Proceedings of the 9th International Conference on Structural Dynamics, EURODYN... Porto, Portugal, 30 June - 2 July 2014
Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Porto, Portugal, 30 June - 2 July 2014 A. Cunha, E. Caetano, P. Ribeiro, G. Müller (eds.) ISSN: 2311-9020; ISBN: 978-972-752-165-4 Seismic performance of straddle-type monorail pre-stressed concrete bridges considering interaction with train under moderate earthquakes Chul-Woo Kim 1, Kazuyuki Ono 2, Mitsuo Kawatani 3, and Takuya Enmei 3 Dept. of Civil and Earth Resources Engineering, Kyoto University, Kyoto 615-8540, Japan 2 Road & Transport Dept., Eight-Japan Engineering Consultants Inc., Osaka 532-0034, Japan 3 Dept. of Civil Engineering, Kobe University, Kobe 657-8501, Japan email: [email protected], [email protected], [email protected], [email protected] 1 ABSTRACT: This study aims to investigate seismic responses and performance of straddle-type pre-stressed concrete (PC) bridges considering train load under moderate earthquakes. The study also examines how elastomeric bearings work for improving seismic performance of the bridge. All investigations were based on a three-dimensional dynamic response analysis of train-bridge interaction system under earthquakes. Observations demonstrated that considering train as dynamic system led to decrease of seismic responses in comparison with those responses considering train as additional mass to the bridge. Elastomeric bearings also improved seismic performance of the bridge. However greater train accelerations were observed at the train on the bridge with elastomeric bearings than the bridge with steel bearings, which would make passengers feel excessive vibrations. KEY WORDS: Monorail; Seismic performance; Train-bridge interaction; elastomeric bearing. 1 INTRODUCTION Monorail system has been successfully adopted as a new transport system in major cities of Japan as it takes short period and low cost in construction compared to the subway system. Improving efficiency and labor saving while satisfies seismic performance is a challenge even in structural design of monorail system. A new type of a steel-concrete composite monorail bridge with a simplified lateral bracing system thus has been proposed in Japan [1]. As for pre-stressed concrete (PC) monorail bridges, adopting longer span (hereafter, advanced bridge) than conventional bridges and elastomeric bearings is proposed to improve efficiency and seismic performance. However, there is concern about large deformations of PC girders caused by longer span and change in vibration characteristics caused by elastomeric bearings. In seismic design of monorail bridges, the effect of the train load is considered as additional mass. However, it is improper to treat train on the monorail bridge just as additional mass in seismic design, since train on monorail bridges is a complicated dynamic system with steering and stabilizing wheels that firmly grasp the track girder of monorail bridges. In addition, differently from railways, the passengers in monorail train might have difficulty in evacuating during earthquakes because of the structural characteristic of the monorail system. Therefore, studies on seismic performance of the monorail bridge and vibration serviceability of monorail train are important technical issues. Bridges in Japan should satisfy level-1 seismic performance under moderate earthquakes, so called level-1 ground motions, and level-2 seismic performance under extreme earthquakes, so called level-2 ground motions [2]. Level-1 seismic performance is defined as the state in an elastic manner without severe damage under moderate earthquakes. Additionally the bridge bearings are kept intact under the level-1 earthquake. A remaining problem to be answered is whether seismic responses of the bridge designed under the level-1 earthquakes stay within elastic range as expected or not, since some measured moderate earthquakes have dominant frequency range which is similar with bridge structures. In other words, even though amplification of a moderate earthquake can be categorized as level-1 ground motion, it could have resonant frequency with bridges and result in a plastic behavior. This study investigates seismic performance of PC monorail bridges with elastomeric bearings as well as adopting longer span than that of conventional bridges. The effect of train load on the seismic performance of the bridge under moderate ground motions is also examined by means of a three-dimensional dynamic response analysis. The validity of the analytical method of train-bridge interaction has been verified by comparing with experiment results on steel monorail bridges [1], [3]. Moreover, the analytical method has been updated to consider seismic behaviors of the steel monorail bridges under moving train [4], [5]. 