Steel · Portal frames & crane runways
Portal frame with second-order effects (AS 4100) calculator
Pinned-base gable portal analysed by the stiffness method for three combinations, then amplified for second-order effects two ways: AS 4100 storey buckling (λc from the column Nom with sway ke from the joint stiffness ratios, δs = 1/(1 − 1/λc), δb for the braced member) and a direct P-Δ iteration with the knee sway. Combined-action checks for columns and rafters use the amplified moments.
Standard: AS 4100-2020 Cl 4.4.2 moment amplification, Cl 4.7.2.2 storey buckling λc, Cl 8.3–8.4 combined actions · P-Δ iteration
Inputs in the worked example
The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.
| Input | Value | Unit |
|---|---|---|
| Span | 24 | m |
| Eaves height | 7 | m |
| Roof pitch | 10 | ° |
| Frame spacing | 7.5 | m |
| Roof dead load | 0.2 | kPa |
| Roof live load | 0.25 | kPa |
| Roof wind uplift (ULS, + up) | 0.75 | kPa |
| Windward wall (ULS) | 0.6 | kPa |
| Leeward wall suction (+ same direction) | 0.35 | kPa |
| Column section | 410UB59.7 | |
| Rafter section | 410UB59.7 | |
| Column out-of-plane restraint spacing (girts / fly braces) | 2.4 | m |
| Rafter out-of-plane restraint spacing (fly braces) | 2.5 | m |
Worked example — results
| Result | Value | Unit |
|---|---|---|
| Rafter rise | 2.12 | m |
| Joint stiffness ratio γ top (γ base = 10) | 2.32 | |
| Sway effective length factor ke | 2.18 | |
| Column Nom (sway) | 1,802 | kN |
| Column φMsx / φNs | 318 / 1,905 | kNm / kN |
| Rafter φMsx / φMb | 318 / 291 | kNm |
| 1.2G + 1.5Q (+ notional 0.002ΣV) | λc 27.3 · δs 1.038 · knee 200 → 200 kNm (P-Δ ×1.000) · uC 70% uR 73% | |
| 1.2G + Wu | λc ∞ · δs 1.000 · knee 206 → 203 kNm (P-Δ ×0.983) · uC 67% uR 72% | |
| 0.9G + Wu | λc ∞ · δs 1.000 · knee 230 → 226 kNm (P-Δ ×0.982) · uC 76% uR 80% | |
| Governing utilisation | 80 | % |
| Eaves sway, 1.2G + Wu (ULS, P-Δ) | 97.0 | mm |
- ✓ δs ≤ 1.4 (moment amplification permitted, Cl 4.4.2.3) — max δs 1.038
- ✓ Columns: combined actions — 76 %
- ✓ Rafters: combined actions — 80 %
Method, formulas and assumptions
- λc by storey buckling (Cl 4.7.2.2): λc = ΣNom/ΣN* for the two columns; ke (sway) = √[(1.6γ1γ2 + 4(γ1 + γ2) + 7.5)/(γ1 + γ2 + 7.5)] with γ2 = 10 (pinned base) and βe = 1.5 for the rafter in double curvature.
- δs = 1/(1 − 1/λc); δb = cm/(1 − N*/Nomb) with cm = 0.6 for the column; column moments × max(δb, δs), rafter moments × δs.
- P-Δ iteration: knee forces ΣN·Δ/h are added until the sway converges; compare the knee moment ratio with δs.
- Combined actions: N/φNs + M/φMs (section), in-plane M ≤ φMs(1 − N/φNcx) and out-of-plane M ≤ φMb(1 − N/φNcy) (Cl 8.4); αm = 1.75 column, 1.13 rafter.
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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.