Weak Storey (B1) Irregularity: Where Does Strength Break Off?

1. What is a weak storey?

If the shear strength of one storey is markedly lower than that of the storey above, deformation concentrates there during an earthquake. That storey is stressed earlier and far more than the rest of the building; in the worst case it collapses while the floors above stay intact.

TBDY 2018 defines this, for reinforced concrete buildings, as B1 — strength irregularity between adjacent storeys (weak storey) among the vertical irregularities (Table 3.6). The measure is the ratio of a storey's effective shear area to that of the storey above:

2. Effective shear area

The effective shear area, a rough proxy for a storey's shear strength, is:

where A_w, A_g and A_k are the cross-sectional areas, in the direction of the earthquake, of columns, reinforced concrete shear walls and masonry infill walls respectively.

Infill walls count at only 15%. One way to read this: infills do carry shear, but they are brittle, their connection to the frame is uncertain and they may be removed during the building's life. The code neither ignores them nor relies on them. What matters is the consequence: upper storeys full of infill appear considerably stronger than a ground storey where they have been removed.

The code also regulates two cases. For infill walls separated from the frame by flexible joints, A_k = 0 (note to Table 3.6, Clause 4.9.1.3(b)): such a wall does not act with the frame, so its shear contribution is not counted. And if a storey has more infill area than the storey above, the infill is ignored entirely in computing η_ci (Clause 3.6.2.3).

3. Two limits: 0.80 and 0.60

• 0.60 ≤ η_ci,min < 0.80: a B1 irregularity exists. The building can be designed, but the behaviour factor R from Table 4.1 is multiplied by 1.25·η_ci,min, and this reduction applies to the whole building in both earthquake directions (Clause 3.6.2.3). A smaller R means a larger design force.
• η_ci < 0.60: never permitted (Clause 3.6.2.3). The building cannot be designed without changing the structural system.

4. Worked example: a building with shops

Consider a building with shops on the ground floor and flats above. Both storeys have 1.2 m² of column area in the earthquake direction. The upper storey has 8 m² of infill; the ground storey has none because of the shop windows. The upper storey's effective shear area is 1.2 + 0.15 × 8 = 2.4 m².

Adding different amounts of reinforced concrete shear wall to the ground storey changes the result as follows (computed with the site's TBDY assessment engine):

With no wall, η_ci = 0.50: the building cannot be designed as it is. 0.6 m² of wall does not remove the irregularity but brings it into the permitted range; R is then multiplied by 1.25 × 0.75 = 0.9375. For a high-ductility RC frame (A11), for example, R = 7.5 is used instead of 8, and for T ≥ T_B the seismic forces grow by 8/7.5 ≈ 1.07, about 7%. With 1.0 m² the ratio reaches 0.92 and the irregularity disappears.

The key lesson of the example: the problem is created as much by the strength that the upper infills add "silently" as by the weakness of the ground storey. The columns are the same on both storeys.

5. Is a weak storey the same as a soft storey?

No, though everyday language often confuses them. TBDY defines them as separate irregularities:

• B1 — weak storey: a strength irregularity, measured by the ratio of shear areas.
• B2 — soft storey: a stiffness irregularity, measured by the ratio of the storey drifts of adjacent storeys; it exists when η_ki > 2.0 (basements excluded).

In buildings with shops they often appear together, because infill adds both strength and stiffness. But a building can have one without the other, so each must be checked separately. The soft-storey animation on the site shows how a stiffness difference concentrates deformation in a single storey.

6. What can be done?

The remedy is to increase the effective shear area of the ground storey, or to reduce the difference between storeys in another way. As the example shows, the most effective option is to add reinforced concrete shear walls in the ground storey; where architecture does not allow it, steel bracing or larger columns can be considered. For existing buildings this is the subject of a retrofit project.

One point worth remembering at the start of design: leaving the ground storey open in the architectural plan while closing the upper storeys with infill is as much a seismic decision as the choice of structural system.