2 TRAIN-BRIDGE INTERACTION WITH GROUND MOTION Bridges are considered as an assemblage of beam elements with six degrees of freedom (DOFs) at each node [3-5]. A car of monorail train has two bogies with pneumatic tires for running, steering and stabilizing wheels. The car’s dynamic behavior is assumed to be sufficiently represented by a discrete rigid multi-body system with 15 DOFs. The combination of the interaction force and wheel load at a contact point of the bridge suggests the equation of forced vibration for monorail train-bridge interaction system. If the interaction system is subjected to ground motion then the problem is solvable by considering an additional inertia force input from acceleration of mass as shown in Equation (1). (1) 1161 850 1500 1500 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 385 5300 5300 5300 5300 385 21200 850 850 1500 1500 (a) Conventional bridge with span length of 21.2m 485 8100 5400 5400 8100 485 850 27000 (b) Advanced bridge with span length of 27m Figure 1. PC girders of the monorail bridge. Front view Side view 22000 5600 950 3700 Side view Front view 22000 950 950 485 30485 5600 3700 28000 28000 950 48530485 750 1000750 100 100 1500 65. 431 2000 1500 2300 71. 920 71. 420 100 1800 100 2500 1350 65. 431 2300 1350 1500 65. 431 100 3000 5000 Φ1000 L =8.0m, n=4 200 100 1900 200 100 1900 1000 2000 100 1800 2000 1500 62. 420 1000 1000 100 100 3000 5000 1000 100 100 L=8.0m, n=4 71. 920 71. 420 2300 2500 100 2350 65. 431 2300 2350 64. 320 62. 420 1000 Φ1000 72. 920 100 64. 320 64. 320 62. 420 500 1000 72. 920 10500 7100 1800 10500 7100 2000 10500 7100 1800 64. 320 200 100 1900 71. 920 71. 420 10500 7100 100 72. 920 200 100 1900 71. 920 71. 420 500 1000 72. 920 500 1000 500 1000 7501000750 3000 5000 62. 420 1000 1000 100 2@2500=5000 100 7000 1000 100 Φ1000 Φ1000 L=6.5m, n=6 L=6.5m, n=6 (a) Conventional bridge (b) Advanced bridge Figure 2. Substructure of monorail bridges. where M, C and K indicate the mass, damping, and stiffness matrices of the bridge, respectively. The force vector is f. Subscripts B, T and BT denote the bridge, train, and bridgetrain interaction, respectively. q and wdenote generalized coordinate vector of the bridge and displacement of train, respectively. äg is the ground acceleration. In this study, the modal analysis is employed assuming that bridge structures deform within elastic range under level-1 ground motions. Details of Equation (1) can be found in references [4], [5]. The differential equations of train-bridge interaction under the ground motion are solved by Newmark’s β method. β of 0.25 was used to obtain stable and accurate solutions. Solutions were obtained with a relative margin of error of less than 0.001. 3 3.1 ANALYTICAL MODEL Bridges This study considered two bridge models: conventional bridge and advanced bridge. Bridge length of the conventional bridge is 22m (span length is 21.2m), while the advanced bridge adopts bridge length of 28m (span length is 27.0m). The general layout and geometry of two bridges are shown in Figure 1, whereas Figure 2 shows those of substructures. The monorail structure has two tram girders and the distance between those tram girders is 3.7m. Reinforced concrete (RC) piers with height of 10.6m were considered in the study. 1162 Figure 3 shows the finite element (FE) model of the monorail bridges. Surface roughness of tram girders and gaps between girders were considered in the dynamic response analysis under moving train and subjected to earthquakes. Half of the total mass of neighboring span (Ld in Figure 3) was also considered: 254.31kN for the conventional bridge and 345.55kN for the advanced bridge. Table 1 shows crosssectional properties and mass per unit length of PC girders. Elastic properties of concrete and elastomeric bearings are summarized in Table 2. It is noteworthy that the elastomeric bearing is proposed for the advanced bridge. The bridge footings of the models were idealized as springs of which properties are shown in Table 3. Figure 4 shows first five natural modes of the conventional and advanced bridges with steel bearings taken from the eigenvalue analysis. The frequencies in parentheses are the results from the FE model considering parked train on the bridge as additional mass. Only horizontal bending modes of tram girders and piers were observed in the first five natural modes. 3.2 Monorail train Figure 5 shows the three-dimensional car model with 15 DOF that is used in this study. The monorail train was assumed to have weight of 338kN/car including passengers. Natural frequencies for bounce and sway motions were 1.207 Hz and 0.912 Hz, respectively. Details of physical properties of train are summarized in reference [4]. Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 Moving Train End of girder G1 girder Ld Ld Center of girder End of girder Ld Ld G2 girder y z x Observation point Ground motion P1 P2 P3 P4 Figure 3. FE model of monorail bridge. 1st mode: 3.099Hz(2.471Hz) Horizontal bending (C/W Pier bending) 2nd mode: 3.370Hz(2.665Hz) Pier bending (C/W Horizontal bending) 3rd mode: 3.833Hz(2.903Hz) Horizontal bending (C/W Pier bending) 4th mode: 4.297Hz(3.819Hz) Horizontal bending 5th mode: 4.299Hz(3.867Hz) Horizontal bending (C/W: Coupled with) (a) Conventional bridge with steel bearings 1st mode: 2.394Hz(1.860Hz) Horizontal bending (C/W Pier bending) 2nd mode: 2.563Hz(1.949Hz) Pier bending (C/W Horizontal bending) 3rd mode: 2.798Hz(2.040Hz) Horizontal bending (C/W Pier bending) 4th mode: 2.934Hz(2.693Hz) Horizontal bending 5th mode: 2.935Hz(2.751Hz) Horizontal bending (C/W: Coupled with) (b) Advanced bridge with steel bearings Figure 4. First five natural modes and frequencies. Table 1. Cross-sectional properties of PC girders. PC girder Conventional Advanced Cross-sectional area (m2) End Center 1.075 0.884 1.075 0.927 Moment of inertia of area (m4) End (Iz) 0.073 0.073 Center (Iz) 0.064 0.071 End (Iy) 0.220 0.220 Center (Iy) 0.206 0.209 End (Ix) 0.307 0.307 Center (Ix) 0.307 0.307 Mass per unit length (t/m) End Center 2.687 2.211 2.864 2.233 Table 2. Elastic properties of concrete and elastomeric bearing. Concrete (N/mm2) Spring constant of elastomeric bearing fck E G kx ky kz kx ky Conventional 50 3.3e104 1.43e104 208 663 162415 342726 3464 Advanced 80 3.8e104 1.65e104 (kN/m) (kN/m) (kN/m) (kN.m/rad) (kN.m/rad) 4 4 Pier 27 2.65e10 1.15e10 fckCompressive stress, E: Young’s modulus, G: Shear modulus Table 3. Spring constant of foundation. Vertical Horizontal Rotational 3.3 3581400 (kN/m) 28275000 (kN/m) 1003300 (kN.m/rad) Ground motions Two moderate design ground motions specified in JRA (Japan Road Association) code [2] and a measured moderate ground motion were considered in the analysis. Figure 6(a) shows Group-1 of Level-1 (hereafter, G1LV1 ground motion) which is the moderate earthquake at a stiff soil site. Figure 6(b) shows Group-2 of Level-1 (hereafter, G2LV1 ground motion) which is the moderate earthquake at a moderate soil site. The moderate ground motion measured in Hobetsu, Yuuhutsu, Hokkaido, Japan, on 26 September 2003 (hereafter HB ground motion, see Figure 6(c)) was also adopted in the seismic response analysis of monorail bridges. In the JRA code, vertical components of the ground motions are not specified, and half scale of the transverse ground motions was adopted in the analysis. For the measured HB ground motion, measured vertical ground motion was considered in the analysis. Figure 6 shows accelerograms and response spectra of the three ground motions. Figure 6(c) shows the natural periods corresponding to the first horizontal (0.323s, 3.099Hz) and advanced bridge with steel bearings (0.418s, 2.394Hz) without considering train. Existence of the natural periods on the dominant range of the response spectrum discloses potential of strong seismic responses. 3.4 Track surface roughness Track surface roughness measured at the conventional bridge is considered in the analysis. Laser displacement sensors were installed to the experimental car to measure surface roughness of tram wheel path, steering wheel path and stabilizing wheel path. The speed of experimental car was 1km/h and sampling 1163 Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 frequency was 200 Hz. Furthermore, surface roughness of joints between girders were also measured by caliper and depth gauge. For the advanced bridge which has longer span than the conventional bridge, the data length of surface roughness is expanded by adding roughness data. Analysis conditions Rayleigh damping was adopted in the analysis, in which the damping constant of the monorail bridge during an earthquake was assumed to be 5%. Dynamic responses of each bridge were obtained by mode-superposition up to the mode related to the frequency near 20Hz: for the conventional bridge with steel bearing, up to the 38th (19.77Hz) mode; up to the 42th (19.86Hz) and 56th (19.64Hz) modes were considered for the advanced bridge with steel and elastomeric bearings in respect. The time interval with Newmark’s β method is 0.005. In investigating the dynamic effect of monorail train on seismic responses of monorail bridges, four scenarios were considered in the analysis: SCN-1 which disregards train’s mass; SCN-2 which considers train as an additional mass on the bridge model; SCN-3 which considers interaction between parked train and the bridge; and SCN-4 which considers interaction between moving train and the bridge. In SCN-2 and SCN-3, train was aligned in such way that the reaction force of P2 pier is the most critical. PEAK = 102 Gal R.M.S = 25.4 Gal Seismic responses In this section, two design ground motions G1LV1 and G2LV1 in JRA code (Figure 6 (a), (b)) were utilized to investigate how adopting longer span and elastomeric bearings result in seismic responses. 