AS 4100 Portal Frame Design — Haunch, Knee Joint & Rafter Stability

Complete AS 4100:2020 portal frame design walkthrough: haunch geometry, knee joint stiffening, rafter buckling under combined axial and bending, in-plane frame stability, and column base detail. The worked example designs a 25 m clear-span industrial portal frame with a 6.0 m eave height and 7.5-degree roof pitch using 530UB92.4 rafters and 310UC118 columns.

The Steel Calculator WASM engine performs portal frame analysis and AS 4100 member checks interactively. This page covers the design methodology for single-storey portal frames — the most common structural system in Australian industrial and warehouse construction.

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

Design Problem Definition

A warehouse portal frame in western Sydney spans 25.0 m clear between column centrelines with a 6.0 m eave height and 7.5-degree roof pitch (1:7.6 slope). The frame spacing is 7.2 m centres. Columns are pinned at the base on reinforced concrete pad footings. The rafter-to-column connection is a rigid haunched knee joint.

Design Data:

Loads (AS 1170 series):

Dead load (roof): 0.15 kPa (sheeting + insulation + purlins) Dead load (ceiling): 0.10 kPa (suspended services, if applicable) Live load (roof): 0.25 kPa per AS 1170.1 Table 3.3 (non-trafficable roof) Wind load: Region A2, terrain category 2.5, importance level 2

Serviceability wind: V_s = 37 m/s (regional), ULS wind: V_u = 45 m/s.

Portal Frame Geometry and Haunch Layout

Frame Dimensions

The portal frame consists of two columns and a rafter with haunched knee joints at each eave:

Haunch Geometry (AS 4100 Clause 5.12)

The haunch is fabricated by welding a tapered plate to the underside of the rafter bottom flange, increasing the section depth from 533 mm to 900 mm at the column face. The haunch web plate is 10 mm Grade 300, fillet-welded to the rafter bottom flange and to a 200 x 16 mm flat plate that forms the bottom flange of the haunch.

Haunch web slenderness check at the deepest section (900 mm depth):

d_1_haunch / t_w_haunch = (900 - 2 x 10.2 - 2 x 16) / 10 = 847.6 / 10 = 84.8

This exceeds 82/sqrt(fy/250) = 82/sqrt(300/250) = 74.9. The haunch web is slender and requires transverse stiffeners. Provide full-depth transverse stiffeners at the column face and at the end of the haunch, plus an intermediate stiffener at the haunch mid-length.

Step 1 — Frame Analysis Results

A second-order elastic analysis (AS 4100 Clause 6.1) was performed with P-Delta effects included. The governing ULS load combination is 1.2G + 1.0W_u (wind uplift) with internal suction of C_pi = -0.30, producing maximum negative moment at the knee joint.

Summary of Design Actions (Factored)

Location N* (kN) M* (kN.m) V* (kN) Notes
Column top (knee) -85.2 -342.5 78.4 Tension + negative moment
Column mid-height -72.1 -128.6 65.2 Combined compression + bending
Column base -58.9 0 52.3 Pinned (moment = 0)
Rafter at knee -64.3 -342.5 112.7 Max negative moment
Rafter quarter-span -38.2 +198.4 28.6 Positive moment region
Rafter at apex -22.7 +86.5 5.1 Near-zero shear

The maximum rafter compression force occurs under dead + live (downward) loading: N*_max = -115.4 kN (compression) combined with M* = -245.6 kN.m at the knee.

Step 2 — Rafter Design: 530UB92.4 (AS 4100 Clauses 5, 6, 8)

Section Properties — 530UB92.4 Grade 300PLUS

Property Symbol Value Units
Depth d 533 mm
Flange width b_f 209 mm
Flange thickness t_f 13.2 mm
Web thickness t_w 10.2 mm
Area A_g 11,800 mm^2
I_x I_x 554 x 10^6 mm^4
Z_x Z_x 2,080 x 10^3 mm^3
S_x S_x 2,370 x 10^3 mm^3
r_y r_y 44.7 mm
J J 555 x 10^3 mm^4
I_w I_w 1,680 x 10^9 mm^6

Section Classification

Flange slenderness: lambda_e = (b_f - t_w) / (2 x t_f) x sqrt(fy/250) = (209 - 10.2) / (2 x 13.2) x 1.095 = 7.53 x 1.095 = 8.25 < 9 (Class 1).

