Nonstructural components and systems (NCSs), often referred to as ... The seismic acceleration demands on NCSs for the two buildings in the recorded.
10NCEE
Tenth U.S. National Conference on Earthquake Engineering Frontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska
SEISMIC DEMANDS ON ACCELERATIONSENSITIVE NONSTRUCTURAL COMPONENTS USING RECORDED BUILDING RESPONSE DATA – CASE STUDY X. Wang1, R. Astroza1, T. Huchinson1, J. Conte1, and R. Bachman2 ABSTRACT This paper investigates seismic demands on acceleration-sensitive nonstructural components using building responses measured on two multi-story reinforced concrete (RC) buildings during a variety of strong earthquake events. The measured data are unique in the sense that they incorporate the building responses at different levels of nonlinearity. The seismic demands on acceleration-sensitive nonstructural components using the recorded responses of the instrumented buildings are evaluated and compared with current code provisions. It is observed that the seismic demands of acceleration-sensitive nonstructural components are sensitive to building nonlinear effects as a result of the building period elongation and the variations of other modal parameters. It is demonstrated that improved seismic demand estimations can be achieved using modal analysis procedures incorporating the modal characteristics of buildings at the corresponding level of nonlinearity.
1 2
Dept. of Structural Engineering, University of California, San Diego, La Jolla, CA 92093-0085 RE Bachman Consulting Structural Engineers, Laguna Niguel, CA 92677
X. Wang, R. Astroza, T. Huchinson, J. Conte, and R. Bachman. Seismic demands on acceleration-sensitive nonstructural components using recorded building response data – case study. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
Seismic Demands on Acceleration-Sensitive Nonstructural Components Using Recorded Building Response Data – Case Study X. Wang1, R. Astroza1, T. Huchinson1, J. Conte1, and R. Bachman 2 ABSTRACT This paper investigates seismic demands on acceleration-sensitive nonstructural components using building responses measured on two multi-story reinforced concrete (RC) buildings during a variety of strong earthquake events. The measured data are unique in the sense that they incorporate the building responses at different levels of nonlinearity. The seismic demands on acceleration-sensitive nonstructural components using the recorded responses of the instrumented buildings are evaluated and compared with current code provisions. It is observed that the seismic demands of acceleration-sensitive nonstructural components are sensitive to building nonlinear effects as a result of the building period elongation and the variations of other modal parameters. It is demonstrated that improved seismic demand estimations can be achieved using modal analysis procedures incorporating the modal characteristics of buildings at the corresponding level of nonlinearity.
Introduction Nonstructural components and systems (NCSs), often referred to as secondary systems, are elements that support the operability of a building but are not considered as part of their primary load bearing system. They usually account for 70-80% of the overall investment of buildings (Taghavi and Miranda, 2003). More importantly, NCSs are critical to the postearthquake operability and survivability of a building. Nonetheless, NCSs are particularly vulnerable to seismic damage and continue to plague the society in the form of excessive economic losses and concerns for life safety (Dhakal, 2010; Miranda et. al., 2012). In view of the seismic vulnerability of NCSs and their significance related to post-earthquake building functionality, design practitioners have been focused on the development of seismic design recommendations for NCSs (ATC 1978, BSSC 1994; BSSC 1994). These works largely form the basis of current seismic design code provisions for NCSs (ASCE 7-05, 2005). Current code provisions provide a simplified equation which include upper and lower bounds to determine the seismic force demands on NCSs. This formulation is intended to be reasonably conservative for nonstructural components in general since it implicitly incorporates the uncertainties associated with design earthquake ground motions as well as structural types and stories of individual buildings (BSSC, 1997). It is noted that the upper bound accounts for the fact that structures are expected to experience significant inelastic deformations during a design earthquake event, which would result in reduced nonstructural spectral acceleration demands at upper floors. In 1 2
Dept. of Structural Engineering, University of California, San Diego, La Jolla, CA 92093-0085 RE Bachman Consulting Structural Engineers, Laguna Niguel, CA 92677
X. Wang, R. Astroza, T. Huchinson, J. Conte, and R. Bachman. Seismic demands on acceleration-sensitive nonstructural components using recorded building response data – case study. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.
