Portal Frame Design Example -- Elastic Analysis and Member Checks per AS 4100

Portal frames are the workhorse of industrial and commercial steel construction. A well-designed portal frame resists gravity and wind loads through moment-resisting connections at the eaves and apex, eliminating the need for bracing in the plane of the frame. This worked example takes you through the complete design of a single-bay portal frame from geometry through to member verification.

Problem definition

A single-bay portal frame for an industrial warehouse in Perth, Western Australia (Region A, Terrain Category 2). The frame is designed to AS 4100:2020 with loads per AS/NZS 1170 series.

Step 1 -- Frame geometry

The portal frame is symmetric about the ridge. The rafter length from eave to apex is:

L_rafter = sqrt((L/2)^2 + (h_r - h_e)^2) = sqrt(15^2 + 4^2) = 15.52 m

The rafter is modelled as a prismatic member with a haunch at each eave. The haunch increases the section depth from 460 mm (rafter) to 610 mm (column) over 2.5 m. In analysis, the haunch is modelled as a tapered element with linearly varying section properties.

Key geometric check: The haunch-to-rafter transition must be gradual. AISC Design Guide 25 recommends a slope no steeper than 1:4 to avoid stress concentrations. Here, (610-460)/2500 = 0.06 or 1:16.7 -- well within limits.

Step 2 -- Load determination (AS/NZS 1170)

Dead load (G)

The roof dead load includes the roof sheeting, insulation, purlins, and services:

Dead load on rafter: w_G = 0.15 x 6.0 = 0.90 kN/m (on plan). Resolved along the rafter slope: w_G,rafter = 0.90 x cos(14.9) = 0.87 kN/m.

Live load (Q)

Per AS 1170.1 Table 3.1, roof live load for non-trafficable roof = 0.25 kPa. Distributed load on rafter: w_Q = 0.25 x 6.0 = 1.50 kN/m.

Wind load (Wu)

Wind loads per AS/NZS 1170.2. For Region A (V_R = 45 m/s), Terrain Category 2, building height 12.0 m:

External pressure coefficients (C_pe) for a gable-roof building with h/d ratio < 0.5 and roof pitch 15 degrees, windward wall:

• Windward wall: C_pe = +0.7
• Leeward wall: C_pe = -0.3
• Windward roof: C_pe = -0.5 (suction)
• Leeward roof: C_pe = -0.5 (suction)

Internal pressure coefficient for a nominally sealed building: C_pi = +0.2 or -0.3 (worst case used).

Critical load combinations (AS 1170.0):

1. 1.35G (gravity only)
2. 1.2G + 1.5Q (gravity + live)
3. 1.2G + Wu + 0.4Q (wind uplift dominant)
4. 0.9G + Wu (minimum gravity + wind)

Step 3 -- Elastic analysis

For a single-bay pinned-base portal frame, the structure has 3 degrees of kinematic indeterminacy (rotation at each eave, rotation at the apex). A second-order elastic analysis is recommended by AS 4100 Clause 4.4 for portal frames where lambda_c (elastic buckling load factor) may be less than 5.0.

Analysis method: Direct stiffness (matrix) method. The frame is discretised into 6 elements: left column, left haunch, left rafter, right rafter, right haunch, right column. Each element uses a 6-DOF beam-column stiffness matrix with geometric stiffness included for P-Delta effects.

Key analysis results (envelope)

Gravity load combination (1.2G + 1.5Q) governs the frame members. Wind uplift (0.9G + Wu) governs the column base connection (tension in anchor bolts).

The peak positive moment occurs in the rafter at the eave (haunch connection). The peak negative moment occurs in the column at the underside of the haunch. Both are near the knee -- this is why the knee connection is the most critical detail in portal frame design.

Frame drift at eave (serviceability, Ws): 12.3 mm = h_e/650. AS 4100 Appendix B suggests h/300 to h/500 for industrial buildings with brittle cladding. At h/650 the frame is acceptably stiff.

Step 4 -- Member capacity checks (AS 4100)

Column check (610UB125)

Section properties: A_g = 16000 mm^2, I_x = 986x10^6 mm^4, Z_x = 3230x10^3 mm^3, S_x = 3680x10^3 mm^3, r_x = 248 mm, r_y = 49.8 mm, k_f = 0.90 (form factor for slender web).

Section capacity (Cl. 8.2): M_sx = f_y x Z_ex = 300 x 3680x10^3 / 10^6 = 1104 kN-m (full plastic) M_sx = min(1104, 1.5 x 300 x 3230x10^3 / 10^6) = min(1104, 1454) = 1104 kN-m phi_Msx = 0.90 x 1104 = 994 kN-m

Member capacity (Cl. 8.4): Effective length: L_ex = 1.5 x 8000 = 12000 mm (sway permitted at eave). L_ey = 4000 mm (fly bracing at mid-height). lambda_nx = (12000/248) x sqrt(300/250) x sqrt(0.90) = 48.4 x 1.095 x 0.949 = 50.3 alpha_b = -0.5 (transverse load at end). alpha_m = 1.75 + 1.05 x (-0.5) + 0.3 x (-0.5)^2 = 1.30 M_bx = alpha_m x alpha_s x M_sx = See AS 4100 Cl. 8.4.4.2 for the full alpha_s calculation.

