Floor Response Spectra for Ultimate and Serviceability Limit States of Earthquakes

Transcription

1 Floor Response Spectra for Ultimate and Serviceability Limit States of Earthquakes SR Uma, J. X. Zhao & A.B. King GNS Science, Lower Hutt, New Zealand. NZSEE Conference ABSTRACT: Earthquake loading standards NZ.: has introduced new provisions for the design of Non-Structural Components (NSC) and building parts taking into account of peak floor acceleration up the height of the building and spectral response of components. In this study, the acceleration demands on NSCs located in ductile lowrise and high-rise buildings of reinforced-concrete moment-resisting frames are analysed under earthquake records with two design levels representing life safety or ultimate limit state, and operational or serviceability limit state. The numerical results on the response of the components are derived using a floor response spectra approach. The floor response spectra up the height of the building have shown peaks near the modal periods which are not reflected by code provisions. This effect is observed both in and conditions, but more pronounced in. Finally, the adequacy of the current provisions of NZS.: in terms of acceleration demands for NSC with short and long periods have been verified. INTRODUCTION Damage associated with Non-Structural Components (NSC) due to earthquakes has proved to contribute a high proportion of the total loss. Previous studies have shown that the loss due to nonstructural components and contents could be in the range of % of the total loss (Taghavi and Miranda, ) for a typical office building. When a building is subjected to earthquake ground motion, it amplifies the motion and hence the components can be subjected to acceleration demands greater than the input ground motions. When the natural period of the component is close to that of the building, the component is subjected to much higher demand than the Peak Floor Acceleration (PFA). The response of the component may be reduced by the ductility of the component itself and its fixings. Therefore, to provide a practical approach for the design of NSC, design standards include factors for (i) increase in PFA up the building, referred as the Floor Height Coefficient (FHC), (ii) spectral response amplification for different periods of component, (iii) ductility of the NSC system, and (iv) a risk factor to reflect the failure consequence. Earthquake loading standard NZS.: has provisions for the design of NSCs, and they are quite different from overseas counter parts. In particular, the provisions on floor height coefficient and component spectral amplification factor are different. Over the last decade, a number of research studies have attempted to assess the behaviour of NSCs and the influence of various parameters on their response, using simplified structural models [Shelton,, Medina et al., ]. The resonance effect in spectral responses of components with periods close to the building modal periods has been reported in previous research studies [Uma et al.,, Medina et al, ]. However, the current NZS provisions on the spectral amplification of components do not relate the period of the component to the period of the building and hence do not allow for such resonance effect. The provisions are based on the study done by Shelton (). This study included -dimensional building models which were subjected to a small number of earthquake records with intensity corresponding to only ultimate limit state () design level and not for serviceability limit state () design level. In this paper, acceleration demands of NSCs in low-rise and high-rise ductile buildings located in high Paper Number

2 h/h h/h seismicity areas are derived using a floor response spectra approach for earthquake records under two design levels representing life safety or ultimate limit state and operational or serviceability limit state. The numerical results of the acceleration demands on NSCs are compared with the design provisions of NZS. and the adequacy of the NZS provisions has been verified. CURRENT NZS PROVISIONS The provisions in NZS. include two factors to determine the design forces: (i) a Floor Height Coefficient (FHC) which represents the variation of peak floor acceleration up the height with reference to the ground motion and (ii) a component amplification factor (CAF) which represents the spectral amplification of the component with reference to PFA. In NZS., the FHC is normalised with respect to the building s site hazard response spectrum coefficient at zero period, C(). Further, the response of the system is reduced by response reduction factor to account for the ductility of connections. The NZS provisions suggest the following expression as the elastic demand on a component with period T p as in Eqn(): where C T C C C T () p p Hi i p C = site hazard coefficient for building period, T for given soil conditions C Hi = Floor height coefficient as in Figure i p C T = Component amplification factor as in Figure Figure shows the envelopes of floor height coefficient (FHC) with two segments (linear and increase with height and constant). This pattern of distribution was considered necessary to reflect higher mode effects. The distribution depends on the height of the attachment of the component relative to the height of the building (h/h). As per the NZS provisions, envelopes are shown for low-rise and highrise buildings considered in this study. Other provisions such as ICC and SEI/ASCE- suggest linear variation up the height of the building. Figure shows the component amplification factor presented with reference to component period T p. The NZ standard uses an amplification factor that is constant at for all components with periods less than., then decreases linearly to. at.s, and remains at. for larger periods. In contrast, SEI/ASCE- provisions based on NHERP studies relate the factor to the ratio of component period to building period, T p /T B, and attempt to capture the amplification near the region when T p /T B equals to. B. Low -rise (NZS) High-rise (NZS). IBC Floor Height Coefficient Floor Height Coefficient FIGURE VARIATION OF FLOOR HEIGHT COEFFICIENT

