Pucher Charts (Plate Internal Forces) In Mathcad

[stillife]

Hi all,

I have just started using Pucher charts to compute internal forces (specifically moments) in plate elements. While the charts are very easy to use once you've understood how they work, it can be tedious to use them over an over, especially if iterations are necessary. I read through the book by Aloph Pucher to try and understand how the influence surface contour plots were generated, but I was unable to find that information. I was wondering if anyone else here has used the plots and knows if they can be generated in mathcad (or any other mathematics based application) with finer intervals. I'm trying to see if the plots are based on solutions to the differentiation of the deflection surface or through some emperical method. I'm hoping that if the plots are created mathematically, it could be possible to use mathematics capability of mathcad (or mathematica) to compute moments by integrating over the loaded areas.

I hope I'm making sense. As I said I've just started using this method so please point out any flaws in my understanding.

Any and all help is appreciated in advance,

Bests,

Ali

[DanMarotta]

Hi Still Life,

I'm not familiar with Pucher charts but I'm sure another Mathcad community member is. Perhaps you could share a little more about yourself by completing your profile so members can tailor their response to fit your needs.

-BostonDan

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[jeanGiraud]

"Pucher charts"

... do you mean the Mathcad coding for the *.PDF FORTRAN code ?

That should be no problem, but you must collect the formulas you

want and start by a project description.

jmG

[BillWadsworth]

If you are working with rectangular plates, this finite difference formulation might be of help. You need to allow for the fact that it is an approximate method particularly in the vicinity of point loads or point supports.

Bill Wadsworth

[MikeArmstrong]

Bill, thanks for sharing the worksheet. As you said in your post it is an approximate method, but is an alternative to doing a FEA analysis. Have you got any simple worksheets which you are willing to share? Maybe a simple beam analysis showing the deflection along the beam as you have in your sheet.

Mike

[BillWadsworth]

Mike,

How about this one for a statically determinate beam?

Bill

[MikeArmstrong]

Lester Wadsworth wrote:

Mike,

How about this one for a statically determinate beam?

Bill

Bill,

Another nice worksheet, cheers for sharing.

Mike

[BillWadsworth]

or this one for any beam, varying inertia, elastic supports, and any number of spans, fixed or free ends. This is one I posted way back on the Collabatory.

BIll

[MikeArmstrong]

Bill,

Cheers, another excellent worksheet.

Sorry to be a pain, but have you got an example of a simply supported beam with a point load so I can start from scratch and adapt to mine own needs.

Mike

[BillWadsworth]

Mike,

If you just strip down the first sheet you get something like this.

You integrate the reactions to get the moments, the moments to get the slopes, and the slopes to get the deflexions. Then, after getting the constants of integration, you get an expression for the deflexions. I did the integrations by hand but the purists would have you do them in Mathcad, I tried once but I got in a tangle over the Macauley terms, trying to use the Heaviside function.. I expect I did not do it right.

regards, Bill

[MikeArmstrong]

Lester Wadsworth wrote:

Mike,

If you just strip down the first sheet you get something like this.

You integrate the reactions to get the moments, the moments to get the slopes, and the slopes to get the deflexions. Then, after getting the constants of integration, you get an expression for the deflexions. I did the integrations by hand but the purists would have you do them in Mathcad, I tried once but I got in a tangle over the Macauley terms, trying to use the Heaviside function.. I expect I did not do it right.

regards, Bill

Cheers again Bill,

I have a few sheets saved similar to the one you posted. Great, at least I know I was on the right track !

I haven't been able to get Mathcad to get the integrations, always had to do them by hand.

Cheers,

Mike

[AjayaMalla]

Pucher charts, as the name implies are meant to aid graphical solution of plate bending/shear. To have those in MathCAD, one would need to code MathCAD for the solution (lots of differential equation solving). Would it be easier to pick up solutions from Roarks instead and code them?

I use the Pucher charts fairly often. Have them digitized in AutoCAD where I can get bending moment readoffs by drawing in my imposed load footprint.

Cheers. Ajaya