A 2-bar planar truss has a pinned support at Node 1 (left) and Node 2 (right). Node 3 is above them, forming a triangle. A horizontal load $P$ is applied at Node 3. Assume $AE/L$ is constant and equal to $k$ for both members. Set up the global stiffness matrix.

A truss has three members meeting at a central unconstrained node (Node 4). Nodes 1, 2, and 3 are pinned to a rigid wall. A vertical load $P$ acts at Node 4. This truss is internally indeterminate to the 1st degree.

Consider the 2-bar truss from Example 1. Suppose the support at Node 2 settles downwards by a known amount $\Delta_{settle}$.

A portal frame has pinned bases (Nodes 1, 4) and rigid upper joints (Nodes 2, 3). It is subjected to a lateral load at Node 2. How many DOFs does this structure have in a general 2D frame analysis?

A continuous beam (which is modeled as a frame with axial stiffness ignored or constrained) has a uniform load $w$ applied along member 1 (between Nodes 1 and 2).

A rigid frame has an internal hinge inserted in the middle of a beam member. How is this modeled in the stiffness method?