3 Amplification factor,c i (T p ) Amplification factor,c i (T p ). NZS. NEHRP Component Period, T p... Component Period, (T p /T B ) FIGURE COMPONENT AMPLIFICATION FACTOR ANALYTICAL MODELS Building models considered represent ductile low-rise and high-rise buildings of Reinforced Concrete (RC) moment resisting frame. Low-rise and high-rise buildings have and storeys respectively with a light roof in addition to the number of storeys. The buildings were designed for a shallow soil site in a high seismicity area (Wellington) using, as per NZS.:, a capacity design approach to ensure ductile behaviour. The nonlinear dynamic simulations were performed on -dimensional models of the buildings in SAP (version.) platform. Cyclic inelastic deformations were modelled using non-linear link (NL Link) elements. These elements were included in beams near the column face for the RC buildings. RC column elements in the ground floor were modelled with fibre hinges to account for axial load-moment-interaction. P-Delta effects were considered in the analyses. Location where non-linearity is modeled FIGURE TYPICL -DIMENSIONAL MODEL FOR STOREY RC FRAME The height of the ground story is.m and other stories are.m high. The bay length is.m. The seismic mass on all the floors is t and t on the roof. Typical configuration of the low-rise RC building is shown in Figure. The first two modal periods of low-rise buildings are.s and.s and those for high-rise buildings are.s and.s. The building sets were analysed under two suites of -year and -year return period earthquake records. The record selection and scaling procedures are discussed below. GROUND MOTIONS Seven horizontal components from seven records were selected and scaled to represent the likely ground motions for a -year return period. Five components were from shallow crustal earthquakes and two components (LAU and K) were from subduction interface earthquakes to represent a possible subduction interface earthquake on the subduction zone beneath Wellington. The other seven components were not used because the matching to the corresponding code design spectra was not as good as for those selected. Eight horizontal components from four records from shallow crustal earthquakes were selected to represent possible ground motion for a return period of years. The

4 ranges of magnitude and source distance for the selected records were made to be the best match to those of the deaggregation results from the probabilistic seismic hazard analyses. These records were scaled to match the design spectra for site class C by a procedure stipulated in the current design standards (NZS.: ). The earthquake magnitudes and the closest source distances to the rupture planes for crustal events are given in Table. The last numerical value in the record name refers to the component number. Table Information on the strong-motion records selected for the present study RECORD NAME COMP. STATION NAME EARTHQUAKE NAME M W R (KM) year return period ARC EW Arcelik Kocaeli, Turkey. DUZ Duzce Kocaeli, Turkey. ELC El Centro El Centro. LAU NS La Union Michoacan. LUC Lucern Landers. K NS HKD -- Japan. TAB NS Tabas Tabas, Iran. year return period A-IV/ / Wildlife Liquef. Array Superstition Hills. B-BRA/ / Brawley Airport Superstition Hills. B-LAD/ / Bishop - LADWP Chalfant Valley. H-PTS/ / Parachute Test Site Imperial Valley. FLOOR HEIGHT COEFFICIENT The median and th percentile values of Floor Height Coefficient (FHC) calculated as peak floor accelerations normalized with site hazard coefficient, C() are plotted under and conditions in Figure, suggesting that the provisions from NZ standards are highly conservative. Figure shows that the FHC is almost constant for all floor levels for both and ground motions, and significantly differs from the first structural modal shape, because (a) PFA is associated with highfrequency contents (possibly over Hz) of the floor acceleration time history; (b) amplification of response at such frequencies may not be large; and (c) Wellington is located in one of the highest seismic hazard and ground motions even for state cause nonlinear structural response which attenuates the floor accelerations at all levels. Another striking result is that FHC values under records are less than that under records, a possible result of the significant nonlinear response of the structure under earthquake loading. The slight increase in FHC at roof level may be a result of high frequency modes. Note that PGA is not the controlling parameter for matching the spectrum and hence PFA/C() at ground floor is not necessarily equal to.. The almost constant PFA distribution along the building height is supported by recorded building response. Two sets of records from a building array in Gisborne, the Gisborne Post Office in NZ ( floors) have nearly the same PFAs at roof, and nd Floor and the free-field records. The PFAs at the basement of this building are always considerably less than those at the free-field, the nd floor and the roof as a result of kinematic soil-structure interaction (Zhao ). The recordings obtained from a building in California during the Northridge earthquake reported by Shelton (Figure ) shows that PFA amplification in this building is very small and only very moderate amplification occurred at roof level.

