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Ground-motion scaling for seismic performance assessment of high-rise moment-resisting frame building
Soil Dynamics and Earthquake Engineering 94 (2017) 125–135
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Ground-motion scaling for seismic performance assessment of high-rise moment-resisting frame building
MARK
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Avik Samantaa, , Yin-Nan Huangb a b
Department of Civil and Environmental Engineering, IIT Patna, Bihta 801103, Bihar, India Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan
A R T I C L E I N F O
A BS T RAC T
Keywords: Ground motion scaling High-rise building Nonlinear analysis Seismic response Performance assessment Seismic hazard
Next generation performance-based earthquake engineering involves the use of a probability framework, which incorporates the inherent uncertainty and variability in seismic hazard, structural and non-structural responses, damage states and economic and casualty losses. One key issue in seismic performance assessment is the scaling of ground motions for nonlinear response-history analysis. In this paper, the impact of ground-motion scaling procedures, including 1) geometric-mean scaling of pairs of ground motions, 2) spectrum-matching of groundmotions, 3) first-mode-based scaling to a target spectral acceleration and 4) maximum-minimum orientation scaling, on the distributions of floor acceleration, story drift and floor spectral acceleration of a sample high-rise building is investigated using a series of nonlinear response-history analyses of a 34-story moment-resisting frame building. The advantages and disadvantages of each ground-motion scaling method are discussed for seismic performance assessment of a 34-story building.
1. Introduction The structural and non-structural damages observed during the 1989 Loma Prieta and 1994 Northridge earthquakes motivated expert practitioners and researchers to develop the first-generation tools for Performance-Based Earthquake Engineering (PBEE), such as those documented in FEMA 273 and 274 [1] and FEMA 356 [2]. The deterministic assessment procedures in those documents provided relations between structural response indices (such as story drifts and inelastic member deformations) and performance levels (such as immediate occupancy, life safety and collapse prevention) and shifted the focus of assessment from forces to displacements and deformations. FEMA 350 [3], which was drafted as part of the SAC Steel Project, extended the first generation tools through the use of probabilistic assessment procedures. In contrast to the first-generation tools for PBEE, where performance assessments are performed using a deterministic approach, the ATC-58 project in the United States develops next-generation tools and guidelines for performance-based seismic design and assessment using a probability framework, which can incorporate the inherent uncertainty and variability in seismic hazard, structural and non-structural responses, damage states and repair costs in the assessment process [4]. A significant amount of research work has been carried out for
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ground motion selection and scaling. Shome et al. [5] suggested that the scaling of ground-motion records to the 5%-damped target spectral acceleration for a given event (magnitude (M) and distance (R) pair) at the fundamental frequency of a structure is efficient to estimate the nonlinear response of the structure for the event. Baker and Cornell [6] considered Intensity Measure (IM) consisting of two parameters, spectral acceleration and epsilon (ε), at a given period to predict the response of a structure when selecting ground motions as ε was found to be an good indicator of spectral shape. Baker and Cornell [7] proposed a spectrum, namely, conditional mean spectrum – considering ε (CMS-ε), that accounts for the correlation in spectral accelerations at different periods and computes the spectral accelerations for a given M-R pair conditional to a given target spectral acceleration at the fundamental period of a structure (T1). PEER report 2009/01 [8] suggested selection of ground motions based on record properties (use the CMS for spectral shape, the proper inelastic spectral displacement target) to precise and accurate prediction of peak inter-story drift ratio response. Haselton et al. [9] proposed an alternative simplified method which allows the analyst to use a general ground motion set, selected without regard to ε, to calculate an unadjusted building collapse capacity by using nonlinear dynamic analysis, and then to correct this capacity using an adjustment factor to include the impact of the expected ε(T1) for the building site and collapse hazard intensity, Sa, col(T1). This eliminates the necessity of considering ε(T1) in selection of
Corresponding author. E-mail addresses: [email protected] (A. Samanta), [email protected] (Y.-N. Huang).
http://dx.doi.org/10.1016/j.soildyn.2017.01.013 Received 1 September 2014; Received in revised form 10 December 2015; Accepted 15 January 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.
Soil Dynamics and Earthquake Engineering 94 (2017) 125–135
A. Samanta, Y.-N. Huang
analysis of high-rise buildings because the loss contributed from shortand long-period spectral demands may both be significant. Scaling methods based solely on the spectral demand at the first-mode period may not be appropriate. Spectrally-matched ground motions to a uniform hazard spectrum (UHS) for a very wide period range may produce overly conservative results since 1) the short- and long-period spectral demands may be governed by different events and 2) the impact of the correlation in spectral demands at different periods is not included in the development of a UHS. The main objective of this paper is to study the impact of groundmotion scaling procedures on the distributions of structural responses of high-rise buildings. A series of nonlinear response-history analysis are performed for a 34-story moment-resisting frame building subjected to ground motions scaled using different methods, namely, 1) geometric-mean scaling of pairs of ground motions, 2) spectrummatching of ground-motions, 3) first-mode-based scaling to a target spectral acceleration, 4) maximum-minimum orientation scaling methods and 5) spectrum-matching method to study the contribution of higher modes. The impact of ground-motion scaling on seismic performance of high-rise building is discussed. We focus not only on the median values of the structural responses (e.g., peak floor acceleration, peak story drift and average floor spectral acceleration) but also on their dispersions.
the ground motion records. Jayaram et al. [10] indicated conventional dynamic structural analysis often involves scaling input ground motions to a target mean response spectrum. The variance in the target spectral acceleration is usually ignored, which can bias the structural response estimates. They proposed a computationally efficient and theoretically consistent algorithm to select and scale ground motions that match target spectral accelerations in both mean and variance. Weng et al. [11] proposed a multimode ground motion scaling (MMS) ground-motion scaling method which includes contributions from the dominating modes and uses the square root of the sum of the squares (SRSS) or complete quadratic combination (CQC) rule in the estimate of seismic demands. They conducted a series of nonlinear response-history analyses for sample low-, medium- and high-rise buildings and concluded that the MMS method is effective in reducing the dispersion in peak seismic demands. Kalkan and Chopra [12] have developed a modal-pushover-based scaling (MPS) method to scale ground motions for use in nonlinear response history analysis of buildings and bridges. The step by step method is useful for first mode dominant structures as well as for structures susceptible to higher mode effect. The MPS procedure has been evaluated (from the prospective of seismic design and not performance assessment) for low- and mid-rise buildings (four-, sixand thirteen story buildings) in the paper. Katsanos et al. [13] reviewed various methodologies developed for selecting appropriate records that can be used for dynamic analysis of structural systems in the context of performance-based design and observed that there are many ways to achieve record selection. They concluded that it is still difficult to limit the bounds of the ensuing structural response dispersion uniformly. NIST [14] provided recommendations related to selecting and scaling ground motions for design and performance assessment of low and medium-rise buildings, and discussed best practices for applying the current rules in building codes and standards. Huang et al. [15] studied four scaling methods, namely, 1) geometric mean scaling of pairs of ground motions, 2) spectrum matching of ground motions, 3) first-mode-period scaling to a target spectral acceleration and 4) scaling of ground motions per the distribution of spectral demands to see the impact of alternate ground-motion scaling procedures on the distribution of displacement responses in single-degree-of-freedom (SDOF) structural systems. The selection and scaling of ground motions for the analysis for high-rise buildings are more challenging than that for shorter buildings. High-rise buildings have longer natural period. The difference in period between the first and higher modes is greater and the highermode effect is more significant for high-rise buildings. One should consider a wide period range when scaling ground motions for the
2. Building description and numerical modeling Fig. 1 presents the plan of the sample 34-story building for this study. The building has four (three) bays in the X (Y) direction and a typical story height of 3.5 m. The building consists of moment resisting frames with steel-concrete composite columns and steel beams. Each column consists of concrete core with a compressive strength of 55 MPa and steel box-section outside the concrete core as main reinforcement. The steel section is bonded to the inside concrete core and the relatively low-strength out-side concrete (with a compressive strength of 20.5 MPa) through shear lugs. Corner reinforcement and steel stirrups are provided near the periphery of the column section. The sample building is located on a rock site in northern Taiwan and designed according to the design spectrum of Fig. 2. In this study, the building was modeled using SAP2000 [16]. The periods of the first three modes of the numerical model for the sample building in the X (Y) direction are 4.58, 1.63 and 0.94 (4.90, 1.76 and 1.02) seconds, respectively. The period of the first torsional mode is 3.5 s. Plastic hinges were assigned to the numerical model for the sample building. Moment hinges per Table 5–6 of FEMA 356 (Steel Beams - Flexure) were assigned at the ends of the beams. P-M2-M3 hinges in SAP2000 were assigned at the ends of the columns to consider the interaction of axial force and bi-axial bending moments. The pushover curves of the building in the X and Y directions are presented in Fig. 3. A series of nonlinear response-history analyses were performed in SAP2000 for the numerical model described above using direct integration method with P-Delta effect included. Mass-and-stiffness proportional damping was used in the analysis with 5% damping ratio assigned at periods of 4.90 and 1.76 s based on the periods of the first and third modes of the sample building.
12 m
11 m
3. Seed ground motions Thirty pairs of seed ground motions were selected from PEER NGA ground motion database with moment magnitude between 6.7 and 7.6, closest site-to-source distance between 3 and 13 km and Site Classes of B and C per ASCE-7 site classification [17] 1. Table 1 presents a list of the thirty pairs of seed ground-motion records used in this study. Each
12 m
10 m
9m
8m
8m 1 The site of the sample building is about 10-km away from the Xin-Cheng fault in Taiwan, which governs the seismic hazard of the site.
