Australian Torsion Design — AS 4100 Clause 5.11

Complete reference for torsional design of steel members to AS 4100:2020. Covers St. Venant (uniform) torsion, warping (non-uniform) torsion, section selection for torsional efficiency, combined torsion and bending interaction, and practical design for spandrel beams and crane girders.

Related pages: AS 4100 Beam Design | Australian Beam Sizes | Combined Loading | Beam Capacity Calculator

Torsional Behaviour Fundamentals

Torsion in steel members arises whenever the applied load does not pass through the shear centre of the cross-section. Two distinct mechanisms resist torsion, and their relative importance depends entirely on the section type:

St. Venant torsion (uniform torsion): Pure shear flow around the section, with no axial strains. Governed by the torsional constant J. Closed sections (CHS, SHS) resist torsion almost entirely through St. Venant action. The shear stress is proportional to the distance from the section centreline and reaches a maximum at the outer surface.

Warping torsion (non-uniform torsion): Flanges bend in opposite directions, creating axial (normal) stresses that vary along the member length. Governed by the warping constant Iw. Open sections (I-sections, channels) resist the majority of torsional moment through warping. The warping normal stresses are largest at the flange tips and at points of torsional restraint.

Torsional Section Properties

The enormous difference between the J values of closed vs open sections (factor of 100-1000) means that closed sections should always be selected when torsion is a primary load effect.

Design for Combined Torsion and Bending — Clause 5.11

AS 4100 does not provide a single explicit formula for the combined torsion and bending interaction. Instead, the stresses from each action are computed separately and combined using an appropriate yield criterion:

Normal stress (from bending + warping): sigma = Mx* / Zx + My* / Zy + Mw* / Ww <= phi x fy

Shear stress (from vertical shear + St. Venant + warping shear): tau = Vx* / Awx + Vy* / Awy + Mt* x t / J + Mw* x Sw / (Iw x t) <= phi x 0.60 x fy

Von Mises equivalent stress (combined normal + shear): sigma_eq = sqrt(sigma^2 + 3 x tau^2) <= phi x fy

For most practical cases where torsion is incidental (spandrel beams, edge beams with cladding), the torsional stresses are small and the simple linear interaction of M*/phi_M + T*/phi_T <= 1.0 is adequate. For members where torsion is a primary load (crane girders, helical stair stringers, curved beams), the full Von Mises check is necessary.

Section Selection for Torsional Loading

The torsional constant J increases with the cube of the wall thickness for closed sections. For a CHS, J = pi x D^3 x t / 4 (thin-wall approximation). For an SHS, J = 2 x t x (b - t)^2 x (d - t)^2 / (b + d - 2t).

Key rules for torsional design:

1. Closed sections always dominate. A CHS 219.1x8.2 has ~270 times the St. Venant torsional stiffness of a 310UB46.2, yet weighs 25% less (42.6 kg/m vs 56.4 kg/m for comparable bending capacity).

2. I-sections are poor in torsion. The warping resistance depends on flange thickness cubed and the distance between flanges. For a 410UB59.7, approximately 85% of the torsional resistance comes from warping, and only 15% from St. Venant. The section works for torsional loads up to about 2-5 kNm before stresses become significant.

3. Channels and angles should never be used as torsion members. Their shear centre lies outside the section, so any transverse load inherently produces torsion. A 200PFC loaded through its web has the shear centre offset by approximately 50 mm from the load line, generating a distributed torque even under a perfectly vertical load.

4. Warping restraint matters. A torsionally loaded I-beam with both ends free to warp experiences approximately half the warping stress of the same beam with warping prevented at one end (typical of a beam rigidly connected to a column). Providing warping fixity increases torsional stresses, which is counter-intuitive but correct — the restraint prevents the beam from relieving itself through warping deformation.

Torsion in Spandrel Beams

Spandrel (edge) beams supporting masonry or precast cladding are the most common case where torsion must be explicitly checked in building design. The cladding load is eccentric to the beam shear centre by approximately:

e = (flange width / 2) + (cladding offset from flange face)

For a 310UB supporting brick veneer on angle shelf: e ~ 150 + 110 = 260 mm.

Distributed torque: mz = w_cladding x e (kNm/m along beam)

For a 6 m edge beam with 8 kN/m cladding load at 260 mm eccentricity: mz = 8 x 0.26 = 2.08 kNm/m. Peak torque at support = mz x L / 2 = 2.08 x 3 = 6.24 kNm.

This is a significant torque for a 310UB section. The flange tip normal stress from warping is approximately: sigma_w = Mw_max / (Iw / w_max) where w_max is the warping function at the flange tip.

For the 310UB46.2: sigma_w ~ 6.24 x 10^6 x 156 / 1.49 x 10^12 x 0.5 ~ 60 MPa at flange tip.

Combined with the bending stress (typically 160-200 MPa under factored loads), the total normal stress at the flange tip could reach 220-260 MPa, approaching the yield stress. This illustrates why spandrel beams are often upsized beyond the bending requirement alone.

Mitigation strategies:

• Specify a CHS or RHS spandrel beam — eliminates warping stress entirely
• Provide intermediate torsional restraints (cross-frames at 2-3 m centres)
• Specify continuous angle along the beam to form a pseudo-closed section with the slab
• Upsize the beam section to reduce the bending stress component of the interaction

Worked Example — 310UB46.2 Spandrel Beam

Problem: A 310UB46.2 Grade 300 spandrel beam spans 6.0 m between columns. It supports the floor slab on one side (vertical load passes near shear centre — negligible torsion from slab) and an architectural precast panel on the other side with an eccentricity e = 200 mm. Panel self-weight = 5.0 kPa x 3.0 m height = 15.0 kN/m (vertical). Total factored dead load on beam (including slab) = 32 kN/m UDL. Factored moment M* = 144 kNm.

