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4 Earthquake Engineering (continued) + ward ' s science 5100 West Henrietta Road • PO Box 92912 • Rochester, New York 14692-9012 • p: 800 962-2660 • wardsci.com This article was originally published by McGraw Hill's AccessScience. Click here to view and find more articles like this. tural non-linearity, effectively damage), although today nonlin- ear analyses are commonly being used. For ordinary design, the actual earthquake forces are reduced via a response-modifica- tion factor, which varies depending on the assumed inherent ductility of the structure, based on its lateral force-resisting system's material (wood, steel, concrete, etc.) and system (mo- ment frame, braced, shear wall, etc.). These reduced forces, with appropriate safety factors, are combined with gravity and other loads in the design of the overall structure. For small buildings, pseudo-static or linear dynamic analytical methods are em- ployed for design and are based on the structure's natural pe- riod (that is, the first mode of vibration). Linear dynamic meth- ods account for the first and higher modes, which analyses are usually more quickly performed in the frequency domain, using techniques based on the fast Fourier transform (FFT). For larger and more important structures, nonlinear dynamic analyses are employed, typically in the time domain. In a nonlinear dynamic analysis, the structure is subjected to earthquake acceleration time histories (actual or synthesized records, scaled to match the site hazard), and member response into the inelastic range is taken into account, including P − Δ effects (that is, the in- crease in overturning moment due to the structure's weight, P, times its lateral deflection, Δ). Dynamic and nonlinear analysis is now quite feasible as a result of the advent of more powerful computers and specialized software—ETABS, SAP2000, ANSYS, STAAD, and LARSA are some of the structural analysis packages more commonly used. Performance-based design employs a variety of structural approaches to reduce damage to acceptable levels, including base isolation, supplemental damping, and active control (Fig. 2). Base isolation involves placing special components, termed isolators, within the structure, which are relatively flex- ible in the lateral direction yet can sustain the vertical load. This technique is more properly termed structural isolation, because it is not always employed at the base. When the earthquake causes ground motions beneath the structure, the isolators allow the structure to respond much more slowly than it would without them, resulting in lower seismic demand on the structure. Isolators may be laminated steel–high-quality rubber pads, sometimes incorporating lead or other energy-absorbing materials, or parabolic dish-shaped base plates, which rely on the structure's own weight trying to "climb" the sloping sides of the "dish" to counteract the lateral force of the earthquake. Supplemental damping involves placing dampers within the structure, which retard the structural response of the normal or undamped structure, again re- sulting in lower seismic demand on the structure. Dampers can be hydraulic cylinders, simi- lar but much larger than those used in automobile shock absorb- ers, or can rely on the energy absorption of steel deformed inelastically. An increas- ingly common application of this type is buckling-restrained braces (BRBs), which consist of a slender steel core surrounded by concrete designed to support the core continuously and prevent buckling under axial compression, together with an interface to prevent undesired interaction (Fig. 3). Active control involves placing hydraulic rams or other actuating devices within the structure, which introduce forces counter to those caused by the earthquake, thus negating some or all of the seismic demand. To determine how much force to apply to which actuator(s) involves a real-time solution of the dynamics of the structure; that is, it is required that sensors measure the ground motion at the base of the structure, a structural analysis for these accelerations be performed on a dedicated processor, and the optimum pattern of forces be determined and applied via quick-response actuators, during a time interval equal to or less than the dynamic response of the structure. Base isolation and supplemental damping are now mainstream structural engineering tools, whereas active control has not been widely employed. Fig. 3: Buckling-restrained braces (BRBs) in a new steel-framed building under construction in California. The BRBs are the diagonal steel members. (Credit: C. Scawthorn)

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