Fig. 1. 2D Plan view of the building.
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the SAC steel project after the 1994 Northridge earthquake. To study the impact of the degree of yielding on the seismic performance of the sample building, three sets of target spectral values were developed corresponding to earthquake return periods of 475 and 2475 years and 200% of the set for an earthquake return period of 2475 years. The target spectra for return periods of 475 and 2475 years were developed following the procedures in the building code in Taiwan and are presented in panels a and b of Fig. 4, respectively, using solid lines. The seven spectral ordinates of each of the two spectra at periods of 1– 7 s in increments of 1 s were used as the target spectral values for Method 1 to scale thirty pairs of seed ground motions. The period range of 1 through 7 s was selected to cover a range of 0.2T1 to 1.5T1, where T1 is the fundamental period of the sample building, as required in building codes. Three sets of thirty pairs of scaled ground motions were developed using Method 1 and the seed ground motions of Table 1. Fig. 5a presents the geometric-mean (termed geomean hereafter) spectra of the thirty pairs of scaled ground motions for a return period of 2475 years. The median of the thirty spectra of Fig. 5a and that for the scaled ground motions for a return period of 475 years are presented in panels b and a of Fig. 4, respectively, using red dash lines. The median spectra match reasonably well to their target in the period range of 0.2T1 to 1.5T1.
Fig. 2. Design spectrum for the site at Taiwan for an earthquake return period of 475 years.
4.2. Method 2: Spectrum-matching method to match the median spectrum for Method 1 Spectrally matched ground motions have been widely used in the building and nuclear industries to compute seismic demands of structural and nonstructural systems. To study the impact of using spectrum-matched ground motions on the response of the sample building, each component of the thirty pairs of seed ground motions was modified to match three target spectra using the computer code RSPMATCH [20]. The three target spectra include the median spectra in panels a and b of Fig. 4 for Method 1 and 200% of that in Fig. 4b for Method 1. Panels a and b of Fig. 6 present the response spectra of the 30 ground motions scaled using Method 2 in the X and Y directions, respectively, for a return period of 2475 years. 4.3. Method 3: Sa (T1) scaling method Shome et al. [5] proposed a method that involves amplitude scaling of ground motion records to a specified acceleration at the first mode period of a structure. The seed ground motions of were scaled to match each of the median spectral acceleration of Fig. 4 for Method 1 at a period of 4.75 s Fig. 5b presents the thirty geomean spectra of the thirty pairs of scaled ground motions for an earthquake return period of 2475 years. The dispersion in spectral accelerations of Fig. 5b in the short and mid period ranges is much greater than that of Fig. 5a. The median of the thirty geomean spectra for Method 3 for an earthquake return period of 475 (2475) years is presented in panel a (panel b) of Fig. 4 using a blue dash-dot line. The median spectra are similar to those for Method 1.
Fig. 3. Pushover curve for thirty-four story building.
pair was rotated to be parallel and perpendicular to the orientation of GMRotI50 [18], which is a rotated geometric-mean spectral demand independent of sensor orientation.
4.4. Method 4: Maximum-minimum orientations 4. Ground motion scaling methods Huang et al. [21] used an orientation-dependent parameter, RSa (θ ), to investigate the orientation of maximum elastic spectral demands for near-fault ground motions. The upper bound on RSa (θ ), equal to 1, occurs when the spectral demands for a given orientation are equal to the maximum demands at all periods considered. The maximum value of RSa (θ ) was termed RSa, max . In Method 4, the two components of each pair of seed ground motions of were first rotated to the orientations parallel and perpendicular to the orientation associated with RSa, max . These two orientations are termed the maximum and minimum orientations, respectively. We note that the spectral demand in the minimum orientation is not necessarily minimum among all orienta-
The following ground-motion scaling procedures are studied in this paper: 4.1. Method 1: Geometric-mean scaling method The first method involves amplitude scaling a pair of seed motions by a single scaling factor to minimize the sum of the squared errors between the target spectral values and the geometric mean (square root of the product) of the spectral ordinates for the pair. The method was used by Somerville et al. [19] to develop ground-motion time series for 127
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Table 1 List of seed ground motions. Record Sequence Number
Earthquake Name
Year
Station Name
Earthquake Magnitude
Closest site-to-fault distance (km)
126 292 779 802 803 825 1085 1161 1182 1193 1197 1198 1462 1489 1493 1494 1497 1501 1507 1515 1517 1519 1527 1530 1531 1541 1545 1546 1550 1551
Gazli, USSR Irpinia, ItalY01 Loma Prieta Loma Prieta Loma Prieta Cape Mendocino Northridge−01 Kocaeli, Turkey Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan
1976 1980 1989 1989 1989 1992 1994 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999
Karakyr Sturno LGPC Saratoga - Aloha Ave Saratoga - W Valley Coll. Cape Mendocino Sylmar - Converter Sta East Gebze CHY006 CHY024 CHY028 CHY029 TCU TCU049 TCU053 TCU054 TCU057 TCU063 TCU071 TCU082 TCU084 TCU087 TCU100 TCU103 TCU104 TCU116 TCU120 TCU122 TCU136 TCU138
6.80 6.90 6.93 6.93 6.93 7.01 6.69 7.51 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62
5.46 10.84 3.88 8.50 9.31 6.96 5.19 10.92 9.77 9.64 3.14 10.97 5.18 3.78 5.97 5.30 11.84 9.80 5.31 5.18 11.24 7.00 11.39 6.10 12.89 12.40 7.41 9.35 8.29 9.79
Fig. 4. Target design spectra for the sample site and the median spectra of the ground motions scaled using Methods 1 and 3.
Fig. 5. Geometric-mean spectra of the 30 pairs of ground motions scaled to the design spectrum for a return period of 2475 years using Methods 1 and 3.
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Fig. 6. Spectra of the 30 ground motions in X and Y directions spectrally matched to the target median spectrum for Method 1 for a return period of 2475 years using Method 2.
minimum (component 2) orientations, respectively. For this set of scaled ground motions, the spectral values for the maximum orientation in the long period range are larger compared to the spectral values obtained by the other three methods (see Fig. 7c). Conversely, in the minimum orientation the spectral values in the long period range are lower (see Fig. 7d) compared to the spectral values obtained by the other three methods. Method 4 is included to study the impact of orientations of ground motions on the distributions of structural responses. Note that the deterministic and probabilistic values for seismic design parameters in ASCE 7–10 [17] and latest version of International Building Code [22] have been defined in the maximum direction rather using geometricmean spectral acceleration.
tions. The term is used because the corresponding orientation is 90 degrees from the maximum orientation. The rotated seed ground motions were then scaled using Method 1, namely, the geometricmean scaling method. Two sets of target spectral values were used corresponding to 100% and 200% of the target spectrum for an earthquake return period of 2475 years (the solid line of Fig. 4b). Fig. 7b presents the thirty geometric-mean spectra of the thirty pairs of scaled ground motions for Method 4 and an earthquake return period of 2475 years. The median of the thirty spectra of Fig. 7b is presented in Fig. 7a using a red dash line. The median spectrum of Fig. 7a matches reasonably well to the target at periods between 0.2T1 and 1.5T1. Panels c and d of Fig. 7 present the spectra of the scaled ground motions for Method 4 in the maximum (component 1) and
Fig. 7. Target design spectra for the sample site, the median spectra, spectra in maximum-minimum orientation and geometric-mean spectra of the 30 pairs of ground motions scaled to the design spectrum for a return period of 2475 years using Method 4.
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4.5. Method 5: Spectrum-matching to match the target spectrum
6. Results of response-history analysis
In Fig. 4, Fig. 6 and Fig. 7a, the spectral ordinates of the median spectra for Methods 1 through 4 are much lower compared to the target values (the solid lines in panels a and b of Fig. 4) at periods smaller than 0.2T1. Higher modes may contribute significantly to structural responses of tall buildings. To study the contribution of higher modes and the impact of the period range used in the scaling process for highrise buildings, ten pairs of ground motions were developed in which ground motions are spectrally matched to the target spectra of Fig. 4b for the entire period range. The spectrally-matched ground motions were developed using the computer code RSPMATCH [20] and the seed ground motions were selected from Table 1. Ten pairs were used because the dispersions in the structural responses for spectrallymatched ground motions are relatively smaller than those for other scaling methods studied herein and do not require as many ground motions to estimate the median and dispersion of structural responses at the same confidence level. Method 5 is included in this study also because the difference in the shape of median spectral ordinates between Methods 2 and 5 is arguably similar to that between CMS and UHS for a given return period. If the shape of a CMS is considered more realistic than that of a UHS, the results for Methods 2 and 5 can be used to evaluate the impact of spectral shape on performance of high-rise buildings.
Nonlinear response-history analysis was performed for the sample building using the thirteen sets of scaled ground motions described in the previous section. The results of peak floor acceleration, peak interstory drift and average floor spectral acceleration response over 5 through 33 Hz are presented in this section. Average floor spectral acceleration is used to represent the seismic demands on secondary systems, of which the frequencies are typically much larger than the fundamental frequency of a tall building. Good-of-fit tests were performed to check the distribution of structural responses. The results show that the distributions of the peak floor acceleration, average floor spectral acceleration and peak inter-story drift responses are approximately lognormal. Therefore, the structural responses of this study are presented with the help of the following parameters assuming lognormal distribution of the responses:
⎛1 θ = exp ⎜⎜ ⎝n
β=
n
⎞
i =1
⎠
∑ ln yi⎟⎟
1 n−1
(1)
n
∑ (ln yi
− ln θ )2
i =1
y16th = θ. e−β y84th = θ.