Web slenderness in combined compression and bending requires the compression depth to be determined. For M* = 342.5 kN.m, the elastic compressive stress in the web extends from the compression flange to a depth of approximately:

y_c = d/2 x (1 + N* x d / (2 x M*)) for major-axis bending with axial compression.

At knee: N* = -64.3 kN, M* = -342.5 kN.m. Estimating y_c ~ 0.55d from the compression flange gives a compression web depth of 293 mm. The web slenderness:

lambda_e = (293 / 10.2) x 1.095 = 28.7 x 1.095 = 31.4 < 82 (Class 2). The section is Class 2 (Compact) for the combined loading condition at the knee.

Section Moment Capacity (Clause 5.2)

M_s = S_x x f_y = 2,370 x 10^3 x 300 = 711.0 kN.m

phi x M_s = 0.90 x 711.0 = 639.9 kN.m

Member In-Plane Capacity (Clause 8.4.2.2)

For a portal frame rafter subject to combined compression and bending, the in-plane interaction check per Clause 8.4.2.2:

N* / (phi x N_c) + M* / (phi x M_s) <= 1.0

Effective length for in-plane buckling: The rafter is restrained by the portal frame stiffness. From the frame buckling analysis, the in-plane buckling load factor lambda_cr = 8.2, giving:

N_omb = 8.2 x N*_max = 8.2 x 115.4 = 946 kN (elastic buckling load for the frame)

For the rafter segment in compression under the critical load combination (N* = 64.3 kN, M* = 342.5 kN.m at the knee):

L_e for rafter in-plane buckling: Approximately 0.85 x S_rafter where S_rafter = rafter length from knee to apex = 12.5 m / cos(7.5 deg) = 12.6 m.

L_e = 0.85 x 12,600 = 10,710 mm

lambda_n = (10,710 / 44.7) x sqrt(300 / 250) = 239.6 x 1.095 = 262.4

At this high slenderness, alpha_c is approximately 0.10 from Table 6.3.3 — the rafter would buckle in-plane well before the applied load is reached if the frame action did not provide restraint. This demonstrates why portal frame analysis MUST use the frame buckling approach (Clause 6.4.3) rather than effective length factors alone.

Out-of-Plane Buckling (Fly Brace Restraint)

Fly braces restrain the rafter bottom flange at 1.8 m centres, corresponding to purlin spacing. The segment between fly braces is:

L_s = 1.8 m, k_t = 1.0, k_l = 1.0, k_r = 1.0 (simple restraint)

L_e = 1.0 x 1,800 = 1,800 mm

lambda_n_ltb = (1,800 / 44.7) x 1.095 = 40.3 x 1.095 = 44.1

alpha_s from Table 5.6.1 at lambda_n = 44.1: approximately 0.908.

Moment modification factor alpha_m: For the rafter segment between fly braces near the knee, the moment varies from near-maximum at the knee to approximately 60% of maximum at the next brace point. From Table 5.6.1 for a linear moment variation:

beta_m = M_min / M_max = 0.60 (moment ratio) alpha_m = 1.75 + 1.05 x beta_m + 0.3 x beta_m^2 = 1.75 + 1.05 x 0.60 + 0.3 x 0.36 = 1.75 + 0.63 + 0.108 = 2.49

But alpha_m is capped at 2.5 per Clause 5.6.1.1, so alpha_m = 2.49 is valid but high. Let's be conservative and use alpha_m = 1.75 for a linear moment gradient (standard practice for purlin-restrained rafter segments).

M_b = alpha_m x alpha_s x M_s = 1.75 x 0.908 x 711.0 = 1,130 kN.m — exceeds M_s, so M_b = M_s = 711.0 kN.m (capped).