Step 1 — Torsional loading: Distributed torque mz* = 1.2 x 15.0 x 0.20 = 3.6 kNm/m (using factored dead load factor for the precast)

Peak torque at support: T* = 3.6 x 6.0 / 2 = 10.8 kNm

Step 2 — Section properties (310UB46.2, Grade 300): J = 0.127 x 10^6 mm^4 | Iw = 1.49 x 10^12 mm^6 | Zx = 1,015 x 10^3 mm^3 | Sx = 1,142 x 10^3 mm^3

Step 3 — Bending stress: sigma_b = M*/Zx = 144 x 10^6 / 1,015 x 10^3 = 142 MPa

Step 4 — Torsional warping stress at support (warping restrained at column): The warping moment at the support for a fixed-warping end with UDL torque is obtained from the differential equation of non-uniform torsion. Using the standard solution for a beam with one end warping-fixed and one free:

Mw_max (at support) ~ mz* x L^2 / 8 (for this boundary condition; exact solution involves hyperbolic functions).

Mw_max ~ 3.6 x 6^2 / 8 = 16.2 kNm (warping moment = torque x lever-arm-type factor)

Warping normal stress at flange tip: w_max = bf x d / 4 = 166 x 309 / 4 = 12,840 mm^2 (approximately, for a doubly symmetric I-section).

sigma_w = Mw_max x w_max / Iw = 16.2 x 10^6 x 12840 / 1.49 x 10^12 = 140 MPa.

This is significant — the warping stress is comparable to the bending stress.

Step 5 — Combined normal stress: sigma_total = 142 + 140 = 282 MPa > phi x fy = 0.90 x 300 = 270 MPa. FAILS.

The combined stress exceeds the design yield stress. The section is inadequate without torsional mitigation.

Step 6 — Mitigation: Option A — Provide an intermediate torsional restraint at midspan, reducing the unbraced torsion length to 3.0 m. This reduces Mw_max to ~ mz* x 3^2 / 8 = 4.05 kNm, and sigma_w to ~ 35 MPa. Combined: 142 + 35 = 177 MPa << 270 MPa. OK.

Specify: Provide a cross-frame or a stiff channel tie at midspan between the spandrel beam and the first interior beam to provide torsional restraint. The tie must resist the bimoment reaction at the restraint.

Alternative Option B — Use CHS 273.1x9.3 (Grade C350L0, fy = 350 MPa): Z = 548 x 10^3 mm^3. Bending stress = 144 x 10^6 / 548 x 10^3 = 263 MPa < phi_fy = 315 MPa. OK on bending.

St. Venant torsion: J = 17.8 x 10^6 mm^4 for CHS 273.1x9.3. tau = T* x D/(2J) = 10.8 x 10^6 x 273.1 / (2 x 17.8 x 10^6) = 82.8 MPa. phi x 0.60 x fy = 0.90 x 0.60 x 350 = 189 MPa > 82.8. OK.

Combined Von Mises: sigma_eq = sqrt(263^2 + 3 x 82.8^2) = sqrt(69169 + 20572) = sqrt(89741) = 300 MPa < 315 MPa. OK.

The CHS section handles the torsion with no special detailing and no intermediate restraint — this is why closed sections are the preferred choice for torsion-loaded members.

Frequently Asked Questions

When is torsion actually critical in steel beam design? Torsion is critical in: (a) spandrel beams supporting heavy cladding (masonry, precast) with eccentricities exceeding 150 mm; (b) crane runway girders where the wheel load can be offset from the girder centreline; (c) curved beams (helical stairs, pedestrian bridges) where the geometry induces torsion under gravity; (d) beams supporting monorail hoists where the load point changes; and (e) canopy beams with off-axis loads. In typical floor beams with slab on both sides, torsion is negligible because the loads are balanced.

How does torsional restraint at the supports affect the design? A connection that prevents warping (rigid welded connection, bolted end plate) increases the warping stresses at the support compared to a connection that is free to warp (simple bearing seat, slotted holes). Paradoxically, a "stronger" connection produces higher torsional stresses. The ideal torsional detail provides vertical and lateral support while allowing warping deformation — a detail known as a "fork" support. In practice, most bolted shear connections provide partial warping restraint, and the conservative approach is to assume full warping fixity.

What is the difference between equilibrium torsion and compatibility torsion? Equilibrium torsion is required for the structure to be in equilibrium — without it, the structure would collapse. Examples: a spandrel beam supporting an eccentric cladding panel, a crane girder. Compatibility torsion arises from the stiffness of connected members and can be redistributed if the member yields — it is not required for equilibrium. AS 4100 requires equilibrium torsion to be designed for explicitly, while compatibility torsion can often be ignored if the structure can redistribute loads after local yielding.

Can I add a continuous steel plate to an I-beam to increase torsional resistance? Adding a continuous plate to close the open section (creating a box section) dramatically increases the St. Venant torsional constant J. For a 310UB with a 10 mm continuous bottom cover plate welded to both flanges: J increases from 0.127 x 10^6 to approximately 150 x 10^6 (factor of ~1000). However, the weld design must develop the full shear flow, and the internal welding may be difficult. A simpler alternative is to select a hollow section from the outset.

This page is for educational reference. Torsional design per AS 4100:2020 Clause 5.11. Verify section properties and torsional constants from manufacturer data. All structural designs must be independently verified by a licensed Professional Engineer or Structural Engineer. Results are PRELIMINARY — NOT FOR CONSTRUCTION.