5. Ground-motion sets used in this study
eβ
(2) (3) (4)
where θ, y16th and y84th are the median (50th), 16th and 84th percentile values, respectively; yi is the response (peak floor acceleration, peak inter-story drift or average floor spectral acceleration) subjected to the ith ground motion and n is the total number of ground motions, which is 30 for Methods 1 through 4 and 10 for Method 5. Table 2 and Table 3 present the medians (θ) and dispersions (β), respectively, in the responses of the sample building for 100% and 200% of ground shaking intensity for an earthquake return period of 2475 years. The trends in the responses for an earthquake return period of 475 years are similar to those for 2475 years and are not presented in Table 2 and Table 3. For peak floor acceleration and average floor spectral acceleration, the results at the 2nd, 18th and 35th (roof) floors are presented in Table 2 and Table 3; for peak interstory drift, the results for the 1st, 17th and 34th stories are presented. In this paper, the 1st floor is at the ground level and the 35th floor is the roof of the sample building. The ith story is defined as the story between the ith and i+1th floors.
A total of thirteen sets of ground motions were used to perform nonlinear response history analysis of this building. Three of them are developed using Methods 1, 2 and 3 for an earthquake return period of 475 years. Five are developed using Methods 1 through 5 for an earthquake return period of 2475 years. The remaining five sets are for 200% of the sets corresponding to the earthquake return period of 2475 years. In Fig. 9a and Fig. 9d, the median of the geometric-mean spectra of the eight sets of scaled ground motions are presented for earthquake return periods of 475 and 2475 years, respectively. In Fig. 9b and Fig. 9e (Fig. 9c and Fig. 9f), the median spectra for the first (second) component of the scaled ground motion sets are presented. The median of the geometric-mean spectra for all cases for an earthquake return period of 475 (2475) years are almost identical in the period region of 0.2T1 to 1.5T1. For the median spectral acceleration at T1 (4.7 s) for the first component of the scaled ground motions for an earthquake return period of 2475 years, the values are 0.12g, 0.11g, 0.12g, 0.15g and 0.11g for Methods 1 through 5, respectively (see Fig. 9e); for the second component, the values are the values are 0.1g, 0.11g, 0.1g, 0.07g and 0.11g for Methods 1 through 5, respectively (see Fig. 9f).
6.1. Peak floor acceleration Median, 84th and 16th percentiles of peak floor acceleration at the
Fig. 8. Spectra of the 10 ground motions in X and Y directions spectrally matched to the target spectrum for a return period of 2475 years using Method 5.
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Fig. 9. Median spectra for component 1, 2 and geometric-mean of the ground motions scaled using Method 1 through 5.
estimation of median in peak floor acceleration response for Method 2 is more obvious in the X direction than in the Y direction. In Fig. 9a, Method 4 provides larger median values compared to the first three methods. Note that Method 4 provides greater median spectral ordinates compared to the first three methods in the X direction (see Fig. 9e). In Fig. 10a and Fig. 11a, Method 5 always produces median values greater than and dispersions similar to Method 2. In Fig. 6 and Fig. 8, Methods 2 and 5 provide similar spectral ordinates in the longer period range and the spectral ordinates are much larger at periods smaller than 1 s for Method 5. For Method 5 larger median value in peak floor acceleration at the 2nd floor is attributed by the higher modes of the sample building which is a reasonable observation for high-rise
2nd and 35th floors in the X (Y) direction are presented in Fig. 10a (Fig. 11a) for Methods 1 through 5. In general, Methods 1 and 3 provide similar median values. The median of peak floor acceleration is about 5–15% (2% to 9%) underestimated by Method 2 compared to the results for Method 1 in the X (Y) direction. The difference is not significant. The trends are slightly different in the X and Y directions which can be explained using the median spectra of Fig. 9 for components 1 and 2. In the X direction (i.e., component 1), Method 2 provides slightly smaller median spectral ordinates in the period region of 2 through 7 s compared to Methods 1 and 3 (Fig. 9b and Fig. 9e) while in the Y direction (i.e., component 2), Method 2 provides similar median spectral ordinates in the long period region compared to Methods 1 and 3 (Fig. 9c and Fig. 9f). As a result, the under-
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Table 2 Median responses of the sample building subjected to ground motions corresponding to 100% and 200% shaking levels for an earthquake return period of 2475 years. GM Intensity
100%, a return period of 2475 yrs
200%, a return period of 2475 yrs
Orientation Response Floor Method 1 Method 2 Method 3 Method 4 Method 5 Response Story Method 1 Method 2 Method 3 Method 4 Method 5 Response Floor Method 1 Method 2 Method 3 Method 4 Method 5
X Y Peak Floor Acceleration (g) 2nd 18th Roof 2nd 0.25 0.20 0.32 0.25 0.22 0.18 0.27 0.23 0.24 0.20 0.31 0.24 0.26 0.22 0.35 0.25 0.30 0.22 0.29 0.32 Peak Story Drift (mm) 1st 17th 34th 1st 38 31 13 33 29 27 11 30 33 31 13 29 46 37 15 25 29 28 11 32 Average Floor Spectral Acceleration (g) 2nd 18th Roof 2nd 0.29 0.22 0.33 0.29 0.26 0.19 0.28 0.26 0.28 0.22 0.33 0.28 0.30 0.24 0.37 0.29 0.43 0.23 0.31 0.43
X
Y
18th 0.19 0.18 0.18 0.18 0.20
Roof 0.30 0.28 0.29 0.26 0.29
2nd 0.49 0.44 0.44 0.52 0.61
18th 0.33 0.32 0.32 0.37 0.38
Roof 0.51 0.48 0.49 0.51 0.52
2nd 0.50 0.45 0.46 0.49 0.63
18th 0.33 0.32 0.32 0.32 0.36
Roof 0.51 0.50 0.48 0.47 0.53
17th 29 30 28 23 29
34th 15 14 14 13 14
1st 80 75 85 87 71
17th 55 48 57 60 51
34th 20 19 19 20 19
1st 74 73 69 53 68
17th 51 55 50 39 51
34th 25 25 24 22 25
18th 0.20 0.19 0.20 0.19 0.23
Roof 0.31 0.29 0.30 0.28 0.31
2nd 0.57 0.51 0.52 0.60 0.85
18th 0.37 0.34 0.35 0.39 0.43
Roof 0.54 0.49 0.52 0.53 0.55
2nd 0.58 0.51 0.54 0.56 0.85
18th 0.36 0.34 0.34 0.35 0.42
Roof 0.53 0.51 0.51 0.50 0.58
provide moderate dispersions in peak floor acceleration compared to the other methods.
buildings. It is also found that the higher-mode effect for acceleration response is more significant at the 2nd floor than at the roof. If the shape of median spectral ordinates for Method 2 is considered more realistic than that for Method 5, the use of Method 5 may overestimate seismic loss of a tall building with acceleration-sensitive equipment and components installed in the lower levels. The dispersion in peak floor acceleration is greatly influenced by the dispersion in spectral ordinates of ground motions in the short period range. In Table 3, Fig. 10a and Fig. 11a, the dispersion in peak floor acceleration is smallest for Methods 2 and 5 (spectrum-matching method) and largest for Method 3 (Sa (T1) scaling method) among the five scaling methods. Dispersion in spectral ordinates is smallest in the short period range for Methods 2 and 5 (see Fig. 6 and Fig. 8). In Method 3, the seed ground-motion pairs are amplitude scaled to match the target spectrum at only first mode period of the building and the dispersion in spectral ordinates is greatly increased in the short period range (see Fig. 5b). The dispersion in peak floor acceleration is therefore significant due to higher-mode effect. Methods 1 and 4
6.2. Peak story drift Median, 84th and 16th percentiles of peak story drift of the first and 34th stories in the X (Y) direction are presented in Fig. 10b (Fig. 11b) for Methods 1 through 5 and three ground-motion intensity levels. In general, the differences in the median values are less than 10% 1) among Methods 1, 2 and 3 in the Y direction, and 2) between Methods 1 and 3 in both the X and Y directions. Median story drift in the X direction for Method 2 is 6–24% smaller than that for Method 1. In the X direction, Method 4 always produces larger median story drift compared to the other four methods (see Fig. 10b) at a given shaking intensity. Median story drift in the X direction for Method 4 is about 10–20% greater than that for Method 1. Although Method 4 has median geomean spectral ordinates similar to the other methods at periods between 0.2T1 to 1.5T1 (see Fig. 9d), it provides larger median
Table 3 Dispersions in the responses of the sample building subjected to ground motions corresponding to 100% and 200% shaking levels for an earthquake return period of 2475 years. GM Intensity
100%, a return period of 2475 yrs
200%, a return period of 2475 yrs
Orientation Response Floor Method 1 Method 2 Method 3 Method 4 Method 5 Response Story Method 1 Method 2 Method 3 Method 4 Method 5 Response Floor Method 1 Method 2 Method 3 Method 4 Method 5
X Y Peak Floor Acceleration (g) 18th Roof 2nd 2nd 0.35 0.18 0.16 0.44 0.18 0.12 0.13 0.15 0.69 0.44 0.39 0.76 0.46 0.27 0.23 0.40 0.12 0.14 0.08 0.21 Peak Story Drift (mm) 1st 17th 34th 1st 0.58 0.43 0.25 0.47 0.14 0.09 0.13 0.10 0.31 0.22 0.28 0.3 0.57 0.42 0.24 0.38 0.12 0.08 0.11 0.11 Average Floor Spectral Acceleration (g) nd th 2 18 Roof 2nd 0.42 0.24 0.18 0.52 0.12 0.12 0.12 0.1 0.74 0.49 0.41 0.81 0.53 0.31 0.23 0.45 0.08 0.17 0.09 0.1
X
Y
18th 0.30 0.12 0.57 0.25 0.13
Roof 0.25 0.15 0.50 0.25 0.08
2nd 0.33 0.18 0.61 0.47 0.12
18th 0.20 0.14 0.40 0.32 0.15
Roof 0.17 0.10 0.30 0.19 0.09
2nd 0.44 0.15 0.73 0.38 0.21
18th 0.32 0.13 0.52 0.25 0.15
Roof 0.24 0.11 0.40 0.19 0.09
17th 0.43 0.07 0.22 0.40 0.05
34th 0.27 0.16 0.39 0.26 0.09
1st 0.56 0.22 0.29 0.54 0.25
17th 0.40 0.15 0.24 0.36 0.16
34th 0.14 0.09 0.15 0.15 0.10
1st 0.54 0.19 0.28 0.45 0.17
17th 0.40 0.10 0.18 0.33 0.09
34th 0.19 0.12 0.26 0.19 0.08
18th 0.35 0.12 0.61 0.32 0.17
Roof 0.28 0.14 0.52 0.28 0.09
2nd 0.41 0.12 0.68 0.51 0.08
18th 0.29 0.14 0.48 0.34 0.17
Roof 0.20 0.09 0.35 0.22 0.09
2nd 0.51 0.10 0.78 0.42 0.10
18th 0.38 0.13 0.58 0.32 0.19
Roof 0.27 0.11 0.45 0.23 0.13
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Fig. 10. Median, 84th and 16th percentile values of different response quantities at different floors in X direction using Methods (1) through (5).
