with a pretty coarse grid displacement model).

ESP, sorry I missed the point, which clearly the OP got.

 

[zekeman]

nuche1973 (Structural)

For those of us who do happen to have a copy of Rourke handy (mine got lost) may I suggest you post the problem with the boundaries so that we can check it against Timoshenko or some other well known reference.

 

[nuche1973]

zekeman:
go to

http://www.hpb.com

, they have several copies starting at $6.00 to $80. (US). That's where I got mine.


There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.

 

[ESPcomposites]

I took the code I developed for panel stability and modified it to accept a pressure load.

http://www.espcomposites.com/software/docs/ePressure_1.0.0.zip

With this FEM solution, you can input arbitrary boundary conditions and plate aspect ratio.

I compared it to Roark's solution for all 4 edges SS and it was within 10%. The interesting part is that Roark's does not have the (1-v^2) term you would expect for a plate. Perhaps it is buried in the coefficients, but that would assume a value for Poisson's ratio.

In any case, you can use this to compare the solutions to Roark's to see if the trend is correct. I haven't checked it out yet. Just download the associated CalculiX open source solver that I have linked in the Excel file.



Brian

http://www.espcomposites.com

 

[ESPcomposites]

I updated the code to better distribute the pressure load to weight the edge loads properly. It now to within 1% for the two cases I checked (both SS on all edges). Have not checked out the edge condition case in question yet.

Brian

http://www.espcomposites.com

 

[zekeman]

nuche1973,

Thanks for the tip

 

[ESPcomposites]

The all edge SS cases matched the FEM to within 1% or so. For the case in question (SS,Free,SS,Clamped) the FEM did not match as well, but in general, the trend was correct with Roark's. Based on this, the Roark's values are probably OK.

Brian

http://www.espcomposites.com

 

[prex]

The reference for Roark uses [ν]=0.2, as also Roark declares in the coefficient tables.
By using that value and this application in the first site below (under Plates -> Simple bending -> Rectangular -> 1 clamped,2 supp., 1 free -> Unif.load), I found values quite close to Roark's ones (within 1% for a/b=1, but with a 3% difference for a/b=3).
So Roark's values are again confirmed, within the limits of the coarse approximation used in the calculation.
However the dependence on [ν] of these particular boundary case is relatively large.
For [ν]=0 (with which primary stresses are calculated) the stress at the free edge goes down by 7% and for [ν]=0.3 it goes up by 3%.
It is also hard to understand how Roark manipulated Moody's tables, a closer reading of the paper would be required for that.

prex

http://www.xcalcs.com

: Online engineering calculations

http://www.megamag.it

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http://www.levitans.com

: Air bearing pads

 

[rb1957]

my recollection is that Moody used v = 0.2 (lord knows why)

 

[JStephen]

I think the issue is that you intuitively expect the stress to continue increasing. And in fact, it does, even though beta decreases, as the tabulated constant is mulitplied by b^2 to get the stress.

 

[nuche1973]

Thanks for the assistance. I appreciate it.

There are days when I wake up feeling like the dumbest man on the planet, then there are days when I confirm it.