Seismic Design of Bridges on Lead‐Rubber Bearings

SEISMIC DESIGN OF BRIDGES ON LEAD-RUBBER BEARINGS By D. H. Turkington,1 A. J. Carr,2 N. Cooke,3 and P. J. Moss4 ABSTRACT: This paper reports on a parametric study of the response of bridge superstructures supported on lead-rubber bearings when subjected to the 1940 El Centro earthquake (N-S component) and the 1966 Parkfield earthquake. The effect of parameters such as lead-plug size and aspect ratio, bearing thickness and yield strength, pier, abutment, and superstructure stiffnesses, and different earthquake records were investigated. The results of the time-history analyses by Turkington (1987) produced clear trends that are used in the design procedure proposed by Turkington et al. (1987, 1989). The trends showed that the presence of lead shifts the natural period of the structure and increases the amount of damping. The mag- nitude of the period change and damping decreases as the natural period of the structure increases or as the pier height increases. Lead-rubber bearings are most effective when used in conjunction with stiff substructures and can be used to redistribute seismic forces between piers and abutments. INTRODUCTION A lead-rubber bearing is a laminated elastomeric bridge bearing containing a cylinder of lead at its center that extends over the full depth of the bearing (Fig. 1). The rubber/steel laminated bearing carries the weight of the struc- ture and provides post-yield elasticity. The lead core deforms plastically, providing damping energy dissipation; its inclusion in a standard elastomeric bearing has two effects on the bridge response. The first is to change the stiffness of the structure, generally resulting in an increase in the natural period. Secondly, it increases the amount of damping because of the hys- teretic properties of the inelastic deformation. Two of the most commonly used procedures for designing bridges with lead-rubber bearings are: (1) In New Zealand, the Ministry of Works and Development (MWD) design guide (1983); and (2) in California, the Dy- namic Isolation Systems (DIS) procedure (1984). Both procedures represent the seismic response of the bridge by a single-degree-of-freedom (SDOF) structure with inelastic spectra. The MWD design procedure assumes that the deck is infinitely rigid. The stiffness of the equivalent SDOF structure is a summation of the stiffnesses of all the piers and abutments; the SDOF structure mass is the total deck superstructure mass. In the DIS procedure, the bearings at the piers and abutments are considered independently, and the response is based on the 'Engr., Crippen Consultants/H. A. Simons, Vancouver, British Columbia, Can- ada. 2Reader, Dept. of Civ. Engrg., Univ. of Canterbury, Christchurch, New Zealand. 3Sr, Lect., Dept. of Civ. Engrg., Univ. of Canterbury, Christchurch, New Zea- land. 4Sr. Lect., Dept. of Civ. Engrg., Univ. of Canterbury, Christchurch, New Zea- land. Note. Discussion open until May 1, 1990. Separate discussions should be sub- mitted for the individual papers in this symposium. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on Jan- uary 11, 1988. This paper is part of the Journal of Structural Engineering, Vol. 115, No. 12, December, 1989. ©ASCE, ISSN 0733-9445/89/0012-3000/S1.00 + $.15 per page. Paper No. 24131. 3000 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. Dowel holes through outer shim 10 mm Outer steel shim Inner steel shims Lead Rubher plug FIG. 1. Lead-Rubber Bearing compressive stress or vertical load on the individual abutments or piers. The MWD design guide has two methods for determining the response. One is to determine the response directly from design-aid charts, but this method is limited since only a few charts are presented and have only been derived for one assumed pier weight. The charts do not give the designer a good feel for the sensitivity of the various parameters associated with the seismic response. The other method presented in the MWD design guide and published by Blakeley (1979) determines the response directly from in- elastic spectra. Inelastic response spectra are produced by computing the response of SDOF structures of different fundamental periods and yield strengths and then plotting the maximum acceleration and displacement re- sponse of these oscillators against the effective period. A problem with this method is that the effective period is not calculated directly, and the response must be estimated through an iterative trial-and-error process. Another sig- nificant problem is that no inelastic spectra are yet presented for the most recent New Zealand Bridge Design Spectra proposed by Priestley and Park (1984). The DIS design procedure is in many ways a "black-box" approach, which does not provide