Estimating floor acceleration in nonlinear multi-story moment-resisting frames

Transcription

1 Etimating floor acceleration in nonlinear multi-tory moment-reiting frame R. Karami Mohammadi Aitant Profeor, Civil Engineering Department, K.N.Tooi Univerity M. Mohammadi M.Sc. Student, Civil Engineering Department, K.N.Tooi Univerity SUMMARY: In thi paper, a new hear building model i ued to tudy floor repone pectra of multi-tory tructure. The torie of hear building model are et to have the lateral tiffne and hyteretic force-deformation behaviour equivalent to the correponding tory of given moment-reiting frame. Incremental dynamic analye are alo performed on different hear building model and the variation of peak floor acceleration with the intenity of earthquake i invetigated. The effect of fundamental period of tructure, trength reduction factor, and level of intallation are alo tudied on the acceleration repone of non-tructural component. A new formulation i propoed for extracting elatic acceleration pectrum of every floor from peak ground acceleration. Thi procedure could be taken a an alternative in uing the reonance factor propoed by Eurocode 8. The effect of nonlinear behaviour of tructure i then conidered by calculating the required influence factor. Keyword: Non-tructural component; Peak floor acceleration; Nonlinear behavior; Dynamic analyi; Shearbuilding model. 1. INTRODUCTION Nontructural component (NSC) are intalled in the floor of a building that are not part of intended load-bearing tructural ytem. Nontructural element are generally claified into three categorie: 1) architectural component; 2) mechanical and electrical component; 3) building content. Viti et al. (1980) preented a computational cheme for developing nonlinear floor repone pectrum (FRS). The reult were hown, auming miile impact on a reactor building. Then the expected reduction value were dicued for eimic or miile impact excitation with repect to the linear cae. Fiouz and Ghafoury Ahtiany (2003) preented a implified method for analyzing econdary ytem uing pectral analyi. Taghavi and Miranda (2005) applied a implified model of a multitory building to develop a method for etimating peak floor acceleration of building. Their preented method can be ued to etimate floor acceleration demand at any floor for a given ground motion record. The dynamic characteritic of building were approximated by uing a implified model baed on the equivalent continuum tructure coniting of a combination of flexural and hear beam. Medina et al. (2006) evaluated peak component acceleration demand for accelerationenitive NSC. Thee ytem were attached to the elatic and inelatic regular moment-reiting frame. The repone of a variety of tiff and flexible multi degree of freedom frame ubjected to a et of 40 far-field ground motion tudied. Villaverde (2006) propoed an approximation method to etimate the eimic repone of nonlinear nontructural component upported by nonlinear tructure. The method wa baed on the procedure previouly developed for analyzing linear nontructural component attached to a linear primary tructure. Furtmuller (2008) preented a procedure to analyze nontructural component mounted on different floor of inelatic primary tructure. Oropeza et al. (2009) invetigated nontructural component repone in the preence of nonlinear behavior of upporting tructure uing floor repone pectra method (FRS). The effect of everal parameter uch a natural frequency of primary and econdary ytem, trength reduction

2 factor and hyteretic model have been tudied. In thi tudy, NSC mounted on elatic and inelatic multi degree of freedom moment reiting frame are analyzed uing modified hear building model and floor repone pectrum method. For thi ake, OpenSee oftware ha been ued for time hitory analyi. The amplification factor and reonance factor of torie have been calculated. Accordingly, the quantitie of Eurocode 8 for computing the force exerted to the econdary ytem have been reformatted for elatic behaviour of primary tructure. The effect of nonlinear behaviour of tructure i then conidered by calculating the required influence factor. 2. EUROCODE 8 EQUATION In Eurocode 8 the following equation i recommended for calculating the force exerted on NSC on a floor of tructure: F SW.. (2.1) q where, S 3. 1 Z. S. H T 1 1 T p (2.2) W : weight of non-tructural element γ : Importance factor q : behaviour factor of NSC S : Floor Repone Spectrum (FRS) α : ratio of ground deign acceleration type (A) to ground gravitational acceleration (g) S: oil type coefficient; T : natural period of NSC T p : natural period of tructure Z: height of intallation location of NSC in tructure H: total height of the tructure In thi formulation S i conidered a peak ground acceleration (PGA) with a given oil type and the effect of inelatic behavior of primary tructure i not conidered. 3. MODELING AND ANALYSIS METHOD In order to tudy the repone of nontructural component in multi degree of freedom tructure, three, five and even-tory moment reiting frame with different natural period and trength are examined, Table 3.1. Thee frame are deigned baed on ASCE 2005 requirement.

