The Investigation of Earthquake Resistance for the PC continuous Rigid Frame Bridge considering Nonlinearity in Superstructure

Transcription

1 The Investigation of Earthquake Resistance for the PC continuous Rigid Frame Bridge considering Nonlinearity in Superstructure (l)graduate School of Civil Engineering, Kyusyu University, , Hakozaki, Higashi-ku, Fukuoka-shi, Fukuoka , Japan doc.kyushu-u. ac.jp (2) Corporation of Fuji P.S., , Tenjin,Chuo-ku, Fukuoka-shi, Fukuoka , Japan LD V02426@niftyserve. or.jp (3)Dept of Land and Watre Development, Kyushu Kyoritsu University, 1-8, Jiyugaoka, Yahatanisi-ku, Kitakyushu-shi, Fukuoka , Japan naritomi@kyukyo-u. ac.jp (4) Corporation ofyachiyo Engineering, , Dote-mati, Omiya-shi, Saitama , Japan okada@yachiyo-eng. co.jp Abstract In this study, a existing PC continuous rigid frame bridge designed by the seismic coefficient method is analyzed considering nonlinearity of superstructure. The effect of nonlinearity of superstructure on the responses of bridges is investigated for different hysteresis loop models. 1 Introduction In case of PC continuous rigid frame bridges which have comparatively long span, narrow deck, and tall piers, therefore small rigidity in the out of plane (transverse direction), seismic safety should be investigated by the nonlinear time history analy-

2 198 Earthquake Resistant Engineering Structures sis. Furthermore, if bridges designed by the former specification which has small design seismic force comparing that of the new specification, the check of the seismic safety is necessary. In this study an existing PC continuous rigid frame bridge designed by the seismic coefficient method (h=0.1) is analyzed in transverse direction considering the nonlinearity of not only substructure but also superstructure, and seismic safety of the bridge is investigated for a large scale earthquake. The effect of different hysteresis loop models of superstructure on the response of bridges is compared. 2 The Bridge Outline An object bridge of analysis in this study is 3 span continuous rigid frame bridge with bridge pier of which the height differs, which is designed by the specification in The figure of this bridge outline is shown in Figure 1, the characteristic of this bridge is shown in Table 1. Because both piers is very high, and it has different height between long pier (called the following, PI) and short pier (called the following, P2), this bridge comes under ' the bridges that behave complicatedly during the earthquake ' in the new specification. Superstructure is prestressed concrete (called PC) member, and piers is reinforced concrete (called RC) members. And both superstructure and piers use hollow cross-section, the width of piers is getting widely from the upper part to the lower part. Analytical model is shown in Figure 2. The superstructure is assumed to be all linear or all nonlinear beam member, and piers are nonlinear beam members. And ~94000 Figure 1: Overall side view (unit:mm) ^ Table 1: The design conditions of the bridge Superstructure Bridge Length Span Length Substructure Specifications Design seismic coefficiei Ground classification 3 span continuous PCrigidframebridge L=2288m 67.4m m m PI: 68.0m P2 : 45.0m Specifications of highway bridges (1980) longitudinal direction kh=0.12 transverse direction k^= class I

3 Earthquake Resistant Engineering Structures 199 / ^ g ' 1r \ -x linear or nonlinear member ) rigid member [^rigid member reduction of longitudinal 3[«^^^- nonlinear member reinforcement c* ^^ -^ reduction of longitudinal reinforcement ( 52.9 m height from ( 20.3 m height from the bottom of the pier s the bottom of the pier ) 1 4 reduction of longitudinal reinforcement ( 17.7m height from the bottom of the pier ), r \ nonlinear member,.a ^'* ^ reduction of longitudinal rcinforcement % ( 28.0 m height from the bottom >f cthe pier )! Figure 2: The analytical model in piers, reduction of longitudinal reinforcement are conducted in two parts of each pier (see Figure 2), so that these cross-section are divided separately. Rigid joint set up between the superstructure and piers. 3 The Eigen Value Analysis This bridge is supposed to have complicate response property by the different heights of piers etc, so that it is very important to understand the vibration characteristic. The result of eigen value analysis is shown in Table 2, and the shape of mode is shown in Figure 3. As a result of these, the effective mass of primary mode in right-angled direction is smaller than 60%, so it is clear that the contribution of the higher order mode cannot ignored. Table 2 The result of eigrn value analysis The degree Period The effective mass ratio Primary Secondary The third Figure 3 : The mode figure 4 Nonlinear Dynamic Analysis 4.1 Skeleton curve Moment-curvature (M- < ) relationship in skeleton curve of pier and superstructure is decided from each cross-section and initial axial force obtained by self weight analysis. The bar arrangement drawings of pier and main girder is shown in Figure 4. M- 0 relationship of the bottom of both piers in transverse direction is shown in

