See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/318529080 STUDY OF COMPARISON OF APPLYING MODES IN RESPONSE SPECTRUM ANALYSIS Conference Paper · April 2017 CITATIONS READS 0 517 3 authors: Kiran Somasundar M Rahul Leslie RMIT University Kerala Public Works Department 1 PUBLICATION 0 CITATIONS 14 PUBLICATIONS 21 CITATIONS SEE PROFILE SEE PROFILE Belarmin Xavier Amal Jyothi College of Engineering 5 PUBLICATIONS 1 CITATION SEE PROFILE Some of the authors of this publication are also working on these related projects: STUDY OF COMPARISON OF APPLYING MODES IN RESPONSE SPECTRUM ANALYSIS View project Pushover Analysis View project All content following this page was uploaded by Kiran Somasundar M on 19 July 2017. The user has requested enhancement of the downloaded file. STUDY OF COMPARISON OF APPLYING MODES IN RESPONSE SPECTRUM ANALYSIS Kiran Somasundar M1 P.G Scholar Department of Civil Engineering Amal Jyothi College of Engineering Kanjirappally kiran110493@gmail.com Rahul Leslie2 Belarmin Xavier3 Dy.Director DRIQ Kerala PWD Trivandrum rahul.leslie@gmail.com Assistant.Professor Department of Civil Engineering Amal Jyothi College of Engineering Kanjirappally belarminxavier@amaljyothi.ac.in Abstract— In the response spectrum analysis, the method prescribed for seismic analysis of multi-storied buildings in IS 1893(part-1)2002, like other similar codes, is the method of combining the modal responses, followed by combining them by the SRSS or CQC to obtain the final response forces for design. This method is referred to, by the authors, as the Indirect method, since it is not the modal loads that are combined, but the modal responses. One drawback often pointed out concerning this method is that the resulting responses lose their signs in the process of combination by SRSS (or CQC). One method to overcome this is known as 'Dominant mode signage', available in few of the analysis and design packages, like STAAD.Pro and MIDAS/Gen. In this paper, a new method of analysis is being investigated, referred to by the authors, as the Direct method, where, instead of combining the modal responses by SRSS, the modal (lateral) loads itself are combined by SRSS before applying on the building model. Keywords—modes, response spectrum analysis MIDAS) have come up with a „Dominant Mode signage‟ feature by which, after determining the forces (BM, AF, SF etc)by SRSSing those from individual modal force sets applies signs to those values with that of the results obtained from analysing for modal loads corresponding to that mode dominant in that direction Thus the results for the seismic analysis in X direction are the modal forces from each mode in X direction combined by SRSS and given the sign of the modal forces of that mode which is dominant in the X direction. Here a new approach is being investigated where, instead of analysis for the modal loads and SRSSing the results, the load themselves are combined by SRSS and applied as a single load on the structure This method, referred to here is the „Direct method‟, is at present recommended only for applying multi modal lateral loads for pushover analysis. II. METHODOLOGY I. INTRODUCTION The codal procedure recommended for Response Spectrum Analysis is referred in this report as the „Indirect Method‟, where the modal loads(ie, the set of lateral loads corresponding to each mode)are applied on the structure, one at a time and the modal forces(ie, the member forces obtained from the analysis for each modal loads(Bending moment BM, Shear force SF, Axial Force AF, etc )are combined by the SRSS(Square Root of Sum of Squares hereafter referred to as SRSS) The procedure has the drawback that, in case of columns, in the process of combination of modal forces from individual modes by SRSS, the interaction of AF‟s with its corresponding BM‟s from within each modal force set is lost, as AF‟s from all modal forces are combined, and finally the interaction is between the combined AF‟s and combined BM‟s Also in the process of combining by SRSS, the signs of forces (AF and BM) are lost, ending up with positive signs for all forces. As a probable solution to the latter (ie, loss of signs), some of the analysis‟ software packages (eg STAAD Pro and A. Response Spectrum Analysis Response spectrum analysis is performed using multimode responses, where the free vibration modes are computed using Eigen vector analysis. The modal parameters for a structure come as pairs of Natural Frequency f (in Hz) and Mode shape ∅ or time period T, which is its reciprocal(in s). The modal parameters