Portal Frame Design Guide — Haunch, Knee, Base Fixity, and Worked Example

Complete portal frame design reference covering elastic and plastic analysis methods, haunch proportioning, knee and apex joint design, base fixity selection, and a worked example for a 20-meter span industrial building. Based on AISC Design Guide 25, Eurocode 3 Part 1-1, and AS 4100.

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

What Is a Portal Frame?

A portal frame is a single-storey structural system consisting of vertical columns rigidly connected to horizontal or pitched rafters, forming moment-resisting frames that resist both gravity and lateral loads without requiring diagonal bracing in the plane of the frame. Portal frames are the workhorse of industrial, warehouse, and agricultural construction worldwide, prized for their ability to provide large clear spans with minimal internal obstructions.

The defining characteristic of a portal frame is the rigid connection at the eave (column-to-rafter joint), which transfers bending moment between the column and rafter. This moment transfer reduces the mid-span bending moment in the rafter by 30–50% compared to a simply supported rafter, allowing lighter sections for the same span. A second rigid connection at the apex (ridge) further redistributes moments, and when combined with a haunch — a deepened section at the eave — the frame can achieve spans of 15 to 60 meters economically.

Portal Frame Geometry and Terminology

A typical portal frame consists of:

• Columns: Vertical members, typically universal beam (UB) or wide-flange (W) sections. Column height is set by clearance requirements plus an allowance for the haunch.
• Rafter: The sloping beam member. Rafter depth is typically 1/40 to 1/55 of the span for hot-rolled sections. The rafter slope (roof pitch) is usually between 5° and 15° for standard profiled metal cladding; steeper pitches (15°–30°) are used in high-snow regions.
• Haunch: A deepened section at the eave where the rafter connects to the column. The haunch increases the moment capacity at the most highly stressed region of the frame. Haunch length is typically 10–15% of the span.
• Knee joint: The rigid connection at the eave, combining the column top, haunch bottom flange, and rafter bottom flange. Bolted end plates or fully welded details are common.
• Apex joint: The rigid connection at the ridge. For symmetrical frames, this carries primarily axial force and a modest bending moment.
• Base: The column-to-foundation connection. Can be nominally pinned, semi-rigid, or fully fixed depending on lateral drift requirements and foundation cost trade-offs.

The frame is usually analysed in its own plane (in-plane behaviour), with out-of-plane stability provided by purlins, girts, and longitudinal bracing systems. Torsional restraint to the rafter compression flange is provided by purlins at regular intervals.

Elastic vs Plastic Analysis

Portal frames can be designed using elastic or plastic analysis, with the choice driven by frame geometry, ductility requirements, and applicable code provisions.

Elastic Analysis (First-Order): The frame is analysed assuming linear material behaviour and small deflections. Internal forces and moments are calculated from applied loads, and members are designed such that the maximum stress does not exceed yield. Elastic analysis is simpler, always permitted by codes, and provides the basis for serviceability checks (deflections). However, it does not capture the reserve capacity of the frame after first yield and typically results in heavier sections.

Plastic Analysis (Rigid-Plastic or Elastic-Plastic): Plastic analysis exploits the ductility of steel to redistribute moments after the formation of plastic hinges. A portal frame designed plastically can carry 30–60% more load than predicted by elastic analysis for the same sections, or can achieve the same capacity with lighter sections. The method requires:

1. Sections that meet the compactness (Class 1 or Class 2) limits to ensure adequate rotation capacity at plastic hinges
2. Adequate restraint at and near hinge locations to prevent lateral-torsional buckling during rotation
3. A frame geometry that permits the formation of a collapse mechanism without instability

Per AISC 360, plastic analysis is permitted under Section C2, with additional requirements for member compactness and bracing. Eurocode 3 permits plastic global analysis for frames with Class 1 sections only. AS 4100 Section 4.5 provides similar provisions.

For a typical portal frame, the first plastic hinge forms at the eave haunch under gravity loads. As load increases, a second hinge forms at the apex or near mid-span, creating a collapse mechanism. The plastic analysis load factor for a properly proportioned frame is typically 1.5 to 1.7 times the factored load.

Second-Order Effects (P-Delta): Whether using elastic or plastic analysis, the stability of the frame must account for second-order effects — the additional moments generated when gravity loads act through lateral displacements. For portal frames with roof slopes less than 15°, the P-Delta effect is primarily an in-plane column phenomenon and can be captured using the amplification factor method (AISC Appendix 8) or a direct second-order analysis.