the designer with a clear picture of the fundamental seismic behavior. There are assumptions that limit the application of the procedure. For example, only a single dissipator, with a characteristic strength of 5% of the superstructure weight, is considered in the design charts. The question of pier flexibility is not adequately addressed. There are a number of problems with both given procedures. The strength of the lead-rubber bearing is defined in an awkward manner, being measured in terms of the characteristic strength Qd, rather than the yield strength F{ (Fig. 2). The procedures account for neither the rotational inertia effects of the superstructure mass nor for the higher mode effects of the piers, and the suggested distribution of the lead-rubber bearings between the piers and abutments is questionable. This paper summarizes the results of a research project initiated in order to investigate the various parameters associated with the design of bridges supported on lead-rubber bearings. Some of the parameters examined are 3001 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. FIG. 2. Shear Properties of Lead-Rubber Bearings bearing height and yield strength, pier and foundation stiffness, deck stiff- ness, and earthquake excitation. The major aim is to develop a design method that will allow designers to more fully utilize the benefits of lead-rubber bearings. The research project was completed in four stages. Stage one evaluated the response of single-degree-of-freedom (SDOF) structures, using a model equivalent to a bridge superstructure supported on lead-rubber bearings and rigid foundations. The second stage examined the response of a bridge su- perstructure supported on lead-rubber bearings and a single pier. The re- sponse using 5-, 10-, and 15-m long piers was studied, and rotational inertia effects about the longitudinal direction of the superstructure were included. The third stage examined the response of two- and four-span bridges with various combinations of pier and abutment stiffness and bearing arrange- ments. Stage four reviewed the research results in order to establish a design procedure. This was successfully established and is described by Turkington (1989). COMPUTER ANALYSES Seismic analyses were carried out using a nonlinear, two-dimensional dy- namic analysis program for two different earthquakes; the 1940 El Centro N-S and the 1966 Parkfield. The models used in the time-history analyses are described in the following. Rigid Foundation Model The rigid foundation model represented a bridge superstructure supported 3002 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. 2.5m Rigid members Bearing shear members Pier cap * tributary pier mass Tributary pier mass Pier flexural members Rigid foundation FIG. 3. Pier Models: (a) Transverse; (b) Longitudinal by bearings on a rigid foundation and consisted of a mass connected to a bilinear spring rigidly fixed at the other end. The mass modeled the super- structure weight, and the shear properties of the bearing were modeled by the bilinear spring. The bilinear properties of the bearings were varied in the study; compression loads per bearing of 280 kN and 450 kN were used. The first load is approximately equal to the minimum of 0.4P50 specified in the New Zealand MWD design brief (1978) for adequate confinement of the lead core. The second load is approximately a maximum and is the rated vertical load at between 50-100% shear strain. Pier Models The concrete piers for the Mangatewai-Iti River bridge on the North Island of New Zealand were modeled in this study. The piers are reasonably typ- ical, being 1.67 m in diameter and supported by cylindrical piles which were considered to act rigidly in the model (Fig. 3). Pier heights of 5, 10, and 15 m were used, pier height being defined as the distance between the top of the pier cap and the base of the pier. The superstructure, consisting of four simply supported pretensioned concrete girders and a reinforced con- crete slab continuous over the pier, is supported by eight bearings at each pier cap. The superstructure weight of 2,240 kN on the pier, or 280 kN per bearing, is the tributary structural dead load and the superimposed dead load. These are the only loads used in seismic design carried out according to the New Zealand MWD bridge design brief (1978). Rotational inertia of the deck was modeled by using four rigid arms and bearings eccentrically located to the pier centerline for the transverse anal- yses [Fig. 3(a)], with degrees of freedom as shown in Fig. 4. The results of a sensitivity study showed that rotational inertia was a reasonably signif- icant factor in the dynamic behavior. The response of 5-, 10-, and 15-m 3003 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. ' Tributary