5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

Earthquake duration effect on the nonlinear response of MDOF system using a new version of Incremental Dynamic Analysis

(IDA)

Ahmad Nicknam1, Azad Yazdani2, Kian Saeedi2 1- Assistant Prof., Department of Civil Eng., Iran University of Science & Technology

2- Assistant prof., Department of Eng., University of Kurdistan 3- M.Sc. student, Department of Civil Eng., Iran University of Science & Technology

A_Nicknam@iust.ac.ir A.Yazdani@uok.ac.ir

kian_saeedi@CivilEng.iust.ac.ir

Abstract In this article we introduce a new version of Incremental Dynamic Analysis (IDA) by which the effect of earthquake duration on the nonlinear dynamic response of the structure seems to be more obvious. We believe that the input energy of earthquakes is a better Intensity Measure (IM) than the spectral acceleration in first mode of the structure vibration (Sa(T1,5%)) for the study of duration effects. We used artificial acceleration time-histories simulated by the specific barrier model modified slightly for this study as well as real records apropriately selcted. Results confirm our proposed aproach. Keywords: strong motion duration, incremental dynamic analysis, artificial earthquakes.

1. INTRODUCTION

The emergence of computers with high computing power, speed and accuracy on the one hand and the need to design irregular, uncommon and important structures on the other hand, leads the engineers to perform the nonlinear analysis such as the well known Incremental Dynamic Analysis approach (IDA). In this method the nonlinear dynamic analysis for the structure is performed using the acceleration time histories which are scaled appropriately and the maximum interstory drift ratio is plotted versus the Intensity Measure, thus the linear and nonlinear responses of the structure and structural collapse are evaluated [1].

One of the important parameters in the study of earthquake records is the strong motion duration. In this study the effects of the earthquake duration on the damage measure (DM) for the MDOF system is calculated and assessed. Since it is not always likely to find enough real earthquake records satisfying the conditions needed for this study, analysis is performed using the generated records compatible to the source, path and site soil condition as well as real records selected appropriately.

For our purpose, primarily some earthquakes (acceleration time histories) having certain durations, the same site soil type which the structure is designed for, and a variety of the magnitudes and distances are simulated, then the a 9story SMRF structure is modeled using the DRAIN-2DX code and the IDA analysis is performed. It seems that, the dependence of the damage measure on earthquakes’ durations is more cleared if the input energy of the earthquakes is selected as the intensity measure in IDA procedure.

2. STRONG MOTION DURATION Empirical observations and analytical studies show how cyclic structural damage is related to energy released during ground shaking. More than 30 definitions of seismic duration are available in literature [2] trying to measure such damage potential [3–5]. Trifunac and Brady [6] define the effective duration tD as the time interval between the 5 and 95% of the root mean square acceleration (RMSA).

5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

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The latter is shown in Equation (1) where tE is the total duration of the seismic event (1)

In this study we use two groups of real records the same as the reference [7]. Iunio Iervolino and Gaetano Manfredi (2006) defined an Index for the duration of earthquakes as

(2)

Then they selected some real records in narrow bins of ID, we use their two groups of bins with ID=5 and ID = 22. The selected time histories are shown in Table 1.

Table 1- real earthquakes selected for analysis[7]

tD , tn are durations according to Trifunac & Novikova and Trifunac & Brady respectively[1]. Since it is

not always likely to find enough real records satisfying the conditions of source, path and site effects of the concerned region, we decided to simulate artificial earthquakes which can be compatible better to our certain conditions and compare the results with real earthquake records.

3. SIMULATING ARTIFICAL TIME-HISTORIES We simulated two groups of time-histories using the SGMSv5 code which uses the Specific Barrier Model of source spectra and accounts for path and site conditions as well [8]. As this code originally is calibrated for the region which the structure is designed for, we just modified the code so that the simulated time histories have certain durations, independent of other parameters. In the original code the duration of the simulated time-history is related to corner frequency and distance from source to site [8]. So we choose reasonable ranges of magnitude and related duration to be sure that our simulated acceleration time-histories are physically reasonable. Two groups are the same in the distance and magnitude while different in durations; duration is 15 seconds for the first group and 25 seconds for the other. 10 time-histories are simulated for each group of duration, so we have 40 time-histories 20 of them real and 20 artificial. The selected magnitude and distances for artificial earthquakes are shown in Table 2.

5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

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Table 2- magnitudes and Distances for simulation of time-histories Record number Magnitude Distance 1 6.5 30 2 6.7 20 3 7 55 4 7.2 35 5 7.3 90 5 6.2 80 7 7.5 100 8 6 70 9 6.4 45 10 7.9 75

