In this lecture, we'll cover:

• Using the primary stiffness matrix to solve for unknown support reactions
• Applying the global force–displacement relationship to obtain nodal forces
• Interpreting the sign and direction of reaction forces in the global reference frame
• Mapping calculated forces back onto the physical structure
• Verifying results using equilibrium considerations for a statically determinate structure

In this lecture, we focus on solving for the unknown support reactions using the primary stiffness matrix. We take the global force–displacement relationship and, instead of using the reduced stiffness matrix, we use the full primary stiffness matrix together with the displacement vector we have already determined. By multiplying the stiffness matrix by the vector of known displacements, we obtain the full set of nodal forces, including the support reactions.

We then interpret each force component in the context of the global coordinate system, carefully considering sign conventions and physical meaning. We map these forces back onto the structure and check whether their directions and magnitudes make sense from a statics perspective. By considering horizontal and vertical equilibrium, and the constraints imposed by member orientation, we confirm that the computed reactions are consistent with what we would expect for a simple statically determinate structure. This reinforces the connection between the stiffness method and fundamental equilibrium principles.

Next up:

In the next lecture, we complete the analysis by calculating the internal axial forces in each member and reviewing the full direct stiffness method procedure.