and dispersion values at a given story for a given shaking intensity. The difference in the distributions of peak story drift between Methods 2 and 5 is much smaller than that in the distributions of peak floor acceleration at the 2nd floor. This observation indicates that the contribution from the higher modes of the sample building on displacement response is smaller than the first mode. In general, the dispersion in peak story drift is smallest for Methods 2 and 5 and largest for Methods 1 and 4 among the five methods
spectral ordinates in the X direction (see Fig. 9e). Conversely, in the Y direction, Method 4 provides lower median spectral ordinates in the long period region compared to the other methods (see Fig. 9f). As a result, median story drift for Method 4 is lower than that for the other four methods in the Y direction (see Fig. 11b). The difference in the responses between Methods 1 and 4 clearly demonstrates the impact of ground-motion orientation on performance of tall buildings. In Fig. 10b and Fig. 11b, Methods 2 and 5 provide similar median 133
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Fig. 11. Median, 84th and 16th percentile values of different response quantities at different floors in Y direction using Methods (1) through (5).
spectral ordinates is small at periods close to T1 and significant in the short period range (see Fig. 5b).
studied herein. It has higher correlation to the dispersion in spectral ordinates at periods close to T1 than that in the short period range. For example, the larger dispersions in peak story drift for Methods 1 and 4 is not surprising since the dispersions in spectral ordinates for those methods are greater than for the other methods in the long period range, where T1 is located (see Fig. 5a and Fig. 7b). The dispersion in peak story drift for Method 3, namely, the Sa(T1) method, is moderate compared to that for the other methods. In Method 3, the dispersion in
6.3. Average floor spectral acceleration Median, 84th and 16th percentiles of floor spectral acceleration averaged over a frequency range of 5 through 33 Hz for Methods 1 through 5 are presented in Fig. 10c and Fig. 11c, for the X and Y 134
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Method 3 is smaller than that for Methods 1 and 4 in the period range close to the fundamental period of the sample building, and therefore Method 3 has smaller dispersions in drift response than Methods 1 and 4. 8. Based on the analysis results of this study, we conclude that optimal ground-motion scaling procedures for performance assessment of a high-rise building depend on the target seismic hazard (spectral accelerations over a wide period range) and the characteristics and positions of structural and nonstructural components in the building (acceleration- or displacement-sensitive components). These factors should be considered in the scaling procedures of ground motions.
directions, respectively, for three ground-motion intensity levels. The trends are generally similar to those for peak floor acceleration and not repeated herein. 7. Conclusions A series of bi-directional nonlinear response-history analyses were performed for a 34-story sample building to study the impact of ground-motion scaling on the performance of high-rise buildings. Ground motions were scaled for a wide range of hazard using the geomean scaling method (Method 1), spectrum-matching method (Methods 2 and 5), Sa(T1) method (Method 3), and maximumminimum orientation scaling method (Method 4). All the scaled ground-motion sets for a given hazard level have similar median geomean spectral ordinates in the period region of 0.2T1 to 1.5T1. Both medians and dispersions in peak floor acceleration, peak interstory drift and average floor spectral acceleration of the sample building are presented and discussed. Major conclusions are summarized as follows:
Acknowledgements This research is supported by grants from Cutting-edge Urban Development Program funded by Ministry of Land, Transport and Maritime Affairs of Korean (Code# ’09R & D A01) and from the National Science Council of Taiwan (NSC 102–2218-E-002–007). Ms. Yu-Wen Chang provided seismology information for cities in Taiwan. Dr. Chyng-Maw Su, Mr. Bruce Li and Mr. Huan-Wei Chen provided information for the 34-story building analyzed in this study. Their assistance is acknowledged.
1. In general, Methods 1 and 3 provide similar median values for both acceleration and drift responses. Method 2 moderately underestimates the median responses computed for Method 1. 2. The difference in the distributions of structural responses between Methods 1 and 4 identifies the impact of orientations of ground motions on the demands of the sample building. In general, median responses in the maximum direction (i.e., the X direction in this study) for Method 4 are about 10–20% greater than that for Method 1. Both methods provide similar dispersions in the responses. 3. The difference in the distributions of structural responses between Methods 2 and 5 identifies the impact of spectral shape on the demands of the sample building. Method 5 provides larger median values for peak floor acceleration and average floor spectral acceleration responses at lower floors of the sample building compared to Method 2 and the other methods due to higher spectral ordinates in the short period range. For peak story drift, Method 5 provides similar median values as Method 2. The impact of higher-mode effect is more significant for acceleration response than for drift. Methods 2 and 5 provide the smallest dispersions in the responses among the five methods studied herein. A smaller dispersion enables the use of a smaller number of ground motions in response-history analysis for stable estimates with acceptable accuracy and confidence level. However, spectrum-matching scaling may not be appropriate when the seismic loss of a building is sensitive to dispersions in the responses. 4. The dispersions in acceleration responses have a higher correlation with the dispersion in spectral ordinates of ground motions in the short period range than at the fundamental period of the sample building. The dispersion in spectral ordinates for Method 3 is greater than that for the other methods in the short period range for a given hazard level, and therefore Method 3 has largest dispersions in acceleration responses. If Method 3 is used in a performance assessment of a high-rise building, spectral shapes of seed ground motions should be selected carefully to avoid the significant dispersion in spectral ordinates in the short period range. 5. For analysis of high-rise buildings sensitive to multi-mode excitation use of Method 3 can be inappropriate as it underestimates the medians and provides highest dispersions for floor acceleration and average floor spectral acceleration responses. 6. If prediction of damage to non-structural components is an objective of the analysis, then an appropriate method is Method 5 which takes into account contributions from higher modes. 7. The dispersions in peak story drift have a higher correlation with the dispersion in spectral ordinates of ground motions in the period range close to the fundamental period of the sample building than in the short period range. The dispersion in spectral ordinates for
References [1] FEMA - Federal Emergency Management Agency . NEHRP Recommended provisions for seismic regulations for new buildings and other structures. Washington, D.C: FEMA 273 (Provisions) and 274 (Commentary); 1997. [2] FEMA - Federal Emergency Management Agency . Prestandard and commentary for the seismic rehabilitation of buildings. Washington, D.C: FEMA 356; 2000. [3] FEMA - Federal Emergency Management Agency . Recommended seismic design criteria for new steel moment-frame buildings. Washington, D.C: FEMA 350; 2000. [4] ATC - Applied Technology Council . Seismic performance assessment of buildings. Volume 1–Methodology. Washington, D.C: FEMA P-58. Federal Emergency Management Agency; 2012. [5] Shome N, Cornell CA, Bazzurro P, Carballo J. Earthquakes, records, and nonlinear responses. Earthq Spectra 1998;14(3):469–500. [6] Baker JW, Cornell CA. A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthq Eng Struct Dyn 2005;34:1193–217. [7] Baker JW, Cornell CA. Spectral shape, epsilon and record selection. Earthq Eng Struct Dyn 2006;35:1077–95. [8] PEER Ground Motion Selection and Modification Working Group . Evaluation of ground motion selection and modification methods: predicting median interstory drift response of buildings [PEER Report 2009/01]. Berkeley: Pacific Earthquake Engineering Research Center, University of California; 2009. [9] Haselton CB, Baker JW, Liel AB, Deierlein GG. Accounting for ground motion spectral shape characteristics in structural collapse assessment through an adjustment for Epsilon. J Struct Eng ASCE 2011;137(3):332–44. [10] Jayaram N, Lin T, Baker JW. A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance. Earthq Spectra 2011;27(3):797–815. [11] Weng YT, Tsai KC, Chan YR. A ground motion scaling method considering highermode effects and structural characteristics. Earthq Spectra 2010;26(3):841–67. [12] Kalkan E, Chopra AK. Modal-pushover-based ground-motion scaling procedure. J Struct Eng ASCE 2011;137(3):298–310. [13] Katsanos EI, Sextos AG, Manolis GD. Selection of earthquake ground motion records: a state-of-the-art review from a structural engineering perspective. Soil Dyn Earthq Eng 2010;30(4):157–69. [14] NIST - National Institute of Standards and Technology. Selecting and scaling earthquake ground motions for performing response-history analyses, NIST GCR 11-917-15. Gaithersburg, Maryland: Prepared by the NEHRP Consultants Joint Venture; 2011. [15] Huang Y-N, Whittaker AS, Luco N, Hamburger RO. Scaling earthquake ground motions for performance-based assessment of buildings. J Struct Eng ASCE 2011;137(3):311–21. [16] CSI. SAP2000 user’s manual, Version 14.1.0. Computers and Structures, Inc., : Berkeley, California; 2009. [17] ASCE - American Society of Civil Engineers. Minimum design loads for buildings and other structures, ASCE/SEI 7-10. Virginia; 2010. [18] Boore DM, Watson-Lamprey J, Abrahamson NA. Orientation-independent measures of ground motion. Bull Seismol Soc Am 2006;96(4A):1502–11. [19] Somerville P, Smith N, Punyamurthula S, Sun J. Development of ground motion time histories for phase 2 of the FEMA/SAC steel project [Report SAC/BD-97/04]. California: SAC Joint Venture: Sacramento; 1997. [20] Abrahamson NA. Non-stationary spectral matching program RSPMATCH. PG & E, Internal Report; 1998. [21] Huang Y-N, Whittaker AS, Luco N. Orientation of maximum spectral demand in the near-fault region. Earthq Spectra 2009;25(3):707–17. [22] ICC - International Code Council . 2012 International building code. Illinois: ICC.Country Club Hills; 2011.
