# Building Behavior

The behavior of a building during an earthquake is a vibration problem. The seismic motions of the ground do not damage a building by impact, as does a wrecker's ball, or by externally applied pressure such as wind, but by internally generated inertial forces caused by vibration of the building mass. An increase in mass has two undesirable effects on the earthquake design. First, it results in an increase in the force, and second, it can cause buckling or crushing of columns and walls when the mass pushes down on a member bent or moved out of plumb by the lateral forces. This effect is known as the pA effect and the greater the vertical forces, the greater the movement due to pA. It is almost always the vertical load that causes buildings to collapse; in earthquakes, buildings very rarely fall overâ€”they fall down. The distribution of dynamic deformations caused by the ground motions and duration of motion are of concern in seismic design. Although duration of strong motion is an important design issue, it is not presently (2004) explicitly accounted for in design.

In general, tall buildings respond to seismic motion differently than low-rise buildings. The magnitude of inertia forces induced in an earthquake depends on the building mass, ground acceleration, the nature of the foundation, and the dynamic characteristics of the structure (Fig. 2.2). If a building and its foundation were infinitely rigid, it would have the same acceleration as the ground: the inertia force F for a given ground acceleration a may be calculated by Newton's law F = Ma, where M is the building mass. For a structure that deforms only slightly, thereby absorbing some energy, the force F tends to be less than the product of mass and ground acceleration. Tall buildings are invariably more flexible than low-rise buildings, and in general, experience much lower accelerations than

Figure 2.2. Schematic representation of seismic forces.

low-rise buildings. But a flexible building subjected to ground motions for a prolonged period may experience much larger forces if its natural period is near that of the ground waves. Thus, the magnitude of lateral force is not a function of the acceleration of the ground alone, but is influenced to a great extent by the type of response of the structure itself and its foundation as well. This interrelationship of building behavior and seismic ground motion also depends on the building period as formulated in the so-called response spectrum, explained later in this chapter.

Consider, for example, the behavior of a 30-story building during an earthquake. Although the motion of the ground is erratic and three-dimensional, the horizontal components in two mutually perpendicular directions are of importance. The fundamental period T1 of a tall building is a function of its stiffness, mass, and damping characteristics, and can vary over a broad range anywhere from 0.05 to 0.30 times the number of stories, depending upon the materials used in the construction and the structural system employed. As a preliminary approximation for steel-framed buildings, the period T1 is approximately equal to 0.15N, where N is the number of stories. A typical 30-story building would have a fundamental period of 4.5 sec, with the periods of the next two higher modes, T2 and T3, approximately equal to one-third and one-fifth of T1.

The second and third modes of vibration for the 30-story building are thus approximately equal to 1.5 and 0.9 sec. During the first few seconds of earthquake, the acceleration of the ground reaches a peak and is associated with relatively short-period components of the range 0 to 0.5 sec, which have little influence on the fundamental response of the building. On the other hand, the long-period components that occur at the tail end of earthquakes, with periods closer to the fundamental period of the building, have a profound influence on its behavior.

The intensity of ground motion reduces with the distance from the epicenter of the earthquake. The reduction, called attenuation, occurs at a faster rate for higher-frequency (short-period) components than for lower-frequency (long-period) components. The cause of the change in attenuation rate is not understood, but its existence is certain. This is a significant factor in the design of tall buildings, because a tall building, although situated farther from a causative fault than a low-rise building, may experience greater seismic loads because long-period components are not attenuated as fast as the short-period components. Therefore, the area influenced by ground shaking potentially damaging to, say, a 50-story building is much greater than for a 1-story building.