APPLICATION OF ENERGY ABSORBING CONNECTERS TO STEEL CONTINUOUS GIRDER BRIDGES

Transcription

1 13 th World Conference on Earthqake Engineering Vancover, B.C., Canada Agst 1-6, 24 Paer No APPLICATION OF ENERGY ABSORBING CONNECTERS TO STEEL CONTINUOUS GIRDER BRIDGES Hiroshi ZUI 1 and Yoshio NAMITA 2 SUMMARY The efficienc of a seismic energ dissiation device is stdied. Steel bellows are connected between girders and abtments in order to redce the damage of steel bridges. The effectiveness of the bellows is verified b the dnamic resonse analses for three-san steel continos girders on rbber bearings. The iers are single colmn te made of reinforced concrete designed nder L1 or L2 earthqake condition of Jaanese code. Their heights are varied in three was. The seismic erformances are examined nder varios combinations of designed iers. Frthermore, estimation formlas concerning the maximm dislacement of serstrctre and iers are develoed b considering the energ balance between seismic int energ and dissiated hsteretic energ, and their validities are evalated b comaring with nonlinear dnamic resonse analses. The estimation formlas rodce good reslts in site of their simlicit, and therefore the are efficient for selection of sitable bellows. INTRODUCTION Passive base isolation sch as rbber bearings can redce damage of bridges de to the increase of the fndamental vibration eriod and the additional daming rovided to dissiate the seismic energ. However, it becomes ossible to case collision between girders or between girders and abtments de to large longitdinal dislacements of the serstrctre sbjected strong earthqakes. This collision reslts in increased failre of ser- and sbstrctres. The varios kinds of mitigation devices sch as rbber te and metal te have been investigated and these stdies show that onding forces can be considerabl redced [1-3]. Most of the roosed devices are effective onl after collision and for comression. Athors have roosed a design method in which steel bellows as energ absorbing devices are connected between girders in a row or between girders and abtments [4]. The are connected to the web of girders. The bellows are effective even before collision and, moreover, both in comression and tension. The 1 Professor, Setsnan Universit, Osaka, Jaan, zi@civ.setsnan.ac.j 2 The same as above

2 characteristics of bellows were investigated b loading tests and finite element method, and the design formlas as to the initial rigidit, the ield strength and the ield dislacement of bellows were develoed. The effectiveness of steel bellows for siml sorted steel girders on metallic bearings and for steel continos girders on rbber bearings was also stdied in the case of their lacement between abtments at both ends [4]. Frthermore, a ractical method was develoed in order to decide the characteristics of bellows b sing the resonse sectrm analsis based on the eqivalent linear method. This method is effective bt reeated dnamic analses are necessar and the dislacements of serstrctre and iers tend to be overestimated. In this aer, the efficienc of steel bellows for steel continos girders on rbber bearings is investigated and a more ractical and simle method for the selection of characteristics of bellows is roosed b considering energ balance between seismic int energ and dissiated hsteretic energ. Comter rograms were develoed sing MATLAB for resonse sectrm analses and non-linear time-histor analses. Dnamic analses are carried ot also b these rograms. ANALYTICAL MODELING OF A STEEL CONTINUOUS GIRDER BRIDGE Analtical model of bridge 4.m 4.m 4.m A model of three-san continos girder is shown in Fig.1. The serstrctre consists of five steel late girders, and the total dead load is 15MN. The characteristics of the ier sed for the analsis are shown in Table 1. The iers are A1 A2 single colmn te made of reinforced concrete. Their P1 heights are varied in three was. P2 Fig. 1 A Continos girder The ier section characteristics were decided for two strength level, small (L1 level) and medim (L2 level). In on rbber bearings the design of ier, effective weight of the serstrctre was assmed to be dead load reaction force (5.MN) to all iers regardless of their heights. The longitdinal strengths and the dislacements are shown in Table 1 at the oint of ield initiation of steel bars and at an ltimate state. The strengths are exressed b the seismic intensities. The intensities of the iers designed b L1 earthqake are abot.4 and the intensit of the ier designed b L2 earthqake is abot.6. Table 2 shows the case of analsis in terms of the combination of ier te. Lead rbber bearings (LRB) are sed for the rose of seismic base isolation. The dimensions of LRB are decided so that the fndamental eriod coincides with the target eriod, and the maximm shearing strain in rbber does not exceed 25%. Table 2 shows combination cases of iers and the maximm dislacements obtained b the static design based on the dctilit design method. In the first colmn of Table 2, S means small strength ier and C means medim strength ier. The nmbers next to S or C show ier heights of P1 and P2. For examle, S618 means the ier combination where P1 and P2 are designed b L1 earthqake and their heights are 6m and 18m, resectivel. Since LRB have non-linear hsteretic Table 1 Characteristics of concrete iers Strength of Piers Small (Level 1) Medim (Level 2) Height of Pier (m) Weight of Piers (kn) Steel Rods Area (cm 2 ) Yield initiation Ultimate state Horizontal strength (Seismic intensit) Strength (kn) Dis. (cm) Strength (kn) Dis. (cm)

