## Damping

Buildings do not resonate with the purity of a tuning fork because they are damped; the extent of damping depends upon the construction materials, type of connections, and the influence of nonstructural elements on the stiffness characteristics of the building. Damping is measured as a percentage of critical damping.

In a dynamic system, critical damping is defined as the minimum amount of damping necessary to prevent oscillation altogether. To visualize critical damping, imagine a tensioned string immersed in water. When the string is plucked, it oscillates about its rest position several times before stopping. If we replace water with a liquid of higher viscosity, the string will oscillate, but certainly not as many times as it did in water. By progressively increasing the viscosity of the liquid, it is easy to visualize that a state can be reached where the string, once plucked, will return to its neutral position without ever crossing it. The minimum viscosity of the liquid that prevents the vibration of the string altogether can be considered equivalent to the critical damping.

The damping of structures is influenced by a number of external and internal sources. Chief among them are

1. External viscous damping caused by air surrounding the building. Since the viscosity of air is low, this effect is negligible in comparison to other types of damping.

2. Internal viscous damping associated with the material viscosity. This is proportional to velocity and increases in proportion to the natural frequency of the structure.

3. Friction damping, also called Coulomb damping, occurring at connections and support points of the structure. It is a constant, irrespective of the velocity or amount of displacement.

4. Hysteretic damping which contributes to a major portion of the energy absorbed in ductile structures.

It is a common practice to lump different sources of damping into a single viscous type of damping. For nonbase-isolated buildings, analyzed for code-prescribed loads, the damping ratios used in practice vary anywhere from 1 to 10% of critical. The low-end values are for wind, while those for the upper end are for seismic design.

The damping ratio used in the analysis of seismic base-isolated buildings is rather large compared to values used for nonisolated buildings, and varies from about 0.20 to 0.35 (20 to 35% of critical damping).

Base isolation, discussed in Chapter 8, consists of mounting a building on an isolation system to prevent horizontal seismic ground motions from entering the building. This strategy results in significant reductions in interstory drifts and floor accelerations, thereby protecting the building and its contents from earthquake damage.

A level of ground acceleration on the order of 0.1g, where g is the acceleration due to gravity, is often sufficient to produce some damage to weak construction. An acceleration of 1.0g, or 100% of gravity, is analytically equivalent, in the static sense, to a building that cantilevers horizontally from a vertical surface (Fig. 2.3).

F1 + F2+ F3+ F4+ F5+ F6 = W = Building weight

Figure 2.3. Concept of 100% g. A building subjected to an acceleration of 100% g conceptually behaves as if it cantilevers horizontally from a vertical surface.

### 2.1.3. Building Motions and Deflections

Earthquake-induced motions, even when they are more violent than those induced by wind, evoke a totally different human responseâ€”first, because earthquakes occur much less frequently than windstorms, and second, because the duration of motion caused by an earthquake is generally short. People who experience earthquakes are grateful that they have survived the trauma and are less inclined to be critical of the building motion. Earthquake-induced motions are, therefore, a safety rather than a human discomfort phenomenon.

Lateral deflections that occur during earthquakes should be limited to prevent distress in structural members and architectural components. Nonload-bearing in-fills, external wall panels, and window glazing should be designed with sufficient clearance or with flexible supports to accommodate the anticipated movements.

### 2.1.4. Building Drift

Drift is generally defined as the lateral displacement of one floor relative to the floor below. Drift control is necessary to limit damage to interior partitions, elevator and stair enclosures, glass, and cladding systems. Stress or strength limitations in ductile materials do not always provide adequate drift control, especially for tall buildings with relatively flexible moment-resisting frames or narrow shear walls.

Total building drift is the absolute displacement of any point relative to the base. Adjoining buildings or adjoining sections of the same building may not have identical modes of response, and therefore may have a tendency to pound against one another. Building separations or joints must be provided to permit adjoining buildings to respond independently to earthquake ground motion.

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