Out-of-plane LTB does not govern for the rafter due to the tight fly brace spacing.

Step 3 — Column Design: 310UC118 (AS 4100 Clause 6)

Section Properties — 310UC118 Grade 300PLUS

Property Symbol Value Units
Depth d 315 mm
Flange width b_f 307 mm
Flange thickness t_f 18.7 mm
Web thickness t_w 11.9 mm
Area A_g 15,000 mm^2
r_y r_y 77.5 mm
S_x S_x 1,980 x 10^3 mm^3
alpha_b — 0.5 Curve c (minor axis)

In-Plane Column Check

For a pinned-base portal frame column, the effective length factor for in-plane buckling is determined from frame stability analysis. For a 6.0 m column height with a rigid knee:

k_e in-plane: approximately 2.2 (sway permitted, pinned base, rigid top)

L_e = 2.2 x 6,000 = 13,200 mm

lambda_n = (13,200 / 77.5) x sqrt(300 / 250) = 170.3 x 1.095 = 186.5

From Table 6.3.3, lambda_n = 186.5 is well into the elastic buckling range. For lambda_n > 100, alpha_c approximately follows:

alpha_c = (90 / lambda_n)^2 x 0.6 = (90 / 186.5)^2 x 0.6 = 0.233 x 0.6 = 0.140

N_s = A_g x f_y = 15,000 x 300 = 4,500 kN

N_c = 0.140 x 4,500 = 630 kN

phi x N_c = 0.90 x 630 = 567 kN in-plane.

Column axial force N*_max = 72.1 kN (compression under dead + live). Utilisation = 72.1 / 567 = 0.127 — axial compression alone is well within capacity.

Combined Actions Check (Clause 8.3)

At column mid-height: N* = 72.1 kN, M* = 128.6 kN.m

Section moment capacity: M_s = S_x x f_y = 1,980 x 10^3 x 300 = 594.0 kN.m phi x M_s = 0.90 x 594.0 = 534.6 kN.m

Interaction per Clause 8.3.4 for a compact doubly-symmetric section:

N* / (phi x N_c) + M* / (phi x M_s) <= 1.0 = 72.1 / 567 + 128.6 / 534.6 = 0.127 + 0.241 = 0.368 — well within capacity.

The 310UC118 column is lightly loaded for a 25 m span portal frame. A 250UC89.5 would also work but the deeper column provides better knee joint stiffness.

Step 4 — Knee Joint Design (Clause 5.12, 8.3, 9)

The knee joint transfers the rafter moment into the column through the haunch. Three limit states control the design:

4a. Haunch Web Shear Buckling

The haunch web at the deepest section (900 mm) is subject to the full rafter moment of 342.5 kN.m. The shear force in the haunch web:

V*_haunch = M* / d_haunch_eff = 342.5 / 0.80 = 428 kN

where d_haunch_eff is the lever arm between flange centroids (approximately 0.89 x 900 = 800 mm).

Haunch web shear capacity (6 mm plate, Grade 300):

V_w = 0.6 x f_y x d_1 x t_w = 0.6 x 300 x 847.6 x 10 = 1,526 kN

The haunch web has ample shear capacity. However, the diagonal compressive stress field at the knee must be checked per Clause 5.12.3:

phi x V_v = 0.90 x 1,526 = 1,373 kN >> 428 kN — shear buckling is not governing.

4b. Knee Diagonal Stiffener

A diagonal stiffener is provided from the rafter inner flange to the column inner flange, aligning with the compression force path. The stiffener force:

F_stiffener = M* / d_haunch_eff x 1/sin(theta)

At the knee, theta is the angle between the rafter and column (90 - 7.5 = 82.5 degrees). sin(82.5 deg) = 0.991.

F_stiffener = 428 x 1/0.991 = 432 kN (compression).

Stiffener size: 100 x 16 mm flat bar, Grade 300. Effective length for buckling = diagonal length between flange weld lines = 1,200 mm.

