Structural Calculations for Beams Using Calculus via Sympy Jul 2022

I find it effective to use closed form solutions and to be able to develop/verify special cases using well-known (and well worn) formulas.

I built a Jupyter notebook. Here is my summary of the contents.

1. Given a beam with fixed ends and a single concentrated load :
   
   (a) Write the equation for the reactions, , , , and ,
   
   (b) Plot the reaction for all possible locations of ,
   
   (c) Build a function, using indefinite integration to determine and for a partial uniform moment, ,
   
   (d) Build a function, using definite integration to determine and for a partial uniform moment, ,
   
   (e) Consider the point load, , located at a distance, , from the left support. What location would result in the maximum moment at the left support?,
   
   (f) Consider a partial uniform load, applied to the beam only over a distance L/2, what location of the uniform load would result in the maximum moment at the left support?,
   
   (g) Determine the solution of for any arbitrary partial uniform loading, ,
   
   (h) Determine the solution of for any arbitrary partial uniform loading, ,
   
   (Bonus 1) Determine the solution of for various ‘checkered’ uniform loadings, ,
   
   (Bonus 2) Determine the solution of for various ‘checkered’ uniform loadings, .

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   My Jupyter Notebook

   Click to see notebook PDF.

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   Live Charts

   Click to see plot; hover over data points to see data values; use finger or mouse to select rectangular area of interest

   Click to see plot; hover over data points to see data values; use finger or mouse to select rectangular area of interest

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