Portal Frame Analysis
A three-dimensional portal frame solved with a 12-degree-of-freedom beam element: four fixed columns tied by four roof beams, with the lateral load applied at the windward eaves. Sway, member forces and reactions come out of the same stiffness matrix a desktop package assembles.
| Member | Length (m) | Axial (kN) | Shear (kN) | Moment A (kN·m) | Moment B (kN·m) |
|---|---|---|---|---|---|
| 0–4 | 5.00 | 2.3 | 5.0 | 15.8 | 9.2 |
| 1–5 | 5.00 | -2.3 | 5.0 | 15.7 | 9.2 |
| 2–6 | 5.00 | -2.3 | 5.0 | 15.7 | 9.2 |
| 3–7 | 5.00 | 2.3 | 5.0 | 15.8 | 9.2 |
| 4–5 | 8.00 | -5.0 | -2.3 | -9.2 | -9.2 |
| 5–6 | 6.00 | -1.015e-16 | 3.955e-16 | 1.188e-15 | 1.186e-15 |
| 6–7 | 8.00 | -5.0 | -2.3 | -9.2 | -9.2 |
| 7–4 | 6.00 | 7.356e-17 | -3.014e-16 | -9.081e-16 | -9.037e-16 |
12 DOF: axial, torsion, bending in both planes · Rigid-jointed beam-column.
K·u = F · 6 DOF per node.
Δ = f(K, H, I) · No closed form for a fixed-base portal; the solver is the calculation.
A clear path from inputs to results.
A three-dimensional portal frame solved with a 12-degree-of-freedom beam element: four fixed columns tied by four roof beams, with the lateral load applied at the windward eaves. Sway, member forces and reactions come out of the same stiffness matrix a desktop package assembles.
How to use
- Set bay span (m).
- Set frame spacing (m).
- Set eave height (m).
- Set lateral load (kn).
- Read the headline metrics, then check the table for the detail.
The formula
Reference: Direct-stiffness linear static analysis under AISC 360 §C2, 12-degree-of-freedom 3D beam element.
Worked example
At the default inputs
- Bay span (m): 8; Frame spacing (m): 6; Eave height (m): 5; Lateral load (kN): 20; Column area (cm²): 120; Column I (×10⁶ mm⁴): 120; Beam area (cm²): 80; Beam I (×10⁶ mm⁴): 90; Analysis: first
- 1
Eave sway: 3.9 mm · Max moment: 16 kN·m · Column axial: 2 kN · Base shear: 20.0 kN
Eave sway: 3.9 mm · Max moment: 16 kN·m · Column axial: 2 kN
Interpreting the result
At 20 kN the eaves move 3.9 mm, a drift of 1/1285 of the height.
Assumptions & limitations
- Fixed bases, rigid joints.
- Linear static; P-Delta not included.
Frequently asked questions
Why does sway grow so fast with height?
The columns bend over a longer lever arm and the stiffness falls with the cube of the height.
Is this a second-order analysis?
No — P-Delta needs a different solver, so a slender frame will sway more in reality.
Methodology last reviewed 2026-10-22. Results are informational and not financial or engineering advice — see our disclaimer.