In this lecture, we'll cover:

• Setting up a new Jupyter Notebook for a truss example, including importing an image for reference
• Importing required Python libraries: copy, math, NumPy, and matplotlib
• Defining material and geometric constants such as Young’s modulus and cross-sectional area
• Constructing the global element stiffness matrix for a truss member in a global coordinate system
• Building the stiffness matrix in quadrants and assembling it using NumPy’s array and concatenate functions
• Rounding output for clarity without altering underlying numerical precision
• Repeating the process for a second element and highlighting the benefit of code reuse

In this lecture, we begin implementing our truss analysis in Python by setting up a Jupyter Notebook and importing the necessary dependencies. We define key material and section properties, initially using simplified values to remain consistent with earlier hand calculations, with the intention of substituting realistic values later. We then focus on constructing the global element stiffness matrix for the first truss member, defining its length and orientation, and explicitly forming the cosine and sine terms required for the matrix entries.

We build the stiffness matrix quadrant by quadrant using NumPy arrays, scale it by $( EA/L )$, and assemble the full 4$\times$4 matrix by concatenating submatrices along the appropriate axes. We also demonstrate how to present results neatly by rounding printed output without affecting the stored numerical values. Finally, we repeat the procedure for a second element by modifying only the angle and length, illustrating both the structure of the stiffness formulation and the efficiency gains that programming provides.

Next up:

In the next lecture, we assemble the primary stiffness matrix in Python, impose boundary conditions, and reduce it to the structure stiffness matrix.