The storey forces (horizontal force, Qi ) are computed as per clause 7.7 of the code: 2.2 Pushover analysis based evaluation of structureNonlinear pushover analysis, or collapse mode analysis, is a simple and efficient techniqueto predict the seismic response of a structure often in lieu of a full dynamic analysis.A pushover analysis provides us with the capacity to monitor initial yielding and grad-ual post elastic plastic behaviour of both inpidual elements and overall structural system(Hasan et al. 2002). In pushover analysis the forces are applied incrementally in every stepuntil the design (or ultimate) force is reached. Using the results from this analysis, the actualnonlinear dynamic response of the structure can be estimated.The non linear pushover analysis in this work is performed using IDARC-2D with forcecontrol (Valles et al. 1996). It is assumed that no in-cycle strength degradation, and thus nonegative stiffness, occurs during the force control. Non linearity both in terms of geometryand material are incorporated. The controlling parameter of the analysis is the base shear(Vb): the analysis stops when the base shear exceeds its design/final value or if the structurecollapses before the design/final base shear Vb is reached. Structural collapse is defined byfailure of Cholesky decomposition of the stiffness matrix, which signifies that the matrix isno longer positive definite.IDARC uses the following system of equations to analyze the structure:[Kt ] { u} = { F} − { Pv} −  Pfr − { Phi } − { Piw} + Ccorr { Ferr } (5)where, [Kt ]= tangent stiffness matrix, { u} is the vector with the increment of lateral dis-placements; { F} is the vector with the increment in lateral forces; { Pv}, { Pfr }, { Phi },and { Piw} are the vector with the increment of forces in viscous dampers, friction dampers,hysteretic dampers, and infill panels respectively; Ccorr is a correction coefficient (usuallytaken as one); and { Ferr } is the vector with the unbalanced forces in the structure.IDARC uses a single step unbalanced force correctionmethod to deal with the unbalancedforce in static pushover analysis. The same approach is also taken in non linear dynamic anal-ysis, as discussed in the next subsection. The force increment is taken to be very small sothat the magnitude of unbalanced force (which is computed when moments, shear and stiff-ness are being updated in the hysteresis model) does not increase beyond acceptable limits(Au and Yan 2008).2.3 Incremental dynamic analysis (IDA) based evaluation of structuresIncremental dynamic analysis (Vamvatsikos and Cornell 2002) conducts a series of non lin-ear dynamic runs of the structure which can then be used to correlate the performance ofthe structure with the seismic demand. The method is highly efficient in terms of predictingthe response of the system and has become a valuable tool in seismic engineering. Simpleroptions like linear static procedure, linear dynamic procedure, non linear static procedure areavailable as given in SAC FEMA (Cornell et al. 2002). However, the degree of accuracy ismuchlesserthaninIDA.Incremental dynamic analysis procedure:Incremental dynamic analysis involves a series of non linear dynamic analysis of a structure.The basic steps are:-1. Select an intensity measure, IM: Intensity measure is a quantity used to describe theintensity of groundmotion ofwhich spectral acceleration, S is themost suitable variable. Sa corresponds to the first natural mode of vibration of the required structure and isobtained for a single horizontal component of earthquake (any one of the earthquakecomponents is sufficient). It is the maximum acceleration that the ground motion willcause in a linear oscillator with a specified natural period and damping. Strictly speak-ing, it is actually the “pseudo spectral acceleration”, defined as the spectral displacementtimes the natural frequency squared:Sa = Sdω2n (6)that is commonly used as a measure of spectral acceleration. However, the differencebetween the two is small enough (for a structure with light damping and short timeperiod) to be neglected (Chopra 2002).2. Select an engineering demand parameter,EDP:Also known as structural statemeasure,EDP is a quantity used to describe the relevant response of structure due to the prescribedseismic loading.Many EDPs are in vogue and its selection depends on the type of struc-tural assessment. For assessing structural damage, peak Inter-story drift ratio, IDR is thenatural choice as it is closely related to the damage caused to the structure (Chopra andGoel 2001). Local failure can be identified easily using IDR and hence this is selectedas the EDP in this paper. The dispersion for IDR is higher as IM increases.3. Increment IM: IMneeds to be incremented successively to capture the entire scenario ofstructural state- from elastic behaviour to its eventual collapse. There are various modelsproposed for increasing IM in repeated loops of which the method of scaling up therecord by a constant step and increasing the step size every run is used here. In thismethod, once non convergence is reached, analysis is performed at an IMin between thelast known convergent scaling up factor and the non convergent scaling up factor.4. Run the time domain analysis: The non linear dynamic analysis is performed usingIDARC-2d which uses a combination of Newmark-Beta integration and pseudo forcemethod. Non linearity both in terms of geometric and material are incorporated. Mate-rial non linearity is accounted by using bilinear hysteretic model (along with stiffnessdegradation, strength deterioration and slip lock). A bilinear hysteretic model suggeststhat as soon as hinge formation occurs at a particular node, it is unable to bear furtherloads i.e. its bending stiffness becomes zero. Mass proportional damping is adopted inthis paper.5. Obtain the EDP: Repeat step 2–4 until structure collapses6. Plot IM versus EDP: from above.The algorithm is described in Fig. 1.As in pushover analyses, IDARC uses a single step unbalanced force correction method todeal with the unbalanced force in non-linear dynamic analysis. The unbalanced force (whichis computed when moments, shear and stiffness are being updated in the hysteresis model)is applied at the next iteration. As mentioned in previous section this is not very accurateas it modifies the actual input loads. As a result when the magnitude of unbalanced forceincreases, so does the error in the model. The unbalanced force is correlated with the timestep for which the integration is performed, so if the time step is small enough, the methodgives quite accurate answers. For a general building, the time step should be smaller than0.005 s (Valles et al. 1996). 通过增量动态分析评估设计低层钢框架英文文献和中文翻译(3):http://www.youerw.com/fanyi/lunwen_56527.html