In this section, we'll cover:

• Introduction to the direct stiffness method
• Application of the method to a simple two-bar truss example
• Clarification of previously covered theory through a complete worked example
• Demonstration of how the method scales to larger structures

In this section, we shift our focus from foundational theory to the practical application of the direct stiffness method. We do this by working through a complete example involving a simple two-bar truss structure. Through this example, we bring together the concepts previously developed—such as material behaviour and element stiffness matrices, and show how they fit into a coherent analysis procedure. The aim is to clarify any remaining uncertainty by demonstrating the full workflow in a concrete way.

Although the structure analysed is deliberately simple, it allows us to demonstrate every essential feature of the direct stiffness method. We see how the procedure generalises, highlighting one of its key strengths: scalability. Once we understand the method in the context of a small truss, we are well equipped to apply it to much larger and more complex structures. We also set the stage for the remainder of the course, where the emphasis will shift towards streamlining implementation and developing computational solutions with Python.

Next up:

In the next lecture, we walk through a step-by-step overview of the full analysis procedure, from forming global stiffness matrices through to computing member forces.