4 200 Earthquake Resistant Engineering Structures Figure 5. Regarding both piers, 'crack-yield-ultimate' in M- <f) relationship is decided using stress-strain curve in the 1996 specification. In the calculation of M- 0 relationship of the superstructure, stress-strain curve of concrete, steel, and PC steel in the specification concrete bridge is used. Definition of each event is a follows. Crack (the case in which the concrete of the edge of tension side cracks) RC yield (the case in which reinforcement bar in tension side firstly yields at the end of web) PC yield (the case in which the tensile stress of the PC reaches the yield stress) Ultimate (the case in which maximum compressive strain of the concrete reaches ultimate strain of ) M- 0 relationship of cross-section at the mid-span of the center span in transverse direction is shown in Figure 6. Reinforcement SD295A Steel for PC SBPR930/ m Reinforcement SD295A / DIG D19 D22 oooo oooo Figure 4: The bar arrangement drawings of pier and main girder xio' Curvature 0(l/cm) * W Figure 5: The skeleton curve at bottom of the piers Curvature 0(l/cm) Figure 6: The skeleton curve at midspan of the center span 4.2 Selection of the Nonlinear Hysteretic Behavior Generally, it is known that PC members have more elastical behavior and small consumption of hysteretic energy in the elasto-plastic area in comparison with RC members. Some nonlinear hysteresis models have been proposed in recent year, for PC member including RC member. Particularly, Okamoto-type hysteresis model proposed by Okamoto at ap, if modification factor for unloading stiffness a ' is

5 Earthquake Resistant Engineering Structures 201 selected appropriately in proportion to the amount of PC steel and reinforcement bar, it is possible to give the hysteresis property of PC cross-section with high accuracy. Then Okamoto-type hysteresis loop would be used to represent the nonlinear hysteresis characteristic of the main girder in this analysis. Okamoto-type hysteresis loop is shown Figure 7. In addition, the beginning point directional type hysteresis loop widely used for PC girder, is also used for the comparison. The value of a' is defined using yield strength of PC steel (M^) and that of reinforcement bar (M%) in the cross-section of girder as shown in equation (1). This is calculated in all cross-sections necessary in frame analysis. The value of a ' for main girder analyzed in this study becomes a '=0.500 ~ These values corresponds to the PRC member according to the research of Okamoto. M, (1) Further, because Okamoto-type hysteresis loop is stiffiiess degrading-type tri-linear model, it is necessary to decide skeleton curve with 3 gradients. As for the main girder treated here, it is almost same that yield point of PC steel and that of reinforcement bar, and stiffness degrading after PC steel yield is remarkable than that of after reinforcement bar yield, so that 3 gradients of 'crack - PC steel yield - ultimate' is chosen in skeleton curve as shown in Figure 7. And, the nonlinearity hysteresis property of RC pier is used Takeda-type hysteresis model shown in Figure 8. My < >y -<t>y -0.8 a Me -Me Figure 7: Okamoto-type hysteresis loop -My Figure 8: Takeda-type hysteresis loop (Degrading tri-linear type model) 4.3 Analytical Method Newmark ]3 method ( ]3 =1/4) in used for integral, and time interval is seconds. The damping constant is made to be 3% in superstructure, and 2% in pier. In this analysis the investigation is carried out for type-1 seismic force specified by the Japan specification for highway bridges. The type-1 seismic force represents the plate boundary type big earthquake. The waveform of type-1 used in this analy-

6 202 Earthquake Resistant Engineering Structures sis is shown in Figure 9. The direction of seismic force is transverse direction of bridge. The result obtained Okamoto-type model, the beginning point directional type model, and the elastic model were compared each other. 5 Result of Analysis Figure 9: Input seismic waveform {Type-1, soil class l(hard soil)} The results obtained by three different models of main girder, i.e.okamoto-type model (OT model), the beginning point directional model (BPD model), and elastic model (EL model) are compared on 5 points of the bridge. There are mid-spans of side spans, the heads of piers, and mid-span of the center span. 5.1 Acceleration and Displacement The largest response displacement and acceleration of superstructure is shown in Table 3. The value in the table is the largest absolute values. From Table 3, the largest displacement occurs in the PI in all cases. The displacement of the PI in BPD model is about 15% larger than those in other two models. Table 3 : Maximum Displacement and Acceleration in Superstructure Transverse Direction Points Maximum displacement / Maximum acceleration OT model BPD model EL model point cm / 561.5gal 64.8cm / gal 49.5cm / 528.6gal point! 76.7cm / SOO.Ogal 88.0cm / 500.9gal 75.6cm / 520.2gal point cm / gal 79.7cm / 828.7gal 75.7cm / 624.0gal point cm / gal 45.1cm / 479.0gal 43.4cm / 474.4gal point cm / 560.7gal 24.9cm / 400.0gal 25 Jem /424.2gal note: point 1 : mid-span of side span (PI side) point 2 : head of the pier PI point 3 : midspan of the center span point 4 : head of the pier P2 point 5 : mid-span of side span (P2 side)

