This Python code solves any 2D truss structure using the joints method.

In order to explain the code, it was used for solving the following truss structure (Engineering Mechanics: Statics. Bedford & Fowler - Problem 6.7)

• The data is uploaded from an excel file with two main sheets

  • Element Sheet shows the start and end joints for each element
  

  • Joint Sheet shows information such as:

    • X, Y coodinates for each joint.
    • Rx, Ry represents the support reactions. If there are 1 in both columns that joint is a pinned support. If just one column has 1 that joint is a roller support.
    • Fx, Fy represents the forces in X and Y direction for each joint.
    

• In the first part of the code the support reactions are solved using the equilibrium equations for 2D structures:

$$ \Sigma F_x = 0 $$

$$ \Sigma F_y = 0 $$

$$ \Sigma M = 0 $$

• After that, all the joints are sorted based on the unknown values.
• The solution process starts with the joints with less unknowns (1 or 2) and uses the equilibrium equations for joints.

$$ \Sigma F_x = 0 $$

$$ \Sigma F_y = 0 $$

• The equation system is solved using the linalg function from numpy
• The quantity of unknowns are updated after solve a joint. The above process is repeated until all the joints are solved.
• Finally, a line-plot with the internal load of each element (in tension[+] or compression[-]) is shown.

• A solution of this example truss obtained using the software MDSolid is shown below.

• Load tha truss data using a grid and straight lines drawn with mouse.