INELASTIC SEISMIC RESPONSE OF ASYMMETRIC STRUCTURES

Abstract

Asymmetric structures when subjected to earthquake ground motion will undergo torsional vibration in addition to lateral oscillations. In elastic region, the lateral-torsional coupled response is characterized by the structural eccentricity, uncoupled frequency ratio (UFR) and damping. In inelastic region, the force-deformation characteristics of the lateral resisting elements are the added system parameters. The observations made by various researchers regarding inelastic torsional response of eccentric system are contradictory and do not provide a satisfactory design criterion. The effects of uncoupled frequency ratio (UFR) on inelastic response have not been understood and UFR has been defined in three different ways. Till 1990, a single system was used by the researchers which cannot represent all types of eccentric structures occurring in practice. Later, a set of nine single storey model was introduced. When a structure is excited well into the inelastic range and an element yields, the centre of resistance no longer remains constant. The past studies have considered strength eccentricity as a constant parameter and concluded that the strength eccentricity cannot be an effective criterion. This is not true. The key is to consider a variable strength eccentricity based on the system parameters to account for different types of eccentric systems. The main objectives of this study are to critically review the codal provisions to assess the additional ductility demand on eccentric systems and to develop improved torsional provisions that account for system parameters related to stiffness and mass distribution. iv Nine generalized single-storey mono-symmetric three element models representing a wide range of stiffness distribution of asymmetric structures are identified. SOOE component of the El Centro earthquake of 1940 is used for seismic response which is still considered to be a very severe earthquake. The equations of motion are solved by step by step integration method. The effects of uncoupled frequency ratio and its various definitions on inelastic torsional response of asymmetric systems are investigated. A mass distribution representative of that in real buildings is identified. The maximum values of mass eccentricity for regular eccentric and irregular eccentric buildings are estimated. The range of variation of eccentricity is limited accordingly. It is shown that the torsional response of all types of eccentric systems with UFR equal to 1.0 is not critical as assumed in most of the previous studies. Therefore, determination of UFR for each eccentric system according to proposed mass distribution is necessary. Using the generalized models, the torsional provisions given in Uniform Building Code of U.S.A 1991, New Zealand Code (NZS-4203) 1992, National Building Code of Canada 1990, Mexican Code 1987 and Bureau Of Indian Standard (IS-1893) 1984 are critically examined. The current torsional provisions in the seismic codes based on the design coefficients a, £ and 5 do not consider all the system parameters except for structural eccentricity. Thus they lead to non-uniform distribution of the additional ductility demand on the elements. Therefore, they do not provide an economical solution. Nine generalized models with three different uncoupled lateral time periods (0.25 sec, 1.0 sec and 2.0 sec) are considered to investigate the effects of strength eccentricity on additional ductility demand on edge elements. The value of structural eccentricity is varied at 1/10 interval and the value of strength eccentricity is varied at 1/6 interval. Thus, a total of 27x11x6 analyses are carried out resulting in 27x11 sets of curves of ductility ratio of rigid-edge-element (REE) and flexible-edge-element (FEE) against normalized strength eccentricity. The intersection of ductility ratio curves of REE and FEE is referred to as effective strength eccentricity. It is found to be a function of structural eccentricity, stiffness eccentricity, torsional stiffness and uncoupled lateral time period of the system. The locus of these intersection points is used to derive the expression for effective design eccentricity that accounts for system parameters mentioned above. A procedure independent of design eccentricity is proposed for providing the additional strength to the system and its distribution among the elements. It permits greater freedom to the designer. The additional ductility demand on the elements of the systems designed based on the proposed formulation is almost nil, that is, much less than that given by Uniform Building Code of U.S.A. 1991, New Zealand Code (NZS-4203) 1992 and is comparable with that of National Building Code of Canada 1990. The overall increase in the strength of the system is least for the proposed formulation, while National Building Code of Canada 1990 requires consistently maximum increase in the overall strength of the system. The proposed formulation provides an effective and economical solution for the design of eccentric systems compared to those given by the various codes.