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NR_77526736-Contributor
6-Contributor
December 8, 2021
Solved

Mathcad Prime - Integrals Are Too Slow

  • December 8, 2021
  • 4 replies
  • 6189 views

Hello everyone:

 

This thread is a continuation (and different question) resulting from this thread: https://community.ptc.com/t5/PTC-Mathcad/Mathcad-Prime-Breaks-in-Integral-Graph-Causing-Problems/td-p/755864

 

The replies in that thread were helpful. However, I still have to take the integral of Werner_E's equation to get the moment graph; and now, I'm trying to take the integral again to get the deflection graph. Is anyone here good enough at taking integrals that you could provide formulas for the integral (as opposed to just using the software to taking the integral) and second integral of the equation in Werner_E's more efficient function V formula? For convenience, here is a link to his formula: https://community.ptc.com/t5/image/serverpage/image-id/48045iEF9ADF38676B3B81/image-dimensions/752x76?v=v2

 

Thanks in advance.

 

Best answer by terryhendicott

Hi,

 

Second post with the fully generic calculations as promised.

The definition of B in my sheet is different to pwb in your calculations.  B is the length of the load. pwb is distance from left of right hand side of load.

Your problem enclosed.  I have added a Modulus of Elasticity, and a section modulus for deflection calculations,

It now is appreciably slower but acceptable speed.

Capture.JPG

Capture2.JPG

4 replies

T
21-Topaz II
terryhendicott21-Topaz II
21-Topaz II
December 9, 2021

Hi,

The enclosed analysis of a generic load on a beam.  From the general shape you can equate any load.  Even a point load is spread over a very small distance in real life.

It calculates the shear and moment in the beam directly.

It calculates the deflection using conjugate beam theory which does use integrals.

On my machine it is fast.

 

I would like to take some more time to make it even more general so multiple loads can be placed on a span.   I'll get around to it.

I have negated moment and deflection so moment is plotted on tension side and deflection scaled by ten is downward.

 

Capture.JPG

 

Cheers

Terry

    T
    21-Topaz II
    terryhendicott21-Topaz IIAnswer
    21-Topaz II
    December 9, 2021

    Hi,

     

    Second post with the fully generic calculations as promised.

    The definition of B in my sheet is different to pwb in your calculations.  B is the length of the load. pwb is distance from left of right hand side of load.

    Your problem enclosed.  I have added a Modulus of Elasticity, and a section modulus for deflection calculations,

    It now is appreciably slower but acceptable speed.

    Capture.JPG

    Capture2.JPG

      N
      NR_77526736-ContributorAuthor
      6-Contributor
      December 21, 2021

      Hello Terry, Thank you very much for the reply and for your time. Unfortunately for me, I'm on V3 so I can't open the file you attached :(. Would you mind screenshotting the equations and posting them in an additional reply? Thanks again 🙂

      L
      LucMeekes23-Emerald IV
      23-Emerald IV
      December 21, 2021

      See this thread: https://community.ptc.com/t5/PTC-Mathcad/Unable-to-evaluate-a-conditional-expression-Prime-6/m-p/764696#M198858

      It contains a V3 of the file, saved in Prime 6, 4, and 2. You should be able to open the Prime2 file.

       

      Success!
      Luc

        N
        NR_77526736-ContributorAuthor
        6-Contributor
        January 3, 2022

        Thanks for the replies. Much appreciated. I’m kinda still clicking around with this spreadsheet at the moment. 

        quick question, after you do the moment equations and you start doing the deflections, you have functions defined that have ‘cong’ in the name. Fcong, xcong, etc. what is the cong standing for? 

        T
        21-Topaz II
        terryhendicott21-Topaz II
        21-Topaz II
        January 4, 2022

        Hi,

         

        The subscript "cong" is short for conjugate beam. 

        https://eng.libretexts.org/Bookshelves/Mechanical_Engineering/Introduction_to_Aerospace_Structures_and_Materials_(Alderliesten)/02%3A_Analysis_of_Statically_Determinate_Structures/07%3A_Deflection_of_Beams-_Geometric_Methods/7.06%3A_Deflection_by_the_Conjugate_Beam_Method

        Capture.JPG

        Cheers

        Terry

         

          T
          21-Topaz II
          terryhendicott21-Topaz II
          21-Topaz II
          January 4, 2022

          Hi,

          I have added some comments that will make understanding it a little easier.

          Capture.JPG

          Cheers

          Terry

            N
            NR_77526736-ContributorAuthor
            6-Contributor
            January 12, 2022

            Thanks for the help Terry and Luc!

             

            To anyone who might be coming to this thread in the future because graphing integrals are going too slow. To the best of my knowledge, the reason why my graph was so slow whereas terry's was fast even though the graph is essentially the same thing is because his equations are broken up into smaller algebraic equations whereas my spreadsheet was trying to graph a large integral. If you do the symbolic solution of the integral of the equation I linked to in the other thread, you'll notice that it spits out another integral. So, his spreadsheet just evaluates the moment at each point whereas mine had to: take the integral, then evaluate some functions, then take another integral, then solve it. So mine had multiple steps to his one step and if you multiply that out by a thousand points along the beam it ends up causing the spreadsheet to take like 30 min to do the graph. 

             

            If this is happening to you, just try to split up your equations into smaller algebraic solutions and it should go faster.

             

            Thanks again.

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