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Soil Dynamics and Earthquake Engineering journal homepage: www.elsevier.com/locate/soildyn
Ground-motion scaling for seismic performance assessment of high-rise moment-resisting frame building
MARK
⁎
Avik Samantaa, , Yin-Nan Huangb a b
Department of Civil and Environmental Engineering, IIT Patna, Bihta 801103, Bihar, India Department of Civil Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei 10617, Taiwan
A R T I C L E I N F O
A BS T RAC T
Keywords: Ground motion scaling High-rise building Nonlinear analysis Seismic response Performance assessment Seismic hazard
Next generation performance-based earthquake engineering involves the use of a probability framework, which incorporates the inherent uncertainty and variability in seismic hazard, structural and non-structural responses, damage states and economic and casualty losses. One key issue in seismic performance assessment is the scaling of ground motions for nonlinear response-history analysis. In this paper, the impact of ground-motion scaling procedures, including 1) geometric-mean scaling of pairs of ground motions, 2) spectrum-matching of groundmotions, 3) first-mode-based scaling to a target spectral acceleration and 4) maximum-minimum orientation scaling, on the distributions of floor acceleration, story drift and floor spectral acceleration of a sample high-rise building is investigated using a series of nonlinear response-history analyses of a 34-story moment-resisting frame building. The advantages and disadvantages of each ground-motion scaling method are discussed for seismic performance assessment of a 34-story building.
1. Introduction The structural and non-structural damages observed during the 1989 Loma Prieta and 1994 Northridge earthquakes motivated expert practitioners and researchers to develop the first-generation tools for Performance-Based Earthquake Engineering (PBEE), such as those documented in FEMA 273 and 274 [1] and FEMA 356 [2]. The deterministic assessment procedures in those documents provided relations between structural response indices (such as story drifts and inelastic member deformations) and performance levels (such as immediate occupancy, life safety and collapse prevention) and shifted the focus of assessment from forces to displacements and deformations. FEMA 350 [3], which was drafted as part of the SAC Steel Project, extended the first generation tools through the use of probabilistic assessment procedures. In contrast to the first-generation tools for PBEE, where performance assessments are performed using a deterministic approach, the ATC-58 project in the United States develops next-generation tools and guidelines for performance-based seismic design and assessment using a probability framework, which can incorporate the inherent uncertainty and variability in seismic hazard, structural and non-structural responses, damage states and repair costs in the assessment process [4]. A significant amount of research work has been carried out for
⁎
ground motion selection and scaling. Shome et al. [5] suggested that the scaling of ground-motion records to the 5%-damped target spectral acceleration for a given event (magnitude (M) and distance (R) pair) at the fundamental frequency of a structure is efficient to estimate the nonlinear response of the structure for the event. Baker and Cornell [6] considered Intensity Measure (IM) consisting of two parameters, spectral acceleration and epsilon (ε), at a given period to predict the response of a structure when selecting ground motions as ε was found to be an good indicator of spectral shape. Baker and Cornell [7] proposed a spectrum, namely, conditional mean spectrum – considering ε (CMS-ε), that accounts for the correlation in spectral accelerations at different periods and computes the spectral accelerations for a given M-R pair conditional to a given target spectral acceleration at the fundamental period of a structure (T1). PEER report 2009/01 [8] suggested selection of ground motions based on record properties (use the CMS for spectral shape, the proper inelastic spectral displacement target) to precise and accurate prediction of peak inter-story drift ratio response. Haselton et al. [9] proposed an alternative simplified method which allows the analyst to use a general ground motion set, selected without regard to ε, to calculate an unadjusted building collapse capacity by using nonlinear dynamic analysis, and then to correct this capacity using an adjustment factor to include the impact of the expected ε(T1) for the building site and collapse hazard intensity, Sa, col(T1). This eliminates the necessity of considering ε(T1) in selection of
Corresponding author. E-mail addresses: [email protected] (A. Samanta), [email protected] (Y.-N. Huang).
http://dx.doi.org/10.1016/j.soildyn.2017.01.013 Received 1 September 2014; Received in revised form 10 December 2015; Accepted 15 January 2017 0267-7261/ © 2017 Elsevier Ltd. All rights reserved.
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analysis of high-rise buildings because the loss contributed from shortand long-period spectral demands may both be significant. Scaling methods based solely on the spectral demand at the first-mode period may not be appropriate. Spectrally-matched ground motions to a uniform hazard spectrum (UHS) for a very wide period range may produce overly conservative results since 1) the short- and long-period spectral demands may be governed by different events and 2) the impact of the correlation in spectral demands at different periods is not included in the development of a UHS. The main objective of this paper is to study the impact of groundmotion scaling procedures on the distributions of structural responses of high-rise buildings. A series of nonlinear response-history analysis are performed for a 34-story moment-resisting frame building subjected to ground motions scaled using different methods, namely, 1) geometric-mean scaling of pairs of ground motions, 2) spectrummatching of ground-motions, 3) first-mode-based scaling to a target spectral acceleration, 4) maximum-minimum orientation scaling methods and 5) spectrum-matching method to study the contribution of higher modes. The impact of ground-motion scaling on seismic performance of high-rise building is discussed. We focus not only on the median values of the structural responses (e.g., peak floor acceleration, peak story drift and average floor spectral acceleration) but also on their dispersions.
the ground motion records. Jayaram et al. [10] indicated conventional dynamic structural analysis often involves scaling input ground motions to a target mean response spectrum. The variance in the target spectral acceleration is usually ignored, which can bias the structural response estimates. They proposed a computationally efficient and theoretically consistent algorithm to select and scale ground motions that match target spectral accelerations in both mean and variance. Weng et al. [11] proposed a multimode ground motion scaling (MMS) ground-motion scaling method which includes contributions from the dominating modes and uses the square root of the sum of the squares (SRSS) or complete quadratic combination (CQC) rule in the estimate of seismic demands. They conducted a series of nonlinear response-history analyses for sample low-, medium- and high-rise buildings and concluded that the MMS method is effective in reducing the dispersion in peak seismic demands. Kalkan and Chopra [12] have developed a modal-pushover-based scaling (MPS) method to scale ground motions for use in nonlinear response history analysis of buildings and bridges. The step by step method is useful for first mode dominant structures as well as for structures susceptible to higher mode effect. The MPS procedure has been evaluated (from the prospective of seismic design and not performance assessment) for low- and mid-rise buildings (four-, sixand thirteen story buildings) in the paper. Katsanos et al. [13] reviewed various methodologies developed for selecting appropriate records that can be used for dynamic analysis of structural systems in the context of performance-based design and observed that there are many ways to achieve record selection. They concluded that it is still difficult to limit the bounds of the ensuing structural response dispersion uniformly. NIST [14] provided recommendations related to selecting and scaling ground motions for design and performance assessment of low and medium-rise buildings, and discussed best practices for applying the current rules in building codes and standards. Huang et al. [15] studied four scaling methods, namely, 1) geometric mean scaling of pairs of ground motions, 2) spectrum matching of ground motions, 3) first-mode-period scaling to a target spectral acceleration and 4) scaling of ground motions per the distribution of spectral demands to see the impact of alternate ground-motion scaling procedures on the distribution of displacement responses in single-degree-of-freedom (SDOF) structural systems. The selection and scaling of ground motions for the analysis for high-rise buildings are more challenging than that for shorter buildings. High-rise buildings have longer natural period. The difference in period between the first and higher modes is greater and the highermode effect is more significant for high-rise buildings. One should consider a wide period range when scaling ground motions for the
2. Building description and numerical modeling Fig. 1 presents the plan of the sample 34-story building for this study. The building has four (three) bays in the X (Y) direction and a typical story height of 3.5 m. The building consists of moment resisting frames with steel-concrete composite columns and steel beams. Each column consists of concrete core with a compressive strength of 55 MPa and steel box-section outside the concrete core as main reinforcement. The steel section is bonded to the inside concrete core and the relatively low-strength out-side concrete (with a compressive strength of 20.5 MPa) through shear lugs. Corner reinforcement and steel stirrups are provided near the periphery of the column section. The sample building is located on a rock site in northern Taiwan and designed according to the design spectrum of Fig. 2. In this study, the building was modeled using SAP2000 [16]. The periods of the first three modes of the numerical model for the sample building in the X (Y) direction are 4.58, 1.63 and 0.94 (4.90, 1.76 and 1.02) seconds, respectively. The period of the first torsional mode is 3.5 s. Plastic hinges were assigned to the numerical model for the sample building. Moment hinges per Table 5–6 of FEMA 356 (Steel Beams - Flexure) were assigned at the ends of the beams. P-M2-M3 hinges in SAP2000 were assigned at the ends of the columns to consider the interaction of axial force and bi-axial bending moments. The pushover curves of the building in the X and Y directions are presented in Fig. 3. A series of nonlinear response-history analyses were performed in SAP2000 for the numerical model described above using direct integration method with P-Delta effect included. Mass-and-stiffness proportional damping was used in the analysis with 5% damping ratio assigned at periods of 4.90 and 1.76 s based on the periods of the first and third modes of the sample building.