3 Table 2 Combination cases of iers and Dislacements obtained b Static Design Name of case Serstrctre Pier P1 (cm) Pier P2 (cm) (cm) Pier LRB Pier LRB S S S S S S C C C C C C P P P P Fig. 2 Force vs. dis. relationshi of hsteretic bi-linear srings Fig. 3 Hsteretic modified Takeda model srings characteristics, the load dislacement crves of LRB are exressed b hsteretic bi-linear srings. The rigidit of nloading is eqal to the initial rigidit. The hsteretic model of bi-linear te is shown in Fig.2. We examine here the behaviors in longitdinal direction, and the serstrctre is treated as rigid bodies. The dislacements of abtment are disregarded since it is rigid enogh. The nmber of degrees of freedom is three in total (serstrctre and two middle iers). The force-dislacement law of iers is reresented b the modified Takeda model which can treat the degradation effects nder cclic loading. Fig.3 shows hsteretic load-dislacement crve of the modified Takeda model. Mechanical characteristics of steel bellows The steel bellow connected between a girder end and an abtment is shown in Fig.4. Two steel lates are bent in semicirclar shaes and are connected to the web of a girder and to the anchored late. Fig. 5 shows loading and nloading aths obtained b the laborator tests and FEM analses [4]. The width of the secimen is 25cm, the radis is 15cm and the thickness is 1.9cm. Strictl seaking, the inclinations of the loading ass after ielding of the comression side are less stee than the tension side, and as nloading-reloading advances to oosite direction, this tendenc becomes more consicos. However, the loading and nloading aths are aroximated b the hsteretic Steel bellows Girder Shoe Abtment Fig. 4 Steel bellows connected to abtment and its cross section

4 bi-linear srings shown in Fig.2 for simlicit. The design formlas were shown in [4] concerning the strctral characteristics sch as ield strength, ield dislacement and maximm strength of bellows. Resonse sectrm and seismic wave The resonse analses are carried ot in the next chater b taking into accont onl the behaviors in longitdinal direction for the whole strctre. Fig. 6(a) shows the sed resonse sectra that are given in Jaanese seismic code for soil te 2 [5]. Time-histor analses are also carried ot in the next chater b taking into accont the non-linear behaviors. As an int data of seismic wave we se acceleration time histories that are obtained from the actal Fig. 5 Loading and nloading aths of secimen earthqakes and so modified as to satisf the sectrm for L2 earthqake (Te II). The seismic wave sed is shown in Fig. 6(b). (b) A time histor of acceleration (a) Resonse sectrm (L2,TeII) Fig. 6 Resonse sectra and a time histor of acceleration APPLICATION OF STEEL BELLOWS TO A STEEL CONTINUOUS GIRDER BRIDGE Calclation reslts of dnamic analses in case withot bellows The cases with sal restrainers (withot bellows) in which the energ absorbing is not exected are calclated first for comarison. In these cases, both of stiffness and daming of the restrainers are ignored becase the are not effective before the dislacement of serstrctre exceeds a certain vale. Fig.7 shows the maximm dislacements of serstrctre and iers obtained b two dnamic resonse analses, the resonse sectrm analses based on the eqivalent linear method and the non-linear time-histor analses. The rocedre of the resonse sectrm analses is as follows. First, the effective dislacements of ier and LRB are assmed, and then eqivalent linear stiffness and the daming ratios of non-linear sring elements are calclated. The resonse vales are calclated from the resonse sectrm analses. Calclations are reeated ntil the differences between the obtained dislacements and the assmed dislacements become within 5% [4]. In Fig.7, s means reslts of the resonse sectrm analses and nl means reslts of the non-linear time-histor analses. The differences between calclated vales b resonse sectrm analses and non-linear time-histor analses are small. The resonse sectrm analses based on the eqivalent linear method can be a ractical and effective means as a design method in case withot bellows. The dislacements of small strength iers are considerabl large in comarison with those of medim strength iers. Some of the dislacements of small strength iers exceed the ltimate dislacement. Fig.8 shows the time-histor resonse of the dislacements of

