EN 1993-1-1 Portal Frame Design — Haunch, Sway Stability, Worked Example

Quick Reference: This guide walks through the complete EN 1993-1-1 design of a single-bay pitched-roof portal frame spanning 25 m with 6 m column height and 10° roof pitch. We cover frame imperfections φ (Cl. 5.3.2), elastic critical buckling factor αcr for sway classification (Cl. 5.2.1), haunch geometry optimisation, in-plane buckling lengths, snap-through stability of rafters, and the full S275 IPE-section worked example. Design follows EN 1993-1-1:2005 supplemented by SCI P397 guidance for haunched portal frames.

PRELIMINARY — NOT FOR CONSTRUCTION. All calculations are illustrative educational examples. Results must be verified by a licensed Professional Engineer before use in any design project.

1. Portal Frame Geometry and Loading

Portal frames are the dominant structural form for single-storey industrial and commercial buildings across Europe. A typical frame comprises two columns and two pitched rafters, connected by moment-resisting eaves joints and an apex joint that may be pinned or moment-resisting.

Worked Example Geometry:

• Span L = 25.0 m, clear height h = 6.0 m to underside of eaves haunch
• Roof pitch θ = 10° → rafter length Lr = 12.5 / cos(10°) = 12.69 m
• Frame spacing = 7.0 m centres

Member Selection (Initial):

• Columns: IPE 400, S275 steel
• Rafters: IPE 360, S275 steel
• Haunch at eaves: fabricated from IPE 450 cut section, length Lh = 2.5 m (10% of span)

Design Loads:

• Dead load (roof cladding + purlins + services): gk = 0.60 kN/m²
• Snow load (CEN 1991-1-3, ground snow sk = 0.80 kN/m², shape coefficient μ1 = 0.80 for 10° pitch): qs = 0.64 kN/m²
• Wind load (CEN 1991-1-4, qp = 0.90 kN/m², external pressure coefficients per Table 7.4a): uplift case controls with suction on roof qw,max = −0.75 kN/m²

2. Frame Imperfections — Cl. 5.3.2

Global frame imperfections are essential for portal frames — the inherent lack of plumb and straightness can significantly reduce the buckling resistance of slender frames.

Initial sway imperfection φ:

φ = φ0 × αh × αm

φ0 = 1/200 (basic value, EN 1993-1-1 Cl. 5.3.2(3))

αh = 2/√h = 2/√6.0 = 0.816 (height-dependent reduction, but 0.667 ≤ αh ≤ 1.0, so 0.816 is valid)

αm = √(0.5(1 + 1/m)) = √(0.5(1 + 1/2)) = √(0.5 × 1.5) = √0.75 = 0.866 for m = 2 columns in the frame row.

φ = 1/200 × 0.816 × 0.866 = 0.00353 = 1/283

Equivalent horizontal forces:

At each column top, apply ΔHEd = φ × NEd where NEd is the axial force at the column top. At the preliminary design stage, estimate NEd from the vertical roof reaction:

VEd = (1.35 × 0.60 + 1.50 × 0.64) × 7.0 × 25.0 / 2 = (0.81 + 0.96) × 175 / 2 = 1.77 × 87.5 = 154.9 kN per column

ΔHEd = φ × NEd = 0.00353 × 154.9 = 0.547 kN per column (applied as horizontal point loads at eaves level in the analysis model).

While small individually, these equivalent horizontal forces generate a base moment that should not be ignored when evaluating the frame's lateral stiffness.

3. Sway Classification — αcr Calculation

The most critical decision in portal frame design is whether second-order effects need to be considered.

αcr = Fcr / FEd

Where Fcr is the elastic critical buckling load and FEd is the design load. EN 1993-1-1 Cl. 5.2.1 provides the classification:

For portal frames, the Horne approximation gives αcr without a full eigenvalue analysis:

αcr = (HEd / VEd) × (h / δH,Ed)

From a first-order elastic analysis of the frame under the equivalent horizontal forces ΔHEd = 0.547 kN at each eaves:

• Total horizontal reaction at base level HEd = 2 × 0.547 = 1.094 kN
• Total vertical load VEd = 2 × 154.9 = 309.8 kN
• Relative horizontal displacement at eaves δH,Ed = 12.4 mm (from elastic frame analysis)

αcr = (1.094 / 309.8) × (6000 / 12.4) = 0.00353 × 483.9 = 1.71

αcr = 1.71 < 3 → Frame is highly sway-sensitive → full second-order analysis required.

This result is typical for portal frames without plan bracing — the slender columns and flexible eaves connections produce significant P-Δ effects. Acceptable solutions include:

1. Increase column size (IPE 450 or 500) to stiffen the frame.
2. Add portal bracing (cross-bracing in the roof plane or vertical bracing in the end bays).
3. Perform a full second-order analysis accounting for P-Δ effects explicitly.