deck masses Superstructure below centre of mass Bearing Superstructure shear member Bearing a SOOG to 3" t» "i =f| O o n> o 3 Q, o V) "^ ID O « 3 3D COMPARISON OF RESPONSE USING ELASTOMERIC, LEAD-RUBBER, OR No BEARINGS Rigid Foundation Model The response of superstructures supported on bearings and rigid founda- tions are reviewed first. The maximum bearing shear force and displacement responses are plotted in Figs. 5(a-d) and Fig. 6, for the 280-kN vertical load only; similar results were obtained for the 450-kN vertical load. Maximum shear forces associated with lead-rubber bearings were gener- ally less than for the elastomeric bearings, but there were a number of ex- ceptions, particularly for bearings with the larger diameter of lead plug. In many cases, the difference in response shear forces between elastomeric and lead-rubber bearings alone was not significant enough to justify the use of the lead-rubber bearings. The better performance of the lead-rubber bearings is seen by comparing the displacements. The maximum displacement of the lead-rubber bearings is clearly less than that of the elastomeric bearings for both earthquake rec- ords. The large displacements of the elastomeric bearings continue for many cycles after the peak response, whereas the displacements of the lead-rubber bearings are quickly damped out (Fig. 6). Roll-out failure of a bearing occurs when rotational equilibrium is ex- ceeded and the bearings roll out of position. This type of failure is discussed further by Buckle (1984). The elastomeric bearings had potential roll-out failure under the Parkfield, but not the El Centra, earthquake, whereas lead- rubber bearings did not suffer potential roll-out failure under either earth- quake. The design procedures generally recommend that the maximum shear strain not exceed 100% for the design earthquake. Figs. 5(b and d) show that this 0.15 p p "— *— r (it e u n u Q -^_ a C_ La te 0.10 0.05 0 -0.05 -0.10 -0.15 1 1 1 1— 75mm dia. lead plug- 2.0 4.0 6.0 Time (sec) 8.0 10.0 FIG. 6. Time-History Shear Displacements of 198-mm Tall Bearings to El Centra 1940 N-S Earthquake 3008 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. 2 -* 1600 1W0 1200 1000 - i£ 800 o 400 JK 600 200 0 Pier height ~5m No bearing Elastomeric (No lead 1 —•— 50mm lead core —"— 75 mm lead core 15m —"=--f=te £Wm 5m _i i I i_ -i L _L 0 i 50 100 150 Rubber Thickness I mm) (a) 280 2L0 200 c QJ S ft 160 o "5. ^ 120 80 0 • No bearing Elastomeric (No lead) • 50mm lead core 75 mm lead core Pier height 15m 10 m _l I I I I I L I L_ J I I 1_ 50 100 150 Rubber Thickness (mm) FIG. 7. Response of 5-, 10-, and 15-m Pier Model to El Centro 1940 N-S Earth- quake: (a) Pier Base Shear Forces; (b) Superstructure Displacements 3007 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. is exceeded by elastomeric bearings for both records, except for those bear- ings with a shearing rubber thickness greater than 110 mm under the El Centra 1940 N-S record. Pier Models The results of the time-history analyses for the combination model of sin- gle pier and bearings are reviewed next. The results for the El Centra 1940 N-S earthquake are shown in Figs. l{a and b). It is clear that there are considerable benefits to be gained by the use of lead-rubber bearings with relatively stiff piers; however, these benefits decrease as the pier stiffness decreases. Similar trends were observed in the results from the Parkfield earthquake. Lead-rubber bearings are most effective when used in conjunction with the five-meter piers, reducing the level of shear force from the maximum value associated with monolithic construction, i.e., no bearings, and reduc- ing the maximum displacement that occurs when elastomeric bearings are used. The trends are similar for the ten-meter piers; the effectiveness of lead- rubber bearings in reduced shear force is less than for the five-meter piers, but they are still effective in reducing the displacements. The effectiveness of lead-rubber bearings in limiting shear force and dis- placement when used in conjunction with the flexible 15-m piers has been reduced to an insignificant amount. The bearing displacements are only be- tween 3-18% of the superstructure displacement, compared to a range be- tween 48-81% for the five-meter piers. DETERMINATION OF EFFECTIVE PERIOD The seismic response of a bridge can be determined directly from elastic response spectra if the effective period Te and effective damping ratio A.,, are known. The effective period can be calculated from the total effective stiffness of the bridge substructure ^2Ke and the total superstructure mass M as follows: I M T - ~ 2 " ^ ( 1 ) The total effective stiffness is a combination of the elastic stiffness of the piers