DYNAMIC RESPONSE ANALYSIS OF THE RAMA 9 BRIDGE EXPANSION JOINT DUE TO RUNNING VEHICLE Tanan Chub-uppakarn 1, Adison Owatsiriwong 2* 1 Department of Civil Engineering, Faculty of Engineering, Prince of Songkla University, Thailand 2 ALPS Consultants Company Limited, Bangkok, Thailand 10500 E-mail: adisorn.alps@gmail.com Abstract: Normally, Running vehicles generate vibration load due to the rounghness of road surface. When vehicles run on a bridge, the vibration of the bridge sometimes becomes fairly large because of amplification by the dynamic interaction of vehicle and bridge. In the expansion joint of Rama 9 Bridge, the oscillating problem due to running vehicles has actually occurred long time. Furthermore, the structure is subject to a continuous degradation due to ageing and environmental factors. In present, working condition of the expansion joint of Rama 9 Bridge is not perfect as design criteria. Therefore, responsible supervisory authority would like to maintenance or part replacement of the structure. Objective of this study is focus on analysis dynamic response of the expansion joint of Rama 9 Bridge due to running vehicle. It has been found that speed of vehicle is quite sensitive to dynamic response of the structure. Therefore, finite element method, popular method, is used to analyze the problem. The solution is used to decide and conduct the problem which generally results in more economical repairs. Keywords: Dynamic, vehicle, Rama 9, Bridge 1. INTRODUCTION One of the most important parts of the Rama 9 Bridge structure is expansion joint between main steel structure and concrete structure. It is used to release thermal stress and transfer vertical load to main structure of the bridge. However, the expansion joint of The Rama 9 Bridge has served its function for over 20 years. In 2004, it was recommended by the inspection report (IMMS, 2004) that parts of this expansion joint be replaced and maintain in-place due to severe damage and malfunction. Therefore, the Expressway Authority of Thailand (EXAT) has recently planned to maintain and part replacement of this important part of the bridge. In order to select economical repair methods, numerical analysis of The Rama 9 bridge expansion joint due to running vehicle is used to conduct problem. In this study, the Finite Element Method (FEM) that is one of the most popular approximate methods for solving problems is used to solve problem. The joint is a roller-shutter type that enables to maintain vehicle loading through bending stiffness of its major components namely sliding plate, tongue plate, rocker plate, and track frame. Those joint components must be assured to have enough bending stiffness and capacity during the course of operation. 2. ANALYSIS ASSUMPTIONS AND DESIGN LOADING 2.1 Analysis Assumptions A series of three dimensional finite element analysis was conducted to explore behavior of The Rama 9 bridge expansion joint due to running vehicle. The component of expansion joint structures was modeled using shell element, while connection between each plate of the structures and track frame was simulated using an interface element at which its axial load carrying capacity was transferred by a set of compression springs as depicted in Fig. 1. The structural damping was also taken into account to constant for all natural frequencies. The properties and parameters of the structure adapted in the analysis are focus on elastic range and small displacement theory. External loads were imposed vertically symmetric to simulate the action of vehicle load and symmetric boundary condition. Therefore, the joint structure can be applied along the plane of symmetry. Track Frame Fig. 1. Finite element model and boundary condition used in the analysis 2.2 Vehicle loading End Support Tongue plate Sliding plate Spring Fastener Rocker plate AASHTO loading of HS20-44 is based on an axle load of 145 kn. This load is divided into two tries that is a load at each end of the axle. The tire contact area for HS20-44 as defined in AASHTO 3.30 shall be assumed as a rectangle with a length in the direction of traffic of
254 mm, and a width of tire of 500 mm. Therefore, the pressure would appear to be equal to 72.5 kn/(254x500) = ~550 kpa. In addition, these two tires on the axle are spaced six feet apart (center-to-center) transverse to the direction of traffic and the successive axles of an HS truck are 4.27 m apart along the direction of traffic. According to the Department of Highway (DOH) s requirement, a Thai truck whose gross weight is 130% of AASHTO HS20-44 will be used for the analysis. 3. NUMERICAL MODELING OF THE RAMA9 BRIDGE EXPANSION JOINT 3.1 Structural elements A series of three dimensional finite element analysis using SAP2000 (Computers and Structures, 2009) were conducted to explore the dynamic and static response of the roller shutter joint under the action of Thai truck (1.3 times HS20-44). The modeling mesh comprising of 494 nodes, 380 shell elements and 32 links elements can be shown in Fig. 1. To reduce the problem size, only half of the typical segment is considered. Symmetric boundary conditions are applied along the plane of symmetry. 