Response of tall Steel Moment Resisting Frames (SMRF) to near-fault pulse-like ground motion

Transcription

1 Resonse of tall Steel Moment Resisting Frames (SMRF) to near-fault ulse-like ground motion R. Ruakhety & R. Sigbjörnsson Earthquake Engineering Research Center (EERC), University of Iceland SUMMARY: his contribution describes a study on the elastic resonse of tall buildings subjected to near-fault ulse-like ground motions, with secial emhasis on the relative imortance of different vibration modes, and their deendence on the redominant eriod of such ground motion. Generic elastic Steel Moment Resisting Frames (SMRF) are analyzed using a set of ground motion records. It is found that the eak inter-storey drift demands of the SMRF models increase as the fundamental eriod of the SMRF aroaches the dominant ulse eriod. Higher mode contributions to eak inter-storey drifts are found to be significant at the uer storeys of the frames, more so for the taller ones. Equivalent ulses, which have been suggested in the literature to reresent near-fault ground motion are found to be inat to simulate the higher mode resonse deficient in redicting both the eak inter-storey drift as well as its distribution along the height of the frames. Keywords: near-fault ground motion, inter-storey drift, higher mode resonse, tall moment resisting frames. I RODUCIO Near-fault ground motions recorded in the forward directivity region contain strong velocity ulses. he concentration of seismic energy in one or a few cycles of strong ulses has an imulsive imact on structures, otentially causing severe damage. his otentially imulsive behaviour became evident after strong earthquakes in the ast, for examle, the 994 Northridge, the 995 Kobe, and the 999 Chi-Chi earthquakes. Evidence of near-fault related damages to engineering structures have been documented since over 60 years. Benioff (955), for examle, reorted strong seismological evidence of near-fault henomenon in exlaining the intensity atterns observed after the 952 Kern County, California, earthquake. Some other studies concerning damaging effects of near-fault ground motions are those of Westergaard (933), Mahin et al. (976), Bertero et al. (978), Anderson and Bertero (987), and Hall et al. (995). Due to the imulsive nature of near-fault ground motions, researchers have used simle mathematical ulses to model them. he use of simle ulses in studying the dynamic resonse of structures has a long history, for examle, Biggs (964) used one-sided ulses of rectangular, triangular, and ram-like shaes to evaluate elastic as well as inelastic resonse of single degree of freedom (SDOF) systems. Biggs found that the ulse amlitude and duration relative to the eriod of vibration of SDOF system are the two imortant arameters controlling the eak elastic resonse. Several mathematical models of simle ulses intended to reresent salient features of near-fault ground motions has since been used in the literature (see Ruakhety 200 for an overview of different models). Simle ulse models are mostly caable of simulating the eak resonse of SDOF systems at long eriods in general, at eriods larger than about 0.7 times the eriod of dominant ground-motion ulse. At shorter eriods, equivalent ulse models fitted to recorded ground motion tyically

2 underestimate the resonse. he satisfactory behaviour at long eriods has led some researchers to the conclusion that seismic resonse of building structures can be characterized by using simle ulse models (Mavroeidis and Paageorgiou 2003, Mavroeidis et al. 2004). Alavi and Krawinkler (2004) conclude that a reasonable equivalence between a near-fault ground motion and a ulse can be established in a range of / from , where is the fundamental eriod of a building, and is the dominant ulse eriod. he general notion that simle ulses may adequately reresent seismic resonse of SDOF systems is often extraolated to seismic resonse of multile degree of freedom (MDOF) structures. he main argument behind such extraolation is that a ulse model that sufficiently simulates the fundamental mode resonse is adequate (Alavi and Krawinkler 2004). Whereas this might be a reasonable hyothesis for low-rise structures redominantly resonding in the first mode of vibration, its validity for tall buildings with significant resonse contribution from higher vibration modes is questionable. his is because simle ulse models lack in describing high-frequency comonents of ground motion, and are therefore inadequate to simulate resonse of higher vibration modes. It is therefore imortant to study, in a systematic manner, how biased simle ulse models are in describing resonse of tall buildings subjected to actual near-field ground motion records. his study focuses on this task with secial emhasis on the relative imortance of higher vibration modes and to what degree they might influence the suitability of surrogating an actual ground motion by a mathematical ulse. In the following sections, the structural models used, the ground motion database, the comutational rocedure, and an overall analysis of the results are resented in sequence. 2. SRUCURAL MODEL Structural models used in this study are single-bay generic steel moment resisting frames (SMRFs). Four different frames with 9, 2, 5, and 8 stories are considered. A lumed mass equal to kn (200 kis) is assigned to each storey. he second moment of inertia of beam in a storey is ket equal to that of the columns suorting it. With this assumtion, the relative stiffness of beams and columns are tuned to obtain a constant drift along the height when subjected to the lateral forces secified in 0.8 IBC (2003). heir stiffnesses are then scaled to obtain a first mode vibration eriod of 0.07H (Goel and Chora 997), where H is the total height of the frame measured in meters. Classical daming model is assumed, and other details including the modal eriods, mode shaes, and modal daming ratios can be found in Ruakhety (2008). 3. GROU D-MOIO RECORDS he set of ground-motion records used in this study is a subset of the database described in Ruakhety (200). Only those records which contain a clear and dominant ulse in their velocity time series are considered. In addition, only forward-directivity affected records are used. he ulse model of Mavroeidis and Paageorgiou (2003) is fitted to each of the selected records. he fitted ulses are called equivalent ulses hereafter and serve to quantify the resonse due to the imulsive art of ground motion. Each of the 9-, 2-, 5-, and 8-storey frames is subjected to those ground motions which satisfy the criteria > 0.7. his results in 35, 43, 50, and 56 being used in structural analysis of the 9-, 2-, 5-, and 8-storey frame, resectively. he selected records are identified in able by their waveform identification numbers (WID) which can be found in Ruakhety (200).