addition, current code provisions also provide an alternative procedure using modal analysis methods to determine building-specific nonstructural seismic design force demands provided that the dynamic characteristics of the structures are determined by analysis prior to the design of NCSs. In the meantime, researchers have been prompted to advance the state of knowledge related to NCSs seismic demands. Miranda and Taghavi (2005) proposed an analytical method for peak floor acceleration (PFA) estimation of generic buildings using a continuous linear-elastic shear– flexural beam model. In addition, several numerical studies have been conducted to study the effects of building nonlinearity on the seismic acceleration demands on NCSs. Rodriguez et al. (2002) and Ray Chaudhuri and Hutchinson (2011) study the PFA response using various building prototypes; Medina et al. (2006) initiated a comprehensive study to investigate floor response spectra (FRS), and similar studies were conducted by Weiser et al. (2013). These studies have provided valuable insight to understanding the seismic demands on accelerationsensitive NCSs. Nevertheless, previous studies have been largely based on data recorded on buildings in their elastic range (e.g., Fathali and Lizundia, 2011) or numerical simulations (e.g., Medina et al., 2006) to account for building nonlinear behavior. This fact warrants further study of the seismic demands of NCSs as the recorded nonlinear building responses become available. To this end, this paper investigates seismic demands on acceleration-sensitive NCSs using data recorded on two multi-story reinforced concrete (RC) buildings during a variety of strong earthquake events. One building corresponds to a 5-story RC building tested on the NEES@UCSD shake table in 2012 (BNCS building), while the other is a 7-story RC hotel building in Van Nuys, California (VNH building). The recorded data are unique in the sense that they incorporate the response of the buildings at different levels of nonlinearity. The objective of this study is to extend the understanding of NCS acceleration demand estimation using the recorded data. The seismic acceleration demands on NCSs for the two buildings in the recorded earthquake events are evaluated and compared with current code provisions. In addition, modal analysis procedures are implemented to achieve improved estimations of NCS acceleration demands for the BNCS building, and the effectiveness of these methods is demonstrated. Building Structures and Recorded Earthquake Motions BNCS test building The BNCS test building was a five-story RC frame structure tested at the NEES@UCSD shake table facility in 2012 (Chen et al., 2013). The building was conceptually designed for a hypothetical site located in a high seismic zone in Southern California (site class D) with spectral accelerations SDS = 1.41 g and SD1 = 0.95 g. As shown in Fig. 1b, the building consisted of two bays in the longitudinal (shaking) direction and one bay in the transverse direction, resulting in a plan dimension of 10.4×6.1 m. A pair of moment resisting frames was placed in the east bays in the longitudinal direction, while two transverse concrete walls were placed on the northwest side of the building to facilitate transverse lateral load resistance. The diaphragm at each floor provided two openings, one on the southeast and the other on the northwest of the building (Fig. 1b). The building floor-to-floor height was 4.3m at each level, resulting in a total building height of 21.3 m above the foundation (Fig. 1a). Each floor of the building was instrumented with four tri-axial accelerometers placed at the corners of the slab. In addition, two tri-axial accelerometers were deployed on the shake table platen to measure the achieved table motions. It is noted that
the building was severely damaged in the last two fixed base tests due to large drift demands (approaching 6% story drift during the last test). Fracture of the longitudinal reinforcement within the frame beams and punching shear mechanisms were detected at levels 2 and 3. The (fixed-base) BNCS building was tested with six earthquake input motions applied to progressively damage the structure, including four spectrally-matched motions conforming to the design spectra shape as well as two long-duration amplitude-scaled motions recorded during a subduction earthquake. Four seismic tests are selected in this study to represent different seismic hazard levels, and the associated parameters of the achieved earthquake input motions are summarized in Table 1. The 5% damping elastic acceleration spectra of the earthquake input motions and the ASCE 7-05 design spectra corresponding to the hypothetical site of the building are also shown in Fig. 1c. As shown in table 1, an equivalent short period spectral accelerations Sa,mean(T0~Ts, ξ=5%) is determined as an average spectral acceleration between T0 and Ts as defined in the ASCE 7-05 design spectra. These values represent a seismic hazard measure of the individual earthquake motions consistent with the code-specified short period spectral acceleration.
N
W
E
2 FB 1 FB 2 FB 4 FB 5 ASCE 7
Stair Opening
Sa (g)
6.1 m
4.3 m
Total Height
21.3 m
1.5 Elevator Shaft
1 0.5 0
0.5
1
1.5
2
Period (s)
5.2 m
5.2 m
W
0
E
(a)
(b)
(c)
Figure 1.
