THE RATIO OF DISPLACEMENT AMPLIFICATION FACTOR TO FORCE REDUCTION FACTOR

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1 3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada Augut -6, 4 Paper No. 97 THE RATIO OF DISPLACEMENT AMPLIFICATION FACTOR TO FORCE REDUCTION FACTOR Mua MAHMOUDI SUMMARY For Seimic deign, it i important to etimate, maximum lateral diplacement of tructure due to ever earthquake for everal reaon. Seimic deign proviion etimate the maximum roof and tory drift occurring in major earthquake by amplifying the drift obtained by elatic analyi with a deflection amplification factor (DAF). Thi factor depend on variou parameter, of which the force reduction factor (FRF) i the mot important one. The main objective of thi paper i to evaluate the ratio of DAF to FRF (DAF/FRF). It i hown that the ratio DAF/FRF equal to the ratio of the ytem ductility factor () to the ductility reduction factor (R ). So the ratio /R wa evaluated intead of DAF/FRF uing the variou R (propoed in current year). The reult indicate that the ratio of DAF/FRF differ to thoe propoed by eimic proviion uch a NEHRP, IBC and Iranian eimic code (tandard no. 8), and they need to be modified. Keyword: Deflection amplification factor, Force reduction factor, maximum lateral diplacement, Ductility factor INTRODUCTION For eimic deign it i important to etimate, maximum lateral diplacement of tructure for everal reaon; thee include: etimating minimum eparation joint width to avoid pounding, etimating maximum tory drift to avoid detruction of non-tructural element and performance of p-delta analyi. Due to economic reaon, preent eimic code allow tructure to undergo inelatic deformation in the event of trong ground motion. A a reult of thi the deign lateral trength i lower than the lateral trength required to maintain the tructure in the elatic range. The deign lateral trength i obtained by dividing the required fully elatic trength to force reduction factor (FRF). So the diplacement (or drift) calculated by analyi of tructure under the deign lateral force i not the real diplacement of the tructure and it i le than the maximum diplacement of the tructure during trong motion. Aitant Profeor, Department of civil engineering, Technical college of Sari, Sari, Iran

2 Seimic deign proviion etimate the maximum roof and tory drift occurring in major earthquake by amplifying the drift obtained by elatic analyi with a diplacement (or deflection) amplification factor (DAF). max = () e C d max i the maximum inelatic deflection (roof or tory drift), e i the elatic deflection Where calculated by elatic analyi and reduction factor (FRF). C d i the deflection amplification factor (DAF). DAF depend on force RATIO OF DAF TO FRF Fig. how the actual repone envelope and idealized elato-platic repone curve and the following three quantitie are defined []. Bae Shear Ratio, C Idealized repone Actual repone C e C y C C w w y e max Drift, y Fig. : General Structural Repone = / () max R = C e / C y (3) R = C / C (4) y Where = ytem ductility factor, R = ductility reduction factor, y = ytem yield diplacement, firt ignificant yield level. C e = fully elatic bae hear ratio, R = tructural overtrength factor, C y = yield trength level and It ha been hown [] that the force reduction factor and deflection amplification factor can be expreed by the following formula: C =

3 FRF = R R ( orr R Y ) (5) DAF = R ( or R Y ) (6) Y = C / C w (7) Where Y = allowable tre factor applied for working tre deign and level. From (5) and (6), the ratio between DAF and FRF i: DAF FRF C w = correponding deign force R R Y = ( or ) = (8) R R R R Y R (8) how that the ratio DAF/FRF for ultimate tre deign and working tre deign i the ame and it would be better to evaluate the ratio intead of DAF/FRF. So it i concluded that the ratio DAF/FRF R depend on the parameter which affect on R, uch a ytem ductility factor, fundamental period of tructure, load-deflection model of material, damping ratio, ite effect and the characteritic of earthquake (PGA, duration and frequency content)[]. RATIO OF DUCTILITY FACTOR TO DUCTILITY FORCE REDUCTION FACTOR Several formula have been uggeted a ductility force reduction factor ( R ) by Newmark and Hall [], Riddell [3], Krawinkler [4] and Miranda [5]. The R factor propoed by Newmark-Hall depend on ductility factor ( ) and fundamental period (T): R = T. 5 (9) R = T >. 5. Ductility factor and fundamental period affect on formula uggeted by Riddell too: R * R = + * T R = * T * T T () T >. Where R * and T * are determined from the table propoed by Riddell in term of ytem ductility factor. The R factor propoed by Krawinkler depend on fundamental period of ytem (T), ductility factor ( ) and train hardening ratio (α ).It i aumed that the value of train hardening ratio i equal to zero in thi paper:

