Assessment of the Torsion Effect in Asymmetric Buildings Under Seismic Load

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1 Assessment of the Torson Effect n Asmmetrc Buldngs Under Sesmc Load M.D. Bensalah Ecole Natonale Supéreur d Hdraulque, Blda, Algére Departement of cvl engneerng, Saad dahlab unverst, Blda, Algera M. Bensab Departement of cvl engneerng, Saad dahlab unverst, Blda, Algera A. Modaress LMMSS-MAT, CNRS UMR8579, Ecole Centrale Pars(ECP), Chatena Malabr, France SUMMARY: Irregular strucres are more and more used n new archtecral desgn. In these strucres the torson phenomenon can nduce mportant stresses especall n the case of a sesmc moton. The new sesmc codes tr to take nto account ths effect and durng the modelng t s dffcult to assess all the parameters that have an nfluence on the behavor of ths knd of strucres. In ths work, a sd on the nfluence of the torson effects on the behavor of strucres s done. Two tpes of buldngs are consdered, one smmetrcal and the other asmmetrcal n terms of rgdt. The proposed strucres consst of a buldng n renforced concrete wth nfntel rgd slabs and frames. The use of a fnte element code whch takes nto account the nonlnear behavor of strucral elements allows temporal analss. A database of 116 sesmc records s used. These sgnals represent earthquakes wth magnde rangng between 6.2 and 7.7. The responses of the two buldngs are compared n terms of maxmum dsplacement at the top, ductlt and reducton factor. Kewords: Torson, Earthquake, Buldngs, Eccentrct, Non-lnear behavour 1. INTRODUCTION The sesmc response of asmmetrc buldng subjected to ground motons ma be sgnfcantl modfed due to torsonal effects. These effects arsen from non-unform dstrbuton of the mass, the stffness, the strength and the torsonal components of the ground movement. Several sdes have been conducted on the subject. Among them the nfluence of the lateral and torsonal frequences have been nvestgated b Goel and Chopra (1991) and the mportance of adequate desgn of vertcal resstng elements on both sdes of centre of stffness, accdental eccentrct effects due to a varet of causes and the effect of torsonal and lateral couplng responses of asmmetrc buldngs have been sded b Congrad (2002), Stathopoulos (2010). In fact, there are two major reasons for the occurrence of the torson effect. The frst s a non-unform dstrbuton n plan of the stffness, mass or strength. The second s the rockng of foundaton Crsafull and Reboredo (2004). However, other factors have been consdered n order to take nto account the torson effect, frstl n terms of ductlt Fajfar (2005) concluded that the de-amplfcaton of dsplacements on the stff sde due to torson, tpcal for elastc torsonall stff strucres, usuall decreases wth ncreasng plastc deformatons. He found also that the tpcal amplfcaton for elastc torsonall flexble strucres usuall decreases wth ncreasng plastc deformatons. Secondl n terms of the strength reducton factor Newmark and Hall concluded that: n the mddle, low and hgh frequenc, spectral dsplacements and forces are the same for an elastc and nelastc sstem. B consequence for moderatel hgh frequences, the prncple of conservaton of energ s the same as that of an elastc perfectl plastc sstem Mranda (1994). Acall the formulaton of the strength reducton factor combnes the effect of over strength (Rs), ductlt (Rµ) and redundanc (R R ) Bhavn (2010) concluded that n terms of demand the desgn reducton factor ncreases wth ncreasng ductlt and the lateral eldng strength of the strucre decreases wth ncreasng nelastc

2 deformaton n terms of capact. The man objectve of the present work s to estmate the nfluence of torson effects nduced on the behavour of an asmmetrcal strucre. Therefore we consdered two tpes of strucres: smmetrcal and asmmetrcal, n order to see the effects of some parameters prevousl cted. We focused our sd specfcall on some parameters such as: the dsplacement, the ductlt, the reducton factor (Re) and the dnamc non accdental eccentrct. To do t, dnamc analses usng the fnte elements software GEFDYN Aubr and Chouvet (1986), Aubr and Modaress (1996) were performed. 2. DESCRIPTION OF THE STUDIED CASES Dnamc analses on a smmetrcal and asmmetrcal strucre were performed usng GEFDYN software Models characterstcs The transverse sectons of the sngle stor-frames chosen to represent the two tpes of strucres (.e. asmmetrcal and smmetrcal strucres) are shown respectvel n Fg.2.1a and 1b. The mass of the slab s assumed unforml dstrbuted along beam elements and the columns are supposed to be mass less. It s also assumed that the slab of the two strucres s nfntel rgd n ts own plane. Besdes, the same rgdt s observed, for each column element n the smmetrcal strucre (.e. k 1 = k 2 = k 3 = k 4 ) whle n the flexble sde of asmmetrcal strucre the rgdt for the elements E R1 and E R4 are k 1 = k 4 = K and n the rgd sde the rgdt of elements E F2 and E F3 are k 2 = k 3 =1.13K. In ths model the sx degrees of freedom are consdered. a b Fgure 1. Geometr and transverse secton descrpton of strucres As regards the total masses 44 tones, the elastc modulus E of the two strucres s equal to 33.4 GPa and the Posson s rato s ν =0.2. The dnamc elastc analss on fxed base gves a fundamental frequenc (f str ) of 6.32 Hz and 7.02 Hz for asmmetrc and smmetrc strucres respectvel. In order to ntroduce the non-lnear propertes of the column elements n the stff and flexble sde, a plastc hnge model has been used. Fg.2.2. dsplas axal force-bendng moment (M-N) dagrams that control the eld functon of the non-lnear plastc hnge columns of the two strucres.