100 50 0 -50 -100 -150 200 h=5% 100 0 0 5 10 15 Time (s) 20 25 0.1 1 10 Period(s) (a) Design ground motion on stiff soil site: G1LV1 Responses at pier top and span center 150 Acceleration(Gal) 4.2.1 300 150 Acceleration (Gal) 4.2 Figure 5. Monorail train model with 15DOF. Acceleration (Gal) 4.1 SESMIC RESPONSE ANALYSIS OF TRAIN-BRIDGE INTERACTIVE PEAK = 118 Gal R.M.S = 32.9 Gal 300 Acceleration (Gal) 4 system of train might act as a damper under earthquakes. The result corresponds to the conclusion in the previous study on steel girder bridges [4]. It is noteworthy, however, that responses of the advanced bridge with elastomeric bearings showed different tendency: considering the interaction between the advanced bridge with elastomeric bearings and moving train (SCN-4) was greater than the other scenarios as shown in Figure 10. 1164 Response acc. (Gal) Acc. (Gal) Acc. (Gal) Acceleration (Gal) Response acc. (Gal) Response acc. (Gal) Response acc. (Gal) Response acc. (Gal) Acceleration (Gal) Acc. (Gal) Acceleration (Gal) Acc. (Gal) Response acc. (Gal) Response acc. (Gal) Acc. (Gal) Acc. (Gal) Acc. (Gal) Acc. (Gal) Acceleration (Gal) Accelerations at the span center and top of P2 pier in the 200 50 transverse direction were examined. Those accelerations of h=5% 0 100 the conventional bridge under the G1LV1 ground motion are -50 -100 shown in Figure 7, and those under the G2LV1 ground motion 0 -150 0.1 1 10 0 5 10 15 20 25 30 are shown in Figure 8. Figure 7 and Figure 8 show that RMS time(s) Period(s) values under the G2LV1 ground motion were greater than (b) Design ground motion on moderate soil site: G2LV1 those values under the G1LV1 ground motion in all scenarios. Thus for the advanced bridge the responses under the G2LV1 Peak= 140 Gal PEAK = RMS= 140 R.M.S = 42.4 Gal 1000 Peak= 140Gal Gal 42.4 RMS= 42.4 GalGal 1000 Peak= -53.3 Gal 200 RMS= 15.7Peak= Gal 200 200 1000 0.323s 0.418s 200 ground motion which led to critical result are discussed200 in 0.323s 0.418s 800 800 800 100 100 100 100 100 order to save space. The responses of the advanced bridge 600 600 600 0 0 0 with steel bearings under the G2LV1 ground motion are 00 400 400 400 -100 shown in Figure 9, and those of the advanced bridge -100 with -100 -100 -100 200 200 200 elastomeric bearings are shown in Figure 10. -200 -200 -200 -200 0 00 -200 0 5 10 15 20 25 30 0.1 0.1 1 10 10 15 20 025 305 0.1 30 1 101 15 25 20 25 30 0 510 0.10.1 In focusing on the response at the span center, responses of0 5 10 0 155 1020 Period (s) Time (s) Natural Natural period (s) period (s) Time (s) Time (s) Time (s) EW direction natural period (s) period (s) natural the conventional bridge of SCN-2 under the G1LV1 ground PEAK =-53.3 53.3 GalRMS= R.M.S 15.7 Gal Peak= Gal RMS= 42.4 Gal Peak= Gal RMS= 15.7= Gal 1000 Peak= 140 Gal RMS= 42.4140 Gal Peak= -53.3 Gal 15.7 Gal 1000 1000 200 motion were greater than those responses of SCN-1. However, 200 200 200 1000 200 1000 0.323s 0.418s 0.323s 0.418s 800 800800 800 the responses100at the span center of the 800 conventional and 100 100 100 100 600 600 600 600motion600 advanced bridges under the G2LV1 ground showed 0 0 00 0 400400 400 400 400 opposite tendency with those responses under the G1LV1 -100 -100 -100 -100 200200 -100 200 200 200 ground motion: i.e. those responses of SCN-1 were greater 0 00 -200 -200 -200 0 -200 -200 0 0 5 10 15 20 25 30 than those of SCN-2. 0.1 1 11 30 110 10 0 15 20 0.1 25 0.1 05 510 10 15 15 (s) 20 25 10.10.1 0 5 10 15 020 5 2510 30 20 25 3030 0.1 0.1 Time Period (s) Natural Natural period (s)period (s) In considering interactionTime between train with Natural period (s) Natural period (s) Time and (s) the bridge Time (s) UD direction (s) Time (s) natural(s)period (s) naturalnatural period (s)period (s) natural period steel bearings (SCN-3 and SCN-4), the responses were (c) Measured ground motion: HB smaller than those not considering the interaction (SCN-1, Figure 6. Accelerograms and response spectra of moderate SCN-2) (see Figures 7, 8 and 9). It shows that the dynamic ground motions. 