and abutments, based on a cracked second moment of area, the elas- tomeric bearing stiffness, and the secant stiffness of the lead-rubber bearings Ks as shown in Fig. 2. The total effective stiffness of the structure was com- puted from the time-history analysis using the maximum inelastic displace- ment response and the associated bearing shear force. The difference between this calculated effective period using Eq. 1 and the effective period based on the initial stiffness of the lead-rubber bearings K„ (Fig. 2) is called the period shift. The period shift has been expressed as a percentage of the total available period shift, which is the difference be- tween the effective periods calculated using the initial K„ and post-elastic tangent stiffness Kd of the lead-rubber bearings. The percentage period shifts from the results of the transverse and longitudinal response of the combined piers and bearings are shown in Figs. 8(a and b) for the El Centra 1940 N- 3008 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. 100 r X •c "> 50 'o o C • - • bv n ° / °*"""-»JL 1 0. 0 n~*°~~J ^ \ . 0 0 \ 0 0 ^Q 1 Yield strength 6.2Y.W f (50mm dia. lead) ——-iL- o , i —*- ^ g_ ^-Yield strength 14.1'/.W ' (75mm dia. lead) _________^# 0 t. _ _ ... 1 _ ,,-J 0.5 1.0 1.5 2.0 initial Period!sec) la) 2.5 100 50 k . Yield strength 6.2% W (50mm dia. lead.) Yield strength 14.1V.W (75mm dia. lead) _1_ _l_ 0.5 1.0 1.5 2.0 Initial Period (sec) (b) 2.5 0.7 "i 0.4 ° 0.3 0.2 0.1 \- 0 • Yield strength 6.2Y.W (50mm dia. lead) 0 0.5 1.0 1.5 Initial Period (sec) (cl 2.0 2.5 FIG. 8. Percentage Period Shifts: (a) El Centra; (b) Parkfieid; Actual Period Shift: (c) El Centra 3009 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. S and Parkfield earthquakes, respectively. These plots show a good rela- tionship between the percentage period shift and the initial period. It is rea- sonable to predict the effective period directly using these results. In order to evaluate the suitability of the effective period for determining seismic response, the calculated effective period was compared with the pe- riod of the peak response measured directly from the time-history plots. This was obtained by measuring the period of the half-cycle immediately before and after the peak response and by doubling the period of the half-cycle immediately before the peak response. The results of this investigation in- dicated a reasonably good correlation between the calculated effective period and that measured from the time-history analyses. The means and standard deviations of the ratio of the two measured periods to the calculated effective period are, respectively, 1.06 ± 0.16 and 1.01 ± 0.25 for the rigid foun- dation model. The ratios for the five-meter and ten-meter piers are 0.89 ± 0.07, 0.95 ± 0.07 and 0.93 ± 0.03, 0.99 ± 0.09, respectively. The amount of viscous damping can be estimated from the effective pe- riod, the response shear force and response displacement (using Eqs. 2 and 3 as described in the next section), or from the acceleration and displacement response spectra. The two damping values should be approximately the same if the effective period is reasonably accurate. The comparisons demonstrated that the effective period can be used as a suitable measure of the seismic response. To get a clearer picture of the effect of pier stiffness on period shift, the actual period shift was plotted for the transverse and longitudinal response of the piers with the El Centra 1940 N-S record [Fig. 8(c)]. The period shift significantly decreases as the pier stiffness decreases and the structural pe- riod increases. DETERMINATION OF EFFECTIVE DAMPING The additional equivalent viscous damping coefficient Ce and the addi- tional damping ratio ke were calculated from the time-history analyses as follows: Wd C, = ' , (2) ce K = (3) 2meM where a)c = 2n/Te; and Wd = the work done in Fig. 2 at the peak displace- ment Xmax. Hysteretic damping coefficients and ratios were calculated from the time- history analyses using Eqs. 2 and 3. They are added to the nominal 5% included in the analyses to account for inherent damping in the remainder of the bridge. The effective damping ratio is the sum of the hysteretic damp- ing ratio and 5%. These calculated values were then compared to the effec- tive damping ratio measured from the elastic acceleration and displacement spectra and showed a reasonably good correlation. Some scatter can be ex- pected when making this comparison between calculated and measured val- ues because the magnitude of the damping ratio depends on the diameter of 3010 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. Yield strengths. 