3 able. Ground-motion records used in this study Number of storeys 9 List of WIDs, 2, 3, 4, 7, 24, 25, 26, 28, 29, 30, 32, 34, 65, 67, 68, 69, 70, 75, 76, 77, 80, 88, 89, 90, 9, 92, 93, 94, 95, 96, 97, 99, 00, 06 2 Same as above and 7, 8, 38, 42, 45, 46, 66, 78 5 Same as above and 5,, 2, 3, 5, 74, 79 8 Same as above and 6, 8, 0, 4, 6, 7 4. SRUCURAL A ALYSIS he resonse of the SMRFs subjected to ground motions listed in able is comuted by using modal suerosition method to be able to identify the contribution from individual modes. he resonse arameter of interest is selected as inter-storey drift ratio IDR as it is related to the story shears and serves as an imortant damage indicator of building structures subjected to strong ground motions. his resonse arameter is able to describe local damage at the story level. If ui( j, t ) reresents the lateral dislacement of storey j due to mode i as a function of time, the i th mode contribution of IDR is comuted as IDR i ( j t) ( j, t) ui, = 00 (4.) h where h is the storey height. By modal suerosition, the total interstory drift at story j can be obtained as ns IDR j, t = IDR j, t (4.2) ( ) ( ) i= i where ns is the number of storeys, which is also equal to the number of vibration modes ignoring the rotational inertia. he maximum IDR is obtained as ( ) ( ) IDRmax j = max IDR j, t (4.3) he time when the IDR is maximum at storey j is denoted as t j, and the contribution of mode i to IDR ( ) max j at storey j is given by δ i, j ( j) ( j) i( j) IDRi j, t if i= = sgn IDR j, t IDR j, t if i> (4.4) where the sgn [ ] oerator reresents signum function. he first mode contribution is always taken as ositive, and the contribution of higher modes is taken as ositive if it is in the same direction as the first mode contribution and vice versa. 5. RESULS In this section, we resent some examles of the results that highlight the contribution of higher vibration modes, and their relative imortance deending on the frequency content of ground motion. he results for a tyical ground motion are resented first, followed by an analysis of average results.

4 5.. Resonse to a tyical ulse-like ground motion he ground motion being considered is the strike-normal comonent of the 987 Suerstition Hills, USA, earthquake recorded at the PS station. A comarison between the recorded ground motion and the equivalent ulse is resented in Fig. showing ground velocity, seudo sectral velocity (PSV), and sectral dislacement (SD). he first mode eriods of the 9-, 2-, 5-, and 8-story SMRFs are shown with vertical lines from left to right resectively. he eriod of the equivalent ulse is 2.25 s. his record is selected because the ulse fitted to this record sufficiently simulates the eak resonse of SDOF systems having vibration eriod equal to the first mode eriod of all the four SMRFs. he total interstory drifts and the contributions of the first three modes of the 2-storey SMRF comuted using the actual record and the equivalent ulse are resented in Fig. 2. Figure. Strike-normal comonent of the 987 Suerstition Hills, USA, earthquake recorded at the PS station. he grey and black lines reresent the actual record and the equivalent ulse, resectively. he vertical lines from left to right reresent the fundamental eriods of 9-, 2-, 5-, and 8-story SMRFs. Figure 2. IDR along the dimensionless height of the 2-story SMRF subjected to the ground motion and its equivalent ulse shown in Fig.. he red, green, and blue bars reresent the contributions of the first, second, and third modes resectively. Maximum interstory drifts considering all modes of vibration are shown with the solid (for actual record) and dashed (for equivalent ulse) lines. Figure 2 shows that the contribution of second mode is significant. he second mode eriod of the 2- storey frame is 0.9s where the record PSV is as high as it is at its first mode eriod of 2.4s (see Fig. ). he effect of second mode causes the maximum interstory drift to migrate to the to floor. he ulse is able to cature the first mode resonse of the frame and therefore the total drift comuted by using the record and the ulse match each other in the lower half of the frame where the resonse is dominated by the first mode. he ulse underestimates the second mode resonse of the frame, and