4. INCREMENTAL DYNAMIC ANALYSIS The well known incremental analysis method (IDA) was a powerful approach in studying the nonlinear response of multi degree of freedom (MDOF) structures due to dynamic loads during the past decade because of its fewer theoretical problems than the static push-over, such as the loading pattern and distribution of the base shear along the height of the structure. In this method each earthquake acceleration time-history is scaled to appropriate increasing levels of intensity measure (IM) and the nonlinear response of the structure is calculated for them and the Demand Measure (DM) is plotted versus the IM thus a response curve is obtained which is called IDA curve [1]. In conventional IDA method it is common to select the spectral acceleration in the first mode of structure and damping of 5 % ( Sa(T1,5%)) as the IM and the Demand Measure (usually max interstory drift ratio) is plotted versus the IM. As it was discussed by Iunio Iervolino and Gaetano Manfredi [7] for SDOF systems selecting these IM and DM is not suitable for studying the effect of duration, and the conventional IDA curves can not distinguish between varying durations. In this study we see it is true for MDOF systems too and we suggest to select the input energy of the earthquakes as the IM to see the effects more obviously. The input energy of the earthquakes here is defined as Specific Energy Density by equation 3

(3)

A 9-story steel moment resisting frame structure is selected as a case study. The plan and lateral load resisting frame is shown in Figs 1 ,2. The loading is similar to table 3 and the steel behavior is considered to be bilinear with 3 % of hardening shown in Fig 3.

Figure 1. Plan of the 9-story building[9]

5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

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Figure 2. lateral load resisting frame of the 9-story building[9]

Figure 3. bilinear behaviour of steel[7]

Table 3- considered loading for the structure[9]

This structure is modeled by DRAIN-2DX code, it has a period of 2.24 seconds and the analysis is performed based on this model.

5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

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M

5. ANALYSIS AND RESULTS The results of the analysis for the real and simulated earthquakes using both the conventional IDA method and our proposed method are shown in Figs 3, 4. Fig 3 shows the comparison between conventional IDA curves and our proposed new IDA curves for the ID=22 group of real records and the 15 seconds duration group of simulated time-histories. Figure 4 shows the median IDA curves summarized for each group. As mentioned before the median IDA curves of the conventional method do not show a meaningful difference or trend depending on duration changes.

(a)

(b)

Figure (3) comparison of conventional IDA and our method’s curves (a) real records ID =22 (b) simulated records T=15 sec

In figure 5 the summarized median curves of our proposed approach of IDA are shown for both real and simulated earthquakes. As we expected the energy based IM can be a better alternative for the IM and we can see the effect of the earthquake duration on the seismic demand of the structures more obviously. Note that IDA curves don’t have physical meaning for the drift ratios above 0.1, because in the literature it is mentioned that the CP performance point should not be considered above this limit [1] thus we should compare the results up to this point. It is clearly seen that there is no meaningful difference or trend in the conventional median curves up to the drift ratio of 0.1, that is, the performance of the structure is the same for earthquakes having different durations. But by considering the median curves of our proposed method we can see the effect of duration more obvious in the nonlinear region of the curves. The structure has a lower performance against the earthquakes of longer durations than the shorter ones. As it could be predicted, by increasing the duration, structure reaches its capacity limits in lower energy levels that mean the duration has a harmful effect on the structures.

5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

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(a) (b)

Figure (4) median of conventional IDA curves (a) simulated records (b) real records

Figure (5) Median of our new IDA curves for simulated and real earthquakes

5. CONCLUSIONS In this paper we proposed a new Intensity Measure (IM) for the Incremental Dynamic Analysis (IDA) method to study the effect of the ground motion duration on the nonlinear dynamic response of the MDOF systems. As it is known the most obvious effect of the duration is on the energy content of the earthquakes, so we select the input energy of the earthquake as the intensity measure instead of the conventional Sa(T1,5%). This selection seems to be promising as we could see the duration effects more clearly. Moreover it has the advantage of considering the effect of all vibration modes of instead of only the first mode therefore would be a better IM for the high structures particularly those with irregularity.

5th National Congress on Civil Engineering, May 4-6, 2010, Ferdowsi University of Mashhad, Mashhad, Iran

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6. REFERENCES

1. Dimitrios. Vamvatsikos and C.Allin Cornell "Incremental Dynamic Analysis", Department of Civil and Environmental Engineering, Stanford University, CA 94305-4020, U.S.A.

2. Bommer J, Magenes M, Hancock J, Penazzo P. The in_uence of strong-motion duration on the seismic response of masonry structures. Bulletin of Earthquake Engineering 2004; 2:1–26.

3. Uang CM, Bertero VV. Evaluation of seismic energy in structures. Earthquake Engineering and Structural Dynamics 1990; 19:77–90.

4. Malhotra PK. Cyclic-demand spectrum. Earthquake Engineering and Structural Dynamics 2002; 31:1441–1457.

5. Kunnath SK, Chai YH. Cumulative damage-based inelastic cyclic demand spectrum. Earthquake

Engineering and Structural Dynamics 2003; 33:499 –520. 6. Trifunac MD, Brady AG. A study on the duration of strong earthquake ground motion. Bulletin of

the Seismological Society of America 1975; 65:581– 626.

7. Iunio.Iervolino,Gaetano.ManfrediandEdoardo.Cosenza"Ground motion duration efects on nonlinear seismic response" Earthquake Engng Struct. Dyn. 2006; 35:21–38

8. Papageorgiou AS, Aki K. A specific barrier model for the quantitative description of inhomogeneous faulting and the prediction of strong ground motion, Part I: description of the model. Bull Seismol Soc Am 1983;73:693–722.

9. Nicolas Luco, Probabilistic seismic demand analysis, SMRF connections, fractures, and near-source effects, doctoral thesis, June 2002