12 m
11 m
3. Seed ground motions Thirty pairs of seed ground motions were selected from PEER NGA ground motion database with moment magnitude between 6.7 and 7.6, closest site-to-source distance between 3 and 13 km and Site Classes of B and C per ASCE-7 site classification [17] 1. Table 1 presents a list of the thirty pairs of seed ground-motion records used in this study. Each
12 m
10 m
9m
8m
8m 1 The site of the sample building is about 10-km away from the Xin-Cheng fault in Taiwan, which governs the seismic hazard of the site.
Fig. 1. 2D Plan view of the building.
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the SAC steel project after the 1994 Northridge earthquake. To study the impact of the degree of yielding on the seismic performance of the sample building, three sets of target spectral values were developed corresponding to earthquake return periods of 475 and 2475 years and 200% of the set for an earthquake return period of 2475 years. The target spectra for return periods of 475 and 2475 years were developed following the procedures in the building code in Taiwan and are presented in panels a and b of Fig. 4, respectively, using solid lines. The seven spectral ordinates of each of the two spectra at periods of 1– 7 s in increments of 1 s were used as the target spectral values for Method 1 to scale thirty pairs of seed ground motions. The period range of 1 through 7 s was selected to cover a range of 0.2T1 to 1.5T1, where T1 is the fundamental period of the sample building, as required in building codes. Three sets of thirty pairs of scaled ground motions were developed using Method 1 and the seed ground motions of Table 1. Fig. 5a presents the geometric-mean (termed geomean hereafter) spectra of the thirty pairs of scaled ground motions for a return period of 2475 years. The median of the thirty spectra of Fig. 5a and that for the scaled ground motions for a return period of 475 years are presented in panels b and a of Fig. 4, respectively, using red dash lines. The median spectra match reasonably well to their target in the period range of 0.2T1 to 1.5T1.
Fig. 2. Design spectrum for the site at Taiwan for an earthquake return period of 475 years.
4.2. Method 2: Spectrum-matching method to match the median spectrum for Method 1 Spectrally matched ground motions have been widely used in the building and nuclear industries to compute seismic demands of structural and nonstructural systems. To study the impact of using spectrum-matched ground motions on the response of the sample building, each component of the thirty pairs of seed ground motions was modified to match three target spectra using the computer code RSPMATCH [20]. The three target spectra include the median spectra in panels a and b of Fig. 4 for Method 1 and 200% of that in Fig. 4b for Method 1. Panels a and b of Fig. 6 present the response spectra of the 30 ground motions scaled using Method 2 in the X and Y directions, respectively, for a return period of 2475 years. 4.3. Method 3: Sa (T1) scaling method Shome et al. [5] proposed a method that involves amplitude scaling of ground motion records to a specified acceleration at the first mode period of a structure. The seed ground motions of were scaled to match each of the median spectral acceleration of Fig. 4 for Method 1 at a period of 4.75 s Fig. 5b presents the thirty geomean spectra of the thirty pairs of scaled ground motions for an earthquake return period of 2475 years. The dispersion in spectral accelerations of Fig. 5b in the short and mid period ranges is much greater than that of Fig. 5a. The median of the thirty geomean spectra for Method 3 for an earthquake return period of 475 (2475) years is presented in panel a (panel b) of Fig. 4 using a blue dash-dot line. The median spectra are similar to those for Method 1.
Fig. 3. Pushover curve for thirty-four story building.
pair was rotated to be parallel and perpendicular to the orientation of GMRotI50 [18], which is a rotated geometric-mean spectral demand independent of sensor orientation.
4.4. Method 4: Maximum-minimum orientations 4. Ground motion scaling methods Huang et al. [21] used an orientation-dependent parameter, RSa (θ ), to investigate the orientation of maximum elastic spectral demands for near-fault ground motions. The upper bound on RSa (θ ), equal to 1, occurs when the spectral demands for a given orientation are equal to the maximum demands at all periods considered. The maximum value of RSa (θ ) was termed RSa, max . In Method 4, the two components of each pair of seed ground motions of were first rotated to the orientations parallel and perpendicular to the orientation associated with RSa, max . These two orientations are termed the maximum and minimum orientations, respectively. We note that the spectral demand in the minimum orientation is not necessarily minimum among all orienta-
The following ground-motion scaling procedures are studied in this paper: 4.1. Method 1: Geometric-mean scaling method The first method involves amplitude scaling a pair of seed motions by a single scaling factor to minimize the sum of the squared errors between the target spectral values and the geometric mean (square root of the product) of the spectral ordinates for the pair. The method was used by Somerville et al. [19] to develop ground-motion time series for 127
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Table 1 List of seed ground motions. Record Sequence Number
Earthquake Name
Year
Station Name
Earthquake Magnitude
Closest site-to-fault distance (km)
126 292 779 802 803 825 1085 1161 1182 1193 1197 1198 1462 1489 1493 1494 1497 1501 1507 1515 1517 1519 1527 1530 1531 1541 1545 1546 1550 1551
Gazli, USSR Irpinia, ItalY01 Loma Prieta Loma Prieta Loma Prieta Cape Mendocino Northridge−01 Kocaeli, Turkey Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan Chi-Chi, Taiwan
1976 1980 1989 1989 1989 1992 1994 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999 1999
Karakyr Sturno LGPC Saratoga - Aloha Ave Saratoga - W Valley Coll. Cape Mendocino Sylmar - Converter Sta East Gebze CHY006 CHY024 CHY028 CHY029 TCU TCU049 TCU053 TCU054 TCU057 TCU063 TCU071 TCU082 TCU084 TCU087 TCU100 TCU103 TCU104 TCU116 TCU120 TCU122 TCU136 TCU138
6.80 6.90 6.93 6.93 6.93 7.01 6.69 7.51 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62 7.62
5.46 10.84 3.88 8.50 9.31 6.96 5.19 10.92 9.77 9.64 3.14 10.97 5.18 3.78 5.97 5.30 11.84 9.80 5.31 5.18 11.24 7.00 11.39 6.10 12.89 12.40 7.41 9.35 8.29 9.79
Fig. 4. Target design spectra for the sample site and the median spectra of the ground motions scaled using Methods 1 and 3.
Fig. 5. Geometric-mean spectra of the 30 pairs of ground motions scaled to the design spectrum for a return period of 2475 years using Methods 1 and 3.
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Fig. 6. Spectra of the 30 ground motions in X and Y directions spectrally matched to the target median spectrum for Method 1 for a return period of 2475 years using Method 2.
minimum (component 2) orientations, respectively. For this set of scaled ground motions, the spectral values for the maximum orientation in the long period range are larger compared to the spectral values obtained by the other three methods (see Fig. 7c). Conversely, in the minimum orientation the spectral values in the long period range are lower (see Fig. 7d) compared to the spectral values obtained by the other three methods. Method 4 is included to study the impact of orientations of ground motions on the distributions of structural responses. Note that the deterministic and probabilistic values for seismic design parameters in ASCE 7–10 [17] and latest version of International Building Code [22] have been defined in the maximum direction rather using geometricmean spectral acceleration.
tions. The term is used because the corresponding orientation is 90 degrees from the maximum orientation. The rotated seed ground motions were then scaled using Method 1, namely, the geometricmean scaling method. Two sets of target spectral values were used corresponding to 100% and 200% of the target spectrum for an earthquake return period of 2475 years (the solid line of Fig. 4b). Fig. 7b presents the thirty geometric-mean spectra of the thirty pairs of scaled ground motions for Method 4 and an earthquake return period of 2475 years. The median of the thirty spectra of Fig. 7b is presented in Fig. 7a using a red dash line. The median spectrum of Fig. 7a matches reasonably well to the target at periods between 0.2T1 and 1.5T1. Panels c and d of Fig. 7 present the spectra of the scaled ground motions for Method 4 in the maximum (component 1) and
Fig. 7. Target design spectra for the sample site, the median spectra, spectra in maximum-minimum orientation and geometric-mean spectra of the 30 pairs of ground motions scaled to the design spectrum for a return period of 2475 years using Method 4.