5 .6 _max(m) t_s 1_s 2_s t_nl 1_nl 2_nl iers and the load dislacement crve of iers in case of S618 in which the difference of ier heights is largest. It can be confirmed that large energ absorbing is demonstrated from the load dislacement histor crve of the iers. To clarif the amonts of the energ absorbing of the iers and LRB qantitativel, the amonts of energ absortion of each set of iers and rbber bearings are calclated. Fig.9 shows the accmlated time-histor resonses in terms of energ absortion of iers and of the bearing, resectivel, for S618 and C618. In case of S618, the amonts of energ absortion of iers are larger than those of LRB, and in case of C618, the amonts of energ absortion of iers are less than those of LRB. The iers with small strength ma case severe damages. The maximm dislacements of serstrctre shown as t in Fig.7 are almost eqal regardless of ier strength. These vales exceed 5cm and collision ma be cased in the exansion joints in these cases. S66 S1212 S1818 S612 S618 S1218 C 66 C1212 C 1818 C612 C 618 C 1218 Fig.7 Calclation reslts of dnamic analses (the maximm dislacements withot bellows) Fig. 8 Reslts of S618 b nonlinear time histor analses (withot bellows) Fig. 9 Energ absorbing of bearings and iers (S618 and C618 withot bellows) Calclation reslts obtained b dnamic analses give large vales comared with the static design shown in Table 2. Effect of steel bellows as energ absorbing connecters In case withot bellows, the maximm dislacements of serstrctre exceed 5cm. In this section, the effects of steel bellows are examined. The bellows are connected between a girder end and an abtment as

6 shown in Fig.1. Yield strengths of S66 S66 steel bellows are so decided as to S1212 S S S1818 make the dislacements of BELS66 BELS66 middle iers less than ield 8 BELS BELS1212 BELS1818 BELS1818 dislacement, and to sress the C66 C66 dislacement of serstrctre 6 C C1212 C1818 C1818 within ca. 1cm-15cm which can BELC BELC66 be absorbed b exansion joint BELC1212 BELC1212 BEL1818 BELC1818 comarativel easil. The ield 2 2 strength of bellows is determined to be abot 2%-4% of the serstrctre weight that t(m ) t(m ) corresonds to times the (a) R es.sec. (b) N on linear Time Hist. seismic force cased b L1 earthqake. The comarison of Fig. 1 Comarison of maximm dislacements the maximm resonse with and withot bellows ( P / W =. 4 ) dislacement of cases with and withot bellows is shown in Fig.1 b sing same height iers model. The same ield strength of bellows, P / W =. 4 is sed for all cases where P is the total ield strength of both side bellows and W is the total weight of serstrctre. In Fig.1, (a) shows the reslts of the resonse sectrm analses and (b) shows the reslts of the non-linear time histor resonse analses. The ordinate of Fig.1 shows normalized ier dislacements sing ield dislacement of each ier. The abscissa of Fig.1 shows dislacements of serstrctre. The reslts with bellows are shown as BEL and their marks are ainted ot with black color. The reslts of the resonse sectrm analses give relativel larger vales than those of the non-linear time histor resonse analses of case with bellows. We observe that the dislacements of serstrctre and iers can be redced to large extent b sing steel bellows. We mst oint ot here that if the same ield strength of bellows are sed, the maximm dislacement of serstrctre becomes almost same regardless of ier strength or height on the reslts of the non-linear time histor analses. Since the resonse sectrm analses give relativel larger dislacements in case with bellows, a more recise design method is needed in order to decide the sitable characteristics of steel bellows. A design method of steel bellows as energ absorbing connecters We note here that the behavior of serstrctre with bellows is similar in case of same ield strength of bellows. Fig.11 shows energ absorbing of hsteretic members in case of small strength and high iers, BELS1818, and in case of medim strength and low iers, BELC66. The energ absorbing amont of bellows is dominant for both cases even thogh the energ absorbing of iers in BELS1818 is considerabl larger than in BELC66. This fact sggests that a continos girder with bellows can be modeled in one nonlinear hsteretic sring and one mass. Man methods have been roosed to estimate the maximm inelastic dislacement of single-degree-of-freedom sstems [6-7]. In most methods, the maximm dislacement is estimated from the maximm dislacement of linear elastic sstems. / Fig. 11 Energ absorbing of bellows, bearings and iers (S1818 and C66 with bellows) /