Haunch Proportioning and Design

The haunch is the most critical single feature of portal frame design. Located at the eave, it must resist the maximum negative moment in the frame while providing a stiff load path from the rafter to the column. Haunch design is as much art as science, guided by the following principles:

Haunch Length: The haunch length (measured along the rafter from the column face) is typically 10–15% of the span. For a 20 m span, this corresponds to 2.0–3.0 m. Longer haunches provide greater moment capacity at the eave but increase fabrication complexity. A common rule of thumb is haunch length = rafter depth + 1.5 m.

Haunch Depth: The haunch depth at the column face is typically 1.5–2.5 times the rafter depth. The depth tapers linearly from the column face to the rafter depth at the haunch tip. The slope of the haunch soffit should not exceed 1:4 (approximately 14 degrees) to avoid excessive strain concentrations.

Haunch Flanges: The haunch bottom flange must be sized to carry the tension force from the eave moment. The force in the bottom flange at the column face is approximately T = M_eave / (d_haunch - t_f/2), where M_eave is the eave moment and d_haunch is the haunch depth. This tension force must be transferred into the column through the knee joint.

Haunch Web: The web of the haunch carries the shear from the rafter. Web stiffeners are typically required at the haunch tip (where the depthed section transitions to the uniform rafter) and at the column face. The stiffener at the column face must transfer the flange tension into the column web.

Stability of the Haunch Region: The bottom flange of the haunch is in compression near the column for the reverse moment case (wind uplift). The haunch web must be checked for shear buckling if the web depth-to-thickness ratio exceeds limits. Lateral-torsional buckling of the haunch segment is restrained by purlins and fly bracing.

Knee Joint Design

The knee joint transfers moment, shear, and axial force between the rafter and column. The two dominant design approaches are:

Bolted Extended End Plate: The rafter and column are connected through a thick end plate bolted to the column flange. The end plate is extended beyond the tension flange to provide additional bolt rows for moment transfer. This is the most common detail in practice because it allows shop welding and field bolting. The extended end plate must be designed for prying action per AISC Manual Part 9.

Key design considerations:

• Bolt diameter and grade: Typically M20, M24, or 7/8-inch diameter A325 or Grade 8.8 bolts
• Number of bolt rows: 4 to 8 rows, with the outer rows in the tension zone resisting the moment couple
• End plate thickness: 20–30 mm, checked for bending and prying
• Column flange and web: Must be checked for local yielding, crippling, and panel zone shear

Fully Welded Knee: The rafter is welded directly to the column with full-penetration groove welds. This detail eliminates bolts but requires on-site welding and NDT inspection. It is used where bolted details are impractical or where the architect demands a clean visual appearance.

Base Fixity

The column base condition has a profound effect on frame behaviour:

Pinned Base: The column is free to rotate at the base, transmitting only shear and axial force to the foundation. Pinned bases are the most common and most economical choice. The foundation is simpler (a pad footing with two or four anchor bolts), and the frame relies entirely on the eave and apex rigidity for lateral stability. Sway deflections are larger than for fixed bases, and column sections must be heavier to resist the full moment at the base.

Fixed Base: The base connection is designed to transfer moment to the foundation, reducing frame sway by 40–60% and allowing lighter column sections. However, the foundation must be sized for the overturning moment, which often doubles the footing size. Fixed bases require a stiff base plate with anchor bolts arranged outside the column flanges, and the anchor bolts must be designed for the full tension from the moment couple.

Nominally Pinned Base with Moment Capacity: Many codes permit a "nominally pinned" base to develop some moment capacity (typically up to 25% of the column plastic moment) without the foundation being designed for full fixity. This "semi-rigid" behaviour reduces frame deflections modestly without the foundation cost of a fully fixed base.

The choice of base fixity is often governed by the inter-storey drift limit (usually h/300 for portal frames) and the perimeter cladding tolerance. If pinned-base sway exceeds the drift limit, a fixed or semi-rigid base is required.

Axial Force Effects on Rafter Design

While the rafter is predominantly a flexural member, the sloping geometry introduces axial compression. For a roof pitch of 10°, the axial force in the rafter is approximately 18% of the vertical reaction (sin 10° ≈ 0.174). This axial force must be considered in the rafter design per the combined axial-flexure interaction equations (AISC H1, EC3 6.3.3, AS 4100 Section 8.4).

For typical portal frames with spans under 30 m, the axial force ratio (P_u / φP_n) is usually less than 0.15, and axial effects reduce the bending capacity by only 5–10%. However, for steep pitches, long spans, or frames with significant tie-rod restraint, axial effects can become dominant and must be checked rigorously.