100 0 -200 -400 -400 0 5 10 15 20 200 0 -200 -400 0 25 time(s) 5 10 15 20 25 time(s) 0 10 200 0 -200 400 200 0 -200 0 5 10 15 20 0 25 time(s) PEAK = 227.4 Gal R.M.S = 52.76 Gal 400 200 0 -200 5 10 15 20 0 25 time(s) 10 0 -200 -400 Acceleration(Gal) Acceleration(Gal) Acceleration(Gal) 200 PEAK = 175.7 Gal R.M.S = 46.79 Gal 400 200 0 -200 -400 0 5 10 15 20 5 10 15 20 200 0 -200 25 time(s) 0 0 -200 -400 PEAK = 221.6 Gal R.M.S = 48.32 Gal 400 200 0 -200 -400 0 5 10 15 20 25 time(s) 10 5 10 15 20 Responses of monorail train Responses of monorail train during earthquakes are also examined to provide information on vibratory sensation of passengers during earthquakes. Accelerations of the third car of monorail train on the conventional bridge are shown in Figure 11, and those on the advanced bridge are shown in Figure 12. For the response of train on the conventional bridge, responses under the G2LV1 ground motion were greater than those under the G1LV1 ground motion as shown in Figure 11. Observations also demonstrated that the response of moving train (SCN-4) was greater than of the response of parked train (SCN-3). For the response of train on the advanced bridge with steel bearings (see Figure 12 (a)), peak responses of moving train on the advanced bridge with steel bearings under the G2LV1 ground motion were greater than those of parked train even though the RMS value of SCN-4 was similar with SCN-3. However adopting elastomeric bearings led to relatively large accelerations on moving train as shown in Figure 12 (b). It could be concluded that responses of both moving and parked trains should be considered to investigate vibratory sensation of passengers during earthquakes. Moreover adopting elastomeric bearings to reduce seismic responses of bridges could increase acceleration responses of train under earthquakes. 5 30 time(s) PEAK = 191.7 Gal R.M.S = 48.65 Gal 400 200 0 -200 0 25 time(s) (4) Case-4: Train moving (a) Pier top (b) Span center Figure 7 Acceleration responses of the conventional bridge with steel bearings under G1LV1 ground motion. 4.2.2 20 -400 0 0 10 20 30 time(s) 600 400 200 0 -200 -400 -600 PEAK = 421.1 Gal R.M.S = 147.3 Gal 0 10 20 30 time(s) 600 400 200 0 -200 -400 -600 PEAK = 260.5 Gal R.M.S = 66.31 Gal 0 10 20 30 time(s) (3) Case-3: Train stop Acceleration(Gal) Acceleration(Gal) Acceleration(Gal) PEAK = 189.7 Gal R.M.S = 36.55 Gal 200 30 time(s) PEAK = 184.3 Gal R.M.S = 47.93 Gal 400 (3) Case-3: Train stop 400 20 -400 0 25 time(s) PEAK = 613.3 Gal R.M.S = 150.7 Gal (2) Case-2: Train as mass (2) Case-2: Train as mass PEAK = 182.6 Gal R.M.S = 36.16 Gal 400 30 time(s) -400 -400 -400 20 600 400 200 0 -200 -400 -600 (1) Case-1: No train R.M.S = 141.9 Gal Acceleration(Gal) 400 Acceleration(Gal) Acceleration(Gal) (1) Case-1: No trainPEAK = 423.9 Gal PEAK = 164.8 Gal R.M.S = 46.79 Gal Acceleration(Gal) -200 200 Acceleration(Gal) 0 PEAK = 230.7 Gal R.M.S = 69.68 Gal 400 Acceleration(Gal) 200 PEAK = 388.6 Gal R.M.S = 73.70 Gal 400 Acceleration(Gal) PEAK = 228.5 Gal R.M.S = 41.83 Gal 400 Acceleration(Gal) Acceleration(Gal) Acceleration(Gal) Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 SEISMIC PERFORMANCE OF MONORAIL BRIDGE Shearing forces of bearings and piers, and bending moments of piers are examined to discuss seismic performance of 10 20 30 time(s) 600 400 200 0 -200 -400 -600 PEAK = 272.7 Gal R.M.S = 70.86 Gal 0 10 20 30 time(s) (4) Case-4: Train moving (a) Pier top (b) Span center Figure 8 Acceleration responses of the conventional bridge with steel bearings under G2LV1 ground motion. monorail bridges under moderate ground motions. 5.1 Seismic performance of bearings The observation point was the bearing on the P3 pier as the shearing force on the P3 pier was greater than that of other piers from a preliminary investigation. Analytical shearing forces of steel bearings on the conventional bridge under G2LV1 and HB ground motions are shown in Figure 13. It shows that responses under the HB ground motion were larger than those under the G2LV1 design ground motion. Responses under the HB ground motion which led to critical results were discussed for the advanced bridge, and those shearing forces of steel and elastomeric bearings are shown in Figure 14. The horizontal lines in Figures 13 and 14 indicate shear capacities of bearings of the bridges: 165.4kN for the conventional bridge; and 221.9kN for the advance bridge. As shown in Figure 13(a), shearing forces of the conventional bridge under the G2LV1 ground motion were smaller than the shear capacity except SCN-2. For shearing forces of SCN-1 (disregarding train) and SCN-2 (considering train as additional mass) scenarios, those shearing forces of steel bearings on both conventional and advanced bridges under the HB ground motion were greater than the respective shear capacities. On the other hands, the scenarios considering train dynamics (SCN-3 and SCN-4) led to remarkably smaller shearing forces than those of SCN-1 and SCN-2. One reason for the result could be train’s dynamic system which acts as damper during earthquakes. 