4 R [ ( ) + ] / C = C () a T b C = +. a T + T According to the table uggeted by Krawinkler the value of a and b are equal to one and.4 repectively when α=. The force reduction factor uggeted by Miranda depend on ductility factor ( ), fundamental period (T), predominant period of the ground motion ( T g ) and ite characteritic. The formula for rock ite i ued in thi paper: R = + Φ () 3 3 Φ = + exp[ (lnt ) ] T T T 5. Uing R factor which are above explained the ratio of to R have been calculated in term of and T. Fig. to how the ratio of to R (DAF/FRF) in term of and T. Fig. indicate relationhip between the ratio of DAF to FRF and ytem fundamental period determined by above aid formula. Several obervation can be made from fig.. The minimum value for DAF/FRF i.85 approximately extracted from Miranda formula. The maximum value for DAF/FRF i.35 related to Miranda and Krawinkler formula. The ratio DAF/FRF i high when the period i low. The ratio will be equal to one when the period i high. The ratio DAF/FRF computed uing formula explained before are hown in Fig. 3 to 6 for =3, 4, 6 and 8 repectively. The minimum value for all cae i.8 approximately. The maximum value increae with increaing of ductility factor. The ratio DAF/FRF i higher than one when the fundamental period i le than.7 ec Period () Fig. : The ratio DAF/FRF veru fundamental period for ytem ductility factor=

5 Period () Fig. 3: The ratio DAF/FRF veru fundamental period for ytem ductility factor= Period () Fig. 4: The ratio DAF/FRF veru fundamental period for ytem ductility factor= Period () NEW. RIDD. KRA. MIRA. Fig. 5: The ratio DAF/FRF veru fundamental period for ytem ductility factor=6

6 The ratio of DAF to FRF Period () NEW. RIDD. KRA. Fig. 6: The ratio DAF/FRF veru fundamental period for ytem ductility factor=8 Fig. 7 repreent the variation of the DAF/FRF due to ductility factor for T=.. The figure how the ratio depend on ductility factor trongly. The minimum value i one for all formula. Fig. 8 to how the relationhip between the ratio DAF/FRF in term of ductility factor computed for T=.3,.5,, and 4 ec. The minimum value for the ratio DAF/FRF in figure 8 and 9 i one and alo equal to.9 and.85 in figure and repectively. The maximum value of the ratio DAF/FRF increae with increaing of ductility factor and decreae due to increaing in T Ductility factor Fig. 7: The ratio DAF/FRF veru ytem ductility factor for fundamental period=. ec.

7 Ductility factor NEW. RIDD. KRA. MIRA. Fig. 8: The ratio DAF/FRF veru ytem ductility factor for fundamental period=.3 ec Ductility factor Fig. 9: The ratio DAF/FRF veru ytem ductility factor for fundamental period=.5 ec Ductility factor NEW. RIDD. KRA. MIRA. Fig. : The ratio DAF/FRF veru ytem ductility factor for fundamental period= ec.

8 Ductility factor Fig. : The ratio DAF/FRF veru ytem ductility factor for fundamental period=4 ec. SEISMIC PROVISIONS OF DAF/FRF In thi ection the DAF/FRF recommended by NEHRP, IBC and Iranian eimic code (tandard no. 8) will be preented. The maximum and minimum value a ratio between DAF and FRF propoed by NEHRP are lited in table [6]. Table : NEHRP- recommended maximum and minimum ratio between DAF and FRF Structural ytem Maximum value Minimum value Bearing wall ytem.6 Building frame ytem.5 Moment reiting frame ytem.9.69 Dual ytem with a pecial moment frame Dual ytem with an intermediate moment frame Inverted pendulum tructure eimic force reiting ytem

9 Table indicate the maximum and minimum value for DAF/FRF recommended by IBC code [7]. Table : IBC- recommended maximum and minimum ratio between DAF and FRF Structural ytem Maximum value Minimum value Bearing wall ytem.67 Building frame ytem.5 Moment reiting frame ytem.9.69 Dual ytem with a pecial moment frame Dual ytem with an intermediate moment frame Inverted pendulum tructure eimic force reiting ytem Iranian eimic code ue only one value for DAF/FRF which i.4 [8]. According to table and, it i oberved that the ratio DAF/FRF i never larger than one except for Inverted pendulum tructure eimic force reiting ytem. CONCLUSION The reult dicued in the previou ection indicate that the minimum value for the ratio between deflection amplification factor (DAF) and force reduction factor (FRF) i.8. The minimum value increae with increaing of ductility factor and decreaing of fundamental period. The ratio DAF/FRF can be much higher than. for ductile frame ytem (high ductility) and tiff building (low fundamental period). The ratio DAF/FRF wa more than.5 for low period ytem. The DAF (C d ) recommended by NEHRP, IBC and Iranian eimic code (tandard no. 8) are low and therefore they need to be modified, epecially for building having high ductility and low period. REFERENCES. Uang C, Maarouf A. Deflection amplification factor for eimic deign proviion. Structural Engineering 994; (8): Mahmoudi M. The effect of period and overtrength on eimic inelatic demand of R/C flexural frame (Perian) A thei preented for the degree of doctor of philoophy in tructural engineering; Tarbiat Modarre Univerity; Iran; Riddell R, Hidalgo P, Cruz E. repone modification factor for earthquake reitant deign of hort perio building Earthquake Spectra 989, 5(3):

10 4. Naar A, Oteraa J, Krawinkler H. Seimic deign baed on trength and ductility demand Proceding of the Earthquake Engineering Tenth World Confrence, Balkema, Roterdam, 99: Miranda E. Site-dependent trength-reduction factor Structural Engineering 993; 9(): NEHRP recommended proviion for the development of eimic regulation for new building. (994). Bldg. Seimic Safety Council; Wahington, D.C. 7. International Building Code (IBC), (). International Code Council. 8. Iranian code of practice for eimic reitant deign of building (tandard no. 8),(999). Building & houing reearch center.