For the remainder of this worked example, we will adopt an IPE 500 column to bring αcr above 3. With the larger column:

Revised δH,Ed ≈ 6.8 mm (stiffer frame) αcr = (1.094 / 309.8) × (6000 / 6.8) = 0.00353 × 882.4 = 3.12

αcr = 3.12 → sway-sensitive, amplified first-order method acceptable.

4. Haunch Design at Eaves

The eaves haunch is the most highly stressed region of any portal frame — it carries peak bending moment combined with significant axial force from the rafter thrust component.

4.1 Haunch Geometry

The haunch is typically fabricated by cutting an IPE section diagonally: the top flange follows the rafter slope, and the bottom flange cuts away at angle θ to create a linear taper.

For our frame:

• Rafter section: IPE 360 (h = 360 mm, b = 170 mm, tf = 12.7 mm, tw = 8.0 mm)
• Haunch section at column face: equivalent to IPE 450 depth (h = 450 mm)
• Haunch length Lh = 10% of span = 2.5 m
• Cutting angle: θ = tan⁻¹((450 − 360) / 2500) = tan⁻¹(90/2500) = 2.06°

The haunch depth at any distance x from the column face: h(x) = hmin + (hmax − hmin) × (1 − x/Lh) = 360 + 90 × (1 − x/2500)

At x = 0 (column face): h = 450 mm At x = 2500 mm (end of haunch): h = 360 mm

4.2 Haunch Section Properties

The haunch cross-section is built up from:

• Rafter IPE 360 (top portion, full section properties)
• Infill web plate matching the rafter web thickness (8 mm)
• Bottom flange from the cut IPE 450 (tf = 14.6 mm, b = 190 mm)

At the column face (x = 0), the haunch provides:

• Ihaunch ≈ IIPE360 + Iinfill ≈ 162.7 × 10⁶ + 110 × 10⁶ = 272.7 × 10⁶ mm⁴
• This is approximately 1.68× the rafter section modulus at the most critical location.

4.3 Stability Check for Haunched Region

EN 1993-1-1 Cl. 6.3.4 provides the general method for lateral-torsional buckling of members with non-uniform cross-section. For the haunched region, use:

• The actual section properties at each quintile point (x = 0, 0.25Lh, 0.50Lh, 0.75Lh, Lh)
• The worst segment between lateral restraints (typically the purlin spacing of 1.75 m governs within the haunch)

With purlins at 1.75 m centres providing lateral restraint to the top flange, and the bottom flange in compression over the haunch region (sagging moment), fly braces at every second purlin are typically required to restrain the bottom flange.

5. In-Plane Buckling Lengths

Determining buckling lengths for portal frame columns is non-trivial because the restraint at the top depends on the rafter stiffness.

EN 1993-1-1 Annex BB.1 method for portal frames:

For a pitched-roof portal frame with pinned bases:

• Column effective length factor kc = Lcr / Lsystem

For our geometry:

• Column height hc = 6.0 m
• Rafter length Lr = 12.69 m
• Rafter-to-column stiffness ratio: (Ir/Lr) / (Ic/hc) = (162.7 × 10⁶ / 12,690) / (482.0 × 10⁶ / 6000) = 12,823 / 80,333 = 0.160

From Annex BB.1 Figure BB.4, for a pinned-base portal with this stiffness ratio: kc ≈ 2.2 for sway buckling mode

Lcr,y = kc × hc = 2.2 × 6.0 = 13.2 m (in-plane buckling length)

For out-of-plane buckling, the column is restrained by side rails at 1.5 m vertical centres: Lcr,z = 1.5 m (governed by side rail spacing)

This large in-plane buckling length is typical for portal frame columns and explains why the IPE 500 is needed — the column slenderness λ̄ = (Lcr / iy) / (π√(E/fy)) = (13,200/204)/86.8 = 64.7/76.2 = 0.85, which is approaching the buckling plateau region.

6. Snap-Through Buckling of Rafters

For pitched-roof portal frames with rafter slope exceeding 10°, snap-through buckling must be checked. At θ = 10°, our frame is at the threshold.

SCI P397 simplified check:

The rafter slenderness should satisfy Lrafter/imin ≤ 60 for single-bay frames:

For IPE 360 rafter: imin = iz = 37.9 mm (minor axis radius of gyration) Lrafter/imin = 12,690/37.9 = 335 → FAIL — snap-through is a concern.

However, purlins at 1.75 m centres provide intermediate lateral restraint to the top flange. The relevant unsupported length for lateral-torsional buckling of the rafter is the purlin spacing, not the full rafter length. With purlin restraints:

Lpurlin/iz = 1750/37.9 = 46.2 → acceptable.