for few of the lower frequencies are considered for further calculations (7 8 4 2, IS:1893(Part 1)-2002), based on the following. Modes for frequencies > 33 Hz need not be considered The number of modes considered should be such that the total mass participation factor should be at least 90% Missing mass correction for modes having frequency beyond 33Hz For the modal parameters considered, the following factors are determined for each mode • Mode participation factor of each mode Pk • Mass participation factor for each mode Mk • Spectral Acceleration coefficient (Sa/g) respective Earthquake forces. Then for each of these earthquake forces, we obtain respective Bending moments. These Bending moments are SRSSed to obtain a single Bending moment. The Design horizontal seismic coefficient Ah is calculated for each mode from (6 4 2, IS:1893(Part 1)-2002) Where,Z-Zone factor I-Importance factor Mode1 Mode 2 Mode 3 Mode 4 Mode 5 R-Response reduction coefficient Sa/g-Spectral Acceleration coefficient where the Horizontal acceleration Sa/g is determined from the Response spectrum curve (Fig 2,IS:1893(Part1)-2002) For each mode we calculate earthquake forces for each level We get respective bending moments for each mode and are SRSSed . Figure 1.Spatial Acceleration coefficient-Period Graph The lateral force due to the modal response (considering the mode participation factor) is obtained for each mode of all the modes considered The the force at each level for each mode is calculated as (7.8.4.5 (c), IS:1893(Part 1)2002) 2)Direct Method of Analysis:Consider five modes. For each mode we obtain respective Earthquake forces for each level. These forces are combined together to obtain a single Earthquake force and bending moment is calculated for this force. Ak -design horizontal seismic coefficient, calculated for mode k ∅ik -mode shape value for mode k for that floor level i Pk -mode participation factor for mode k Wi- mass at that floor level i B. Combination of modes 1)Indirect Method of Analysis: Consider five modes for a building. For each of the five modes, we can calculate Mode1 Mode 2 Mode 3 Mode 4 Mode 5 For each mode, respective earthquake forces are calculated and combined by SRSSing Table 2 : Time period and Frequency Perio d (sec) 0.694 0.222 0.123 0.085 0.065 Freq(Hz) 1.441 4.51 8.098 11.78 15.31 For kth mode, we should check for mass participation Bending moment Earthquake force. is calculated for this combined Where, n = no. of levels m = no. of modes Table 3 : Mass participation Mode Mk (kN) I II 115.5 16.31 III IV V 5.424 2.686 1.237 Mode participation factors are calculated thereafter Table 4 : Mode Participation 3)Dominant mode method: When activated, all modal combination results will have the same sign as when the dominant mode shape alone would have if it were excited and then the scaled results were used as a static displacements result. Mode I II III IV V Mk(kN) 115.5 16.31 5.424 2.686 1.237 Design horizontal seismic coefficient is given by, C. Calculations A lumped mass model is taken for the study having 23.57kN each.Rectangular plate of size 0.4x0.23 and 0.3x0.4 are taken for modelling.Height is 18 m with seven floors and plate thickness of plate is 0.1m.After applying the loads we obtain the modes shapes for each floor out of which we select five modes. 1 0 0.151 0.389 0.58 0.763 2 0 -0.53 -1 -0.98 -0.41 3 0 0.824 0.861 -0.24 -1 = 0.16 I = Importance factor =1 R = Response reduction coefficient =3 Earthquake force is calculated finally by Table 1 : Mode Shapes MODES> LEVELS V 1 2 3 4 5 Z = Zone factor 4 0 -1 -0.047 0.999 -0.285 5 0 1 -0.838 0.027 0.813 Time period and frequency is also obtained from software Combination of modes is explained earlier to get the final results. Period 0.693 0.221 0.123 0.084 0.065 Sa/g 1.441 2.5 2.5 1.1273 1.0979 Ah 0.0384 0.0667 0.0667 0.03 0.0292 Indirect method Direct method III. CONCLUSION The theoretical study of different types of application of modes gave different results. That is for the same Earthquake Forces acting on a structure, when applied in two methods gave different results. The advantage of the new methods (i.e., Direct method and Dominant mode method)will preserve the sign of the Bending moment and gives more accurate values. For checking the methods in an economical manner, we have to compare these methods with a time history analysis results and check which methods gives reinforcement Asc that is closer in values to the reinforcement required by the time History analysis. IV. 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