In this lecture, we'll cover:

• Labelling nodes, members and determining total degrees of freedom
• Determining member orientation angles measured anti-clockwise from the global positive x-axis
• Constructing the global element stiffness matrix for each truss member
• Preparing for assembly of the 12 $\times$ 12 primary stiffness matrix

In this lecture, we focus on applying the stiffness method to a larger, 8‑bar truss structure. We begin by carefully defining the structure: labelling the six nodes, identifying the eight members, and determining that the system has 12 degrees of freedom, leading to a 12 $\times$ 12 primary stiffness matrix. We emphasise the importance of systematically labelling everything at the outset, as this underpins the entire analysis process.

We then move member by member, determining each element’s orientation angle measured anti-clockwise from the global positive x-axis, always taking node i as the origin. Particular attention is given to how angles are defined, especially for members that appear horizontal but run in the negative global x-direction, or for members requiring a full anti-clockwise sweep (e.g. 300°, 240°, 270°). Once each member’s length and angle are known, we directly substitute into the previously derived global stiffness matrix formulation. The process is deliberately repetitive: once we understand it for one element, we simply repeat it for all eight members.

By the end of the lecture, we have calculated the global stiffness matrix for every individual member. This sets us up for the next step — assembling these element matrices into the overall 12 $\times$ 12 primary stiffness matrix for the complete truss structure.

Next up:

In the next lecture, we assemble the individual element stiffness matrices into the full 12 $\times$ 12 primary stiffness matrix for the 8-bar truss.