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2.4 Computing the drift capacityIf dynamic behaviour is taken into account, the drift capacity of a structure depends on theearthquake record. As stated above, the 1991 Uttarkashi (as captured from station: Bhatwari)and 2001 Bhuj (as captured from station: Ahmedabad) earthquake ground motion records(Fig. 2) are adopted in this paper. Both of these events predate the current edition of IS 1893.Non-linear dynamic analysis for each earthquake record is run from a very small value ofSa to the value of Sa where the structure collapses. The drift capacity of the structure, usedto identify the point of collapse, is computed as follows (Yun et al. 2002): 1. Elastic time history analysis (Chopra 2002) is performed on an accelerogram recordwhich produces a point on an Sa—IDR graph. The slope of the straight line joining thispoint and the origin gives the elastic slope of accelerogram (Se).2. Similarly, Se corresponding to other accelerograms are found and the median elasticslope is obtained.3. Non-linear time history analysis of the building subjected to the relevant accelerogramis performed. The points are plotted on the Sa-IDR graph.4. Drift capacity of the structure is determined from the slope of the above curve (subjectto certain limiting conditions) as described below (Fig. 3), and is measured in terms ofIDR.In Fig. 3, Line 1 represents the line whose slope is equal to the median elastic slope (Se).Lines 2 and 3 represent the two rather extreme cases that may arise during an IDA run. It isoften seen that on scaling the record beyond a certain level, many members start failing inquick succession. Line 2 represents this case. Due to progressive degradation of the stiffnessmatrix, the slope of Sa versus IDR curve decreases. The structure is assumed to have failedas soon as the slope drops below a limiting value (in the range 0.2Se ∼ 0.3Se)—in this paperwe have taken the limit conservatively as 0.3Se. Nevertheless, the drift capacity computedthis way must be limited to 0.10. Line 3 shows another case in which structural members donot fail in quick succession. As a result, the Sa versus IDR curve remains fairly linear and itsslope does not deviate much from Se. For this case as well, structural failure is said to occurwhen IDR reaches a value of 0.10.3 Seismic investigation of three lowrise steel framesIn this section, we analyse the seismic capacities of three steel moment frames designed to ISstandards (members are designed as laterally unsupported). All are assumed to be located inzone V. The allowable deflections, moments and shears (per IS codes) for the three buildingsare ascertained first; the corresponding demands (per IS codes and using equivalent base shearin static pushover analyses) are computed. The demands under two real earthquake records(Fig. 2)—Uttarkashi and Bhuj—are obtained through a full dynamic analysis. Finally, thevalues of deflection, moment and shear in the frames corresponding to first yield and col-lapse are computed through incremental dynamic analysis. The capacities and demands arecompared at the end and a critical appraisal of the codal provisions is made in Sect. 4. 3.1 Single storeyed portal frameA simple portal steel moment resisting frame (a one storey one bay frame with columnheight 4m and beam length 6m) located in Zone V, designed according to the current IScodes (BIS 2002, 2007), is taken as our first example (Fig. 4). The natural period of thestructure is 0.374 s. Pushover analysis of the structure, time history analysis as well as Incre-mental Dynamic Analysis are performed as described below. The building is assumed to bean industrial building with no crane load. The structural steel has a yield stress of 250MPa.As per IS1893:2002, the design base shear coefficient (Ah) is 0.09. The factored seismicweight of the structure is 117 kN, giving the value of design base shear (Vb) as 10.5 kN.As the structure is a single storeyed portal frame, this entire load is applied to the upperleft node of the frame and the structure is designed as per this load. The column and beamsections thus obtained are ISMB 200 and ISMB 300 respectively. The horizontal deflectionis 3.2mm based on elastic analysis whereas the allowable value is 16mm (= height/250).Other codes specify different criteria for deflection. The Immediate Occupancy level inSAC-FEMA (2000) corresponds to IDR = 1% which amounts to storey height/100. Euro-code EC8 (Marino et al. 2005) presents a drift limit of 1%for structureswith no non-structural 3.1.1 Pushover analysisIDARC, with its force control option, is used for pushover analysis of the portal frame. Thestructural response is fairly linear up to Ah = 0.64 beyond which the response becomesnon linear and finally the structure fails (Fig. 5), failure being defined as the point when thestiffness matrix no longer remains +ve definite. The structural drift at the last known safestate (Ah = 1.07) is 30%.The structural drift at the design value of Ah = 0.09 (which occurs at the design shearof Vb = 10.5 kN) is 3.2mm. The deflection limit as per IS code of 0.4% is reached whenAh = 0.46 or Vb = 53.5 kN. First yielding of the structure (at Ah of 0.64 and IDR of 0.56%i.e., a peak displacement of 22.4mm) occurs at the bottom of the right column. 3.1.2 Time history analysisIn order to estimate the seismic demands more accurately, we now perform time historyanalysis of the structure subjected to Uttarkashi and Bhuj earthquake records.More accurateestimates of the corresponding capacities, both at yield and at collapse, are estimated laterfrom an incremental dynamic analysis of the structure.A bilinear hysteresis stress strain model is selected for performing the time history analy-sis. Coefficient of damping is chosen to be 5%. The analysis is run for 60 s for Bhuj and 20 sfor Uttarkashi (Figs. 6, 7).For Bhuj (Uttarkashi) ground record, the peak base shear (Fig. 6) in the portal frame (Vb)is found to be 46.4 kN (39.0 kN) at time 40.3 s (4.56 s), and the peak displacement (Fig. 7)is found to be 0.195% (0.29%) also at time 40.3 s (4.56 s). The figures in parenthesis in theprevious sentence refer to the Uttarkashi ground record.Detailed results, for both Bhuj and Uttarkashi records, are summarized in Table 2.Thesewill be discussed in detail along with the results of the other two structures, in Sect. 4.3.1.3 Incremental dynamic analysisAs discussed in Sect. 2.4, failure of a dynamically excited structure can also be given in termsof Sa and the structural capacity in terms of drift ratio is presented here. We keep linearlyamplifying the record and thus incrementing the IM (Fig. 8). The first yielding for Bhuj record anywhere in the structure occurs for an Sa of 0.88 g (at centre of the beam).