5 therefore underestimates the maximum drifts in the uer half of the frame. Similar results were observed for other frames, which can be found in Ruakhety and Sigbjörnsson (20) IDR at the roof In this section, the accuracy with which simle ulses can redict the eak IDR at the roof of the 9-, 2-, 5-, and 8-story frames is investigated. Each frame is subjected to the above mentioned ground motion records. For each frame, the maximum interstory drift at the roof IDRmax( ns ) is comuted from Eqn. 4.3 by substituting j= ns. he maximum interstory drift at the roof corresonding to a ground k, r k, motion record k and its equivalent ulse are denoted by IDRmax( ns ) and IDRmax( ns ) resectively. he ability of the equivalent ulse to reresent a ground motion k is evaluated by comuting an error term( E k), which is defined as: E k k, r max k, max ( ns) ( ns) = IDR IDR (5.) A value of E greater than indicates that the ulse is redicting smaller interstory drift than the record. he errors introduced in IDR by using an equivalent ulse instead of an actual record are indicated in Fig. 3. he errors are lotted against the normalized eriod. he results indicate that the IDR at the roof comuted by using an equivalent ulse is, on average,.4 times smaller than that comuted by using an actual record. he errors dislay a decreasing trend with increasing values of /. his can be exlained by the fact that as the value of / increases, the higher mode eriods get closer to the ulse eriod where the ulse can adequately reresent the actual ground motion. he figure shows that the erformance of an equivalent ulse is satisfactory if the fundamental eriod of the frame is about.5 times larger than the ulse eriod. For the 9-, 2-, and 5-story frames considered here, this imlies that an equivalent ulse can adequately reresent an actual ground motion if the ulse eriod is smaller than.26s,.6s, and.9s resectively. Considering the relationshi between moment magnitude and ulse eriod resented in Mavroeidis and Paageorgiou (2003), these ulse eriods corresond to moment magnitudes of 6.0, 6.2, 6.4, and 6.5 resectively. his observation leads to the conclusion that simle ulse models cannot adequately reresent recorded ground motions of large earthquakes in the eriod range of the frames considered in this study, i.e., those having first mode eriods less than 3.3s. his also indicates the imortance of highfrequency comonents of near-fault ground motion in the total resonse of tall buildings. Figure 3. Errors in the comutation of interstory drift ratio at the roof of 9-, 2-, and 5-story SMRF due to the use of an equivalent ulse instead of an actual ground-motion record.

6 5.3. Height-wise distribution of inter-storey drifts In this section, the height-wise distribution of inter-storey drifts of SMRFs and its deendence on the fundamental eriod of the frame relative to the ulse eriod is investigated. For each frame, maximum inter-storey drift at each storey is comuted for the corresonding records and their equivalent ulses. hese results are divided into three grous satisfying the conditions 0.7 <.3,.3 < 2.0, and 2.0, resectively. he mean value of the maximum interstory drift is denoted by δ.he results are resented in Fig. 4. It is observed that the inter-storey drift is the largest for the first grou of ground motions where the fundamental eriod of the frame is within times the ulse eriod. his case is shown with blue lines in Fig. 4. For this case, the drift demand along the height of the frame remains almost constant excet at the to 30% of its height where higher mode contributions become imortant. Because the higher mode eriods in this case lie in the region where the ulse PSV is much smaller than the record PSV, the inter-storey drift demands redicted by the ulses are dominated by the first mode. his exlains why the ulses underestimate inter-storey drift demands at the higher stories of the frames. As the fundamental eriod of the frame is increased to.3-2 times the ulse eriod, the first modes of the frames are excited by ground-motion comonents with smaller amlitudes and therefore the drift demands decrease. On further increasing the fundamental eriod of the frames relative to the ulse eriod, drift demands reduce further. It can also be observed that the location of maximum inter-storey drift along the height of the frame migrates towards the to of the frame if is relatively larger than. his haens due to larger contributions from higher modes; when the first mode eriod is much larger than the ulse eriod, the higher mode eriod aroaches the ulse eriod where the ground motion is characterized by larger amlitudes. he differences between the inter-storey drifts redicted by an actual records and their equivalent ulses are the smallest for the third grou of ground motions with > 2.0. Figure 4. Mean interstory drifts of the 9-, 2-, and 5 -story SMRF. he solid and the dashed lines reresent the results obtained by using the actual records and their equivalent ulses resectively. Blue, red, and green lines corresond to 0.7 <.3,.3 < 2.0, and 2.0, resectively. 6. CO CLUSIO S It is found that the higher mode contributions to maximum interstory drifts of tall frames subjected to near-fault ground motions are imortant. he imortance of higher modes is larger at the uer ortions of the frame and increases as the height of the frame increases. Maximum interstory drifts deend strongly on the ratio of the fundamental eriod of vibration of the frame and the ulse eriod. When the fundamental eriod of the frame is close to the ulse eriod, interstory drift demands are larger than when it is much larger or much smaller than the ulse eriod. Simle ulse models as the