7 Matsda et al. show that a estimation method based on non-linear energ absortion resonse sectra gives more recise vales than a estimation method based on linear energ absortion resonse sectra [8]. Single-degree-of-freedom model sed is shown in Fig.12. The calclated the nonlinear histor absortion energ b sing bi-linear model of the erfect elasto-lasticit. So as not to deend on the size of mass, the absortion energ is converted into the eqivalent velocit. T T E = f ( ) & dt = f ( ) d, Ve = 2E / m (1) We calclated the eqivalent velocit sing the seismic wave shown in Fig.6(b). Since second stiffness of lastic region in bellows hsteretic crves affects the amont of absortion energ, the ratio of second stiffness to first stiffness is assmed to be.5 and is taken into accont. Fig.13 shows the non-linear sectra in which the eqivalent velocit is lotted for the elastic eriod. As shown in Fig.14, hsteretic absorbing energ in a ccle of the bi-linear sring is exressed as follows. Whs = 4(1 γ ) P ( max ) (2) When we assme that onl members of steel bellows absorb int seismic energ, total seismic energ is exressed: E = n W hs (3) where n means hsteretic nmber when assming that the bi-linear sring reeats hsteretic crve b the maximm dislacement. The maximm dislacement of the serstrctre with bellows is estimated from the following rocedre. 1) B assming the ratio, P / W, ield strength of bellows to total weight of serstrctre, the eqivalent velocit, V e, is read ot from the elastic eriod sing Fig.13. 2) The total seismic energ, E, is conted backward from V e. 3) Select the coefficient n. 4) Estimate the maximm dislacement from the balance between E and the absorbing hsteretic energ n Whs. E max = + (4) 4n(1 γ ) P B this method the maximm dislacement can be resmed withot reeating the calclation. Fig.15 shows the comarison of estimated maximm dislacement and calclated maximm dislacement from non-linear dnamic analsis. m ax(m ) Ve(m/s) m = W / g Hsteretic bisring li Fig.12 Single-degree-offreedom model P /W =.2 P /W =.25 P /W =.3 P /W =.35 P /W = Elastic Period T (s) Fig.13 Non-linear sectra of h t ti Absorbing energ γ = k / k 2 1 W W hs hs P Fig. 14 Hsteretic absorbing energ of bi-linear srings n=2.5 n=3. n=3.5 n=4. calclated P/W Fig. 15 Estimated maximm dislacement from energ balance P k 1 k 2 max = 4(1 γ ) P ( max )