14.1V. W 175mm dia. lead) 6.2Y.W (50mm dia. lead) 0.5 1.0 1.5 Initial Period (sec) (a) \ H1 ! o Is 30 20 10 - - \ D t i \°~-^~ % V °^x Yield strengths — 14,1'AW (75mm dia.lead) 6.2'/.W(50mm dia.lead) 1—-4K**—®F- 1 1 0.5 1.0 ' 1.5 Initial Period (sec) lb) 2.0 2.5 Calculated — Measured from Response Spectra — Proposed Design Curve Yield strength 14-1Y.W 0.5 1.0 1.5 Initial Period (sec) (c) 2.5 FIG. 9. Normalized Additional Damping versus Initial Period for El Centro 1940 N-S: (a) Calculated Design Curves; (b) Measured Design Curves; (c) Proposed Design Curves 3011 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. lead cylinder in the bearing, the vertical load on the bearing, the overall bearing dimensions, and the earthquake characteristics. The damping ratios obtained from the hysteretic behavior of the lead-rub- ber bearings were normalized by dividing by the period calculated using the post-elastic tangent stiffness of the lead-rubber bearings, because damping varies with both bearing stiffness and pier stiffness. The normalized damping ratios for the El Centro 1940 N-S earthquake obtained by calculation and measured from the response spectra are plotted in Figs. 9(a and b), respec- tively. Fig. 9(c) shows two proposed design curves for estimation of the effective damping ratio. The results of this study show there is a strong relationship between the normalized additional damping and the initial pe- riod. The proposed design method uses this relationship to predict the ef- fective damping ratio. The results also clearly show that lead-rubber bearings can be effective in providing additional damping but that the effectiveness decreases signifi- cantly as the pier stiffness decreases. The amount of additional damping is also dependent on the earthquake characteristics. The largest amount of ad- ditional damping occurred with the more vibratory earthquake El Centro 1940 N-S, while the impulsive Parkfield earthquake was associated with the least amount of additional damping. EFFECT OF BEARING HEIGHT AND DIAMETER OF LEAD PLUG ON RESPONSE The height of a lead-rubber bearing will depend on the design constraints for a given bridge, but this study showed that a taller bearing results in a greater effective period and a greater amount of effective damping. These increases will generally reduce the seismic response of the bridge, but the particular advantage of each depends on the characteristics of the earthquake response spectra. The maximum height of bearing will be limited by either roll-out failure or the vertical load capacity at the maximum displacement. The seismic response is not sensitive to the yield strength of the dissipator as long as the strength is within the range of approximately 4-10% of the superstructure weight. The reason is that an increase in effective damping is generally offset by a reduction in period shift, but the extent depends on the earthquake characteristics. The minimum diameter of lead is governed by service lateral loads; the maximum diameter depends largely on the max- imum expected design ground accelerations. The lead-rubber bearings will not be effective if the yield strength approaches the forces associated with the maximum ground acceleration. Bearing displacements decrease with decreasing pier stiffness, and the sig- nificance of bearing properties, e.g., stiffness and yield strength, also de- creases. For very flexible piers, the bearing properties became insignificant. BRIDGES WITH PIERS AND ABUTMENTS OF DIFFERENT STIFFNESSES The transverse responses of two-span bridges with pier heights of 5, 10, and 15 m, rigid abutments, and two different bearing heights and lead-plug diameters were investigated. The results of the time-history analyses for El Centro 1940 N-S indicated that the trends of effective period and effective damping established for the individual piers and bearings are also valid for 3012 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. the continuous superstructure. An effective dissipator yield level must be established that combines the characteristics of all the bearings, so that the bridge can be represented as a SDOF structure. The effectiveness levels of the lead dissipators at the piers and abutments in providing period shift and additional damping are generally different. The following method is suggested for determining the effective yield level. Check the effectiveness of the lead at the piers and abutments by repre- senting the bridge as an SDOF structure with an effective period that is a function of the total mass and total effective stiffness. The effective mass of an individual pier or abutment can be determined approximately as a pro- portion of the total mass according to its effective stiffness relative to the total effective stiffness of the bridge. The following expression illustrates this relationship: K Me = -~-M (4) Once