7 one used in this study are not caable of simulating the higher mode resonse of tall structures. It is found that the accuracy with which a simle ulse model can reresent an actual ground motion deends on the fundamental eriod of the frame relative to the ulse eriod. On average, simle ulses result in elastic interstory drift demand.4 times smaller than actual near-fault ground motions. For a simle ulse to adequately simulate the elastic interstory drift demands of a tall frame, the fundamental eriod of vibration of the frame has be to at least.5 times larger than the ulse eriod. However, the most severely affected structures are those whose fundamental eriod is close to the ulse eriod. hese results indicate that simle ulse models might not be an adequate relacement for ulse-like ground motions to redict the elastic seismic resonse of tall buildings in the near-fault region. hese results, obtained for elastic structures, should not be extended to inelastic structures. Develoment of ductility in structural members, and the lengthening of vibration eriod due to inelasticity might result in the relative imortance of different modes of vibration that are different than those for elastic structures. In such cases, the initial elastic eriod of the building relative to the ulse eriod and the maximum ductility allowed in the structure will both lay an imortant role in determining the relative imortance of different modes of vibration. A systematic study of such systems with different models of inelasticity and their distribution in the structural system is currently being undertaken in order to extend the results resented here to inelastic building models. REFERE CES Alavi, B. and Krawinkler, H. (2004) Behavior of moment-resisting frame structures subjected to near-fault ground motions. Earthquake Engineering and Structural Dynamics 33:6, Anderson, J. C. and Bertero, V. V. (987) Uncertainties in establishing design earthquakes. Journal of Structural Engineering, ASCE 3:8, Benioff, H. (955) Mechanism and strain characteristics of the white wolf fault as indicated by the aftershock sequence. in Earthquakes in Kern County, Califormia During 952, ed. Oakesshott, G. B., Division of Mines, CA, Bertero, V. V., Mahin, S. A. and Herrera R. A. (978) Aseismic desgin imlications of near-fault San Fernando earthquake records. Earthquake Engineering and Structural Dynamics 6:,3-4 Biggs, J. M. (964) Introduction of strucutral dynamics, McGraw-Hill, New York Goel, R. K. and Chora A. K. (997) Period formulas for moment-resisting frame buildings. Journal of Structural Engineering 23:, Hall, J. F., Heaton,. H., Halling, M. W. and Wald D. J. (995) Near-source ground motion and its effects on flexible buildings. Earthquake Sectra :4, IBC (2003) International Building Code (IBC) International Code Council, Birmingham, Alabama Mahin, S. A., Bertero, V. V., Chora, A. K. and Collins, R. G. (976) Resonse of the Olive view hosital main building during the San Fernando earthquake. echnical Reort 976-0, Earthquake Engineering Research Center, University of California, Berkely. Mavroeidis, G. P. and Paageorgiou A. S. (2003) A mathematical reresntation of near-fault ground motions. Bulletin of the Seismological Society of America 93:3,099-3 Mavroeidis G.P., Dong, G. and Paageorgiou, A. S. (2004) Near-fault ground motions, and the resonse of elastic and ineasltic single-degree-of-freedom (SDOF) systems. Earthquake Engineering and Structural Dynamics 33:9, Ruakhety, R. (2008) Evaluation of equivalent ulses to redict the inelastic resonse of generic frames subjected to near-fault ground motions. Master s thesis, University of Pavia, Italy Ruakhety, R. (200) Contemorary issues in earthquake engineering research: rocessing of accelerometric data, modeling of ineasltic structural resonse, and quantification of near-fault effects. PhD thesis, University of Iceland, Reykjavik. Ruakhety, R. and Sigbjörnsson, R. (20) Can simle ulses adequately reresent near-fault ground motions? Journal of Earthquake Engineering 5:8, Westergaard, H. M. (933) Earthquake-shock transmission in tall buildings. Engineering ews Record 22:22,