5 - - NZS RC PFA/C() FIGURE. FLOOR HEIGHT COEFFICIENT - - NZS RC PFA/C() The large difference between the code provision and the result presented here are caused by a number of factors: ) The PFA height distribution adopted in the current design code are based on the results from Shelton () study where the PFA height coefficient distribution is largely the envelope of the PFA computed from the time history analyses. The results presented in the present study are median and th percentile values. We expect that the different definition in the presented result can cause large differences when the number of records used in both studies are very small; ) The number of records used in the Shelton () study and the present study is very small and the small number of record can lead to large differences between median as well as percentile values and the envelop values. The envelop values will be affected very strongly by using different selected records while median and percentile values are much less sensitive to the record selections; and ) The code provisions are based on the results of -dimensional building models. For building with moderate and large eccentricity the torsion response of the buildings may lead to PFAs larger than those from -D models in the present study. While from a design safety point of view selecting envelope values for PFA may be preferred, the large sensitivity may lead to over-conservative/(under-estimates in rare occasions) of PFAs. Using median value and standard deviation the estimated PFAs under a given probability may be more reasonable. SPECTRAL RESPONSE OF COMPONENTS Figure shows the component amplification factor (CAF) under and conditions. The component periods are normalized by the first modal periods of the buildings. Under conditions, CAF increases significantly with increasing floor level for the -storey building at T p /T B =. The CAF increases from less than at the first floor to just over at the roof. CAFs under conditions, however, are markedly smaller than those under conditions within a range of T p /T B =. to., a possible result of the nonlinear response developed under the conditions. Also, CAF does not have dominant peaks at T p /T B = under conditions. The variation pattern for the normalized floor spectra for the -storey building with repect to floor level and the normalized spectral period are similar to those of the -storey building, though the normalized spectra at the modal periods of the structure are considerably less than those for the -storey buildings under conditions. Under conditions, the normalized spectra have no dominant peaks at T p /T B = for the -storey building, again a possible result of nonlinear response developed in the building under strong shaking. Invariably amplification is observed near the higher (second and third) modal periods both in and conditions.

6 Sac/C() Sac/C() Sac/C() Sac/C().. RC st nd.. RC st th. rd. th. Roof. th T p /T B T p /T B... RC st nd rd Roof... RC st th th th T p /T B FIGURE. SPECTRAL AMPLIFICATION OF COMPONENTS T p /T B FEMA suggests a cut off period of.s for rigid (stiff) components, with larger period components being treated as flexible. Note that motions for components with periods very close to zero are not amplified up the height of the building. NZS provisions are conservative by suggesting a spectral amplification factor of for rigid components with periods close to zero. Table gives the observed maximum amplifications for components with respect to C() near the first mode and second mode periods of the respective buildings. Table. Maximum spectral amplification of components at first and second mode periods Amplification W.R.T. C() T B year () Year () First Mode Second Mode First Mode Second Mode ACCELERATION DEMANDS The acceleration demands on NSCs for the buildings considered were evaluated using Eqn.(). The C() values from site response spectra as per NZS.: are.g for a -year return period and.g for a -year return period. The median and th percentile values of C Hi and C i (T p ) corresponding to first mode (FM) and second mode (SM) periods were used to compute acceleration demands at all floor levels.