BNCS test building: (a) structural skeleton, (b) plan layout, and (c) 5% damping elastic acceleration spectra of the achieved earthquake input motions.
Table 1.
Summary of earthquake input motions of the BNCS building Test Seed record name FB-1 Canoga Park - 1994 Northridge FB-2 LA City terrace - 1994 Northridge FB-4 ICA - 2007 Pisco (Peru) FB-5 TAPS Pump #9 - 2002 Denali 1 2
PGA1 Sa,mean(T0~Ts, ξ=5%) Scaling (g) method2 (g) 0.21 0.40 SM 0.18 0.44 SM 0.25 0.47 AS 0.64 1.38 SM
PGA = peak ground acceleration as achieved on the shake table platen; SM = spectral matching; AS = amplitude scaling
Van Nuys hotel building The Van Nuys hotel (VNH) building is a seven-story RC building constructed in 1966 in the Los
Angeles area. According to ASCE 7-05, the site-specific design spectral accelerations (site class D) are SDS = 1.30 g and SD1 = 0.70 g, respectively. The building plan configuration was nearly identical at each floor with a slightly different layout at the ground floor (Fig. 2b). The plan dimension of the building was 45.7×18.9 m, including eight bays in its longitudinal direction and three bays in its transverse direction. The lateral force resisting system consisted of interior column-slab frames and exterior column spandrel beam frames (Naiem, 2000). The total height of the building was 20.04 m, with 4.15 m at level 1 and 2.65 m from level 2 to level 6, and 2.64 m at level 7 (Fig. 2a). As presented in Fig. 2, the building was instrumented with sixteen uniaxial accelerometers to measure the horizontal accelerations at the ground floor, second floor, third floor, sixth floor, and the roof. The building structure was severely damaged in the 1994 Northridge earthquake as a result of column shear cracking in the longitudinal exterior frames, significantly impairing its lateral load capacity (Ivanović et al., 2000). Several strong earthquake events, between the 1971 San Fernando and 1994 Northridge earthquakes, were recorded by the VNH building. The 1971 San Fernando (Mw=6.6) and 1994 Northridge (Mw=6.7) earthquakes were near-field events, while other recorded earthquakes were far-field events with moment magnitudes ranging between 4.6 and 7.2 (Trifunac et al., 2000). Four earthquake events with relative high acceleration demands selected in this study are summarized in Table 2. Since there were no free-field motion records near the building, the accelerations recorded at the ground floor are considered as the input ground motions for the building in this study. The 5% damping elastic acceleration spectra of the recorded ground motions are also provided in Fig. 3. Compared with the ASCE 7-05 design spectra, NOR represents an event comparable with a design earthquake event, while the remaining three events are within the serviceability levels of the building. N
20.04 m
2.65 m per floor
Typical Floor
Ground Floor
(a)
18.6 m
4.15 m
45.7 m
45.7 m
Figure 2.
18.6 m
2.64 m
45.7 m
(b)
Van Nuys hotel building layout (with sensor locations): (a) elevation, and (b) plan. Current Code Provisions for Acceleration-Sensitive NCSs
Determination of seismic demand on acceleration-sensitive NCSs involves the evaluation of PFA and FRS. Current code provisions (ASCE 7-05, 2006) provide a simplified equation (Eq. 13.3-1) to determine the horizontal seismic design force 𝐹! : 𝐹! =
0.4𝑎! 𝑆!" 𝑊! 𝑧 1 + 2 1 𝑅! 𝐼! ℎ
where 𝑊! is the component operating weight; 𝑆!" is the short period spectral acceleration; 𝑧 is the height in structure of attachment point; ℎ is the total height of structure; 𝑎! is the component amplification factor; 𝐼! and 𝑅! are component importance factor and response modification factor, respectively. It is noted that 0.4𝑆!" in Eq. 1 represents the peak ground acceleration (PGA) provided the spectral shape of the ground motion is consistent with ASCE 7-05 design spectra. The structure acceleration amplification factor, 𝑎! , is empirically defined as 1 + 2𝑧/ℎ, i.e., a linear amplification of the PGA along the building height (BSSC, 1997). Moreover, the component amplification factor, 𝑎! , is defined as 1.0 for rigid components and 2.5 for flexible components. The frequency to distinguish between rigid and flexible components is taken as 0.06 s (16 Hz). The seismic force demand Fp is bounded between 0.3𝑆!" 𝐼! 𝑊! and 1.6𝑆!" 𝐼! 𝑊! . The upper bound is introduced to account for reduced nonstructural spectral acceleration demands at upper floors during design earthquake events as a result of significant inelastic deformations of the structure, while the lower bound accounts for the fact at very short periods, the structural inelastic acceleration demands approaches the PGA at the ground lower floor, where ductility effects do not reduce seismic demands. Table 2.