Stiffener buckling check:

I_st = (16 x 100^3) / 12 = 1.333 x 10^6 mm^4 A_st = 1,600 mm^2 r_st = sqrt(1.333 x 10^6 / 1,600) = 28.9 mm

lambda_n = (1,200 / 28.9) x 1.095 = 41.5 x 1.095 = 45.5

alpha_c from Table 6.3.3 at lambda_n = 45.5 (Curve b, alpha_b = 0.0): approximately 0.920.

N_c_stiffener = alpha_c x A_st x f_y = 0.920 x 1,600 x 300 = 441.6 kN phi x N_c_stiffener = 0.90 x 441.6 = 397.4 kN < 432 kN — marginally inadequate.

Increase stiffener to 120 x 16 mm: A_st = 1,920 mm^2, r_st = 34.6 mm, lambda_n = 38.0, alpha_c = 0.940.

N_c = 0.940 x 1,920 x 300 = 541.4 kN, phi x N_c = 487.3 kN > 432 kN — acceptable.

4c. Column Web at Knee

The column web at the knee joint must transfer the rafter compression force into the column. The compression force from the rafter bottom flange:

C = M* / d_rafter + N*_rafter / 2 = 342.5 / 0.521 + 64.3 / 2 = 657.4 + 32.2 = 689.6 kN

Check column web local yielding (Clause 5.13, web bearing analogy):

b_bf = t_f_rafter + 2.5 x (t_f_column + r_column) = 13.2 + 2.5 x (18.7 + 10.2) = 13.2 + 72.3 = 85.5 mm

R_by = 1.25 x b_bf x t_w_column x f_y = 1.25 x 85.5 x 11.9 x 300 = 381,500 N = 381.5 kN

This is less than the applied 689.6 kN. A horizontal stiffener is required on the column web at the rafter bottom flange level. Provide a 200 x 16 mm plate welded to the column web and flanges.

Step 5 — In-Plane Frame Stability (Clause 8.4)

The portal frame is classified as a sway frame (Clause 6.4.3) because the lateral stiffness depends entirely on frame action. The elastic buckling load factor from frame analysis:

lambda_cr = N_omb / N* = 946 / 115.4 = 8.2 > 5.0

Since lambda_cr > 5.0, second-order effects are moderate and the amplified first-order moment approach (Clause 8.4.2.2) is valid. The moment amplification factor:

delta_b = 1 / (1 - 1 / lambda_cr) = 1 / (1 - 1 / 8.2) = 1 / 0.878 = 1.14

The amplified moment at the knee: M*_amplified = 1.14 x 342.5 = 390.5 kN.m.

Recalculating the rafter at the knee with amplified moment (N* = 64.3 kN):

M_s = 711.0 kN.m, phi x M_s = 639.9 kN.m

N* / (phi x N_c_inplane) + M*_amplified / (phi x M_s) must be checked with the in-plane buckling capacity from the frame analysis. For the frame-governed buckling mode:

phi x N_c_frame = 0.90 x lambda_cr x N*_rafter = 0.90 x 8.2 x 64.3 = 474.5 kN

64.3 / 474.5 + 390.5 / 639.9 = 0.136 + 0.610 = 0.746 — adequate with second-order amplification.

Step 6 — Serviceability (Deflection and Drift)

Eave Drift Under Wind (AS 1170.0 Appendix C)

Serviceability wind load: w_s_wind = 0.70 kPa (windward wall pressure at SLS)

Horizontal deflection at eave (approximated from frame flexibility):

delta_eave = w_s_wind x h_eave^4 / (8 x E x I_column) x frame_stiffness_factor

For a pinned-base frame: delta_eave approximately 18 mm.

Drift limit per AS 1170.0: h_eave / 150 = 6,000 / 150 = 40 mm. 18 mm < 40 mm — acceptable.

Rafter Deflection (Total Load)

The rafter deflects under gravity loading with a maximum at approximately quarter-span. The vertical component:

delta_rafter_max approximately 38 mm.

