Torsional Irregularity (A1): Why Does a Building Twist in an Earthquake?

1. Why does a building twist?

The earthquake force acts on the building's mass and can be thought of as concentrated at the centre of mass. The building resists with its stiffness, whose "centre" depends on how the structural members are arranged in plan. If the two centres do not coincide, the earthquake also applies a torsional moment: the building both sways and twists.

The typical case is a building whose lift and stair walls are grouped in one corner of the plan. The edge with the walls moves little, the opposite edge a lot. Columns on the far edge are stressed much more than the average drift would suggest.

2. The torsional irregularity factor η_bi

TBDY 2018 defines this among the plan irregularities as A1 — torsional irregularity (Table 3.6). At each storey the largest storey drift in the earthquake direction is compared with the average:

If η_bi > 1.2 an A1 irregularity exists. With no torsion both edges drift equally and η_bi = 1.

3. The amplification factor D_bi

In buildings with torsional irregularity, the additional eccentricity used in analysis is amplified by a factor (Equation 4.29):

The values below were computed with the site's TBDY assessment engine:

In the first row η_bi is exactly 1.2: at the limit, but no irregularity. In the second, η_bi = 1.5 and the additional eccentricity is multiplied by (1.5/1.2)² = 1.5625.

4. When one edge moves backwards

The third row is instructive: Δ_min = −2 mm. The building twists so much that the stiff edge moves against the earthquake direction. Δ_min must then be entered as negative, giving η_bi = 10 / 4 = 2.5.

The detail looks small but changes the result. Clipping Δ_min to zero would cap η_bi at 2.0; taking its absolute value would give 10 / 6 = 1.67. Both understate the real torsion. This error was found and fixed in the site's engine during a 2026 audit; the engine now handles negative Δ_min correctly.

5. η_bi > 2.0: is it prohibited?

A common misconception: in TBDY 2018, torsional irregularity is not prohibited, however large. Under Clause 3.6.2.1 it only affects the choice of analysis method. But because the D_bi formula is defined only for η_bi ≤ 2.0, beyond that range there is no defined way to amplify the additional eccentricity in the equivalent lateral force method, and modal analysis is recommended.

The contrast with the weak-storey irregularity is useful: there, η_ci < 0.60 is never accepted (TBDY-03). Torsion has no such absolute limit — but its absence does not make it good design.

6. What to do in design

The real remedy for torsional irregularity lies in the plan, not the calculation: placing walls and stiff members symmetrically, or at least spread towards the perimeter, brings the centre of rigidity closer to the centre of mass. Perimeter walls raise torsional stiffness most effectively because they are furthest from the axis of rotation.