Earthquake events of the VNH building Motion
Earthquake
WHI 1987 Whittier SMA 1991 Sierra Madre LAN 1992 Landers NOR 1994 Northridge 1 2
Mw 5.9 5.6 7.2 6.7
Rupture distance The accelerometer at the ground floor measuring the longitudinal component did not work 2
2
(a)
1 0.5 0
WHI SMA LAN NOR ASCE 7
1.5
Sa (g)
Sa (g)
(b)
SMA LAN NOR ASCE 7
1.5
1 0.5
0
0.5
1
Period (s)
Figure 3.
PGA (g) Sa,mean(T0~Ts, ξ=5%) (g) Long. Trans. Long. Trans. 2 2 N/A 0.14 N/A 0.31 0.06 0.05 0.09 0.13 0.04 0.04 0.18 0.07 0.44 0.37 1.13 1.12
R1 (km) 41 44 186 4
1.5
2
0
0
0.5
1
1.5
2
Period (s)
Elastic acceleration spectra of the recorded ground motions of the VNH building (5% damping): (a) longitudinal, and (b) transverse.
To account for the dynamic characteristics of individual structures, current code provisions allow the modal response spectrum analysis (MRSA) procedure for the evaluation of NCS seismic force demands (ASCE 7-10 Eq. 13.3-4): 𝐹! =
𝑎! 𝑎! 𝑊! 𝐴 (2) 𝑅! 𝐼! !
where 𝑎! is the peak floor acceleration at level 𝑖 determined by MRSA; 𝐴! is the torsional
amplification factor. In Eq. 2 the improved estimate of PFA, 𝑎! , is adopted to replace the empirical linear distribution 0.4𝑆!" (1 + 2𝑧/ℎ). AC156 (ICC, 2012) also develops a required response spectrum (RRS) for shake table qualification testing of NCSs on the basis of ASCE 7-05 (2006) code provisions. Assuming the component modification factors 𝐼! and 𝑅! both equal to 1.0 in Eq. 1, the spectral accelerations for rigid and flexible components, 𝐴!"# and 𝐴!"# respectively, are defined as: 𝐴!"# = 0.4𝑆!" 1 + 2𝑧/ℎ , 𝐴!"# = 𝑆!" 1 + 2𝑧/ℎ (3) Instead of using a constant value for flexible components in all period range, the RRS is divided into three period intervals based on the fundamental period of individual components for the determination of the component spectral acceleration 𝐴! . Similar to ASCE 7-05 (2006) design provisions, the upper bound of 𝐴!"# is 1.6𝑆!" while the lower bound of ARIG is 0.4SDS. Observed Seismic Demands of Acceleration-Sensitive NCSs Structure Acceleration Amplification Factor (as) The structure acceleration amplification factor as represents the dynamic amplification effects of the structure to earthquake motions. Therefore, the factor is critical for PFA estimation – the seismic demands on rigid NCSs. As shown in Fig. 4a, the structural acceleration amplification factors of the BNCS building at the roof range between 1.5 and 2.5, which are lower than the code-specified value (3.0 at the roof) for all earthquake events. The highest amplification is related to FB-4 due to the fact that the spectral shape of this long-duration subduction earthquake greatly differs from that of a code-confirming spectrum, as the spectral peaks are located near the fundamental period of the building. The lowest amplification, as observed in FB-5, is caused by period elongation associated with the building nonlinearity that significantly reduced the spectral acceleration of the building at the fundamental mode. Similarly, the amplification factors of the VNH building in both directions are much smaller than the code values in all earthquake events other than LAN (Figs. 4b and 4c). As for NOR, an earthquake that is comparable to a design earthquake event for the VNH building, the amplification factors in both directions are about 1.3 at the roof, significantly lower than the code-specified value. LAN is the only event that the amplification factors exceed the code-specified values. However, this large-distance lowamplitude event (PGA=0.04 g), with the ground motion spectra dominated by long-period peaks, is non-typical of an earthquake event that is considered in the design codes in the United States. The results demonstrate that the empirical linear distribution 1 + 2𝑧/ℎ slightly overestimates the structure amplification effects in the lower level (less than design level) earthquakes but it significantly overestimates the amplification effects in the design level earthquakes. This is due to the fact that the empirical linear distribution is developed to envelope structure amplification effects absent knowledge of the dynamic characteristics of structures. However, the estimation of floor spectral acceleration demands (which is the product of the structure and component amplification effects) can be effectively reduced by taking into account of the upper bound values in the simplified code equation, as discussed later in Fig. 8.
