Checks the torsional resistance of an open section built of rectangular plates at the ultimate limit state, to SIA 263:2013, with the torsion constant summed element by element and the warping of a double tee as an option. Every step shows its formula and the clause it comes from.

What it checks

Section from the shape (double tee I or H, tee, channel U, angle L, or rectangular plates entered one by one): the mid-line plates, the area A, the second moment I_y and the thickest plate t_max.
Each element: its ratio h/t and the coefficient β_i, taken as 1/3 above h/t = 10, and its contribution K_i = β_i · h_i · t_i³.
Torsion constant K = Σ β_i · h_i · t_i³, each element rotating by the same amount per unit length. K_exact, with the exact coefficients throughout, is shown beside it.
Ultimate torsional resistance T_R = τ_y,k · K/t_max. The stress τ_v = T_v · t/K peaks in the thickest plate.
Design torsional resistance T_Rd = T_R/γ_M1, with γ_M1 from clause 4.1.3, and the peak shear stress τ_max = τ_y,k · M_x,Ed/T_R.
Torsional resistance of the open section: M_x,Ed ≤ T_Rd, with the reserve T_Rd/M_x,Ed beside it.
Warping, optional: a prismatic double tee built in at one end with a torque at the other.

What you enter and what you get

You enter τ_y,k from table 1 of your copy of SIA 263, the shape and its dimensions h, b, t_w and t_f (or each plate), γ_M1 and the design torsional moment M_x,Ed as a magnitude. For the warping case, only the bar length is added.

You get each element's contribution, K, T_R, T_Rd, τ_max and the utilisation with a pass or fail, and a drawing of the section to check against the one you mean. With the Basic plan, it prints as an A4 calculation note.

Assumptions and limits

τ_y,k is entered from table 1, not derived as f_y/√3.
The plates are welded into the section, so there are no fillets to neglect and no taper to idealise: the area and second moments are exact.
Taking β_i as 1/3 above h/t = 10 overstates K a little, because the exact series has not quite reached 1/3 there. In the worked example the difference is 3.4 %.
For a rolled profile the plate sum is below the true value: about 23 % on an HEA 340. Use the rolled-profile module, which takes K from the tables.
Uniform torsion unless the warping case is chosen. Where the section is prevented from warping, part of the torque is carried by warping, and at the restrained section that part can be the whole of it.
Not covered: torsion combined with axial force, bending or shear, distortion of the section, local buckling of a wall under the torsional shear, the connections and fatigue.

Worked example

A welded double tee with h = 330 mm, b = 300 mm, t_w = 9.5 mm and t_f = 16.5 mm in τ_y,k = 205 N/mm², under M_x,Ed = 20 kNm in uniform torsion; it does not pass the torsional resistance check, with η = 1.71. These are the module's own results for its worked example, computed when this page was built.

Inputs
Input	Value	Ref.
Characteristic shear yield strength τ_y,k	205 N/mm²	§ t.1
Shape	Double tee — I or H
Overall depth h	330 mm
Flange width b	300 mm
Web thickness t_w	9.5 mm
Flange thickness t_f	16.5 mm
Resistance factor γ_M1	1.05	§ 4.1.3
Design torsional moment M_x,Ed	20 kNm
Warping	Not considered — uniform torsion only

Calculation: Common values
Step	Value	Ref.
Characteristic shear yield strengthEntered from table 1, not derived.	τ_y,k = 205 N/mm²	§ t.1
Resistance factor	γ_M1 = 1.05	§ 4.1.3
Overall depth	h = 330.0 mm
Overall width	b = 300.0 mm
AreaThe sum of the rectangles of the outline. Exact for a section built of plates; for a ROLLED profile it is short by the root fillets, 4,7 % on an HEA 340.	A = 12,722 mm²
Thickest plateDerived from the section rather than entered. The peak shear stress of an open section is T_v·t/K, so it occurs here.	t_max = 16.5 mm
Second moment of area about yReported so the section can be recognised. Not used by the torsion check: the plate model is 4,6 % below the tabulated value for I_y, because the fillets sit near the web where they count for I_y and not for I_z.not used	I_y = 264,213,316 mm⁴
Element 1 — h/t and βThe mid-line plate is 300.0 × 16.5 mm, so h/t = 18.18, above 10, so β is taken as 1/3.	β₁ = 0.3333
Element 1 — contributionβ·h·t³	K₁ = 449,213 mm⁴
Element 2 — h/t and βThe mid-line plate is 300.0 × 16.5 mm, so h/t = 18.18, above 10, so β is taken as 1/3.	β₂ = 0.3333
Element 2 — contributionβ·h·t³	K₂ = 449,213 mm⁴
Element 3 — h/t and βThe mid-line plate is 313.5 × 9.5 mm, so h/t = 33.00, above 10, so β is taken as 1/3.	β₃ = 0.3333
Element 3 — contributionβ·h·t³	K₃ = 89,596 mm⁴
K with the exact coefficients throughoutTaking β as 1/3 above h/t = 10 is 3.4 % above the exact series here. That rule is followed; this is the size of it.not used	K_exact = 955,167 mm⁴
Torsion constantK = Σ β_i·h_i·t_i³, the elements summed because each rotates by the same amount per unit length while keeping its own shape.	K = 988,021 mm⁴

Calculation: Check 1 — uniform torsion
Step	Value	Ref.
Governing element — thickest	t_max = 16.5 mm
Peak shear stress at M_x,EdThe stress is linear in the torque, so τ_max = τ_y,k·M_x,Ed/T_R.	τ_max = 334.00 N/mm²
Ultimate torsional resistanceT_R = τ_y,k·K/t_max. The flow turns back within the thickness of each plate, so the stress is τ_v = T_v·t/K and peaks in the THICKEST one.	T_R = 12.28 kNm
Design torsional resistanceT_Rd = T_R/γ_M1	T_Rd = 11.69 kNm
Torsional resistance of the open sectionM_x,Ed ≤ T_Rd	η = 1.711 · Fail171 % of the capacity used

How this module is verified

Verified clause by clause against SIA 263:2013 and against independent calculations used on real projects, before release.

Questions

Why is K_exact shown if it is not used?

The rule of 1/3 above h/t = 10 overstates K slightly. K_exact shows by how much.

Can I use this module for a rolled I or H section?

Use the rolled-profile module instead. The plate sum leaves out the root fillets, which carry torsion, so it falls short of the tabulated K. Keep this module for angles and welded sections.

Can I print the calculation?

The full calculation is shown on screen, free and without an account. A print-ready A4 calculation note is part of the Basic plan.

Norm: SIA 263:2013 · Page updated: 27 October 2026

Open steel section of rectangular plates in torsion to SIA 263

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