Using our free member design calculator, the computed member moment capacity: phi_Mbx = 598 kN-m at the critical column section.

Interaction check (Cl. 8.4.5.1): N* = 175 kN (compression at haunch). phi_Ns = 0.90 x 300 x 16000 / 1000 = 4320 kN. N*/phi_Ns = 175/4320 = 0.04 < 0.15. Use simplified interaction: N*/phi_Ns + M*/phi_Mb = 0.04 + 185/598 = 0.35 -- OK.

Rafter check (460UB82.1)

Section properties: A_g = 10500 mm^2, I_x = 372x10^6 mm^4, Z_x = 1615x10^3 mm^3, S_x = 1830x10^3 mm^3. k_f = 0.95.

Section moment capacity: phi_Ms = 0.90 x 300 x 1830x10^3 / 10^6 = 494 kN-m.

Member moment capacity (rafter in-plane, L_e = 0.85 x 15.52 = 13.2 m for pinned apex -- the rafter buckles in an S-shape between eave and apex under gravity load): phi_Mb = 312 kN-m (from detailed alpha_s calculation per Cl. 8.4.4.2).

Interaction check: N*/phi_Ns = 15/(0.90 x 300 x 10500/1000) = 0.005. M*/phi_Mb = 210/312 = 0.67 -- OK. The rafter has ~33% reserve capacity.

Deflection check (serviceability)

Under service live load (Qs = 0.25 kPa), the vertical deflection at the apex is: delta_apex = 28.7 mm = Span/1045. The industry-accepted limit for portal frames is Span/400 = 75 mm. The frame is well within limits. Adequate pre-camber (Span/500 = 60 mm) would further improve appearance.

Step 5 -- Connection design

The three critical connections in a portal frame are the knee (column-to-rafter), the apex (rafter-to-rafter), and the base (column-to-footing).

Knee connection (eave moment connection)

The knee transfers M* = 210 kN-m, V* = 55 kN, N* = 22 kN from the rafter into the column. A haunched extended end plate is typical.

Apex connection

The apex typically has lower moment (M* = 95 kN-m) but the rafter depth is shallower, making bolt lever arms shorter. A flush or extended end plate with 2 rows of M20 8.8/TB bolts per side is sufficient.

Base connection

Under wind uplift (0.9G + Wu), the column base experiences tension. Four M30 holding-down bolts cast into the footing are checked for combined tension and shear per AS 4100 Cl. 9.2.2.3. Holding-down bolt tension capacity includes the concrete pull-out cone per AS 3600.

Step 6 -- Portal frame optimisation

The initial design passes all checks with reasonable utilisation ratios. However, there are optimisation opportunities:

The final optimised design uses 610UB125 columns, 410UB59.7 rafters, 3.0 m haunches, 20 mm end plates, and 60 mm pre-camber. Total steel weight: 7.8 tonnes per frame.

Key Takeaways

• Portal frames resist lateral loads through frame action, not bracing. The moment connections at the eaves and apex are what make them work.
• The knee is the most highly stressed region. Haunch geometry, stiffener detailing, and end plate thickness all require careful attention.
• Second-order effects matter. P-Delta amplifies moments in portal frames and should be included via a rigorous second-order analysis or moment amplification per AS 4100 Cl. 4.4.
• Wind uplift can govern base connection design. Max gravity gives max in-plane moments, but minimum gravity + wind gives max anchor bolt tension.
• Pre-camber improves appearance. A pre-camber of Span/500 to Span/300 removes most visible dead-load sag.

Educational reference only. All portal frame designs must be independently verified by a licensed Professional Engineer. Results are PRELIMINARY -- NOT FOR CONSTRUCTION.

Frequently Asked Questions

How does the portal method differ from a full stiffness analysis for portal frames?

The portal method assumes points of contraflexure at beam and column midpoints and distributes shear based on a simple tributary-width rule. It gives quick approximate moments within 15-20% of a rigorous analysis, but it cannot capture haunch effects, varying section properties, or P-Delta amplification. For final design, a second-order direct stiffness analysis (or at minimum a first-order analysis with B2 amplification) is required by AS 4100.

What is the minimum roof pitch for a portal frame?

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

Can I use cold-formed sections for portal frames?

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 for the primary frames. Cold-formed portal frames must be designed per AISI S100, not AISC 360 or AS 4100 hot-rolled provisions. See our cold-formed steel design guide for more detail.

How are haunches proportioned?

Haunch length is typically 10-15% of the span. The haunch depth varies linearly from the column depth at the eave to the rafter depth at the haunch tip. The slope should not exceed 1:4 (approximately 14 degrees). A common rule of thumb: haunch length = rafter depth + 1.5 m.

What software tools can verify portal frame analysis?

SteelCalculator.app provides browser-based portal frame analysis and member design checks for AS 4100, AISC 360, EN 1993, and CSA S16. For professional use, SpaceGass, Microstran, SAP2000, and STAAD.Pro are widely used in Australian practice. See our Designer Hub analysis page for a free interactive tool.