Additionally, rafter-to-rafter ties at the apex (connecting the two rafters at the ridge) prevent the anti-symmetric snap-through mode by forcing the rafters to buckle in the same direction. These ties should be specified as a minimum of one row per rafter pair, typically an angle or channel section.

7. Member Design Checks

7.1 IPE 500 Column — S275

Section Properties:

• h = 500 mm, b = 200 mm, tw = 10.2 mm, tf = 16.0 mm
• A = 11,550 mm², iy = 204 mm, iz = 43.4 mm
• Wpl,y = 2200 × 10³ mm³

Design Forces (from second-order analysis):

• NEd = 165 kN (compression)
• My,Ed = 285 kN·m (sagging at eaves)
• Vz,Ed = 72 kN

Cross-Section Classification (Cl. 5.5): Flange c/tf = (200 − 10.2 − 2×21)/2/16.0 = 73.9/16.0 = 4.62 ≤ 9ε = 9×0.924 = 8.32 → Class 1 Web c/tw = (500 − 2×16 − 2×21)/10.2 = 426/10.2 = 41.8 ≤ 72ε = 66.5 → Class 1

Section flexural-buckling resistance (Cl. 6.3.3):

λ̄y = (Lcr,y/iy) / λ₁ = (13,200/204) / 86.8 = 64.7/86.8 = 0.745 χy = 1/(0.717 + √(0.717² − 0.745²)) → curve a (α=0.21): Φ = 0.5(1 + 0.21(0.745 − 0.2) + 0.745²) = 0.5(1 + 0.114 + 0.555) = 0.835 χy = 1/(0.835 + √(0.835² − 0.745²)) = 1/(0.835 + √0.141) = 1/(0.835 + 0.376) = 0.826

Nb,Rd = χy × A × fy / γM1 = 0.826 × 11,550 × 275 / 1.00 = 2622 kN

Interaction check (EN 1993-1-1 Eq. 6.61 — Method 1):

NEd/Nb,Rd + My,Ed/Mpl,Rd ≤ 1.0

Mpl,Rd = 2200 × 10³ × 275 / 1.00 = 605 kN·m

165/2622 + 285/605 = 0.063 + 0.471 = 0.534 → OK at 53% utilisation.

7.2 IPE 360 Rafter — S275

Section Properties:

• h = 360 mm, b = 170 mm, tw = 8.0 mm, tf = 12.7 mm
• A = 7273 mm², iy = 149 mm, iz = 37.9 mm
• Wpl,y = 1020 × 10³ mm³

Design Forces (at 5 m from eaves, near apex):

• NEd = 42 kN (compression thrust)
• My,Ed = 195 kN·m (sagging)

LTB check: With purlins at 1.75 m centres as lateral restraint, Lcr,LT = 1.75 m.

λ̄LT = √(Wpl,y × fy / Mcr) = √(1020 × 10³ × 275 / 985 × 10⁶) = √(280.5 × 10⁶ / 985 × 10⁶) = √0.285 = 0.534

For IPE sections h/b = 360/170 = 2.12 > 2.0 → use buckling curve b (αLT = 0.34):

ΦLT = 0.5(1 + 0.34(0.534 − 0.2) + 0.534²) = 0.5(1 + 0.114 + 0.285) = 0.699 χLT = 1/(0.699 + √(0.699² − 0.534²)) = 1/(0.699 + √0.204) = 1/(0.699 + 0.451) = 0.870

Mb,Rd = χLT × Wpl,y × fy / γM1 = 0.870 × 1020 × 10³ × 275 / 1.00 = 244.0 kN·m

Utilisation: My,Ed/Mb,Rd = 195/244 = 0.80 → OK.

8. Serviceability — Deflections

Horizontal deflection at eaves (wind): Under the characteristic wind load combination, the horizontal drift at eaves level should not exceed h/150 = 6000/150 = 40 mm per EN 1993-1-1 Cl. 7.2.1. With the IPE 500 column, δh ≈ 28 mm → OK.

Vertical deflection at apex (snow): The snow-load deflection at the apex should not exceed L/200 = 25,000/200 = 125 mm. First-order analysis with the IPE 360 rafter gives δv ≈ 68 mm → OK.

9. Summary

Related Pages

• EN 1993-1-1 Beam Design — IPE 300 Worked Example, χLT
• EN 1993-1-1 Column Design — HEA 200 Example, Buckling Curves
• EN 1993-1-8 Base Plate Design — T-Stub, Concrete Bearing
• EN 1993-1-8 Bolt Design Guide — Fv,Rd, Fb,Rd
• EN 1993-1-2 Fire Design — Section Factor, Critical Temperature