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jonesn31-Visitor
1-Visitor
March 10, 2018
Solved

Moment-Curvature Analysis - Rotations and Displacements

  • March 10, 2018
  • 3 replies
  • 9132 views

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??

Best answer by Fred_Kohlhepp

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

Capture.PNG

3 replies

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
March 10, 2018

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

F
Fred_Kohlhepp23-Emerald I
23-Emerald I
March 12, 2018

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:

Capture.PNG

    F
    Fred_Kohlhepp23-Emerald IAnswer
    23-Emerald I
    March 12, 2018

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

    Capture.PNG

      J
      jonesn31-VisitorAuthor
      1-Visitor
      March 13, 2018

      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!

       

       

      F
      Fred_Kohlhepp23-Emerald I
      23-Emerald I
      March 13, 2018

      interesting problem!

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