1
0.4
FB FB FB FB
0.2
1 2 3 as (PFA/PGA)
1 2 4 5
(c)
0.8 0.6 0.4 SMA LAN NOR
0.2 0 0
1 2 3 as (PFA/PGA)
Normalized Height (z/h)
0.6
Normalized Height (z/h)
Normalized Height (z/h)
Figure 4.
(b)
0.8
0 0
1
1
(a)
0.8 0.6 0.4
WHI SMA LAN NOR
0.2 0 0
1 2 3 as (PFA/PGA)
Structure acceleration amplification factor: (a) BNCS building, (b) VNH building – longitudinal, and (c) VNH building – transverse.
Component Amplification Factor (ap) Component amplification factor ap reflects the dynamic amplification effect of NCSs. As nonlinear effects of NCSs are addressed by component modification factor Rp, this study focuses on the evaluation of acceleration demands on NCSs that remain elastic. In this study 5% damping is considered in the evaluation of FRS, and the component amplification factors are calculated as the ratio between the FRS and PFA. As shown in the BNCS building results (Fig. 5), the observed component amplification factor peaks are tuned with the longitudinal modal periods of the building (the details of modal properties of the BNCS building are discussed later in the paper). In addition, the variation of the peaks along the height of the building closely resembles that of the mode shapes. As is evident in the case of FB-1 and FB-4, the peak value of the first mode increases nearly monotonically as the building height increases (Figs. 5a and 5b), and in FB-5 the peak of the second mode markedly reduced at the fifth floor – the location of the “node” of the second mode (Fig 5c). Similar observations on the component amplification factors are also reflected in the results of the VNH building (Fig. 6). In addition, it is clearly observed that a constant value of 2.5 is not capable to capture the elastic dynamic amplification effects of NCSs given that the natural period of a component is tuned with one of the modal periods of the primary structure. However, these are not unexpected results since the codespecified component amplification factors, analogous to those of ground motion design spectra, are intended to provide an average estimate of the amplification effects of NCSs in the period range of interest (0.06 s to 0.6 s) rather than at specific spectral peaks. Unlike the case that increased building nonlinearity reduces structural amplification effects, the component amplification factors are more complicatedly affected by building nonlinear behavior. As building response remains slightly or moderately inelastic (Figs. 5a and 5b), the observed component amplification factor peaks are dominated by the periods tuned with the building fundamental period, while in the case of significant building nonlinearity, the component amplification factors tuned with the higher mode periods increase sharply and become dominant at the lower floors, but at higher floors the maximum amplification remains related to the first mode of the building (Fig. 5c). These observations are also confirmed by the NOR results of the VNH building in the longitudinal and transverse directions, as shown in Figs. 6b and 6e. However, it is also noted that the component amplification factor peaks are tuned with
the higher mode periods of the building in the less than design earthquake event WHI (Fig. 6c). This may be resulted from the fact that the frequency content of the motion is concentrated around the frequency tuned with one of the higher mode of the building and very low spectral values near the fundamental period of the building (Fig. 3b). 1