7 NZS. suggests maximum spectral amplifications for components with periods up to.s. With reference to that, in this study, the components with periods less than or equal to.s will be referred as short-period components and others as long-period components. The numerical results on acceleration demands on NSCs obtained for low-rise and high-rise buildings are presented and compared with NZS envelopes in Figures.. Low-rise building The computed demands are less than the NZS envelope for both categories of short- and long-period components (SM and FM) in conditions as a result of the lesser amplification observed in conditions. However, the demands exceed NZS envelopes marginally in upper stories for long-period components and in lower stories for short-period components, for conditions where the higher component amplification was observed.. High-rise Building For high-rise building as shown in Figure, long period components experienced larger demand under conditions especially in upper stories. However, the demands on short period components in and are less than that arrived from NZS providions. The adequacy of NZ provisions for the categories of components in low and hig-rise buildings under and design levels are summarised in Table. Table. Adequacy of NZS provisions for short and long period components Component category Low-rise building High-rise building Short period Adequate Marginal- lower stories Adequate Adequate Long period Adequate Marginal- upper stories Adequate Inadequate-upper stories Med th NZS RC FM.... Med th NZS RC FM Med th NZS RC FM.... Med th NZS RC FM

8 Med th NZS RC SM.... Med th NZS RC SM Med th NZS RC SM.... Med th NZS RC SM FIGURE. ACCELERATION DEMANDS ON COMPONENTS SUMMARY Acceleration demands on non-structural components in low and high-rise buildings of reinforcedconcrete moment-resisting frame were derived. General observations are as follows: The amplification of component response has dominant peaks at the building modal periods in conditions, possibly because there is minor to moderate nonlinear structural response at this level of ground shaking for Wellington which is a high seismicity area. These peaks are reduced considerably under conditions, a possible result of severe nonlinear structural response under strong ground shaking. A general practice is that the design of parts is carried out under conditions with the implicit assumption that criteria are thereby satisfied. However, from the limited numerical results, such an assumption may not always be valid and the design provisions may need to be revised to address the larger amplification due to resonance effect especially in conditions. Overall conclusions are: Code provisions are adequate in conditions for both short-period and long-period components in the low-rise and high-rise building categories considered in this study. However, in conditions, the code provisions are (i) adequate for short-period components in high-rise buildings (ii) inadequate for long-period components in upper stories of high-rise buildings and (iii) marginally inadequate for short-period components in lower storeys and for long-period components in upper storeys of low-rise buildings. With highly conservative values for FHC and marginally adequate values for spectral amplification factor within NZS provisions, the design of components with periods less than.s is likely to be safe. Spectral amplification factors represented using T p /T B may be useful when periods of both component and structure can be estimated. In cases where these periods cannot be adquately estimated, NZS provisions appears to be adequate and conservative for the components that are adequately fixed, as being the recommended practice, to have a period less than.s

9 under and conditions for the buildings investigated in the present study. The observations and conclusions were derived from the limited numerical studies and may only be appropriate for buildings of similar typology located in shallow soil conditions. In a note of caution, the authors feel that the numerical results obtained from this study need calibrations against recordings from instrumented buildings. ACKNOWLEDGEMENTS The authors wish to thank Dr Jim Cousins for his review of the manuscript. Also, the support from Dr. Darrin Bell and his team of Connell Wagener for the design of buildings is much appreciated. The research fund from FRST Programme CX is gratefully acknowledged. The reviewer s comments were helpful to add value to the paper. REFERENCES: FEMA.. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and Other Structures. Federal Emergency Management Agency: Washington D.C. ICC, International Building Code. International Code Council: Falls Church, VA.,. Zhao, J.X.. The estimation of structural modal parameters from the responses of the Gisborne Post Office building in recent earthquakes. Bulletin of the New Zealand National Society for Earthquake Engineering,, - Medina R.A., Shankaranarayanan R. and Kingston K.M.. Floor response spectra for light components mounted on regular moment resisting frames. Engineering Structures., -. NZS.:. Structural Design Actions Part : Earthquake Actions- New Zealand. New Zealand Standards: New Zealand. SEI/ASCE-. American Society of Civil Engineers (ASCE). Minimum design loads for buildings and other structures. SEI/ASCE Standard no. -: Reston (VA). Shelton R.. Seismic response of building parts and non-structural components. Study Report, BRANZ, New Zealand. Taghavi S. and Miranda E.. Response assessment of non-structural building elements. PEER Report /, The Pacific Engineering Research Center: Berkeley, CA. Uma S.R., Zhao J. and King A.B.. Statistical distribution of floor response spectra due to different types of earthquake ground motions. WCEE, October -, Paper No. --: Beijing.