# Structural Calculations for Beams Using Calculus via Sympy Jul 2022

Something about calculus and Sympy is lovable
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, .

My Jupyter Notebook

Click to see notebook PDF.

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