Report - PEER - University of California, Berkeley

In Fig.2 the quantities relevant for the seismic response of an ideal elasto-plasticSDOF system can be visualised. Seismic demand is expressed in terms ofaccelerations and displacements, which are the basic quantities controlling the seismicresponse. Demand is compared with the capacity of the structure expressed by thesame quantities. Fig.2 helps to understand the relations between the basic quantitiesand to appreciate the effects of changes of parameters. The intersection of the radialline corresponding to the elastic period of the idealised bilinear system T with theelastic demand spectrum S ae defines the acceleration demand (strength) required forelastic behaviour, and the corresponding elastic displacement demand S de . The yieldacceleration S ay represents both the acceleration demand and capacity of the inelasticsystem. The reduction factor R is equal to the ratio between the accelerationscorresponding to elastic (S ae ) and inelastic systems (S ay ). If the elastic period T islarger than or equal to T C , which is the characteristic period of ground motion, theequal displacement rule applies and the inelastic displacement demand S d is equal tothe elastic displacement demand S de . From triangles in Figs.1 and 2 it follows that theductility demand µ is equal to R. Fig.2 also demonstrates that the displacements S ddobtained from elastic analysis with reduced seismic forces, corresponding to designacceleration S ad , have to be multiplied by the total reduction factor, which is theproduct of the ductility dependent factor R and the overstrength factor, defined asS ay /S ad . The intersection of the capacity diagram and the demand spectrum, called alsoperformance point, provides an estimate of the inelastic acceleration and displacementdemand, as in the capacity spectrum method. This feature allows the extension of thevisualisation to more complex cases, in which different relations between elastic andinelastic quantities and different idealisations of capacity diagrams are used, e.g., forinfilled frames (see Fig.7a). Unfortunately, in such cases the simplicity of relations,which is of paramount importance for practical design, is reduced. Note that Fig.2does not apply to short-period structures.Fig.2 can be used for both traditional force-based design as well as for theincreasingly popular deformation-controlled (or displacement-based) design. In thesetwo approaches, different quantities are chosen at the beginning. Let us assume thatthe approximate mass is known. The usual force-based design typically starts byassuming the stiffness (which defines the period) and the approximate global ductilitycapacity. The seismic forces (defining the strength) are then determined, and finallydisplacement demand is calculated. In direct displacement-based design, the startingpoints are typically displacement and/or ductility demands. The quantities to bedetermined are stiffness and strength. The third possibility is a performanceevaluation procedure, in which the strength and the stiffness (period) of the structurebeing analysed are known, whereas the displacement and ductility demands arecalculated. Note that, in all cases, the strength corresponds to the actual strength andnot to the design base shear according to seismic codes, which is in all practical casesless than the actual strength. Note also that stiffness and strength are usually relatedquantities. All approaches can be easily visualised with the help of Fig.2.360