3 Fgure 2. Axal force - bendng moment nteracton The ductlt was calculated for both strucres consdered. Frst, n the case of smmetrcal strucre the sstem dsplacement ductlt demand was calculated b the followng Eqn.2.1 Paula (1999): = u μ (2.1) Where ( u ) s the ultmate nelastc dsplacement and ( ) s the eld dsplacement of the sstem. In the case of asmmetrcal strucre the ductlt demand depends on the two angles of twst of the sstem ( θ andθ to ). The frst s the ultmate angles of twst ( θ ) whch depends on the stffness and moment of torson of the sstem. It s defned as Eqn. 2.2: V + evx M tor θ = = (2.2) 2 2 K K x K tor x Where M tor s the torsonal moment; V s the strength n drectons; e vx s the strength eccentrct nduced b the torsonal moment and K tor s the torsonal stffness of sstem; x and are respectvel the dstance from each element (Column) to the centre of rgdt (or gravt). Moreover, knowng that the ultmate dsplacement u obtaned n the asmmetrcal case s not necessarl dentcal n the stff sde u 1 compared to that n the flexble sde u2, the optmal angle of twstθ to, whch corresponds to the strength eccentrct must be calculated b the followng Eqn. 2.3: u1 u 2 θ to = (2.3) L L: s the length of strucre. Where the dsplacement ductlt demand must be lmted to Eqn. 2.4: u ( u1 + X 1θ ) μ = = (2.4) In whch the angle of twst, θ, s found to be less than the optmal value; gven b Eqn.(2.2). However, whenθ > θ, the sstem dsplacement ductlt demand needs to be lmted to Eqn. 2.5: to

4 u ( u2 X 2θ ) μ = = (2.5) Where X 1 s the dstance from elements E R 1 to the centre of mass and X 2 s the dstance from elements E F 2 to the centre of mass. As regards to the strength reducton factor (Re) t reflects the capact of the strucre to dsspate energ through nelastc behavor. Ths does not depend onl on the characterstcs of the sstem, but also on the ground moton nfluenced b the perod of vbraton and the dsplacement ductlt rato Mranda (1994). Ths factor s defned as the rato of the elastc strength demand to the nelastc one Eqn F el R e = (2.6) F Where (F el ) the maxmum lateral elastc strength s obtaned from lnear analss under ground moton, and (F ) s the lateral eldng strength obtaned from non-lnear analss and correspondng to the strength obtaned at the ultmate capact dsplacement under the same ground moton Mranda (1994) Input ground motons The sd used 116 sesmc records wth a magnde varng between 6.2 and 7.7. The parameters that ncorporate the amplde and duraton of the ground moton are lkel to be more relable predctor of damage than parameters that capre onl the amplde of the earthquake. Aras ntenst (Ia) s an earthquake severt measure that correlates well wth several strucral demand measures. Ths ntenst s defned as follows Eqn. 2.7: I Aras T d [ a() t ] ² [ m/s] = π dt 2g 0 (2.7) Where: t s the ground acceleraton T s the duraton of the earthquake and g s the gravt acceleraton Iervolno (2005). The effect of the predomnant perod T p (s) s also sded as the Aras ntenst, the mean perod (T m ) and the peak ground acceleraton PGA (a gmax ) for the gven nput moton. The ranges of varaton of these parameters for the nput motons used are reported n Table 2.1. Table 2.1. Characterstcs of nput moton data Parameter Range a max [g] T p [s] I a [m/s] All sgnals are consstent wth the response spectra of Tpe sol A of Eurocode8. 3. RESULTS AND DISCUSSION Several analses (lnear dnamc (EL), nonlnear dnamc (NL) and Push over (NSP)) were performed. Then the results n terms of capact curves (base shear/top dsplacement), ductlt and