3 Table 3.1: Examined frame characteritic frame pan length ytem type pan torey (m) moment reiting frame height of torie 5 3 The modified hear building model were contructed in order to conduct expanded parametric tudie on variou frame with different tiffne and trength. To prepare thee model, tory hear-floor diplacement curve are attained by performing nonlinear tatic analye on the frame. Then they are replaced by triple-line curve and ued a the behavioral curve for hear building model tabulated in Table 3.1. Thi hear building model i enough accurate and offer acceptable reult for the purpoe of thi tudy. In thi tudy, eight period are conidered for each frame: 1/4, 1/3, 1/2, 2/3, 1, 4/3, 2 and 4 econd. In order to achieve the proper period of hear-building model the initial tiffne of firt tory i adjuted proportionally, keeping the tiffne ratio of torie unchanged. Floor ma and triple tiffne ratio and trength ratio are not changed in the floor, Fig Figure. 3.1: Method of changing period of tructure by keeping tiffne ratio contant. In order to change the trength and exerciing variou trength reduction factor (R), maximum floor hear force (F e ) i calculated auming the tructural behavior completely elatic. Then the model i analyzed by applying the elected earthquake. Floor hear trength (yielding trength) i conidered a F e /R to exercie different trength reduction factor. The ratio of econdary trength to the yielding trength i remained unchanged in the tory. In thi tudy elatic behavior and four trength reduction factor (2, 3, 4 and 5) are conidered a well, Fig Figure. 3.2: Force-diplacement curve for producing a frame with inelatic behaviour.

4 4. PEAK FLOOR ACCELERATION In thi ection the effect of linear and nonlinear behavior are tudied on the peak acceleration applied on non-tructural element. Peak floor acceleration of elatic tructure (PFA e ) would be applied on rigid NSC (with very low period) The effect of NSC location on the tructure One of the mot important parameter affecting peak floor acceleration i the location of NSC in the tructure. According to Fig. 4.1, the NSC attached to the higher floor of tructure will experience more acceleration. Thi trend i almot the ame for all tructure with different period (up to 4.0 ec); however, the height wie ditribution of acceleration would be more uniform in the tructure with higher period. Figure. 4.1: Peak floor acceleration of 7-tory elatic frame with eight different period The effect of primary ytem period The maximum PFA e of top floor and minimum PFA e of firt floor are preented in Fig. 4.2 for eventory elatic frame with different period. According to the figure, a the natural period increae, maximum PFA e decreae and minimum PFA e increae. Figure. 4.2: Peak floor acceleration of even-tory elatic frame with different period The effect of earthquake intenity Another parameter conidered in thi tudy i the effect of applied earthquake intenity on PFA e. Thi effect on average PFA e i hown in Fig. 4.3 for the firt and top floor of a 7-tory frame ubjected to 15 far-field record. A it ha been oberved, an increae in earthquake intenity caue the decreae of PFA e in the firt floor and increae in the higher floor. Thi effect wa not conidered in Eurocode 8 or any other proviion.

5 Figure. 4.3: Average PFA e for the firt and top floor of a 7-tory frame ubjected to 15 far-field record. 5. FLOOR RESPONSE SPECTRUM (FRS) The period of econdary ytem (T ) can affect the repone of NSC. The average elatic repone pectrum (FRS e ) i plotted for the floor 1 to 7 of even-tory frame with a period of 0.67 econd ubjected to 15 far-field record, Fig In thi figure the effect of NSC period i clearly oberved. A it i een, FRS e reache it maximum when the period of econdary ytem i equal to the natural period of the primary ytem. PFA e and maximum FRS e of the above mentioned frame i hown in Fig A an example maximum FRS e value for 7 th tory i five time PFA e, een in the figure. Figure. 5.1: Average FRS e of the 7-tory frame with a period of 0.67 econd. Figure. 5.2: PFA e and maximum FRS e of a 7-tory frame with a period of 0.67 econd. 6. AMPLIFICATION FACTOR () The ratio of PFA e to Peak Ground Acceleration (PGA) i called amplification factor () and defined a: PFA e (6.1) PGA

6 Thi factor i hown in Fig. 6.1 for 3, 5, and 7-tory elatic tructure with a period of 0.67 econd. The value of amplification factor reulted from other expreion (λ=1+z/h, Eurocode 8; λ=1+3z/h, UBC 97; λ=1+2z/h, ASCE 2010) imilar to Eqn. 2.2 are preented in thi figure a well. According to the reult obtained here the number of torie (up to even) ha no ignificant effect on the amplification factor. Moreover, the value of amplification factor obtained in Eurocode 8 are higher for lower floor and lower for higher floor comparing to the calculated quantitie. Figure. 6.1: Average amplification factor for 3, 5, 7-tory elatic tructure with a period of 0.67 econd. Baed on the reult obtained in thi reearch, the following relation eem more appropriate for calculating amplification factor (λ) in comparion with that of Eurocode 8: 3. Z H (6.1) 7. ELASTIC RESONANCE FACTOR, E Floor elatic reonance factor (β e ) i derived from dividing elatic acceleration pectrum (FRS e ) by peak floor acceleration (PFA e ) a: FRS e e (6.2) PFAe The Eqn. 2.2 i ued to calculate elatic reonance factor ( e ) in Eurocode. In thi equation the expreion in bracket could be conidered a e.. Fig. 7.1 how e a per Eurocode (Eqn. 2.2) for Z/H=1.0. The reonance factor i negative for T /T p ratio more than 4.32 which i not rational. Figure. 7.1: Reonance factor according to Eurocode 8 formulation. The tudied frame (3, 5, and 7-tory with 0.67 ec. period), are ubjected to 15 earthquake record and their average reonance factor are hown in Fig The elatic reonance factor reulted from Eurocode are hown in thi figure a well. According to the figure, Eurocode underetimate the