2
1
(a)
6
5
6
(c) 6
(b) ap
ap
ap
42
20 0 0.5 0 1 0 1.5 P 0.5 2 1 eriod (s) 1.5 2 0 Perio 2.5 d (s) 3
H eig H ht ei (z/ gh h) t (z /h a ) p
20 0 0.5 0 1 0 1.5 P 0.5 2 1 eriod (s) 1.5 2 0 Perio 2.5 d (s) 3
H eig H ht ei (z/ gh h) t (z /h a ) p
ap
42
1 0.8 0.61 0.40.8 0.20.6 0 0.4 0.2
(c)
64
64
42
1 0.8 0.61 0.40.8 0.20.6 0 0.4 0.2
1 20 0.8 0.6 0 1 0.40.8 0.5 0 1 0.20.6 0 1.5 0 0.4 P 0.5 2 1 eriod (s) 1.5 0.2 2 0 Perio 2.5 d (s) 3
Component amplification factor of BNCS building: (a) FB-1, (b) FB-4, and (c) FB-5 (ap > 2.5 denoted by warm colors and ap ≤ 2.5 denoted by cold colors). 1
2
3
4
5
6
1
2
3
4
5
6
(a)
(a)
0.8 0.6
(d)
20 0 0 0
0.5 1 0.5 Perio 1.5 1 d (s) 1.5 Perio 2 2.5 d (s)
1 0.8 0.6 1 0.4 0.8 0.2 0.6 0 0.4 0.2 0
eig Hei ht gh (z/ t (z h) /h )
2
3
0.6 0.4
42
2
H
ap ap
eig Hei ht gh (z/ t (z h) /h )
3
(e)
4
4
4
2
0
0
0
0.5
1
0
0.5
1
0.5
1 Perio 1.5 d (s)
2
0
1 0.8 0.6 0.4 0.2
z/h )
0 0
ht (
z/h )
ht (
0 0
2 1 0.8 0.6 0.4 0.2
eig
ht (
z/h )
1 Perio 1.5 d (s)
eig
0.5
H
0 0
2 1 0.8 0.6 0.4 0.2
H
2
0.2 0
ap
6
ap
6
ap
6
0.4 0.2
0.5
1 Perio 1.5 d (s)
eig
0.5 1 0.5 Perio 1.5 1 d (s) 1.5 Perio 2 2.5 d (s)
1 0.8 0.6 1 0.4 0.8 0.2 0.6 0 0.4 0.2 0
H
ap ap
(c)
(b)
6
64
42 20 0 0 0
1 0.8
2
0
H
6
1
(b)
64
Figure 6.
5
4
(b) 6
64
Figure 5.
4
3
H eig H ht ei (z/ gh h) t (z /h )
(a) 6
3
2
Component amplification factor of VNH building: (a) LAN – longitudinal, (b) NOR – longitudinal, (c) WHI – transverse, (d) LAN – transverse, and (e) NOR – transverse. Acceleration Demand Estimation with Modal Analysis Procedures
As the seismic demands of acceleration-sensitive NCSs are markedly influenced by the modal characteristics of the primary structure, two modal analysis procedures are conducted in this study to demonstrate their effectiveness of improving the acceleration demand predictions: 1) the standard modal time history analysis (MTHA) method, and 2) the modal response spectrum analysis (MRSA) method (Chopra, 2001). MTHA requires time history analysis of linear modal single-degree-of-freedom (SDOF) systems, and it is considered “exact” in the sense
that the method leads to exact modal contributions for elastic buildings. In contrast, MRSA, as a code-specified alternative for PFA evaluation (Eq. 2), is an approximate method that involves modal combination rules for the calculation of acceleration demands. Note also that MRSA only estimates the PFAs instead of floor acceleration time histories, and thus it cannot be applied for the evaluation of FRS. The modal parameters of the BNCS building are identified using the data recorded from white noise (WN) and pulse base excitation tests (Astroza et al., 2013). The modal parameters related to the first three longitudinal modes of the building identified from the 3.5% g WN test prior to the first (fixed base) seismic test, defining the undamaged (reference) state for the building, are summarized in Table 3. It is observed that the accumulated effective modal weight of the first three longitudinal modes exceeds 95% of the total (inertial) weight of the building and its NCSs, and therefore the contribution of these modes is sufficient for the purpose of modal combination. In addition, well-spaced longitudinal modal periods of the building justify the use of SSRS modal combination rule in this study. Table 3.