8 The model sed in the non-linear dnamic analsis is S1218 in Table 2. LRB When n = 3 is adoted, the sring f b estimated maximm dislacement gives the vale of the safe side with a m = W / g excetion of the case P / W =. 4. f inert = αkhw Pier f The maximm dislacements of iers sring are estimated from the balance of forces acting on the ier as shown in Fig.16 Forces acting to a ier Fig.16. f = fb + f iner (5) where f b is the sring force of the LRB, f is the sring force of the ier and f iner is the inertia force of the ier. Assming iers are within elastic range: f = k, f iner = α khw (6) where k is ier stiffness within elastic range and k H is seismic coefficient obtained from the resonse sectra (Fig.6(a)) according to the elastic eriod of the ier, 2π W /( gk ) where W is the effective weight of the ier. In Eq. (6), α is the modified coefficient smaller than 1 for the rose of adjsting the inflence that neither the dislacement nor the acceleration becomes maximm at the same time. The sring force of the bearing, f b is obtained as follows: fb = Pb + kb2( T b ) (7) where P b and b is the ield strength and the ield dislacement of the LRB, resectivel. k b2 is the second stiffness of the LRB after ielding, and T is the dislacement of the serstrctre. Sbstitting Eqs. (6) and (7) into Eq. (5): = P + k ) + k W /( k + k (8) { } ) b b2 ( T b H b2 Evalation of the estimation method The exact estimation of the maximm dislacements of the serstrctre and the iers is imortant in erformance-based seismic design. Non-linear time histor analses are carried ot in order to evalate the roosed estimation method throgh the comarison with exact reslts. The maximm dislacements T _max(m) L R B S 61 8 t_es 1_es 2_es t_cal 1_cal 2_cal P/W _m ax LRB S1218 t_es 1_es 2_es t_c al 2_cal 2_es P/W (a) S618 (b) S1218 Fig. 17 Maximm dislacements estimated b the roosed method and obtained b non-linear analses

9 estimated b the roosed method and the maximm dislacements obtained b non-linear analses are shown in Fig.17. The reslts of model S618 are shown in (a) and the reslts of model S1218 are shown in (b) in Fig.17. In Fig.17, t means the maximm dislacements of the serstrctre, and 1 and 2 means the maximm dislacements of Pier 1 and Pier 2, resectivel. Also, _es exresses the estimated vales and _cal shows the calclated vales b non-linear time histor analses. The coefficients n in Eq.(4) and α in Eq.(6) are assmed to be 3 and.6, resectivel, for all cases. Thogh the roosed method tends to overestimate the maximm dislacements, it gives a relativel good estimation of the maximm dislacements for both serstrctre and iers. Steel bellows decrease the maximm dislacement of serstrctre within 15cm and the enable iers to be within the range of elasticit even for the ier designed for L1 earthqake. It can be seen that the maximm dislacements become small as the ield strength of the bellows is enlarged to some extent bt frther enlarging cannot be effective. Practicall, the recommended vales of the ratio of P / W are from.2 to.3 according to the extent of the maximm dislacement which the serstrctre demands in these models. CONCLUSION The effect of the steel bellows as girder connecters of energ absorbing te have been stdied b means of the non-linear time histor analses for continos girders on rbber bearings. Also, a ractical method is roosed to estimate the maximm dislacement of the serstrctre and iers sing energ balance when the steel bellows are attached between girders and abtments. The main conclsions of these stdies are: Steel bellows redce considerabl the dislacements of serstrctre and seismic forces to iers. Calclation vales obtained from the develoed estimation method agree fairl well with those of the non-linear time histor analses. Desired characteristics of steel bellows are satisfied b means of adjsting the ield strength of the bellows. REFERENCES 1 JANKOWSKI R, Wilde K, FUJINO Y Redction of onding effects in elevated bridges dring earthqakes Earthqake Engineering and Strctral Dnamics, 2: 29, OBATA M. et al. Mechanical behaviors of a shock absorbing bridge restrainer late JSCE Jornal of Strctral Mechanics and Earthqake Engineering, No.612, 1999: (in Jaanese) 3 KOSHITOUGE M. et al. Energ absortion erformance of the clindrical rbber shock absorber JSCE Jornal of Strctral Mechanics and Earthqake Engineering, No.675, 21: (in Jaanese) 4 ZUI H. et al. Alication of energ absorbing connecters to steel girder bridges IABSE Smosim, "Towards a better bilt environment - innovation, sstainabilit, information technolog", Melborne, Setember Jaan Road Association Secifications of Highwa Bridges JRA, Miranda E, Riz-Garcia J Evalation of aroximate methods to estimate maximm inelastic dislacement demands Earthqake Engineering and Strctral Dnamics, 22: 31, Riddell R., Garcia J. E., Graces E. Inelastic deformation resonse of SDOF sstems sbjected to earthqakes Earthqake Engineering and Strctral Dnamics, 22: 31, Matsda T. et al. A consideration on the dislacement based design of seismicall isolated highwa bridges JSCE Jornal of Strctral Engineering, 23: Vol.46A, (in Jaanese)