Reentrant corners

Buildings that have suffered seismic damage due to re-entrant corners occasionally feature in earthquake reconnaissance reports. Although re-entrant geometries can take many shapes, what they share in common from a seismic design perspective, is their potential for damage resulting from the different dynamic properties of each wing (Fig. 8.10). For example, when the building in Fig. 8.11 is shaken in the y direction, the left-hand area of the building, and the wing to the right, react quite differently. The left-hand area deflects horizontally a relatively small amount due to its greater depth and inherently greater horizontal stiffness. The more flexible wing moves further and at a different period of vibration. It swings about the stiffer area, possibly damaging floor diaphragms at the junction of the two wings. As a result of the large horizontal deflections, the right-hand end columns of the right-hand wing might also sustain damage. Effectively, the right-hand wing is subject to

Plan

▲ 8.10 Typical re-entrant corner forms.

Entrant Corners

▲ 8.11 The dynamic response of a re-entrant configuration and potential floor diaphragm damage area.

▲ 8.10 Typical re-entrant corner forms.

▲ 8.11 The dynamic response of a re-entrant configuration and potential floor diaphragm damage area.

▲ 8.12 A typical definition of an irregular re-entrant configuration is where A > 0.15B.
Seismic Collectors Entrant Corners
▲ 8.13 Irregular plan configurations improved by seismic separation gaps.

torsional rotation about the stiffer and stronger left-hand area. Shaking in the x direction highlights the same configuration problem.

The attitude of most codes towards re-entrant corners is to require structural engineers to undertake a 3-D dynamic analysis where the length of a projecting area of building causing a re-entrant corner exceeds approximately 15 per cent of the building plan dimension (Fig. 8.12). An engineer will design the re-entrant structure to avoid either diaphragm tearing or excessive horizontal deflections. This can be achieved by fine-tuning the relative stiffness of the wings. However, if they are long or their diaphragms weakened by penetrations for vertical circulation or other reasons in the critical region where they join, that approach may not be structurally sound. The building might best be separated into two independent structures.

Separation is a common solution for re-entrant corner buildings (Fig. 8.13). How it is achieved is explained later in this chapter. Although a building might be perceived as a single mass if its blocks are seismically separated, it actually consists of two or more structurally independent units, each able to resist its own inertia forces including torsion. Where possible, separation gaps are provided adjacent to, or through, areas where floor diaphragms are penetrated or discontinuous.

Plan

Plan

Slot in diaphragm

Slot in diaphragm x

Plan

▲ 8.14 A slot in the diaphragm destroys its ability to span between shear walls for y direction forces. (X direction structure not shown.)

Plan

▲ 8.14 A slot in the diaphragm destroys its ability to span between shear walls for y direction forces. (X direction structure not shown.)

Diagonal steel bracing across slot

Diagonal steel bracing across slot

Vierendeel frame

Vierendeel frame x

▲ 8.15 Plans of two diaphragms where structural integrity across a slot is restored by steel bracing and frame-action.

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