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4.5. Method 5: Spectrum-matching to match the target spectrum
6. Results of response-history analysis
In Fig. 4, Fig. 6 and Fig. 7a, the spectral ordinates of the median spectra for Methods 1 through 4 are much lower compared to the target values (the solid lines in panels a and b of Fig. 4) at periods smaller than 0.2T1. Higher modes may contribute significantly to structural responses of tall buildings. To study the contribution of higher modes and the impact of the period range used in the scaling process for highrise buildings, ten pairs of ground motions were developed in which ground motions are spectrally matched to the target spectra of Fig. 4b for the entire period range. The spectrally-matched ground motions were developed using the computer code RSPMATCH [20] and the seed ground motions were selected from Table 1. Ten pairs were used because the dispersions in the structural responses for spectrallymatched ground motions are relatively smaller than those for other scaling methods studied herein and do not require as many ground motions to estimate the median and dispersion of structural responses at the same confidence level. Method 5 is included in this study also because the difference in the shape of median spectral ordinates between Methods 2 and 5 is arguably similar to that between CMS and UHS for a given return period. If the shape of a CMS is considered more realistic than that of a UHS, the results for Methods 2 and 5 can be used to evaluate the impact of spectral shape on performance of high-rise buildings.
Nonlinear response-history analysis was performed for the sample building using the thirteen sets of scaled ground motions described in the previous section. The results of peak floor acceleration, peak interstory drift and average floor spectral acceleration response over 5 through 33 Hz are presented in this section. Average floor spectral acceleration is used to represent the seismic demands on secondary systems, of which the frequencies are typically much larger than the fundamental frequency of a tall building. Good-of-fit tests were performed to check the distribution of structural responses. The results show that the distributions of the peak floor acceleration, average floor spectral acceleration and peak inter-story drift responses are approximately lognormal. Therefore, the structural responses of this study are presented with the help of the following parameters assuming lognormal distribution of the responses:
⎛1 θ = exp ⎜⎜ ⎝n
β=
n
⎞
i =1
⎠
∑ ln yi⎟⎟
1 n−1
(1)
n
∑ (ln yi
− ln θ )2
i =1
y16th = θ. e−β y84th = θ.
5. Ground-motion sets used in this study
eβ
(2) (3) (4)
where θ, y16th and y84th are the median (50th), 16th and 84th percentile values, respectively; yi is the response (peak floor acceleration, peak inter-story drift or average floor spectral acceleration) subjected to the ith ground motion and n is the total number of ground motions, which is 30 for Methods 1 through 4 and 10 for Method 5. Table 2 and Table 3 present the medians (θ) and dispersions (β), respectively, in the responses of the sample building for 100% and 200% of ground shaking intensity for an earthquake return period of 2475 years. The trends in the responses for an earthquake return period of 475 years are similar to those for 2475 years and are not presented in Table 2 and Table 3. For peak floor acceleration and average floor spectral acceleration, the results at the 2nd, 18th and 35th (roof) floors are presented in Table 2 and Table 3; for peak interstory drift, the results for the 1st, 17th and 34th stories are presented. In this paper, the 1st floor is at the ground level and the 35th floor is the roof of the sample building. The ith story is defined as the story between the ith and i+1th floors.
A total of thirteen sets of ground motions were used to perform nonlinear response history analysis of this building. Three of them are developed using Methods 1, 2 and 3 for an earthquake return period of 475 years. Five are developed using Methods 1 through 5 for an earthquake return period of 2475 years. The remaining five sets are for 200% of the sets corresponding to the earthquake return period of 2475 years. In Fig. 9a and Fig. 9d, the median of the geometric-mean spectra of the eight sets of scaled ground motions are presented for earthquake return periods of 475 and 2475 years, respectively. In Fig. 9b and Fig. 9e (Fig. 9c and Fig. 9f), the median spectra for the first (second) component of the scaled ground motion sets are presented. The median of the geometric-mean spectra for all cases for an earthquake return period of 475 (2475) years are almost identical in the period region of 0.2T1 to 1.5T1. For the median spectral acceleration at T1 (4.7 s) for the first component of the scaled ground motions for an earthquake return period of 2475 years, the values are 0.12g, 0.11g, 0.12g, 0.15g and 0.11g for Methods 1 through 5, respectively (see Fig. 9e); for the second component, the values are the values are 0.1g, 0.11g, 0.1g, 0.07g and 0.11g for Methods 1 through 5, respectively (see Fig. 9f).
6.1. Peak floor acceleration Median, 84th and 16th percentiles of peak floor acceleration at the
Fig. 8. Spectra of the 10 ground motions in X and Y directions spectrally matched to the target spectrum for a return period of 2475 years using Method 5.
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Fig. 9. Median spectra for component 1, 2 and geometric-mean of the ground motions scaled using Method 1 through 5.
estimation of median in peak floor acceleration response for Method 2 is more obvious in the X direction than in the Y direction. In Fig. 9a, Method 4 provides larger median values compared to the first three methods. Note that Method 4 provides greater median spectral ordinates compared to the first three methods in the X direction (see Fig. 9e). In Fig. 10a and Fig. 11a, Method 5 always produces median values greater than and dispersions similar to Method 2. In Fig. 6 and Fig. 8, Methods 2 and 5 provide similar spectral ordinates in the longer period range and the spectral ordinates are much larger at periods smaller than 1 s for Method 5. For Method 5 larger median value in peak floor acceleration at the 2nd floor is attributed by the higher modes of the sample building which is a reasonable observation for high-rise
2nd and 35th floors in the X (Y) direction are presented in Fig. 10a (Fig. 11a) for Methods 1 through 5. In general, Methods 1 and 3 provide similar median values. The median of peak floor acceleration is about 5–15% (2% to 9%) underestimated by Method 2 compared to the results for Method 1 in the X (Y) direction. The difference is not significant. The trends are slightly different in the X and Y directions which can be explained using the median spectra of Fig. 9 for components 1 and 2. In the X direction (i.e., component 1), Method 2 provides slightly smaller median spectral ordinates in the period region of 2 through 7 s compared to Methods 1 and 3 (Fig. 9b and Fig. 9e) while in the Y direction (i.e., component 2), Method 2 provides similar median spectral ordinates in the long period region compared to Methods 1 and 3 (Fig. 9c and Fig. 9f). As a result, the under-
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Table 2 Median responses of the sample building subjected to ground motions corresponding to 100% and 200% shaking levels for an earthquake return period of 2475 years. GM Intensity
100%, a return period of 2475 yrs
200%, a return period of 2475 yrs
Orientation Response Floor Method 1 Method 2 Method 3 Method 4 Method 5 Response Story Method 1 Method 2 Method 3 Method 4 Method 5 Response Floor Method 1 Method 2 Method 3 Method 4 Method 5
X Y Peak Floor Acceleration (g) 2nd 18th Roof 2nd 0.25 0.20 0.32 0.25 0.22 0.18 0.27 0.23 0.24 0.20 0.31 0.24 0.26 0.22 0.35 0.25 0.30 0.22 0.29 0.32 Peak Story Drift (mm) 1st 17th 34th 1st 38 31 13 33 29 27 11 30 33 31 13 29 46 37 15 25 29 28 11 32 Average Floor Spectral Acceleration (g) 2nd 18th Roof 2nd 0.29 0.22 0.33 0.29 0.26 0.19 0.28 0.26 0.28 0.22 0.33 0.28 0.30 0.24 0.37 0.29 0.43 0.23 0.31 0.43
X
Y
18th 0.19 0.18 0.18 0.18 0.20
Roof 0.30 0.28 0.29 0.26 0.29
2nd 0.49 0.44 0.44 0.52 0.61
18th 0.33 0.32 0.32 0.37 0.38
Roof 0.51 0.48 0.49 0.51 0.52
2nd 0.50 0.45 0.46 0.49 0.63
18th 0.33 0.32 0.32 0.32 0.36
Roof 0.51 0.50 0.48 0.47 0.53
17th 29 30 28 23 29
34th 15 14 14 13 14
1st 80 75 85 87 71
17th 55 48 57 60 51
34th 20 19 19 20 19
1st 74 73 69 53 68
17th 51 55 50 39 51
34th 25 25 24 22 25
18th 0.20 0.19 0.20 0.19 0.23
Roof 0.31 0.29 0.30 0.28 0.31
2nd 0.57 0.51 0.52 0.60 0.85
18th 0.37 0.34 0.35 0.39 0.43
Roof 0.54 0.49 0.52 0.53 0.55
2nd 0.58 0.51 0.54 0.56 0.85
18th 0.36 0.34 0.34 0.35 0.42
Roof 0.53 0.51 0.51 0.50 0.58
provide moderate dispersions in peak floor acceleration compared to the other methods.