1165 0 -200 -400 -400 0 10 20 0 30 time(s) 10 20 400 PEAK = 154.3 Gal R.M.S = 43.01 Gal 200 0 -200 -400 30 time(s) 0 10 200 0 -200 PEAK = 393.0 Gal R.M.S = 112.6 Gal 400 400 Acceleration(Gal) Acceleration(Gal) 200 0 -200 PEAK = 142.1 Gal R.M.S = 40.05 Gal 200 0 -200 0 30 time(s) 10 20 -400 30 time(s) 0 10 200 0 -200 200 0 -200 -400 -400 0 10 20 0 30 time(s) 10 20 400 200 0 -200 -400 30 time(s) 30 time(s) 0 -200 200 0 -200 -400 0 10 20 400 200 0 -200 0 10 0 10 20 0 -200 0 5 10 15 20 25 time(s) PEAK = 264.3 Gal R.M.S = 77.35 Gal 400 200 0 -200 -400 10 PEAK = 156.2 Gal R.M.S = 43.28 Gal 0 -200 20 0 30 time(s) -200 -400 0 5 10 15 20 25 time(s) PEAK = 245.3 Gal R.M.S = 62.51 Gal 400 200 0 -200 -400 0 10 20 30 time(s) PEAK = 176.4 Gal R.M.S = 62.5 Gal 200 0 -200 0 5 10 15 20 25 30 Time (s) 20 30 time(s) SCN-4: Moving train (Rear axle) (a) G1LV1 ground motion (b) G2LV1 ground motion Figure 11. Acceleration responses of train on the conventional bridge with steel bearings. Under the HB ground motion, maximum shearing forces at the steel bearing on the conventional bridge were 187.1kN for the SCN-1 scenario and 446.8kN for the SCN-2 scenario, whereas those maximum shearing forces crossed the shear capacity of 165.4kN. Moreover, those maximum shearing forces of the steel bearing on the advanced bridge were 242.9kN in SCN-1 and 321.9kN in SCN-2, which also crossed the shearing capacity of 221.9kN. 20 30 time(s) 800 600 400 200 0 -200 -400 -600 -800 PEAK = 733.9 Gal R.M.S = 106.7 Gal 0 10 20 30 time(s) 200 0 -200 0 10 20 30 time(s) PEAK = 266.2 Gal R.M.S = 91.81 Gal 400 200 0 -200 -400 0 10 20 30 time(s) SCN-3: Parked train (3rd car, front axle) Acceleration(Gal) 0 Acceleration(Gal) PEAK = 163.7 Gal R.M.S = 43.86 Gal 200 10 PEAK = 284.7 Gal R.M.S = 83.44 Gal 400 SCN-3: Parked train (3rd car, front axle) 400 400 -400 30 time(s) 200 -400 0 10 (4) SCN-4: Train moving (b) Span center (a) Pier top Figure 10. Acceleration responses of the advanced bridge with elastomeric bearings under G2LV1 ground motion. Acceleration(Gal) 200 Acceleration(Gal) PEAK = 249.6 Gal R.M.S = 51.52 Gal 400 -400 30 time(s) (4) SCN-4: Train moving (b) Span center (a) Pier top Figure 9. Acceleration responses of the advanced bridge with steel bearings under G2LV1 ground motion. 400 20 -400 30 time(s) 0 (3) SCN-3: Train stop PEAK = 267.7 Gal R.M.S = 65.87 Gal Acceleration(Gal) PEAK = 187.1 Gal R.M.S = 47.93 Gal 400 Acceleration(Gal) Acceleration(Gal) 20 PEAK = 169.7 Gal R.M.S = 58.57 Gal 200 -400 30 time(s) PEAK = 153.4 Gal R.M.S = 43.13 Gal (3) SCN-3: Train stop Acceleration(Gal) 10 (2) SCN-2: Train as mass PEAK = 242.0 Gal R.M.S = 66.01 Gal 400 Acceleration(Gal) Acceleration(Gal) Acceleration(Gal) PEAK = 176.0 Gal R.M.S = 46.98 Gal 400 20 Acceleration (Gal) 20 (2) SCN-2: Train as mass Acceleration(Gal) 0 400 Acceleration(Gal) 10 Acceleration(Gal) 0 1166 0 -200 -400 -400 -400 200 -400 30 time(s) PEAK = 341.0 Gal R.M.S = 84.32 Gal 400 200 0 -200 -400 0 10 20 Acceleration(Gal) Acceleration(Gal) 400 20 PEAK = 223.1 Gal R.M.S = 65.95 Gal 400 (1) SCN-1: No train (1) SCN-1: No train PEAK = 202.7 Gal R.M.S = 48.39 Gal Acceleration(Gal) 0 -200 200 Acceleration(Gal) 200 PEAK = 430.3 Gal R.M.S = 117.6 Gal 400 Acceleration(Gal) PEAK = 242.8 Gal R.M.S = 53.98 Gal 400 Acceleration(Gal) Acceleration(Gal) Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 30 time(s) 600 400 200 0 -200 -400 -600 PEAK = 373.7 Gal R.M.S = 98.74 Gal 0 10 20 30 time(s) SCN-4: Moving train (Rear axle) (b) Elastomeric bearings (a)Steel bearings Figure 12. Acceleration responses of train on the advanced bridge under G2LV1 ground motion. The scenario SCN-2 that considers train as mass and is adopted in the bridge design code resulted in safest design even though the scenario is too idealized. The scenario SCN-1 of disregarding train, which occurs in actual situation, provided greater seismic responses than those scenarios considering train dynamics. It is noteworthy that the shearing forces of elastomeric bearings were clearly smaller than the shear capacities in all scenarios. Seismic performance of elastomeric bearings is sufficient under moderate ground motions. 