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Mar 09, 2018
08:12 PM

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Mar 09, 2018
08:12 PM

Moment-Curvature Analysis - Rotations and Displacements

Hello PTC Community,

I am attempting to utilize my Moment-Curvature Interaction (M-C) to calculate beam rotations and displacements. Currently, I have a worksheet that writes my M-C data to a text file (not included here); the attached worksheet reads the data file, creates a linear interpolation function describing moment as a function of curvature. Next, I have a simply-supported beam loaded with equal symmetrically placed point loads (0.5P); I have defined the moment diagram as a piecewise linear function of length (x).

__My goal is map curvatures across the length of the beam, using moments as the method for "matching" the curvatures to length.__ The next step(s) of calculating rotations and displacements are straightforward after this.

The attached Mathcad Prime 3.0 file attempts to solve for the corresponding curvature that satisfies M(c)=M(x), where c = curvatures from the interaction diagram, and x = position along the length of beam. However, the curvatures I calculate using the Solve Block and "Minerr" are nowhere close to being correct.

Can anybody help with ideas of how to translate curvatures to position??

Solved! Go to Solution.

1 ACCEPTED SOLUTION

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Mar 12, 2018
01:43 PM

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Mar 12, 2018
01:43 PM

The problem you have centers around solving for curvature around moments, when your moment is non-linear. If we adjust that:

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Mar 09, 2018
10:28 PM

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Mar 09, 2018
10:28 PM

Hi,

You have worked the problem once in Excel.

Prime has a "vlookup" function as well. Just do what you did in Excel but do it in Prime.

Cheers

Mar 12, 2018
08:44 AM

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Mar 12, 2018
08:44 AM

Your solution technique will work, but it's based on the assumption that EI (stiffness) is constant along the beam. Your input data does not support that:

Mar 12, 2018
01:43 PM

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Mar 12, 2018
01:43 PM

Mar 12, 2018
06:04 PM

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Mar 12, 2018
06:04 PM

Fred,

Thanks so much for your helpfulness. Unfortunately, I am unable to open you attached .zip file. The attached screenshot shows the error page that is displayed when I try to download the attachment. I do agree with your statement that EI will be non linear.

Mar 12, 2018
06:34 PM

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Mar 12, 2018
06:34 PM

What web-browser are you using? (Chrome, Edgy, Firefox, Internet Exploder, Opera, Safari,...)

Luc

Mar 12, 2018
06:45 PM

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Mar 12, 2018
06:45 PM

I was using Google Chome when I encountered the issue. I tried Firefox, and it worked. Any ideas why this was happening? I had no problems downloading other attachments elsewhere in the PTC Community.

Mar 13, 2018
08:23 AM

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Mar 13, 2018
08:23 AM

let's try again.

This was the only switch:

Mar 13, 2018
01:43 AM

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Mar 13, 2018
01:43 AM

Fred & others,

I am happy to report "success". It turns out that my initial guess value within the Solve Block wasn't adequate to calculate the correct curvatures. I was prompted to change my initial guess from "1/1000 inches" to "1/10000 inches" by looking at Fred's file. Otherwise, I had everything else I needed. I did make some changes to the way I defined my length and curvature vectors -- Fred's method of creating these vectors was much nicer looking than mine.

Attached is a PDF of the Mathcad solution. Thanks to all that helped along the way!

Mar 13, 2018
08:26 AM

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Mar 13, 2018
08:26 AM

interesting problem!