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FIGURE 35.9 Energy response of traditional structure: (a) damageability limit state and (b) collapse limit state (Uang and Bertero 1986).

Figure 35.9a provides the energy response of a 0.3-scale, six-story concentrically braced steel structure as measured by Uang and Bertero (1986). The seismic input consisted of the 1978 Miyagi-Ken-Oki Earthquake signal scaled to produce a peak shaking table acceleration of 0.33g, which was deemed to represent the damageability limit state of the model. At this level of loading, a significant portion of the energy input to the structure is dissipated, with both viscous damping and inelastic hysteretic mechanisms having substantial contributions. If the intensity of the signal is elevated, an even greater share of the energy is dissipated via inelastic deformation. Finally, for the collapse limit state of this model structure at 0.65g peak table acceleration, approximately 90% of the energy is consumed by hysteretic phenomena, as shown in Figure 35.9b. Evidently, the consumption of this quantity of energy has destroyed the structure.

From an energy perspective, then, for proper aseismic design, one must attempt to minimize the amount of hysteretic energy dissipated by the structure. There are basically two viable approaches available. The first involves designs that result in a reduction in the amount of energy input to the structure. Base isolation systems and some active control systems, for example, fall into that category. The second approach, as in the passive and semiactive control system cases, focuses on the introduction of additional energy dissipating mechanisms into the structure. These devices are designed to consume a portion of the input energy, thereby reducing damage to the main structure caused by hysteretic dissipation. Naturally, for a large earthquake, the devices must dissipate enormous amounts of energy.

The SDOF system with a control element is displayed in Figure 35.3, while the governing integro-differential equation is provided in Equation 35.3. After integrating with respect to x, an energy balance equation can be written and the other terms are as previously defined.

As an example of the effects of control devices on the energy response of a structure, consider the tests of a one-third scale three-story lightly reinforced concrete framed building conducted by Lobo et al. (1993). Figure 35.10a displays the measured response of the structure due to the scaled 1952 Taft

where the energy associated with the control element is

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