Worked Example: 20 m Span Portal Frame

Problem Statement: Design a portal frame for an industrial warehouse with a 20 m clear span, 6 m eave height, 10° roof pitch, and 6 m frame spacing. The frame is fabricated from A572 Gr 50 steel (Fy = 345 MPa). Gravity loads: dead load 0.35 kPa, live load 0.25 kPa (roof), superimposed dead 0.15 kPa. Wind load per ASCE 7: main wind force-resisting system.

Step 1 — Determine frame geometry:

• Span = 20.0 m
• Column height = 6.0 m
• Roof pitch = 10° (rise = 20.0 × tan(10°) / 2 = 1.76 m)
• Rafter slope length = √(10.0² + 1.76²) = 10.15 m
• Haunch length = 2.5 m (12.5% of span)
• Haunch depth at column face = 900 mm (1.8 × assumed rafter depth of 500 mm)
• Assumed rafter section: W460 × 52 (410 UB 53.7 in Australian designation)
• Assumed column section: W460 × 68 (460 UB 67.1)

Step 2 — Calculate loads on the frame:

Load on the rafter per unit plan length (tributary width = 6 m frame spacing):

• Dead load: w_DL = (0.35 + 0.15) × 6.0 = 3.0 kN/m
• Live load: w_LL = 0.25 × 6.0 = 1.5 kN/m

ASCE 7 LRFD load combination 2: 1.2D + 1.6L + 0.5Lr

• Factored gravity: w_u = 1.2 × 3.0 + 1.6 × 0 + 0.5 × 1.5 = 4.35 kN/m (live load not critical for roof)

ASCE 7 LRFD load combination subject to wind: 1.2D + 1.0W + 0.5L Wind load (simplified for example): 0.8 kPa design pressure, 6 m spacing → w_wind = 4.8 kN/m on windward wall, 2.4 kN/m suction on leeward wall.

Step 3 — Elastic first-order analysis:

For symmetrical gravity load on a pinned-base frame with a 10° pitch, the eave moment is approximately:

M_eave ≈ w_u × L² / 8 × (1 / (1 + 2h/L × (I_c/I_r) × (L/h)))

Where I_c/I_r is the ratio of column to rafter moment of inertia. For the assumed sections, I_c/I_r ≈ 1.3.

M_eave ≈ 4.35 × 20² / 8 × (1 / (1 + 2 × 6/20 × 1.3 × (20/6))) = 217.5 × (1 / (1 + 4.33)) = 217.5 × 0.188 = 40.8 kNm

The mid-span rafter moment is correspondingly reduced:

M_mid ≈ w_u × L² / 8 - M_eave = 217.5 - 40.8 = 176.7 kNm

Step 4 — Check rafter section (W460 × 52) at mid-span:

Section properties for W460 × 52 (AISC Manual Table 1-1):

• Z_x = 1090 × 10³ mm³ = 1090 cm³ (plastic modulus)
• φM_p = 0.9 × 345 × 1090 × 10⁻³ = 338.7 kNm

M_mid = 176.7 kNm < φM_p = 338.7 kNm, ratio = 0.52. OK.

Check LTB for unbraced length (assumed purlin spacing = 1.5 m): For W460 × 52 with L_b = 1.5 m, L_p ≈ 2.1 m > L_b, so LTB does not reduce capacity. Plastic moment capacity applies.

Step 5 — Design haunch at eave:

Eave moment M_eave = 40.8 kNm (elastic). For plastic design, the eave moment at factored load may approach the plastic moment of the haunch section.

Haunch depth at column face = 900 mm (2.0 × rafter depth). Axial force in rafter at eave ≈ 4.35 × 20 / 2 × sin(10°) = 7.6 kN (negligible).

Bottom flange tension force at column face: T ≈ M_eave / (d_haunch × 0.9) = 40.8 / (0.9 × 0.9) = 50.4 kN.

Check the bottom flange plate (welded to rafter bottom flange): Assuming a continuous plate 200 mm wide × 15 mm thick: A_g = 3000 mm², φT_n = 0.9 × 345 × 3000 × 10⁻³ = 931.5 kN >> 50.4 kN. The plate is far oversized for the elastic moment; the demand under plastic redistribution will be higher.

Step 6 — Check column section (W460 × 68):

The column carries the eave moment of 40.8 kNm plus an axial load from the rafter vertical reaction: P_u = w_u × L / 2 = 4.35 × 10 = 43.5 kN.

