Torsion in Structures: Beams, Sections and Buildings

Bending and axial force get most of the attention in structural engineering, but members can also be twisted. Torsion is that twisting action: a moment applied about the long axis of a member, trying to rotate one end relative to the other. It arises whenever a load is applied off-centre, as when a balcony slab hangs off the side of an edge beam, a canopy is bracketed off a column, or a building’s stiff core sits to one side of its plan.

Torsion is often secondary, but when it is overlooked it causes distinctive cracking, excessive rotation and occasionally failure. This article explains the intuition, the key formulas, why section shape matters so much, a simple worked comparison, how torsion appears at building scale, and the most common mistakes.

The intuition: wringing a towel

Wring out a wet towel and you are applying torsion. Each cross-section of the towel rotates slightly more than the one before, and the fibres follow a spiral. In a solid member, twisting produces shear stresses that run around the section, greatest at the outer surface and zero at the centre. Those shear stresses combine to produce tension and compression on diagonal planes at roughly 45 degrees to the axis.

That diagonal tension is why a concrete beam under significant torsion develops spiral cracks that wrap around its faces, and why a piece of chalk twisted until it breaks fails along a helical surface. Ductile steel, by contrast, can twist through large angles before it fails, although open steel sections may suffer large rotations and warping long before their strength is reached.

Key formulas

For a solid circular shaft of diameter d carrying a torque T, the maximum shear stress at the surface and the angle of twist over a length L are:

τ_max = T·r / J and θ = T·L / (G·J)

Here r is the outer radius, G is the shear modulus of the material (about 81 GPa for steel, roughly 40 per cent of its Young’s modulus) and J is the polar moment of inertia, or torsion constant. For a solid circle, J = π·d⁴/32; for a hollow tube, J = π·(D⁴ − d⁴)/32. The product G·J is the torsional stiffness, the twisting counterpart to the bending stiffness E·I described in our article on moment of inertia.

Non-circular sections need different expressions. For a thin open rectangle of length b and thickness t, the torsion constant is approximately J ≈ b·t³/3. For a thin-walled closed section, the shear flow around the wall is q = T / (2·A_m), where A_m is the area enclosed by the centreline of the wall, so the shear stress is τ = T / (2·A_m·t). These expressions explain the single most important lesson about torsion: closed sections are dramatically stiffer and stronger in twisting than open ones.

Open versus closed sections: a worked comparison

Take a steel strip 200 mm long and 10 mm thick. Used as a flat plate, its torsion constant is approximately 200 × 10³ / 3 ≈ 67,000 mm⁴.

Now fold the same strip into a closed square tube with a centreline of 50 mm by 50 mm and weld the seam. The enclosed area is A_m = 2,500 mm². For a thin-walled closed section, J = 4·A_m²·t / s, where s is the perimeter of the centreline, 200 mm. So J = 4 × 2,500² × 10 / 200 = 1,250,000 mm⁴.

The same amount of steel is roughly twenty times stiffer in torsion when it forms a closed tube, and the advantage grows rapidly as walls get thinner. Cut a slit along the tube and it collapses back to nearly the stiffness of the flat strip. This is why hollow sections and box girders are preferred where twisting is significant, and why I-sections and channels, which are open shapes, are weak in torsion. Our comparison of H-beams and I-beams discusses how these rolled shapes behave.

Open sections also suffer warping: under torsion their flanges bend in opposite directions, so plane sections do not stay plane. Restraining that warping at supports adds stiffness but introduces extra stresses. Channels have an additional complication, because their shear centre lies outside the web, so a load through the web actually twists the section.

Torsion in beams: equilibrium and compatibility

Engineers distinguish two kinds of torsion. Equilibrium torsion is needed to keep the structure standing. A cantilevered canopy or balcony fixed only to the side of an edge beam, with no other support, can only be held up if the beam resists the twist; if the beam cannot, the canopy rotates and falls. This must be designed for explicitly. Our article on cantilever structural design covers how such elements are anchored.

Compatibility torsion arises because connected members rotate together. A slab built monolithically with an edge beam tries to twist the beam as it deflects, but if the beam cracks and softens in torsion, the slab simply redistributes moment and becomes more like a simply supported span at that edge. Eurocode 2 allows compatibility torsion to be neglected in the ultimate design in many cases, but minimum reinforcement in the form of closed links and longitudinal bars is still required to control cracking.

In reinforced concrete, torsion is resisted by a space-truss mechanism: closed links around the perimeter and longitudinal bars at the corners act as ties, while the concrete between spiral cracks acts as inclined compression struts. Open U-shaped links are ineffective; the links must be closed and properly anchored, which is a frequent site inspection point. The detailing principles are covered in our guide to rebar reinforcement.

Torsion at building scale

Whole buildings can twist too. Under wind or earthquake, the lateral load acts roughly through the centre of mass or the centre of the exposed area, while the building resists it around its centre of stiffness, determined by the positions of cores, shear walls and frames. If the two do not coincide, the building rotates in plan as well as swaying. A stair or lift core placed at one end of a long floor plate is a classic cause.

Plan torsion increases the movements and forces at the far corners of the building, which can govern the design of perimeter columns and facade joints. Designers reduce it by arranging stiff elements symmetrically and as far from the centre as practical, which increases the torsional lever arm. Tube structures and perimeter frames, discussed in our article on tall building structural systems, are extremely effective against plan torsion for exactly this reason.

Common mistakes

Hanging loads off one side of a beam without checking twist. Brackets, canopies, signage and cladding supports introduce torsion into beams that were designed only for bending.
Using open sections where twisting dominates. An I-beam carrying an eccentric load can rotate excessively; a hollow section or added restraint is usually better.
Detailing torsion links as open stirrups. Concrete torsion needs closed links with proper hooks and corner bars.
Ignoring the shear centre. Loads applied away from the shear centre of channels and angles cause unintended twist.
Asymmetric stiffness in plan. Placing cores and walls on one side of a building invites plan torsion under lateral load.

Frequently asked questions

What is torsion in a beam?

Torsion is twisting about the beam’s long axis, caused by loads applied off its centreline or shear centre. It produces shear stresses around the section and diagonal tension that can lead to spiral cracking in concrete or excessive rotation in steel.

Why are hollow sections better in torsion?

In a closed section, shear can flow continuously around the whole perimeter, using the large enclosed area as a lever arm. An open section has no closed path, so it relies on the thin walls alone. For the same material, a closed tube can be tens of times stiffer in torsion than an open shape.

What causes torsion in buildings?

Torsion arises when lateral loads from wind or earthquake act away from the centre of stiffness of the building’s resisting structure, such as when cores or shear walls are placed asymmetrically. The building then rotates in plan as well as swaying.

How is torsion resisted in reinforced concrete?

By closed links around the perimeter of the section together with longitudinal bars, particularly at the corners. After cracking, these act with diagonal concrete struts as a three-dimensional truss that carries the twisting moment.

What is the difference between torsion and bending?

Bending rotates a member about an axis across its section, stretching one face and compressing the other. Torsion rotates it about its own long axis, producing shear around the section. Many real members carry both together, and their effects must be combined in design.

Fixing a canopy, balcony or heavy bracket to an existing beam? Talk to our consultancy or get in touch.