5 reducton factor are presented Numercal smulatons The results obtaned n terms of ultmate lateral strength (Vu) respectvel n asmmetrcal (A S ) and smmetrcal (S Y ) strucres are shown n Fg.3.3a and 3b. As t can be seen, the lateral strength n both drectons X and Y (Vx and V respectvel) for the smmetrcal strucre s greater than the one for the asmmetrcal strucre. a b Fgure 3. Base shears versus Top dsplacements n both drectons X and Y Secondl, n terms of ductlt μ versus respectvel ntenst aras and predomnant perod are shown n Fg.3.4 and Fg.3.5, As t can be seen, the ductlt ncreases wth ncreasng nput moton (Aras ntenst) and decrease wth ncreasng predomnant perod respectvel n asmmetrcal (AS) and smmetrcal (SY) strucres. However the reducton factors evoluton s shown n Fg.3.6 and Fg.3.7 respectvel. As t s shown n Fg.3.7, the reducton factor decreases when the domnant perod of the earthquake ncreases. Unlke n the case of ntenst aras varatons Fg.3.6 the reducton factor ncrease wth decreasng nput motons. Fgure 4 Ductlt versus Intenst aras

6 Fgure 5. Ductlt versus Predomnant perod Fgure 6. Reducton factor versus Intenst aras Fgure 7. Reducton factor versus Predomnant perod The results obtaned n terms of the normalzed dnamcs eccentrct (defned as the dnamc eccentrct dvded b the statc eccentrct) are shown n Fg.3 8, t was observed an amplfcaton of eccentrctes n the elastc and plastc behavor on hghl range of aras ntenst, and ts decrease on the non lnear behavor on low aras ntenst. These effects are due to the creaton of plastc hnges.

7 Fgure 8. Normalzed dnamcs eccentrctes versus Intenst aras 4. CONCLUSIONS Ths work demonstrates that the torsonal response n strucres subjected to earthquake ma be nfluenced b man parameters. Some of these effects as the ultmate top dsplacement, ductlt, reducton factor and the dnamc eccentrct are presented. It was found that for the sded cases: 1. In terms of capact the lateral eldng strength of the asmmetrcal strucre s hgher than the one of the smmetrcal strucre n both drectons. 2. The ductlt ncreases wth ncreasng nput moton (Aras ntenst) and decrease wth ncreasng predomnant perod wth sgnfcant varaton n asmmetrcal strucre than those smmetrcal strucres. 3. The reducton factor decreases when the domnant perod of the earthquake ncreases. Unlke the reducton factor ncrease wth decreasng nput motons. 4. The normalzed eccentrct ncrease when Aras ntenst s low on the elastc and nelastc doman and decrease when t s hgh. To generalze the obtaned results, and sd the exstence of correlatons between the strucral characterstcs and the nput moton parameters, the parametrc sd has to be pursued for other cases such as multstor models wth b-drectonalt of nput motons. REFERENCES Goel, R.K. and Chopra, A.K. (1991). Effects of Plan Asmmetr n Inelastc Sesmc Response of One-Stor Sstems. Journal of Strucral Engneerng 117:5, Congrad, I. and Budescu, M. (2002). Evaluaton of the Sesmc Torson Effects on strucres. EOvdus Unverst Annals of Constructons 3:4, Stathopoulos, K.G. and Anagnostopoulos, S.A. (2010). Accdental desgn eccentrct: Is t mportant for the nelastc response of buldngs to strong earthquakes?. Sol Dnamcs and Earthquake Engneerng 30:9, Crsafull, F., Reboredo, A. and Torrs, G. (2004). Consderaton of Torsonal Effects n the Dsplacement Control of Ductle Buldngs. 13th World Conference on Earthquak Engneerng, Fajfar, P., Marusc, D. and Perus, I. (2005). Torsonal effects n the Pushover-Based Sesmc Analss of buldngs. Journal of Earthquake Engneerng 9:6, Mranda, E., Eer, M. and Bertero, V., Eer, M. (1994). Evaluaton of strength reducton factors for earthquake resstant desgn. Earthquake Spectra10:2, Bhavn, P. and Dhara, S. (2010). Formulaton of response reducton factor for RCC framed stagng of elevated water tank usng statc pushover analss. Proceedngs of the World congress on Engneerng. Vol III: Aubr, D., Chouvet, D., Modaress, A. and Modaress, H. (1986). GEFDn: Logcel d Analse de

8 Comportement Mecanque des Sols par Elments Fns avec Prse en Compte du Couplage Sol-Eau-Ar. Manuel scentfque, Ecole Centrale Pars, LMSS-Mat. Aubr, D. and Modaress, A. (1996). GEFDn: Manuel scentfque. Ecole Centrale Pars, LMSS-Mat. Iervolno, I. and Cornell, C.A. (2005). Record Selecton for Nonlnear Sesmc Analss of strucres. Earthquake Spectra 21: 3, Paula, T. (1999). A Smple Sesmc desgn strateg Based on Dsplacement and Ductlt Compatblt. Earthquake Engneerng and Engneerng Sesmolog 1:1,