How the stiffness method works

What this module covers

• Write the axial stiffness of a bar and say which of its three inputs go wrong most often
• Explain the two-node bar matrix from equilibrium rather than by quoting it
• Show that the global matrix is the local one seen from a rotated viewpoint
• Assemble a global stiffness matrix by adding element contributions
• Apply boundary conditions by striking out rows and columns, and say what that means physically
• Recover reactions from the struck-out rows and member forces from the displacements
• Use the equilibrium residual and the condition number as health checks on a solve

Lessons

1. 9.1

   The element and its transformation

   Where the 4×4 bar matrix comes from, why every row sums to zero, and why the global form contains no new physics.

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2. 9.2

   Assembly and boundary conditions

   Adding element contributions into the global matrix, and what striking out a row physically means.

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3. 9.3

   Solving, and recovering what you actually wanted

   Displacements first, then reactions from the struck-out rows, then member forces from the displacements — in that order, and never any other.

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