7 reonance factor where NSC and tructural period are cloe together. Thi fact i confirmed by Oropeza et. al.; their propoed value are alo indicated in the above mentioned figure. Figure. 7.2: Average e for 3, 5, and 7-tory frame with the period of 0.67 ec. ubjected to 15 record. Maximum reonance factor (β emax ) i almot independent of the number of torie (up to 7), Fig. 7.2, i.e. β e i almot independent of NSC location. Baed on the above mentioned point, the following equation i uggeted for calculating elatic reonance factor (β e ): 1.2 e T T p 2 (7.1) Thi equation i compared with Eurocode and Oropeza et. al (2009) in Fig According to thi figure, elatic reonance factor more accurately (and more conervatively) can be calculated by Eqn. 7.1 comparing to Eqn The effect of primary tructure period (T p ) The effect of natural period of primary tructure i tudied on β emax parameter for a even-tory frame and hown in Fig It can be concluded that β emax decreae a natural period of primary tructure increae. The expreion, (0.5/T p ) 0.3, i propoed here to encounter the effect of T p on β e ; β emax remain unchanged for the period le than 0.5 ec. The reult obtained from uggeted equation are drawn in Fig. 7.3.

8 Figure. 7.3: Comparing β emax of 3, 5, and 7-tory tructure ubjected to 15 far-field record. Baed on what explained o far, the Eqn. 7.1 hould be modified in order to oberve the effect of primary tructure period (T p ), a: e 2 T T p T p (7.2) 8. THE EFFECT OF INELASTIC BEHAVIOR OF PRIMARY SYSTEM A it wa mentioned earlier the trength reduction factor (2, 3, 4, and 5) were conidered for examining the effect of inelatic behavior of primary ytem. The peak floor acceleration of nonlinear tructure (PFA p ), would be different from PFA e. The ratio of PFA p to PFA e i called inelatic behavior influence factor (η) and defined a: PFAp PFA p. PFA e (8.1) PFA e Having PFA e and η, PFA p could be calculated from Eqn In Fig. 8.1 the average value of parameter α are hown for 3, 5 and 7-tory inelatic tructure with the period of 0.67 ec. and the trength reduction factor (R) of 3 and 5. According to thi figure, the number of torie or trength reduction factor ha no ignificant effect on η. Moreover, inelatic behavior influence factor decreae a the NSC location level decreae. Conidering Fig. 8.1, the following expreion i uggeted for calculating η value and the obtained reult are hown there a well. 0.5 Z H 0.85 (8.2) Figure. 8.1: Average parameter η in 3, 5, and 7-tory inelatic tructure with the period of 0.67 ec. and reduction factor (R) of 3 and 5, ubjected to 15 far field record.

9 9. SUMMARY AND CONCLUSION Here, the effect of period of econdary and primary ytem, nonlinear behavior and height of primary ytem are tudied on peak acceleration exerted on non-tructural element located on different floor. A method i uggeted for calculating peak floor acceleration of linear and nonlinear tructure in moment reiting frame (up to even torie) by modifying proviion Eurocode 8. The equation ued in thi method are: F S. W. (9.1) Where, S i acceleration pectrum and calculated a follow: S. S Z (1 3 ) 0.5. H e T T p T p for elatic tructure (9.2) Accordingly, the incremental dynamic analye are alo performed indicating that the higher earthquake intenitie caue the decreae of peak floor acceleration in lower floor and it increae in higher floor of tructure. REFERENCES Viti, G., Olivieri, M., Travi, S. (1981). Development of non-linear floor repone pectra. Nuclear Engineering and Deign 64, Fiouz, A., Ghafoury Ahtiany, M. (2003). Simple method of analyze econdary ytem, The Contruction Indutry Portal of Iran. Miranda, E., Taghavi, SH. (2005). Approximate floor acceleration demand in multitory building. I: formulation. Journal of Structural Engineering 131, Miranda, E., Taghavi, SH. (2005). Approximate floor acceleration demand in multitory building. I: formulation. Journal of Structural Engineering 131, Medina, R., A., Sankaranarayanan, R., Kington, K. M. (2006). Floor repone pectra for light component mounted on regular moment-reiting frame tructure. Engineering Structure 28, Villaverde, R. (2006). Simple method to etimate the eimic nonlinear repone of nontructural component in building, Engineering Structure 28, Furtmuller, T. (2008). Seimic repone of econdary tructure mounted on ductile frame, PAMM, Oropeza, M., Favez, P., Letuzzi, P. (2010). Seimic repone of nontructural component in cae of nonlinear tructure baed on floor repone pectra method, Bull Earthquake Engineering 8, Eurocode 8: Deign of tructure for earthquake reitance. Karami Mohammadi, R., Amini, M. (2011). More efficient hear building model of eccentrically braced frame, 6th International Conference on Seimology and Earthquake Engineering.