Check combined axial-flexure per AISC H1-1a: For W460 × 68: φP_n ≈ 1600 kN, φM_nx ≈ 450 kNm. P_u / φP_n = 43.5 / 1600 = 0.027. Since this is less than 0.2, use H1-1a: P_u / (2φP_n) + M_u / φM_n ≤ 1.0. = 0.027 / 2 + 40.8 / 450 = 0.014 + 0.091 = 0.105 << 1.0. OK.

Step 7 — Check serviceability deflections:

Rafter mid-span deflection under service (unfactored) loads: w_service = 3.0 + 1.5 = 4.5 kN/m. Δ_max ≈ 5 × w × L⁴ / (384 × E × I) = 5 × 4.5 × 20000⁴ / (384 × 200000 × 1.47 × 10⁸) / (cos 10°) ≈ 35 mm.

Deflection limit for roof beams with no ceilings: L/180 = 20000/180 = 111 mm. 35 mm < 111 mm. OK.

Sway deflection at eave under wind: Δ_sway ≈ 25 mm. Allowable sway = h/300 = 6000/300 = 20 mm. Sway is slightly high — consider increasing column size or specifying a nominally fixed base to reduce sway to within the limit.

Design Summary: W460 × 52 rafter and W460 × 68 column are adequate for the 20 m span portal frame. The haunch extends 2.5 m along the rafter, tapering from 900 mm depth at the column face to 450 mm at the haunch tip. Base detail may need to be upgraded to a nominally fixed base to meet the h/300 drift limit under wind.

Engineering Best Practices

• Always check the frame under both gravity-dominant and wind-dominant load combinations. The critical case for the haunch bottom flange is often gravity (tension), while the top flange and reverse haunch checks govern for wind uplift.
• Provide fly bracing (torsional struts) from the purlin line to the rafter bottom flange at the haunch tip and at regular intervals to restrain the compression flange against lateral-torsional buckling.
• For frames with spans exceeding 30 m, consider a tied portal (a tie rod connecting the eave points) to reduce the thrust on foundations and reduce column bending moments.
• The haunch-to-rafter transition (tip stiffener) must be detailed to avoid a sudden change in section properties. A gradual taper with a web stiffener at the transition point provides a smooth load path.
• Thermal expansion of the roof cladding can induce significant forces in portal frames longer than 60 m. Provide expansion joints or sliding purlin connections at intervals not exceeding 60 m.
• Always model the base condition realistically. A "pinned" base that develops unintended fixity from four-anchor-bolt detailing can attract moments that overload the anchor bolts and foundation.

FAQ

Q: How does the portal method differ from a full stiffness analysis for portal frames? A: The portal method assumes points of contraflexure at beam and column midpoints and distributes shear based on simple tributary-width rules. It gives quick approximate moments within 15–20% of a rigorous elastic analysis but cannot capture haunch effects, P-Delta amplification, or the influence of base fixity. For final design, a direct stiffness analysis (either first-order with amplification or second-order) is required by all major codes.

Q: What is the minimum roof pitch for a portal frame? A: The minimum practical roof pitch for a portal frame with standard profiled metal cladding is approximately 5° (about 1:11.4). Below this, rainwater drainage becomes unreliable, and ponding can occur. Portal frames can accommodate pitches up to about 30°, beyond which the frame behaves more like an A-frame and rafter axial forces become dominant.

Q: Can cold-formed sections be used for portal frames? A: Yes. Cold-formed portal frames using C or Z sections with bolted knee and apex connections are common in agricultural and light industrial buildings up to about 18 m span. Beyond 18 m, hot-rolled sections are typically required. Cold-formed portal frames must be designed per AISI S100, not AISC 360 or AS 4100 hot-rolled provisions.

Q: How are haunch stiffeners proportioned? A: Haunch tip stiffeners (at the transition from haunch to uniform rafter) must resist the vertical component of the flange force change. The stiffener width should match the haunch flange width minus the web thickness, and the thickness should be at least the web thickness. The stiffener must be welded to both flanges and the web with fillet or groove welds capable of transferring the tension/compression force differential. A full-depth stiffener on both sides of the web is recommended.

References

• AISC Design Guide 25 — Frame Design Using Web-Tapered Members
• AISC 360-22 — Specification for Structural Steel Buildings
• AISC Steel Construction Manual, 16th Edition
• Eurocode 3 (EN 1993-1-1) — Design of Steel Structures
• AS 4100:2020 — Steel Structures
• SCI P399 — Design of Steel Portal Frame Buildings to Eurocode 3
• Steel Construction Institute P252 — Design of Single-Span Steel Portal Frames to BS 5950

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