7 Earthquake Resistant Engineering Structures point] point] point a) OT model ^ 1000 points points b) BPD model _ 1000 points c) EL model^^ Figure 10 : Time history response displacement and acceleration Figure 10 shows the response displacement and acceleration in point 2 or S. The largest acceleration in OT model becomes gal, but judging from the waveform shown in Figure 10 a), this appears to the pulse coming from the numerical calculation. 5.2 Bending Moment and Curvature in the Superstructure The largest bending moment and the largest curvature of the superstructure in 2 nonlinear member models is shown in Table 4. From these 2 tables, the value in BPD model exceeds that in OT model in all examination points. M- < hysteresis loop of each examination point is shown Figure 11. Because of the consideration of reinforcement bar in OT model, it is confirmed that the hysteresis damping effect in OT model is higher than that in BPD model. In Figure 12, M- 0 hysteresis curve of the bottom of the pier in each model is shown. As the result in comparison with 2 nonlinear models for the superstructure it is confirmed that the damage degree of pier in OT model is smaller than that in BPD model. It is thought that OT model which have higher nonlinearity than BPD model is selected, so that the energy absorption is done in the superstructure, and the energy absorption of the substructure is controlled. Comparing with the hysteresis loop of OT model and EL model, response of EL model is slightly bigger than that

8 204 Earthquake Resistant Engineering Structures of OT model, but neither reaches the yield point of reinforcement bar. Judging from these results, it appears to be important that the superstructure should be modeled as nonlinear member for understanding the real behavior of bridges. Points point 1 point2 point 3 point 4 point 5 Table 4 : Maximum bending moment and curvature Maximum bending moment (tfcm) / Maximum curvature ( I/cm) OT model BPD model 4.71E+05 / 3.89E E+05 / 4.47E E+05 / 1.13E E+05 / 1.45E E+05 / 4.63E E+05 / 4.86E E+05 / 3.39E E+05 / 3.82E E+05 / 1.13E E+05 / 1.18E-06 Curvature 0(l/cm) a) point Curvature 0(l/cm) 4.0 X 10 d) point4 ' Curvature <f»(l/cm) * 10"* Curvature 0(I/cm) XlO"* b) point2 e) points Curvature 0(1/cm) c) points Figure 11: Moment-curvature hysteresis loop in superstructure

9 xio' 4.0 Earthquake Resistant Engineering Structures 205 a) OT model Curvature <>(I/cm) * '"" b) BPD model Curvature 0(l/cm> Xl( Curvature 0(l/cm) * ^ c) EL model Curvature 0(l/cm) X 10 * Figure 12: Moment-curvature hysteresis loop in substructure (left : bottom of PI right: bottom of P2) Comparing the damage of the pier with OT and BPD models, it is thought that the cross-section with much amount of reinforcement bar can be expected the high hysteresis damping so Okamoto-type model is preferable for the seismic safety of this type of bridge. 5.3 The comparison of ductility In each examination point of the superstructure and the substructure, the allowable curvature ductility factor and the largest response curvature ductility factor are shown in Table 5. The allowable curvature ductility factor is calculated by the following equation. (2)

10 206 Earthquake Resistant Engineering Structures Points Table 5 : Allowable ductility and Maximum ductility Points point 1 point2 point 3 point 4 point 5 The base of PI (long piar) The base of P2( short piar) a) in superstructure allowable ductility OT model b) in substructure allowable ductility OT model Maximum ductility BPD model Maximum ductility BPD model EL model In equation (2), (/> is the yield curvature, $ ^ is the ultimate curvature, and a is the safety coefficient. The safety coefficient in the substructure is a =3.0 for type 1 seismic force by the specification of highway bridge. And, it is no rule about the safety coefficient of the superstructure, so that same value of 3.0 is adopted for superstructure. Neither the superstructure nor the substructure is exceed the allowable ductility factor. And, about the part of reduction of longitudinal reinforcement bar, though the allowable ductility factor is 2.0-^3.5, the response ductility factors in all crosssection don't reach the yield point of the reinforcement. 6 Conclusions As a result of investigation for the seismic safety on the existing bridge designed by seismic coefficient method (k=1.0), it is proved that seismic safety is sufficient for type-1 seismic force (k=0.7) even if the modeling of the superstructure is evaluated in safety side. In the analysis considering the nonlinearity of the superstructure, by applying hysteresis model with high energy absorption, it was found that the degree of the damage on the substructure is reduced. Therefore, it can be said that the hysteresis absorption capacity of the superstructure is useful for the improvement in the earthquake resistance of the whole bridge system. References 1) Japan Road Association : Specification of highway bridge, I -common edition, in -concrete bridge design, and V -seismic design edition, December ) S.Okamoto and H.Kato : The seismic response property of PC building, Prestressedconcrete, Vol 33, No.4, pp52-63,