Limit: span / 250 = 25,000 / 250 = 100 mm. 38 mm < 100 mm — acceptable but a pre-camber of 15 mm is specified for appearance and drainage.

Portal Frame Summary — Design Checks

Limit State Clause Capacity (phi-R) Design Action D/C Ratio Status
Rafter section moment Cl. 5.2 639.9 kN.m 390.5 kN.m 0.610 PASS
Rafter out-of-plane LTB Cl. 5.6 639.9 kN.m 390.5 kN.m 0.610 PASS
Column combined actions Cl. 8.3 Interaction 1.0 0.368 0.368 PASS
Column in-plane buckling Cl. 6.3.3 567 kN 72.1 kN 0.127 PASS
Knee stiffener buckling Cl. 6.3.3 487.3 kN 432 kN 0.886 PASS
Haunch web shear Cl. 5.11 1,373 kN 428 kN 0.312 PASS
Eave drift SLS 40 mm 18 mm 0.450 PASS
Rafter deflection SLS 100 mm 38 mm 0.380 PASS
Frame stability (lambda_cr) Cl. 6.4.3 5.0 minimum 8.2 > min PASS

Frequently Asked Questions

How does AS 4100 handle the knee joint in a portal frame?

AS 4100 does not provide a specific clause for knee joints — the knee region is treated as a haunched beam-column junction and designed using Clauses 5, 6, and 8 for combined actions. The haunch web must be checked for shear buckling under the diagonal compression field from the rafter moment transfer. Diagonal stiffeners are typically required when the haunch depth-to-web-thickness ratio exceeds 82/sqrt(fy/250). For a 530UB92.4 haunch with d1/tw = 54 at the knee, a full-depth diagonal stiffener from the rafter inner flange to the column inner flange is specified to prevent web buckling and to transfer the compression force smoothly into the column.

What effective length factors apply to portal frame columns per AS 4100?

AS 4100 Clause 6.4 refers to a frame buckling analysis for portal frames rather than prescribing fixed effective length factors. For a pinned-base portal frame with a rigid knee joint, the in-plane effective length factor ke for the column typically ranges from 2.0 to 2.5 for symmetrical single-bay frames. For a fixed-base portal frame, ke reduces to approximately 1.5 to 1.8. These values are determined by elastic buckling analysis (Clause 6.4.3) rather than the simple alignment chart approach used for multi-storey frames. The out-of-plane effective length is governed by fly brace spacing, typically at purlin locations every 1.5-2.0m.

When are haunches required in AS 4100 portal frames?

Haunches are required at the eaves (rafter-to-column connection) when the bare rafter section alone cannot resist the high negative moment at the knee joint. Per AS 4100 Clause 5.12, the haunch increases the section depth at the joint, providing additional moment capacity and stiffness. A haunch depth of 2.0 to 2.5 times the rafter depth is typical for Australian portal frames, with a haunch length of approximately 10% of the frame span measured from the column centreline. Haunches may also be required at the apex for frames with steep roof pitches exceeding 15 degrees, where the apex moment approaches the eaves moment magnitude.

How does AS 4100 Clause 8 handle in-plane frame stability?

AS 4100 Clause 8.4.2.2 governs in-plane frame stability through the amplified first-order moment approach. The moment amplification factor delta_b = 1/(1 - N*/N_omb) where N_omb is the elastic in-plane buckling load of the frame determined from a frame buckling analysis. For portal frames, the amplification factor is applied to the first-order bending moments from lateral loads and frame imperfections. The storey drift amplification factor delta_s per Clause 8.4.2.3 is used when the frame is classified as sway-sensitive. For typical industrial portal frames with roof pitches under 10 degrees, second-order effects increase moments by 10-20% at the knees.

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Related Pages

This page is for educational reference. All resistance formulae are per AS 4100:2020 with AS/NZS 3679.1 section properties. Verify the applicable edition of the National Construction Code for your project jurisdiction. Results are PRELIMINARY — NOT FOR CONSTRUCTION without independent review by a registered structural engineer (CPEng/RPEQ).