In this lecture, we'll cover:

• Defining a Python function to calculate member length and orientation from node data
• Extracting node indices and coordinates from arrays using correct indexing
• Determining whether a member lies along an axis or within one of four quadrants
• Computing the orientation angle using the dot product formula and applying the correct quadrant offset
• Looping through all members to store calculated lengths and orientations automatically

In this lecture, we focus on building a reusable Python function to calculate the length and orientation of any truss member. We begin by carefully extracting the correct node indices and their coordinates from predefined arrays, paying particular attention to Python’s zero-based indexing. From these coordinates, we compute the vector components $dx$ and $dy$, which allow us to determine both the member’s length and its orientation.

We then explore how to calculate the member’s orientation angle with respect to the horizontal axis. To do this robustly, we distinguish between members aligned with the coordinate axes and those located in one of the four quadrants. Using the dot product formula, we compute the acute angle between vectors and then apply the appropriate angular offset depending on the quadrant. Finally, we automate the process by looping through all members, calling our function for each one, and storing the resulting lengths and orientations. By the end of the lecture, we have a flexible and fully automated approach that can be applied to any truss geometry without modifying the core code.

Next up:

In the next lecture, we assemble the primary and structure stiffness matrices programmatically, completing the automated matrix construction phase of the solver.