the effective mass of the individual pier or abutment has been de- termined, the yield strength can be assessed and the effectiveness of the lead- rubber bearing can be measured. Lead-rubber bearings on stiff supports gen- erally provide the greatest period shift and the largest increase in damping and will therefore contribute more significantly to the overall effective dis- sipator yield level. The effective abutment mass and effective abutment yield strengths were calculated for the response of the two-span bridges. The results show good correlation with the period shifts in Fig. 8(0). DECK FLEXIBILITY The effect of deck flexibility was measured by comparing the response of bridges with rigid and flexible decks. Deck flexibility does not generally pose much of a problem with short bridges because of their squat aspect ratios. Thus, only the four-span bridge response was examined. Different arrangements of 5-m and 10-m piers and elastomeric and lead-rubber bear- ings at piers and abutments were used in this study. The results of the time-history analyses showed that the largest difference in maximum deck displacement between the rigid and flexible decks was 2.4 mm, which is only 4% of the total deck displacement. It is therefore sufficiently accurate to model the deck as a rigid element for decks with a length-to-width ratio of less than eight, and it may be applicable to bridges with more slender deck plan shapes. REDISTRIBUTION OF RESPONSE FORCES BETWEEN PIERS AND ABUTMENTS The bearing arrangements of two four-span bridges were chosen to illus- trate how a combination of elastomeric and lead-rubber bearings can be used to redistribute seismic response forces away from problem areas, such as weak foundations, or to provide a more uniform shear or bending moment in piers. The bearings in one bridge with three ten-meter piers were selected to 3013 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. reduce the overall seismic response and to distribute the seismic forces ap- proximately evenly between piers and abutments. This bearing arrangement produced abutment shear forces (325 kN) only 12% greater than the pier shear forces (289 kN). A second arrangement was selected to isolate the piers and to resist most of the seismic force at the abutment; in this case, the abutment shear forces were (524 kN) 3.0 times greater than those at the piers (174 kN). The overall displacement responses of the two models were approximately the same, 64.4 mm and 60.0 mm, respectively. The other bridge had a central ten-meter pier and two adjacent five-meter piers. The bearings were selected to isolate the five-meter piers; another arrangement was selected to resist the major proportion of seismic force at the five-meter piers. The overall displacement responses again were very similar, 58.9 mm and 59.6 mm, but the bearing shear forces at the five- meter piers were quite different for the two bearing arrangements, 213 kN and 405 kN, respectively. The bearing shear forces at the abutments and central ten-meter pier were", respectively, 519 kN, 206 kN and 250 kN, 266 kN for the two bearing arrangements. PIER DESIGN The basic assumption made in all the time-history analyses is that the piers behave elastically during the earthquake. However, the underlying seismic design philosophy for bridges, particularly urban bridges, is that they should still be standing after being subjected to an earthquake of a larger magnitude than the design earthquake, so that emergency services can use them. In order to assess the likely behavior of the piers during a larger earth- quake, the writers ran the time-history analyses of a number of 5-, 10-, and 15-m piers for the El Centro 1940 earthquake. The pier behavior was then changed from elastic to elasto-plastic, taking a flexural strength of the pier as 1.5 times the moment from the El Centro response. The time-history anal- yses were then re-run using the larger Parkfield earthquake. A study of these ductilities revealed that the 15-m piers remained elastic, but displacement ductilities of 1.7 and 1.4, respectively, were undertaken by the ten-meter and five-meter piers. These limited ductilities can be achieved by suitable confinement reinforcement in the hinge region and suitable shear reinforcement based on flexural overstrength in the whole pier. CONCLUSIONS 1. The inelastic seismic behavior of most typical bridges supported on lead- rubber bearings can be reasonably represented by an elastic SDOF structure with an effective period and effective damping. The effective period and effective damping can be determined from the correlation between period shift and nor- malized damping with the initial natural period of the structure. This is calculated using the initial stiffness of the lead-rubber bearings and the elastic pier and abutment stiffnesses. 