Checks the torsional resistance of a solid rectangle h × t at the ultimate limit state, to SIA 263:2013, with the coefficients α and β from the exact Saint-Venant series. Every step shows its formula and the clause it comes from.

What it checks

Aspect ratio h/t, the long side over the short side.
Stiffness coefficient β, derived from the exact Saint-Venant series rather than read off a table. It reproduces the tabulated values to 0.0007.
Stress coefficient α, with τ_max = T_v/(α · h · t²) at the middle of the long side.
Torsion constant K = β · h · t³.
Ultimate torsional resistance T_R = τ_y,k · α · h · t².
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 solid rectangle: 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 long side h, the short side t, γ_M1 and the design torsional moment M_x,Ed as a magnitude. M_x,Ed is the applied moment; T_R is the resistance the section develops against it.

You get h/t, α, β, K, 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.
h is the longer side. α and β are defined against h/t from 1 upwards, so the ratio must be taken that way round.
The peak stress is at the middle of the long side and goes with t², so the short side governs it.
Uniform torsion only. If the bar is prevented from warping anywhere along its length, part of the torque is carried by warping. The closed-form solution covers a double tee and no other section, so this module does not offer it.
A solid rectangle is the stiffest open shape in torsion for its area and still far behind a closed cell. Where torsion governs, the answer is a closed section, not a thicker solid one.
Not covered: torsion combined with axial force, bending or shear (the interaction modules do that), distortion of the section, the connections and fatigue.

Worked example

A solid rectangle 200 × 67 mm 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
Long side h	200 mm
Short side t	67 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
Aspect ratio	h/t = 2.99
Stiffness coefficientDerived from the exact Saint-Venant series rather than read off a table; it reproduces the tabulated values to 0,0007.	β = 0.2630
Stress coefficientτ_max = T_v/(α·h·t²), at the middle of the long side.	α = 0.2669
Torsion constantK = β·h·t³	K = 15,818,172 mm⁴

Calculation: Check 1 — uniform torsion
Step	Value	Ref.
Governing element — thickest	t_max = 67.0 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 = 83.45 N/mm²
Ultimate torsional resistanceT_R = τ_y,k·α·h·t²	T_R = 49.13 kNm
Design torsional resistanceT_Rd = T_R/γ_M1	T_Rd = 46.79 kNm
Torsional resistance of the solid rectangleM_x,Ed ≤ T_Rd	η = 0.427 · Pass43 % 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 compute α and β instead of reading them from a table?

The exact Saint-Venant series gives them for any h/t without interpolation, and reproduces the tabulated values to 0.0007.

How does a solid rectangle compare with other sections?

A rolled H has roughly a twelfth of the torsional stiffness of a solid rectangle of the same area, and the rectangle in turn has a small fraction of a tube's.

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

Solid rectangular steel section in torsion to SIA 263

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