Stiffness Method | Lecture 7 Solving the Stiffness Equation & Displacements + MATLAB Frame Example

📚 In Lecture 7 of the Stiffness Method series, we finally solve the global stiffness equation — the core of structural analysis:
𝐊 · 𝐝 = 𝐅.
We bring everything together to compute nodal displacements, reactions, and internal forces, using both manual and MATLAB approaches.

In this lecture, we will cover:
✅ Applying boundary conditions (fixed, pinned, and roller supports)
✅ Reducing the stiffness matrix and force vector
✅ Solving for unknown displacements using the reduced system
✅ Reconstructing the full displacement vector
✅ Checking accuracy and global equilibrium
✅ Worked example: 2D portal frame under UDL + point load
✅ MATLAB / Octave coding of the beam / frame stiffness matrix

This lecture follows directly from Lecture 6 (Load Vector & Equivalent Nodal Forces) and marks the transition to interpreting structural responses — introducing displacements before moving on to reactions and internal member forces in the next lecture.

👷‍♀️ Delivered by Dr Margi Vilnay – Senior Lecturer in Structural Engineering, Chartered Engineer, and Senior Fellow of the Higher Education Academy.

📺 Watch the full Stiffness Method playlist here: http://bit.ly/3VuvFfk
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