buildings. It is also found that the higher-mode effect for acceleration response is more significant at the 2nd floor than at the roof. If the shape of median spectral ordinates for Method 2 is considered more realistic than that for Method 5, the use of Method 5 may overestimate seismic loss of a tall building with acceleration-sensitive equipment and components installed in the lower levels. The dispersion in peak floor acceleration is greatly influenced by the dispersion in spectral ordinates of ground motions in the short period range. In Table 3, Fig. 10a and Fig. 11a, the dispersion in peak floor acceleration is smallest for Methods 2 and 5 (spectrum-matching method) and largest for Method 3 (Sa (T1) scaling method) among the five scaling methods. Dispersion in spectral ordinates is smallest in the short period range for Methods 2 and 5 (see Fig. 6 and Fig. 8). In Method 3, the seed ground-motion pairs are amplitude scaled to match the target spectrum at only first mode period of the building and the dispersion in spectral ordinates is greatly increased in the short period range (see Fig. 5b). The dispersion in peak floor acceleration is therefore significant due to higher-mode effect. Methods 1 and 4
6.2. Peak story drift Median, 84th and 16th percentiles of peak story drift of the first and 34th stories in the X (Y) direction are presented in Fig. 10b (Fig. 11b) for Methods 1 through 5 and three ground-motion intensity levels. In general, the differences in the median values are less than 10% 1) among Methods 1, 2 and 3 in the Y direction, and 2) between Methods 1 and 3 in both the X and Y directions. Median story drift in the X direction for Method 2 is 6–24% smaller than that for Method 1. In the X direction, Method 4 always produces larger median story drift compared to the other four methods (see Fig. 10b) at a given shaking intensity. Median story drift in the X direction for Method 4 is about 10–20% greater than that for Method 1. Although Method 4 has median geomean spectral ordinates similar to the other methods at periods between 0.2T1 to 1.5T1 (see Fig. 9d), it provides larger median
Table 3 Dispersions in the responses of the sample building subjected to ground motions corresponding to 100% and 200% shaking levels for an earthquake return period of 2475 years. GM Intensity
100%, a return period of 2475 yrs
200%, a return period of 2475 yrs
Orientation Response Floor Method 1 Method 2 Method 3 Method 4 Method 5 Response Story Method 1 Method 2 Method 3 Method 4 Method 5 Response Floor Method 1 Method 2 Method 3 Method 4 Method 5
X Y Peak Floor Acceleration (g) 18th Roof 2nd 2nd 0.35 0.18 0.16 0.44 0.18 0.12 0.13 0.15 0.69 0.44 0.39 0.76 0.46 0.27 0.23 0.40 0.12 0.14 0.08 0.21 Peak Story Drift (mm) 1st 17th 34th 1st 0.58 0.43 0.25 0.47 0.14 0.09 0.13 0.10 0.31 0.22 0.28 0.3 0.57 0.42 0.24 0.38 0.12 0.08 0.11 0.11 Average Floor Spectral Acceleration (g) nd th 2 18 Roof 2nd 0.42 0.24 0.18 0.52 0.12 0.12 0.12 0.1 0.74 0.49 0.41 0.81 0.53 0.31 0.23 0.45 0.08 0.17 0.09 0.1
X
Y
18th 0.30 0.12 0.57 0.25 0.13
Roof 0.25 0.15 0.50 0.25 0.08
2nd 0.33 0.18 0.61 0.47 0.12
18th 0.20 0.14 0.40 0.32 0.15
Roof 0.17 0.10 0.30 0.19 0.09
2nd 0.44 0.15 0.73 0.38 0.21
18th 0.32 0.13 0.52 0.25 0.15
Roof 0.24 0.11 0.40 0.19 0.09
17th 0.43 0.07 0.22 0.40 0.05
34th 0.27 0.16 0.39 0.26 0.09
1st 0.56 0.22 0.29 0.54 0.25
17th 0.40 0.15 0.24 0.36 0.16
34th 0.14 0.09 0.15 0.15 0.10
1st 0.54 0.19 0.28 0.45 0.17
17th 0.40 0.10 0.18 0.33 0.09
34th 0.19 0.12 0.26 0.19 0.08
18th 0.35 0.12 0.61 0.32 0.17
Roof 0.28 0.14 0.52 0.28 0.09
2nd 0.41 0.12 0.68 0.51 0.08
18th 0.29 0.14 0.48 0.34 0.17
Roof 0.20 0.09 0.35 0.22 0.09
2nd 0.51 0.10 0.78 0.42 0.10
18th 0.38 0.13 0.58 0.32 0.19
Roof 0.27 0.11 0.45 0.23 0.13
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Fig. 10. Median, 84th and 16th percentile values of different response quantities at different floors in X direction using Methods (1) through (5).
and dispersion values at a given story for a given shaking intensity. The difference in the distributions of peak story drift between Methods 2 and 5 is much smaller than that in the distributions of peak floor acceleration at the 2nd floor. This observation indicates that the contribution from the higher modes of the sample building on displacement response is smaller than the first mode. In general, the dispersion in peak story drift is smallest for Methods 2 and 5 and largest for Methods 1 and 4 among the five methods
spectral ordinates in the X direction (see Fig. 9e). Conversely, in the Y direction, Method 4 provides lower median spectral ordinates in the long period region compared to the other methods (see Fig. 9f). As a result, median story drift for Method 4 is lower than that for the other four methods in the Y direction (see Fig. 11b). The difference in the responses between Methods 1 and 4 clearly demonstrates the impact of ground-motion orientation on performance of tall buildings. In Fig. 10b and Fig. 11b, Methods 2 and 5 provide similar median 133
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Fig. 11. Median, 84th and 16th percentile values of different response quantities at different floors in Y direction using Methods (1) through (5).
spectral ordinates is small at periods close to T1 and significant in the short period range (see Fig. 5b).
studied herein. It has higher correlation to the dispersion in spectral ordinates at periods close to T1 than that in the short period range. For example, the larger dispersions in peak story drift for Methods 1 and 4 is not surprising since the dispersions in spectral ordinates for those methods are greater than for the other methods in the long period range, where T1 is located (see Fig. 5a and Fig. 7b). The dispersion in peak story drift for Method 3, namely, the Sa(T1) method, is moderate compared to that for the other methods. In Method 3, the dispersion in
6.3. Average floor spectral acceleration Median, 84th and 16th percentiles of floor spectral acceleration averaged over a frequency range of 5 through 33 Hz for Methods 1 through 5 are presented in Fig. 10c and Fig. 11c, for the X and Y 134
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Method 3 is smaller than that for Methods 1 and 4 in the period range close to the fundamental period of the sample building, and therefore Method 3 has smaller dispersions in drift response than Methods 1 and 4. 8. Based on the analysis results of this study, we conclude that optimal ground-motion scaling procedures for performance assessment of a high-rise building depend on the target seismic hazard (spectral accelerations over a wide period range) and the characteristics and positions of structural and nonstructural components in the building (acceleration- or displacement-sensitive components). These factors should be considered in the scaling procedures of ground motions.
directions, respectively, for three ground-motion intensity levels. The trends are generally similar to those for peak floor acceleration and not repeated herein. 7. Conclusions A series of bi-directional nonlinear response-history analyses were performed for a 34-story sample building to study the impact of ground-motion scaling on the performance of high-rise buildings. Ground motions were scaled for a wide range of hazard using the geomean scaling method (Method 1), spectrum-matching method (Methods 2 and 5), Sa(T1) method (Method 3), and maximumminimum orientation scaling method (Method 4). All the scaled ground-motion sets for a given hazard level have similar median geomean spectral ordinates in the period region of 0.2T1 to 1.5T1. Both medians and dispersions in peak floor acceleration, peak interstory drift and average floor spectral acceleration of the sample building are presented and discussed. Major conclusions are summarized as follows:
Acknowledgements This research is supported by grants from Cutting-edge Urban Development Program funded by Ministry of Land, Transport and Maritime Affairs of Korean (Code# ’09R & D A01) and from the National Science Council of Taiwan (NSC 102–2218-E-002–007). Ms. Yu-Wen Chang provided seismology information for cities in Taiwan. Dr. Chyng-Maw Su, Mr. Bruce Li and Mr. Huan-Wei Chen provided information for the 34-story building analyzed in this study. Their assistance is acknowledged.
1. In general, Methods 1 and 3 provide similar median values for both acceleration and drift responses. Method 2 moderately underestimates the median responses computed for Method 1. 2. The difference in the distributions of structural responses between Methods 1 and 4 identifies the impact of orientations of ground motions on the demands of the sample building. In general, median responses in the maximum direction (i.e., the X direction in this study) for Method 4 are about 10–20% greater than that for Method 1. Both methods provide similar dispersions in the responses. 3. The difference in the distributions of structural responses between Methods 2 and 5 identifies the impact of spectral shape on the demands of the sample building. Method 5 provides larger median values for peak floor acceleration and average floor spectral acceleration responses at lower floors of the sample building compared to Method 2 and the other methods due to higher spectral ordinates in the short period range. For peak story drift, Method 5 provides similar median values as Method 2. The impact of higher-mode effect is more significant for acceleration response than for drift. Methods 2 and 5 provide the smallest dispersions in the responses among the five methods studied herein. A smaller dispersion enables the use of a smaller number of ground motions in response-history analysis for stable estimates with acceptable accuracy and confidence level. However, spectrum-matching scaling may not be appropriate when the seismic loss of a building is sensitive to dispersions in the responses. 4. The dispersions in acceleration responses have a higher correlation with the dispersion in spectral ordinates of ground motions in the short period range than at the fundamental period of the sample building. The dispersion in spectral ordinates for Method 3 is greater than that for the other methods in the short period range for a given hazard level, and therefore Method 3 has largest dispersions in acceleration responses. If Method 3 is used in a performance assessment of a high-rise building, spectral shapes of seed ground motions should be selected carefully to avoid the significant dispersion in spectral ordinates in the short period range. 5. For analysis of high-rise buildings sensitive to multi-mode excitation use of Method 3 can be inappropriate as it underestimates the medians and provides highest dispersions for floor acceleration and average floor spectral acceleration responses. 6. If prediction of damage to non-structural components is an objective of the analysis, then an appropriate method is Method 5 which takes into account contributions from higher modes. 7. The dispersions in peak story drift have a higher correlation with the dispersion in spectral ordinates of ground motions in the period range close to the fundamental period of the sample building than in the short period range. The dispersion in spectral ordinates for
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