Checks the torsional resistance of a general single closed cell with up to six walls of differing thickness at the ultimate limit state, to SIA 263:2013, by Bredt's formula. Every step shows its formula and the clause it comes from.

What it checks

Perimeter over thickness Σ s_i/t_i, summed over the wall segments, and the thinnest wall t_min.
Torsion constant K = 4Ω²/Σ(s_i/t_i), Bredt's formula.
Ultimate torsional resistance T_R = 2 · Ω · t_min · τ_y,k, from τ(s) = T_v/(2Ω · t(s)). The flow is constant round the cell, so the stress peaks in the thinnest wall: the opposite of an open section.
Design torsional resistance T_Rd = T_R/γ_M1, with γ_M1 from clause 4.1.3.
Peak shear stress τ_max = τ_y,k · M_x,Ed/T_R, since the stress is linear in the torque.
Torsional resistance of the closed cell: M_x,Ed ≤ T_Rd, the same shape as the general condition E_d ≤ R_d. The reserve T_Rd/M_x,Ed is shown beside it.

What you enter and what you get

You enter τ_y,k from table 1 of your copy of SIA 263, the area enclosed by the wall mid-line Ω, the number of wall segments n (1 to 6) and, for each, its length along the mid-line s_i and its thickness t_i, then γ_M1 and the design torsional moment M_x,Ed as a magnitude. A pair of identical walls may be entered once with the length doubled.

You get Σ s_i/t_i, K, the governing wall t_min, T_R, T_Rd, τ_max and the utilisation with a pass or fail. 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.
Ω is not the area of the material but the area the closed shear flow runs around. K goes with its square, so a cell twice as large in both directions is sixteen times as stiff in torsion.
One cell only. Bredt's formula as written closes a single circuit. In a multi-cell box the flows in the shared webs add and the cells have to be solved together. Nothing in the module detects that you have entered one cell of a several-cell section.
The cell must stay closed. Any cut, service hole or discontinuity in the wall that breaks the closed shear flow removes almost all of the resistance.
Uniform torsion only.
Not covered: torsion combined with axial force, bending or shear (the interaction modules do that), distortion of the section, local buckling of a wall under the torsional shear, the connections and fatigue.

Worked example

A cell enclosing Ω = 8,779.69 mm², entered as two wall segments of 187.4 mm, each 6.3 mm thick, in τ_y,k = 205 N/mm², under M_x,Ed = 20 kNm. 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
Area enclosed by the wall mid-line Ω	8779.69 mm²
Number of wall segments n	2
Length along the mid-line s₁	187.4 mm
Thickness t₁	6.3 mm
Length along the mid-line s₂	187.4 mm
Thickness t₂	6.3 mm
Resistance factor γ_M1	1.05	§ 4.1.3
Design torsional moment M_x,Ed	20 kNm

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
Area enclosed by the mid-line	Ω = 8,780 mm²
Perimeter over thickness	Σ s_i/t_i = 59.49
Thinnest wall	t_min = 6.3 mm
Torsion constantK = 4Ω²/Σ(s_i/t_i), Bredt's formula.	K = 5,182,739 mm⁴

Calculation: Check 1 — uniform torsion
Step	Value	Ref.
Governing wall — thinnest	t_min = 6.3 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 = 180.79 N/mm²
Ultimate torsional resistanceT_R = 2·Ω·t_min·τ_y,k, from τ(s) = T_v/(2Ω·t(s)). The flow is constant round the cell, so the stress peaks in the THINNEST wall — the opposite of an open section.	T_R = 22.68 kNm
Design torsional resistanceT_Rd = T_R/γ_M1	T_Rd = 21.60 kNm
Torsional resistance of the closed cellM_x,Ed ≤ T_Rd	η = 0.926 · Pass93 % 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 does the thinnest wall govern?

The shear flow is constant round the cell, and the stress is that flow divided by the local thickness. A short thin panel therefore governs the whole section, however little of the perimeter it occupies, and thickening the other walls does not recover it.

Can I check a box with an internal web?

Not with this module. A shared web carries the flows of two cells, which add, and the cells must be solved together.

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

Thin-walled closed steel cell in torsion to SIA 263

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