In this lecture, we'll cover:

• How to determine element (member) forces once global nodal displacements are known
• How to transform nodal displacements from global to local coordinate systems
• How to apply the transformation matrix for members at different orientations
• How to compute axial forces using local longitudinal displacements
• How to interpret nodal displacements and prepare results for visualisation in a Jupyter Notebook

In this lecture, we focus on determining element forces after solving for the global nodal displacements of the structure. We take each member in turn and transform its nodal displacements from the global coordinate system into the local reference frame using the appropriate transformation matrix. For inclined members, this involves applying the rotation defined by the member angle, while for members aligned with the global axes the local and global displacements coincide. Once we obtain the local longitudinal displacements at each end of a member, we substitute them into the axial force expression to compute the internal force.

We repeat this process systematically for each member, demonstrating that the procedure is identical regardless of orientation: transform, extract local displacements, and calculate the axial force. We also interpret the physical meaning of the global nodal displacements, identifying the direction of movement under the applied load. Finally, we conclude by transitioning from the hand-worked solution to implementing the full procedure in a Jupyter Notebook, where we will automate the calculations and visualise the structural displacements.

Next up:

In the next lecture, we begin Section 7, where we implement the 8-bar truss solution in Python and start generalising our code for reuse with different structures.