Steel Frame Analysis Tutorial -- Portal Method to Matrix Stiffness

Steel frame analysis is the bridge between architectural layout and member design. Before you can check whether a beam or column is adequate, you need the internal forces and moments that the structure must resist. This steel frame analysis tutorial covers the key methods used in practice — from quick manual techniques for preliminary design to the matrix stiffness method that powers modern structural analysis software.

Portal method for approximate analysis

The portal method is a quick manual technique for low-to-medium rise buildings. It assumes points of contraflexure at midpoints of all beams and columns, and distributes storey shear to columns in proportion to their relative stiffness. The portal method typically gives moments within 15-20% of a more rigorous analysis.

Procedure summary

Total storey shear is accumulated from the roof downward. Interior columns take twice the shear of exterior columns. Column moments = column shear x (storey height/2). Beam moments are determined by joint equilibrium.

Moment distribution method (Hardy Cross)

This manual iterative approach analyses continuous beams and rigid frames through successive cycles of balancing unbalanced moments at joints. Key parameters: stiffness factor K = 4EI/L, distribution factor DF = K/sum(K), carry-over factor COF = 0.5.

Worked example

A two-span continuous beam (8 m + 6 m) with 40 kN/m UDL. After moment distribution: fixed-end moments of ±213.3 kN-m and ±120.0 kN-m are balanced through distribution factors of 0.429 and 0.571 at the interior support. Final moment at the interior support is -173.3 kN-m.

Matrix stiffness method (direct stiffness)

This is the foundation of virtually all structural analysis software. The frame is discretised into line elements connected at nodes (3 DOF per node in 2D). The 6x6 element stiffness matrix is transformed from local to global coordinates, assembled into the structure stiffness matrix K, reduced for boundary conditions, and solved as K * U = F.

Portal frame example

A single-bay portal frame (12 m span, 6 m columns, pinned bases, 30 kN/m UDL on rafter) solved by the matrix stiffness method gives: horizontal knee displacement of 15.3 mm, apex displacement of 32.1 mm, column base moment of 126 kN-m.

Educational reference only. All frame analysis results must be independently verified by a licensed Professional Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.

Try It Yourself

Ready to try this yourself? Use our free Load Combinations Calculator to generate ASCE 7, EN 1990, AS/NZS 1170, and NBC load combinations, then check your members with the Beam Capacity Calculator.