In this lecture, we'll cover:

• How to use the primary stiffness matrix to compute reaction forces
• Substituting known nodal displacements back into the global force–displacement equations
• Interpreting the resulting reaction force vector in terms of the structure’s degrees of freedom
• Relating calculated reaction forces to their physical locations on the structure

In this lecture, we focus on solving for the reaction forces once the structural model has been fully assembled. We begin by revisiting the complete force–displacement relationship using the primary (global) stiffness matrix. By substituting the known nodal displacements into this system of equations, we determine the reaction forces through a straightforward matrix multiplication. This reinforces the idea that, once the global stiffness matrix has been constructed, extracting meaningful structural results becomes a systematic process.

We also interpret the resulting reaction force vector in a physical context, linking specific entries in the vector to particular degrees of freedom and nodes on the structure. By identifying how values such as the applied and reaction forces correspond to individual nodes, we strengthen our understanding of how the mathematical formulation connects directly to the structural behaviour. Overall, we see that after assembling the global stiffness matrix and solving for nodal displacements, calculating reaction forces is a natural and relatively simple final step in the analysis process.

Next up:

In the next lecture, we determine the axial force in each member by transforming global displacements into local coordinates and then transition to implementing the solution in Python.