20 30 time(s) 10 20 30 time(s) PEAK = 242.9 kN, R.M.S = 58.52 kN V Vlim 0 10 PEAK = 180.0 kN, R.M.S = 57.16 kN V Vlim 0 10 20 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 PEAK = 446.8 kN, R.M.S = 102.7 kN V Vlim 0 10 20 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 PEAK = 321.9 kN, R.M.S = 118.4 kN V Vlim 0 10 V Vlim 0 10 20 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 PEAK = 93.50 kN, R.M.S = 22.27 kN V Vlim 0 10 20 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 0 10 20 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 V Vlim 0 10 20 30 time(s) (4) SCN-4: Train moving (a) G2LV1 ground motion (b) HB ground motion Figure 13. Shear forces at steel bearings of the conventional bridge. 5.2 Seismic performance of piers A brief procedure to assess seismic performance of RC pier is as [2], 1) to decide failure mode utilizing the ratio of shear capacity times pier height to the capacity of bending moment; 2) to compare the analytical cross-sectional shearing force with the limit state if failure mode is shearing failure, or to compare the analytical cross-sectional bending moment with the limit state if failure mode is flexural failure mode. Preliminary investigations showed that failure modes of all models were the flexural mode. To examine the seismic performance at the pier base, the bending moment estimated from the seismic response analysis was compared to the flexural capacity for cracking of concrete Mc and the flexural capacity for failure of RC piers Mu. The maximum capacities for cracking of concrete, yielding of reinforcing bars and failure of the pier are calculated. To examine the flexural capacity, it is necessary to consider all axial reinforcements of the cross-section. The flexural capacity for cracking of concrete Mc is defined as the bending moment when the stress at the edge in the cross-section of the pier reaches the flexural strength of concrete, which can be calculated as Equation (2). M c Wi ( f bd N i / Ai ) V Vlim 0 10 20 30 time(s) 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 0 PEAK = 55.16 kN, R.M.S = 23.08 kN V Vlim 10 20 30 time(s) V Vlim 0 10 20 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 PEAK = 82.15 kN, R.M.S =36.35 kN V Vlim 0 10 20 30 time(s) (3) SCN-3: Train stop PEAK = 108.4 kN, R.M.S = 26.44 kN (2) where, Wi, fbd, Ni and Ai are the section modulus considering reinforcing bars, the flexural strength of concrete, compressive axial force at the cross-section and the sectional area considering of reinforcing bars, respectively. Shear force (kN) V Vlim Shear force (kN) Shear force (kN) PEAK = 86.49 kN, R.M.S = 19.47 kN 20 PEAK = 96.55 kN, R.M.S = 28.73 kN (3) SCN-3: Train stop 400 300 200 100 0 -100 -200 -300 -400 PEAK = 51.93 kN, R.M.S = 19.02 kN (2) SCN-2: Train as mass Shear force (kN) PEAK = 78.05 kN, R.M.S = 19.83 kN Shear force (kN) Shear force (kN) (2) SCN-2: Train as mass 400 300 200 100 0 -100 -200 -300 -400 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 (1) SCN-1: No train Shear force (kN) 400 300 200 100 0 -100 -200 -300 -400 Shear force (kN) Shear force (kN) (1) SCN-1: No train 20 Shear force (kN) V Vlim 0 400 300 200 100 0 -100 -200 -300 -400 Shear force (kN) 10 PEAK = 187.1 kN, R.M.S = 56.97 kN Shear force (kN) V Vlim 0 400 300 200 100 0 -100 -200 -300 -400 400 300 200 100 0 -100 -200 -300 -400 PEAK = 109.4 kN, R.M.S = 30.80 kN V Vlim 0 10 20 Shear force (kN) PEAK = 101.6 kN, R.M.S = 30.07 kN Shear force (kN) 400 300 200 100 0 -100 -200 -300 -400 Shear force (kN) Shear force (kN) Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 30 time(s) 400 300 200 100 0 -100 -200 -300 -400 PEAK = 48.98 kN, R.M.S = 19.43 kN V Vlim 0 10 20 30 time(s) (4) SCN-4: Train moving (b) Elastomeric bearing (a) Steel bearing Figure 14. Shear forces at bearings of the advanced bridge under HB ground motion. The flexural capacity for failure of the pier Mu is defined as the bending moment for failure of the pier. The bending moment is calculated according to Equation (3). M u C (d e x) Tsc (d e dc ) Tst e (3) where, C’, T’sc and Tst are the axial compressive force of concrete, the axial compressive force of reinforcing bars, and the axial tensile force of reinforcing bars, respectively. For the conventional bridge with steel bearings under the G2LV1 and HB ground motions, the analytical bending moment with flexural capacities of the P2 pier are shown in Figure 15. The bending moment and flexural capacities for the advanced bridge under the HB ground motion are shown in Figure 16. Therein Mc was 20180kN.m and Mu was 3370 kN.m. Observations demonstrated that the monorail bridges satisfy Level-1 seismic performance as expected since in all scenarios the bending moment was smaller than the limit states of flexural failure but greater than the flexural capacities for clacking. Considering train dynamics in the seismic response analysis reduced the bending moments at the RC piers drastically comparing the scenario of considering train as additional which is the conventional approach. For the bridge with elastomeric bearings, bending moments were remarkably smaller than the limit state of flexural failure and were not cracked. It demonstrates that the elastomeric bearings were a good option to improve seismic performance of the bridge. 