In this lecture, we'll cover the following:

• How to compute reaction forces from the global stiffness matrix and displacement vector.
• How to construct the global displacement vector including restrained and free degrees of freedom.
• How to verify vertical force equilibrium.
• How to account for self-weight contributions at restrained nodes.
• How to visualise the distribution of reaction forces across the mesh.

We begin by assembling the global displacement vector, carefully inserting zero displacements at restrained degrees of freedom and computed values elsewhere. By multiplying this vector by the global stiffness matrix, we obtain the global force vector, from which the reaction forces can be extracted. A key detail is the manual inclusion of self-weight at restrained nodes, which would otherwise be omitted and lead to a vertical force imbalance.

We then verify the correctness of the model by checking vertical force equilibrium, comparing the total applied load (calculated using element areas and self-weight via the shoelace formula) with the total reaction force. Finally, we generate a visual representation of the reaction forces across the mesh, using arrows to indicate both magnitude and direction. This allows us to qualitatively assess whether the distribution of reactions is physically reasonable, providing confidence in the model before moving on to displacement visualisation.

Next up

In the next lecture, we will extract and visualise the deflected shape, comparing it with the OpenSeesPy benchmark to assess the accuracy of our custom solver.