Integrated Seismic Design of Structure and Control Systems

In this chapter, structural control techniques aimed at reducing the vulnerability of existing or new structures, built in medium and high seismic risk areas, are described. The description is focused on the passive control and, in particular, on the passive supplemental energy dissipation techniques. The effectiveness of the largest and most popular dissipation devices, such as hysteretic and viscous, by highlighting the significant reduction of seismic demand on the main structure to be protected through the evaluation of earthquake damage indices is briefly described.

In this chapter, the supplemental passive energy dissipation devices, metallic or hysteretic dampers, frictional, viscoelastic and viscous (linear and non-linear) dampers, developed and studied over the years, are briefly described. For each type of device, the physical, mechanical and technological aspects are analysed by describing the construction, hysteretic behavior, physical models, advantages, and disadvantages. Then, the more appropriate mathematical laws to model their dynamic behavior, with particular reference to the viscous and viscoelastic, are described. Finally, a comparison between all the different types of device is reviewed and the main recommendations, reported in the international codes with specific reference to the viscous and viscoelastic, are explained.

In this chapter, the principal elements of the dynamic response of linear undamped and damped single and multi degrees-of-freedom systems are described in time domain both in terms of the relative motions of the mass and in state space form. In a first stage, the analysis of the dynamic response of linear simple-degree-of-freedom systems in the time domain is described by defining the main dynamic characteristics of the undamped system and, then, evaluating the damped natural frequency of the system and response factor. The modal strain energy method is described to evaluate the damping ratio of the SDOF system equipped with viscous and viscoelastic devices. As for linear multi-degrees-of-freedom systems the decoupling procedure for modal analysis and the proportional damping model are described. Even for these systems the effect of damping, assumed to be proportional, on the natural frequencies is evaluated and the modal strain energy method with regard to viscous and viscoelastic devices is illustrated. Then, the concept of the state of a system, the definition of the state space and its properties are discussed. Finally, with reference to both single-degree-of-freedom that multi-degrees-of-freedom systems the representation of their dynamic response in state space is illustrated.

This chapter deals with the theory of viscoelasticity and the discrete models such as, for example, the Kelvin and Maxwell models. The aim of this chapter is to assess the dynamic behavior of viscoelastic dissipative bracing systems taking into account the presence of the brace. In fact, the viscoelastic damper is modeled as the Kelvin model, whose behavior is dependent, in itself, on frequency; the viscoelastic damper-brace component can be studied through the Poynting-Thomson model which presents even more dependence on the frequency. Similarly, the viscous (linear or non-linear) damper-brace component can be studied through the Maxwell model, characterized by a frequency dependent dynamic response. In both cases, because of the frequency dependence, in the dynamic field, dynamic “reduced” magnitudes correspond to the static magnitudes of the viscoelastic dissipative bracing system, in other terms, between the static and dynamic behavior, there is a reduction in the effectiveness of the viscoelastic dissipative bracing system.

This chapter deals with the integrated design of the elastic structural system and the viscoelastic dissipative bracing system to achieve an expected seismic design displacement. The variables that characterize the design problem, their domain and the steps of the proposed methodology are illustrated and commented in details by taking into account the concepts described in the previous chapters. A set of seven historical unscaled acceleration records is selected to develop dynamic analyses by testing the proposed integrated design methodology. With reference to an equivalent SDOF integrated system, a cost index, assumed as an optimized objective function and defined on the design variables, is described in order to find the optimal design in economic terms, or rather, the economically optimal combination of the design variables for each expected seismic target performance. Finally, the extension of the results, developed on the substitute structure, to a viscoelastically and proportionally damped MDOF framed integrated system is explained in order to design the least expensive regular system.

This chapter deals with the proposed parametric analysis of the integrated design methodology by considering the set of acceleration records selected in the previous chapter. With reference to an equivalent SDOF integrated system, starting from the evaluation of the average displacement spectrum, combinations of the design variables, which are the lateral stiffness of the structural system, the static stiffness and the static damping coefficient of the viscoelastic dissipative bracing system, are evaluated for different values of the period of the system and of the seismic design displacement considered. Subsequently, the minimum of the cost index is searched for each group of cost ratios in order to find the optimal values of the design variables. This is followed by an economic comparison between the optimal integrated structural/control system and the optimal elastic braced structural system or the optimal elastic unbraced structural system without dampers for each target performance. In the last part, a validation of the proposed procedure is performed by verifying that an optimal single-degree-of-freedom integrated system achieves the expected seismic design displacement. Finally, the extension of this methodology to a proportionally damped multi-degrees-of-freedom framed integrated system is developed on the basis of specific hypotheses to demonstrate the effectiveness of the proposed integrated design methodology.