Modal parameters of the first three longitudinal modes of BNCS building in its undamaged state Mode
Period (s)
1-L 2-L 3-L accumulated
0.79 0.19 0.10 /
Modal participation Effective modal Percentile factor weight (kN) weight (%) 1.25 3685.5 83.1 -0.37 334.6 7.5 0.27 257.2 5.8 / 4277.3 96.4
The modal parameters of the first three identified longitudinal modes of the building following the seismic tests FB-1, FB-4, and FB-5 are provided in Table 4. The progression of the modal parameters indicates that building nonlinearity affects the building periods most significantly. The modal participation factors (MPFs) are observed to be less sensitive to the nonlinear effect than the building periods, however larger variation of the MPFs is detected on the third mode. The mode shapes, though not shown in the paper for brevity, remain similar to those of their respective undamaged states for the first mode but show slightly larger differences for the higher modes at different damage states. Using the identified modal parameters, MTHA and MRSA are conducted to estimate the floor acceleration responses. Constant damping ratios, 7% for FB-1, 5% for FB-4, and 6% for FB-5, respectively, are applied to all three modes considered in MTHA, and they are used consistently in MRSA for the calculation of ground motion response spectra. These values represent equivalent viscous damping ratios for a linear SDOF including different sources of energy dissipation mechanisms (e.g., material nonlinear hysteresis). As shown in Fig. 7, the results indicate that both modal analysis procedures produce reasonable estimates of the PFAs as well as the profiles along the building height in the three seismic tests. These observations suggest that the PFA responses can be reasonably estimated using modal combination of equivalent linear SDOF systems by considering period elongations and the variation of modal parameters related to the building nonlinear effects. The accuracy of results may be further improved by conducting
nonlinear SDOF time history analysis and investigating the damping effects of the building, however these studies are out of the scope of this paper. Modal periods and MPFs of BNCS building of the three seismic events Motion FB-1 FB-4 FB-5
Mode 1-L Period (s) MPF 0.92 1.23 1.19 1.22 1.56 1.21
1
Mode 2-L Period (s) MPF 0.21 -0.40 0.23 -0.41 0.31 -0.36 1
0.8
0.6
0.4
ASCE7 MRSA MTHA Recorded
0.2
Figure 7.
1
(b)
0.2
0.4 PFA (g)
0.6
Normalized Height (z/h)
Normalized Height (z/h)
(a)
0 0
Mode 3-L Period (s) MPF 0.11 0.31 0.12 0.38 0.16 0.19 (c)
0.8
0.6
0.4
ASCE7 MRSA MTHA Recorded
0.2
0 0
0.2
0.4 0.6 PFA (g)
0.8
Normalized Height (z/h)
Table 4.
0.8
0.6
0.4
ASCE7 MRSA MTHA Recorded
0.2
0 0
0.5
1 1.5 PFA (g)
2
Result comparison of peak floor accelerations of the BNCS building: (a) FB-1, (b) FB-4, and (c) FB-5.
The floor acceleration time histories calculated with the MTHA method are then used to evaluate the FRS, and the obtained FRS are compared with the RRS calculated using code-specified equations as well as the FRS calculated using recorded data. These spectral acceleration demands at selected floors are presented in Figs. 8. It is noted that although RSS of an individual building at each floor is uniquely associated with the site-specific SDS in design practice, the RRS presented in Fig. 8 is evaluated using motion-specific Sa,mean(T0~Ts, ξ=5%) associated with each earthquake input motions (in Table 1) to replace the site-specific SDS in Eq. 3. In addition, the RRS evaluated without considering the upper bound effects are also included in Fig. 8. It is noted that the RRS at the second floor are not affected by the upper bound limit. As shown in Fig. 8, The FRS obtained using MTHA are in reasonable agreement with those calculated with the recorded data at each floor. The comparison indicates that MTHA is capable of capturing the FRS peak spectral values related to the structural modes as well as the spectral shapes. It is noted, however, that the FRS at the fifth floor and the roof for FB-5 imply that the structure could have experienced abrupt change of dynamic characteristics, evident by two dominant spectral peaks located in the long period region resembling the fundamental period at the beginning and the end of the test. The MTHA method, due its linear approximation assumption, is not capable of simulating this aspect, but the overall spectral shape and the peak values at the higher modes are accurately reflected. In the period range of interest (0.06 s to 0.6 s), the RRS at the second floor are in good
agreement with the recorded FRS for the three tests, while the bounded RRS at the fifth floor and the roof are less consistent with the recorded results. In addition, it is observed that accounting for upper bound values effectively improve comparisons with measured spectral acceleration demands at the fifth floor and roof compared to those obtained without considering these effects. During the design level earthquake (FB-5), while the bounded RRS remains higher than the recorded FRS at the fifth level, which is associated with the “node” of the second mode, the bounded RRS at the roof achieves a reasonable estimate in the period range of interest. AC156 (w/o Upper Bound) AC156 (w/ Upper Bound) MTHA Recorded 2nd Floor