1167 M Mc Mu -20000 0 10 20 0 -10000 M Mc Mu -20000 0 30 time(s) 10 20 10000 0 -10000 M Mc Mu -20000 0 30 time(s) 10 10000 0 -10000 M Mc Mu -20000 0 10 20 PEAK = 10930 kN･m, R.M.S = 2550 kN･m 20000 10000 0 -10000 M Mc Mu -20000 30 time(s) 0 10 20 PEAK = 8549 kN･m, R.M.S = 2861 kN･m 10000 0 -10000 M Mc Mu -20000 30 time(s) 0 0 -10000 M Mc Mu -20000 0 10 20 20000 10000 0 -10000 M Mc Mu -20000 30 time(s) 0 10 10 20 0 -10000 M Mc Mu -20000 0 10 20 30 time(s) 10000 0 -10000 M Mc Mu -20000 0 10 10000 0 -10000 M Mc Mu -20000 10 20 10 20 30 time(s) PEAK = 2156 kN･m, R.M.S = 629.5 kN･m 20000 10000 0 -10000 M Mc Mu -20000 0 10 20 30 time(s) PEAK = 2422 kN･m, R.M.S = 706.1 kN･m 20000 10000 0 -10000 M Mc Mu -20000 0 30 time(s) 20000 10000 0 -10000 CONCLUSION M Mc Mu -20000 30 time(s) This study investigates how train on monorail bridges acts on seismic responses of monorail bridges. The study also examined the seismic performance of the conventional type monorail bridge with steel bearings and the advanced type monorail bridge which adopts longer span than that of the conventional bridge under moderate ground motions. Efficacy of the elastomeric bearing is also examined. Summarized results are as follows. (1) The failure mode was flexural failure, and monorail bridge design satisfies Level-1 seismic performance since in all scenarios the bending moment was smaller than the limit states. (2) Dynamic system of train could act as a damper during earthquakes. (3) Elastomeric bearings were a good option to improve seismic performance of the bridge. However, adopting elastomeric bearings to reduce seismic responses of bridges could increase acceleration responses of train under earthquakes. (4) Seismic responses of both moving and parked trains should be considered to investigate vibratory sensation of passengers during earthquakes. 1168 20 PEAK = 6059 kN･m, R.M.S = 1795 kN･m 0 (4) SCN-4: Train moving (a) G2LV1 ground motion (b) HB ground motion Figure 15. Bending moment at the pier base of the conventional bridge with steel bearings. 6 0 10 20 30 time(s) (3) SCN-3: Train stop PEAK = 6260 kN･m, R.M.S = 1669 kN･m 20000 0 30 time(s) 20000 30 time(s) Bending Moment (kN・m) 10000 Bending Moment (kN・m) Bending Moment (kN・m) 20000 20 PEAK = 6655 kN･m, R.M.S = 1355 kN･m (3) SCN-3: Train stop PEAK = 4174 kN･m, R.M.S = 1253 kN･m M Mc Mu -20000 (2) SCN-2: Train as mass PEAK = 5279 kN･m, R.M.S = 1368 kN･m Bending Moment (kN・m) 10000 Bending Moment (kN・m) Bending Moment (kN・m) 20000 0 -10000 30 time(s) 20000 (2) SCN-2: Train as mass PEAK = 3221 kN･m, R.M.S = 847.9 kN･m 20 10000 (1) SCN-1: No train Bending Moment (kN・m) PEAK = 5149 kN･m, R.M.S = 1424 kN･m 20000 Bending Moment (kN・m) Bending Moment (kN・m) (1) SCN-1: No train Bending Moment (kN・m) -10000 10000 PEAK = 2553 kN･m, R.M.S = 785.1 kN･m 20000 Bending Moment (kN・m) 0 PEAK = 10920 kN･m, R.M.S = 2442 kN･m 20000 Bending Moment (kN・m) 10000 PEAK = 8657 kN･m, R.M.S = 2542 kN･m 20000 10 20 30 time(s) Bending Moment (kN・m) PEAK = 4149 kN･m, R.M.S = 1404 kN･m 20000 Bending Moment (kN・m) Bending Moment (kN・m) Bending Moment (kN・m) Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014 PEAK = 2931 kN･m, R.M.S = 1368 kN･m 20000 10000 0 -10000 M Mc Mu -20000 0 10 20 30 time(s) (4) SCN-4: Train moving (a) Steel bearings (b) Elastomeric bearings Figure 16. Bending moment at the pier base of the advanced bridge under HB ground motion. REFERANCES [1] [2] [3] [4] [5] [6] C.H. Lee, C.W. Kim, M. Kawatani, N. Nishimura, T. Kamizono, Dynamic response analysis of monorail bridges under moving trains and riding comfort of trains, Engineering Structures 27 , 1999-2013, 2005. Japan Road Association (JRA), Specifications for Highway Bridges, Part V: Seismic Design, Maruzen, Tokyo, Japan, 2013. C.H. Lee, M. Kawatani, C.W. Kim, N. Nishimura, Y. Kobayashi, Dynamic response of a monorail steel bridge under a moving train, Journal of Sound and Vibration 294, 562-579, 2006. C.W. Kim, M. Kawatani, Effect of train dynamics on seismic response of steel monorail bridges under moderate ground motion, Earthquake Engineering & Structural Dynamics 35, 1225–1245, 2006. C.W. Kim, M. Kawatani, T, Kanbara, N. Nishimura, Seismic behavior of steel monorail bridges under train load during strong earthquakes, Journal of Earthquake and Tsunami 7, No.2,1350006 1-17, 2013. C.W. Kim, M. Kawatani, K.B. Kim, Three-dimensional dynamic analysis for bridge–vehicle interaction with roadway roughness, Computers & Structures 83, 1627–1645, 2005.
© Copyright 2024