# Torsion

Torsion was introduced in Chapter 2. In summary, if the Centre of Mass (CoM) of a building is not coincident with the Centre of Resistance (CoR) a torsional moment acts in the horizontal plane causing floor diaphragms to twist about the CoR (see Fig. 2.16). The rotation affects columns located furthermost from the CoR most severely. They are subject to large horizontal deflections, sometimes damaging them so seriously they collapse under the influence of their vertical gravity forces. Numerous torsion failures were observed during the 1994 Northridge and 1995 Kobe earthquakes (Fig. 8.1). Based upon post-earthquake observations of building failures, torsion is recognized as one of the most common and serious horizontal configuration problems.

Architects and engineers prevent building damage arising from torsion by using several approaches. Firstly, they minimize the distance in plan between the CoM and CoR. Remember that even with a perfectly symmetrical structural configuration some degree of torsion still occurs due to torsional motions within the ground shaking. Codes specify a minimum design eccentricity to account for this and unavoidable out-of-balance or asymmetrical distribution of gravity forces in a building with respect to the CoR. Every

▲ 8.1 Collapse of a concrete frame building at ground floor level due to torsion, 1995 Kobe, Japan earthquake.

(Reproduced with permission from EERI. David R. Bonneville, photographer).

▲ 8.1 Collapse of a concrete frame building at ground floor level due to torsion, 1995 Kobe, Japan earthquake.

(Reproduced with permission from EERI. David R. Bonneville, photographer).

Shear wall

Plan

(a) No torsional resistance

Shear wall

Plan

(a) No torsional resistance

Plan

(b) Excellent torsional resistance

▲ 8.2 Two structural configurations, each with four shear walls, with contrasting abilities to resist torsion.

Reaction force from shear wall y x

Reaction force from shear wall

Plan

▲ 8.3 A building plan illustrating how vertical structure resists torsion. Most gravity-only structure and the movement of the building in the y direction is not shown.

Plan

▲ 8.3 A building plan illustrating how vertical structure resists torsion. Most gravity-only structure and the movement of the building in the y direction is not shown.

building, no matter how symmetrically configured in plan, requires torsion resistance.

Secondly, designers provide a minimum of two lines of vertical structure parallel to each of the main orthogonal axes of a building yet horizontally offset from each other. The horizontal off-set or lever-arm between each line of structure should be as large as possible to maximize both the latent torsion-resisting strength and stiffness. When the building in Fig. 8.2(a) twists in plan, its shear walls offer no significant resistance because they warp, flexing about their weak axes. In contrast, when the plan in Fig. 8.2(b) twists about the CoR which is centrally located, each of the four walls reacts along its line of strength against the horizontal deflection imposed upon it by the rotation of the floor diaphragm. Long lever-arms between pairs of walls provide the best possible resistance against torsion.

How exactly does vertical structure resist torsion? Consider the building in Fig. 8.3. It is very well configured structurally to resist torsion - two perimeter shear walls in each direction. Assuming a torsional eccentricity e between the resultant line of action of inertia forces acting in the y direction and the CoR, the building twists clockwise. Its diaphragm rotates as a rigid unit. A diaphragm is usually very stiff and strong in its plane, especially if constructed from reinforced concrete. When twisting occurs about the CoR, which is the point through which the resistance from all the shear walls acts, the shear walls acting in the y direction deflect in opposite directions a small amount Ay. These movements are additive to the shear wall deflections due to the y direction forces that are not shown. Each shear wall also twists a little. This source of torsional resistance is neglected because the twisting strength of an individual wall is so low. As each wall is pushed, it resists the imposed deflection in the direction of its strength (the y direction) and applies a reaction force. The value of these reaction forces multiplied by the lever arm between them represents a moment couple that partially resists the torsional moment causing diaphragm rotation.

Also due to the diaphragm rotation, the x direction shear walls deflect horizontally Ax in opposite directions. Like the y direction shear walls, they react against the movement that deflects them. They apply equal and opposite reaction forces upon the diaphragm creating another moment couple. Even though no x direction seismic forces act on the building, because these two shear walls orientated parallel to the x axis are strongly connected to the diaphragm, they nonetheless participate in resisting torsion. The two torsion-resisting couples formed by the

Diaphragm rotation

Plan

(a) Four inner walls slightly increase torsional resistance

Diaphragm rotation

Plan

(a) Four inner walls slightly increase torsional resistance

Diaphragm rotation

Plan

(b) Diaphragm rotation increases where inner walls alone resist torsion

Diaphragm rotation

Plan

(b) Diaphragm rotation increases where inner walls alone resist torsion

▲ 8.4 Structure located close to the CoR is less effective at resisting torsion.

▲ 8.4 Structure located close to the CoR is less effective at resisting torsion.

▲ 8.5 An example of a torsionally unbalanced system.

pairs of parallel shear walls combine to resist the torsional moment and provide torsional equilibrium. Any structural damage is unlikely since only minimal diaphragm rotation occurs.

The four extra shear walls added in plan (Fig. 8.4(a)) enhance torsional resistance slightly. Even if the new walls are identical to the perimeter walls because they are closer to the CoR they are subject to 50 per cent smaller displacements when the diaphragm twists and the lever-arms between them are less. With a lesser resisting force (proportional to horizontal displacement) and half the lever arm their torsion-resisting contribution is only 25 per cent of that provided by the perimeter walls. If the perimeter walls are removed, and horizontal forces and torsion are now resisted by the inner walls alone, the two torsion-resisting couples must offer the same resistance as before since the value of the torsion moment is unchanged. We can neglect any torsional resistance from the slender perimeter columns. Since the lever-arms between the inner walls are half of the original lever-arms wall reaction forces double. This means that these walls will need to be considerably stronger and that the diaphragm will twist further. The structural configuration in Fig. 8.4(b) is therefore twice as torsionally flexible as that in Fig. 8.2(b) i but it might still be structurally adequate especially if the perimeter gravity-only columns can sustain the ensuing horizontal movements without damage.

