Dynamic Analysis

Symmetrical buildings with uniform mass and stiffness distribution behave in a fairly predictable manner, whereas buildings that are asymmetrical or with areas of discontinuity

Figure 2.10. Reentrant corners in L-, T-, and H-shaped buildings. (As a solution, add collector elements and/or stiffen end walls.)

Figure 2.10. Reentrant corners in L-, T-, and H-shaped buildings. (As a solution, add collector elements and/or stiffen end walls.)

or irregularity do not. For such buildings, dynamic analysis is used to determine significant response characteristics such as: 1) the effects of the structure's dynamic characteristics on the vertical distribution of lateral forces; 2) the increase in dynamic loads due to torsional motions; and 3) the influence of higher modes, resulting in an increase in story shears and deformations.

Static methods specified in building codes are based on single-mode response with simple corrections for including higher mode effects. While appropriate for simple regular structures, the simplified procedures do not take into account the full range of seismic behavior of complex structures. Therefore, dynamic analysis is the preferred method for the design of buildings with unusual or irregular geometry.

Two methods of dynamic analysis are permitted: 1) elastic response spectrum analysis; and 2) elastic or inelastic time-history analysis. The response spectrum analysis is the preferred method because it is easier to use. The time-history procedure is used if it is important to represent inelastic response characteristics or to incorporate time-dependent effects when computing the structure's dynamic response.

Structures that are built into the ground and extended vertically some distance above-ground respond as either simple or complex oscillators when subjected to seismic ground motions. Simple oscillators are represented by single-degree-of-freedom systems (SDOF), and complex oscillators are represented by multidegree-of-freedom (MDOF) systems.

A simple oscillator is represented by a single lump of mass on the upper end of a vertically cantilevered pole or by a mass supported by two columns, as shown in Fig. 2.11.

The idealized system represents two kinds of structures: 1) a single-column structure with a relatively large mass at its top; and 2) a single-story frame with flexible columns and a rigid beam. The mass M is the weight W of the system divided by the acceleration of gravity g, i.e., M = W/g.

The stiffness K of the system is the force F divided by the corresponding displacement A. If the mass is deflected and then suddenly released, it will vibrate at a certain

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