A 2×2 frame: natural frequencies and buckling by the finite element method
A demo analysis of a steel frame — the same tasks I solve for clients in Abaqus, MATLAB and Mathcad. A model of 100 elements and 288 degrees of freedom: six natural frequencies, mode shapes and three buckling modes, with a 6-page report.
- 2.184 Hz
- first frequency
- 52.79
- first buckling factor λ₁
- 0.0014%
- max. deviation from theory
The task
Show an engineering calculation end to end: input data and assumptions, the model, the results and — above all — a check you can trust.
What I did
- Stiffness, mass and geometric stiffness matrices for beam elements
- Natural frequencies and modes, mass participation factors
- Linear buckling analysis: critical load factors and column effective lengths
- The report: inputs, model, method, results, validation, conclusions
Proof
- Against closed-form solutions — cantilever, simply supported beam, Euler columns — the difference is at most 0.0014%
- Mesh convergence: with 10 elements per member the result is within 0.005% of the reference
- The sum of reactions equals the applied load: 840.00 kN
Materials
10 · Click any item to enlarge it
What else you can hand over to me
- A house concept: plan, elevations, section, renders
- An interactive 3D model of an object for your website
- Frame or truss analysis: natural frequencies and buckling
- MATLAB and Mathcad tasks with a commented report
- Pile capacity and pile group settlement to Russian codes (SP)
Pine House: a concept for a 131 m² single-storey house
Plan, elevations, section, site plan and 3D from one model — so every dimension agrees