Although the previous figures illustrate shear walls resisting seismic forces, moment and braced frames can also provide adequate torsion resistance. Replace the shear walls with one- or multi-bay moment frames and the principles outlined above still apply. The building will be less torsionally stiff due to the lesser stiffness of the frames but still perform adequately, especially if the frames are located on the perimeter of the building.

In the examples considered so far, a recommended torsion-resistant structure comprises a minimum of four vertical elements, like shear walls or moment frames, with two in each direction. However, in some situations the number of elements can be reduced to three (Fig. 8.5). Any y direction forces are resisted by one shear wall, albeit long and strong especially given an absence of redundancy, and x direction forces resisted by two walls. When torsion induces diaphragm rotation, the two x direction walls, in this case with a long lever-arm between them, form a moment couple. They provide torsional stability or equilibrium irrespective of the direction of loading - but only so long as they remain elastic. Most shear walls and frames are designed for relatively low seismic forces if they incorporate ductile detailing. So when

one x direction wall yields as a result of inertia forces in the x direction as well as torsion it temporarily loses its stiffness and the COR migrates towards the stiffer end, increasing torsional eccentricity. The system becomes torsionally unstable.

Site boundary

Site boundary

Street frontage

Street frontage

▲ 8.6 Poor configuration of a typical corner building with shear walls as boundary walls.

This configuration consisting of three vertical structural elements is described by structural engineers as a torsionally unbalanced system. It is not recommended unless the x direction walls or frames are much stronger than minimum requirements. They must be capable of resisting horizontal forces with little or no ductility demand and therefore possibly possess far more strength than normal. Researchers are currently responding to the undesirable situation where code torsion provisions are based upon elastic structural performance and have yet to account for the effects of anticipated inelastic or ductile behaviour.8 Until research findings update guidelines, architects should avoid torsionally unbalanced systems unless satisfying the criterion above.

The beginning of this section recommended that designers minimize torsional eccentricity. But to what extent? When is torsional eccentricity too great? A structural engineer can provide an answer for a particular building, but only after undertaking a complex 3-D computer analysis to calculate dynamic stresses and horizontal displacements. As a rule-of-thumb, keep the eccentricity in each orthogonal direction to less than 25 per cent of the building dimension measured normal to the direction of force under consideration.

Fire resistant infill "

(if strong, separated from frame)

▲ 8.7 An improved horizontal configuration for a corner building. Horizontal forces are resisted by symmetrical moment frames.

The worst-case torsion scenario, as shown in Fig. 8.6, is common for buildings on urban corner sites. The two sides away from the street are bounded by fire-resistant walls which, even if not specifically designed as shear walls, act as such. The two street frontages are relatively open. The CoR is therefore located at the back corner of the building. Assuming the building weight is evenly distributed in plan the eccentricities in both directions equal 50 per cent of the building plan dimensions.

If you design a corner building use one of three strategies to reduce torsional eccentricities. First, avoid designing strong rear walls. Substitute them with fire-resistant infilled moment frames. Infills of either lightweight construction or reinforced masonry that are separated on three sides from the frames, as discussed in Chapter 10, are suitable. Both those frames - which also carry gravity forces - require identical frames along the street frontages to balance them torsionally (Fig. 8.7).

Secondly, in an alternative, but less popular strategy, the two strong rear walls remain, but are separated in-plan from the rest of the building

Plan

Soft

Non-structural

Tie between wall

Soft

Non-structural

Tie between wall

Plan

▲ 8.8 An alternative approach to achieving satisfactory configuration of a corner building by separating the strong walls from the rest of the structure and providing new moment frames to resist all seismic forces.

Plan

▲ 8.8 An alternative approach to achieving satisfactory configuration of a corner building by separating the strong walls from the rest of the structure and providing new moment frames to resist all seismic forces.

(Fig. 8.8). Horizontal separation joints between the walls and floor diaphragms prevent the walls playing any role in seismic resistance. New moment frames just inside the walls resist inertia forces in both directions. The final step is to detail the wall-to-diaphragm connections at each level. Ties must resist inertia forces acting normal to the walls arising from their self-weight. The connections need to be strong along one axis, but able to slide or move freely along the other. The associated detailing complexities explain why this is a less preferred option.

The third strategy for reducing torsional eccentricity involves ' softening' the rear walls by designing and constructing them as many short walls. For example, a single 20 m long wall might be designed and built as five 4 m long walls. The vertical joints between the walls, necessary for ensuring structural separation, require treatment for fire resistance. This approach needs to reduce torsional eccentricity sufficiently to make it attractive. Even softened walls can be far stronger and stiffer than moment frames.

(a) Undesirable configuration caused by an eccentric structural core

Plan

The strategy of substituting potentially strong walls with infilled frames or constructing the walls from light-weight and relatively weak but fire-resistant materials, thereby rendering them non-structural, is often a viable solution to reduce torsion. Its usage is not confined solely to the perimeters of buildings. It can overcome eccentricities associated with, for example, eccentrically placed cores or shafts that might normally function as horizontal force-resisting elements (Fig. 8.9).

(a) Undesirable configuration caused by an eccentric structural core

Light-weight or separated non-structural infill walls

Moment frame

Plan

(b) Eccentric core, but regular horizontal configuration

Light-weight or separated non-structural infill walls

Moment frame

Plan

(b) Eccentric core, but regular horizontal configuration

▲ 8.9 Avoiding torsional eccentricity from an eccentric structural core by making the core non-structural.