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Figure 8. Comparison between FRS and RRS of the BNCS building. Conclusions This paper investigates seismic demands on acceleration-sensitive NCSs using the data measured on two multi-story RC buildings during a variety of strong earthquake events. One building corresponds to a 5-story RC building tested on the NEES@UCSD shake table in 2012 (BNCS building), while the other is a 7-story RC hotel building in Van Nuys, California (VNH building). The recorded data are unique in the sense that they incorporate building responses at different levels of nonlinearity. The acceleration demands on nonstructural components in the
instrumented buildings are evaluated and the results are compared with current code provisions. In an attempt to improve the seismic demand estimation, modal analysis of the BNCS building is also conducted using the modal characteristics identified from the WN base excitation tests of the building. Important findings of this study are summarized as the following: • The empirical linear distribution in current code provisions, in most cases, results in overestimation of the structure acceleration amplification effects, in particular when building response is strongly nonlinear. This is due to the structure period elongation and the reduced ground motion spectral acceleration associated with the building fundamental mode. To account for reduced demands attributed to building nonlinearity, current code provisions impose upper bound values to provide, as intended, generally conservative estimate of the seismic design forces on acceleration-sensitive NCSs regardless of specific building types and their dynamic characteristics. • Assuming a damping ratio of 5% for the acceleration-sensitive NCSs, a constant value of 2.5 is not capable of capturing the dynamic amplification effects of NCSs with its natural period tuned with one of the modal periods of the primary structure. Nevertheless, it is recognized that the code-specified value is intended to provide an average estimate of the amplification effects of NCSs in the period range of interest (0.06 s to 0.6 s) rather than at specific spectral peaks. • For NCSs in the period range of interest (0.06 s to 0.6 s), the spectral acceleration demands on acceleration-sensitive NCSs calculated using the simplified equation coupled with the upper bounds in most cases result in a reasonable and conservative estimate of elastic spectral acceleration demands during a design earthquake event. • With the presence of building nonlinearity, the component amplification factor tuned with the higher mode periods increases significantly and becomes dominant at the lower floors, but at higher floors the peak amplification effect remains correlated to the first mode of the building. • Modal analysis procedures are effective in improving NCS acceleration demand predictions. Nevertheless, the procedures require the identification of structural period elongation and modal parameters accounting for building nonlinear effects. These aspects are critical to the accuracy of modal procedures and are therefore recommended for further research. This study focuses on the acceleration demands on NCSs using data recorded on two multi-story RC buildings from a variety of strong earthquake events. Consequently, the results discussed herein are limited to structures similar to those presented in this study and may not be representative of those of tall buildings or other structure types. The objective of this study is to extend the previous research findings of NCS acceleration demand estimation with the investigation on unique recorded data, and to provide recommendations on future research for improving seismic design of NCSs. Acknowledgments This study is completed as part of a research collaboration between four academic institutions (University of California, San Diego, San Diego State University, Howard University, and Worcester Polytechnic Institute), four government or other granting agencies (the National Science Foundation, the Englekirk Advisory Board, the Charles Pankow Foundation, and the California Seismic Safety Commission), over 40 industry partners, and two oversight committees. Through the NSF-NEESR program, partial funding is provided by grant number CMMI-0936505. Support is also provided by NEES@UCSD and NEES@UCLA staff, Dr. Robert Englekirk, Mr. Mahmoud Faghihi,
Dr. Matthew Hoehler, and Prof. Ken Walsh. This work would not be possible without the many hours of dedicated graduate student contributions, in particular, Consuelo Aranda, Michelle Chen, Hamed Ebrahimian, Elias Espino, Giovanni De Francesco, Jin-Kyung Kim, Steven Mintz, Elide Pantoli, Hae-Jun Park, and Francesco Selva. Opinions and findings of this study are of the authors and do not necessarily reflect those of the sponsors.
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