Moment-Curvature Analysis - Rotations and Displacements

[jonesn3]

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??

[terryhendicott]

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

[Fred_Kohlhepp]

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:

[Fred_Kohlhepp · Accepted solution]

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

[jonesn3]

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. 

[LucMeekes]

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

Luc

[jonesn3]

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. 

[Fred_Kohlhepp]

let's try again.

This was the only switch:

[jonesn3]

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!

[Fred_Kohlhepp]

interesting problem!