2. The seismic performance of bridges supported on lead-rubber bearings were generally better than bridges supported on elastomeric bearings. The use of lead- rubber bearings provides significant benefits over the use of elastomeric bearings by reducing the displacement response and the number of cycles at the maximum response, although generally little advantage is gained in force response. 3014 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. 3. Lead-rubber bearings combined with elastomeric bearings can provide an effective means of distributing the response forces between piers and abutments as required. 4. The use of taller lead-rubber bearings results in a greater effective period shift and a greater amount of effective damping. Thus, the seismic performance of the bridge is generally improved. The maximum height of the bearings are limited by either roll-out failure or by the vertical load capacity at maximum displacement. Lead-rubber bearings reduce the risk of roll-out failure because of their smaller displacements. 5. The seismic response is not significantly affected by the diameter of the lead plug, provided that the yield strength is within the range of 4-10% of the deck superstructure weight. 6. The characteristics of the earthquake records affect the performance of the lead-rubber bearings. Vibratory earthquake records generally result in greater amounts of additional damping than do more impulsive earthquakes; the larger magnitude earthquakes generally result in greater period shifts. 7. The effectiveness of lead-rubber bearings and elastomeric bearings signif- icantly reduces as the stiffness of the pier decreases and the natural period of the structure increases. 8. Piers should be designed to remain elastic for at least the design earthquake and reinforcement detailed for limited ductility so that the bridge can perform satisfactorily during a greater magnitude earthquake. APPENDIX I. REFERENCES Blakeley, R. W. G. (1979). "Design of bridges incorporating mechanical dissipating devices. Seismic design of bridges." Bulletin 43, Part 2, New Zealand National Roads Board (NZNRB), Road Research Unit. Buckle, I. G. (1984). "Factors affecting the performance of lead-rubber energy dis- sipators." Bulletin 73, New Zealand National Roads Board, Road Research Unit, 157-170. Dynamic Isolation Systems. (1984). Seismic base isolation using lead-rubber bear- ings—Design procedures for bridges. Dynamic Isolation Systems, Berkeley, Calif. New Zealand Ministry of Works and Development. (1978). "Highway bridge design brief." Civil Division Publication CDP 701/6, New Zealand Ministry of Works and Development, Wellington, New Zealand. New Zealand Ministry of Works and Development. (1983). "Design of lead-rubber bridge bearings." Civil Division Publication 818/A, New Zealand Ministry of Works and Development, Wellington, New Zealand. Priestley, M. J. N., and Park, R. (1984). "Strength and ductility of bridge substruc- tures." Bulletin 71, New Zealand National Roads Board, NZNRB, Road Research Unit, 6-7. Turkington, D. H. (1987). "Seismic design of bridges on lead-rubber bearings." Re- search Report 87/2, Civ. Engrg. Dept., Univ. of Canterbury, Christchurch, New Zealand. Turkington, D. H., et al. (1987). "Seismic design of bridges on lead-rubber bear- ings." Proc, Pacific Conf. on Earthquake Engineering, Wairakei, New Zealand, 389-400. Turkington, D. H., et al. (1989). "A design method for bridges on lead-rubber bear- ings." J. Struct. Engrg., ASCE, 115(12), 3017-3030. APPENDIX II. NOTATION The following symbols are used in this paper: 3015 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d. Ce = additional equivalent viscous damping coefficient; Fi = shear force at first yield of lead-rubber bearing; Kd = post-elastic stiffness of lead-rubber bearing; Ke — effective shear stiffness of pier or abutment; ^,Ke = total effective shear stiffness of bridge; Ks = secant stiffness of lead-rubber bearing; Ktl = unloading stiffness of lead-rubber bearing; M = total mass of superstructure; Me = effective mass associated with pier or abutment; P = vertical compression force on bearing; P50 = specified maximum value of vertical compression load at 50% bearing shear strain; Qd = characteristic yield strength of bearing; Te = effective period of bridge; V = bearing shear force; Wd — work done in hysteresis loop; •X'max = maximum superstructure displacement; K = effective damping ratio; and a)e = effective frequency. 3016 J. Struct. Eng. 1989.115:3000-3016. D ow nl oa de d fro m a sc el ib ra ry .o rg b y W A LT ER S ER IA LS P RO CE SS o n 05 /0 1/ 13 . C op yr ig ht A SC E. F or p er so na l u se o nl y; al l r ig ht s r es er ve d.