3.2 Material Properties and Damping High-strength steel Gr. SM53C with F y = 359 MPa is used for tongue plate, sliding plate and rocker plate, while the high-strength steel Gr. SM58Q with F y = 458 MPa is used for track frame (support device). The Young s Modulus (E) of steel is 2.0 x 10 5 MPa; Poisson ratio is 0.30 with mass density of 7850 kg/m 3. The spring fasteners are made of steel Gr. S35C whose yield strength equal to 400 MPa (min). The hinge joint is made of steel Gr. SM53C whose yield strength equal to 359 MPa, while the connecting pin is made of SUS316 steel having yield strength of 205 MPa. Damping of material can be modeled using Rayleigh s damping equation. The damping ratio of n th frequency mode can be written by i i (1) 2 i 2 and are free parameters that can be determined from regression analysis if at least 2 set of data are known. Without testing data, we consider here a simple case where of =0.1142. The value of, determined from linear model, is 0.00029. Dampings introduced by connecting bolts and hinge joints as well as elastomeric cushion are excluded from the analysis due to lack of support evidence. 3.3 Loading Loading acting to roller shutter joint is mainly due to weight of HS-20 truck that occurs when the truck passing through the joint. Axle weight and load distance of the HS-20 truck adopted for the analysis is shown in Fig.2. This actual load pattern can be well represented by a series of finite size impulses marching in time as shown in Fig. 3 and Tables 1 to 3. This presents the idealized loading for one wheel of HS20-44 truck. 145 kn 145 kn 36 kn Symmetric line 2a) HS20-44 design load pattern 2b) Pressure wheel load acting to FE model Fig. 2. The AASHTO HS20-44 design load pattern Function Value 1.0 Fig. 3. Impulse load function and load parameters Table 1. Load pattern for HS-20 truck passing at speed of 30 km/h arrival time (s) 0.0228 0.0696 0.1164 0.1597 0.2101 0.2569 6.00E-03 6.00E-03 6.00E-03 6.00E-03 6.00E-03 6.00E-03 Table 2. Load pattern for HS-20 truck passing at speed of 60 km/h arrival time (s) 0.0114 0.0348 0.0582 0.0798 0.1050 0.1284 t d = s/v a Varies length Tongue plate Sliding plate Rocker plate t 1 4.27 m Time t 1 = interval time, t d = arrival time, v a = vehicle speed, s = dominate distance 3.00E-03 3.00E-03 3.00E-03 3.00E-03 3.00E-03 3.00E-03 Table 3. Load pattern for HS-20 truck passing at speed of 100 km/h arrival time (s) 0.0068 0.0209 0.0349 0.0479 0.0630 0.0770 1.00E-03 1.00E-03 1.00E-03 1.00E-03 1.00E-03 1.00E-03
3.4 Modeling of spring fastener, end support and hinge joint The spring fastener is modeled as hook element, so that it carries only tension. A spring constant of 1205 N/mm is used. The end support is modeled as gap element, so that it can sustain only compressive force. The initial distance of gap and hook is specified as 1x10-3 mm. Hinge joint is modeled as horizontal shear link element. Conceptually, the link must be able to carry axial force as well as transverse shear forces in both vertical and horizontal directions. The bending stiffness of horizontal link is neglected due to its stocky shape. To provide a complete load path, additional vertical link element is required at load transfer point to track frame. It is assumed that the vertical link can transfer load from the sliding plate to track frame only in its axial direction. 3.5 Analysis method Implicit time integration by Hilber-Hughes-Taylor (HHT) method with =1/2 (unconditionally stable) is adopted for the transient analysis. Lump mass model is used to speed up solution time. The time increment t 0.1 milliseconds is used throughout the analysis. Due to presence of gap and hook, the analysis commonly becomes nonlinear during the time step. To obtain nonlinear solution, full Newton-Raphson method with automatic time step adjustment is adopted. To assist convergence of the solution, smaller time increment is usually required when nonlinear response of the structure is detected. The relative convergence tolerance for force residual is set as 1x10-3. 4. ANALYSIS RESULT 4.1 Vertical displacement Vertical displacements at mid of tongue plate, sliding plate and rocker plates are plotted versus time. It was found that the maximum vertical displacement occurs at rocker plate due to its larger span. The maximum vertical displacement at mid of rocker plate under static load is 0.264 mm. Next step, considered moving load condition, deformation of the structure is controlled by slow speed of HS20-44 truck as shown in Figs. 4 to 6. The vertical deformation at middle span of roller joint plate at speed of 30, 60, 100 km/h is 0.412 mm, 0.235 mm, and 0.257 mm respectively. The plot of dynamic response factor defined by the ratio between dynamic and static response is shown in Fig. 7. According to the results, the vehicle at traveling speed of 30 km/h induces maximum dynamic response factor of about 1.58. Figure 8 illustrates the von Mises stress at bottom layer of joint plates. Fig. 4. Vertical displacement at vehicle speed of 30 km/h Fig. 5. Vertical displacement at vehicle speed of 60 km/h Fig. 6. Vertical displacement at vehicle speed of 100 km/h Fig. 7. Plot of dynamic response factor for varying truck speed 4.2 Force in spring fasteners The history of tensile force in spring fasteners is plotted in Figs. 10 to 12 for traveling speed 30, 60 and 100 km/h, respectively. It can be shown that the maximum tensile force occurs when the truck travel at the lowest speed (30 km/h). The maximum tensile force is equal to 980 N causing tensile stress of 1.65 MPa which is significantly less than the allowable value for the steel Gr. S35C (0.5F y = 200 MPa). The location and element numbering of the spring fasteners are shown in Fig. 9. 13.3MPa 10.5 MPa Time = 0.0585s Time = 0.063s
6.4MPa 6.5MPa Time = 0.1604 Time = 0.214s 6.7MPa 14.9MPa Time = 0.2809s Time = 0.2859s Fig. 8. Contour of von Mises stress at bottom of plate at speed 30 km/h S28 S27 H18 H19 H24 S26 Fig. 12. Time history plot of tensile force at spring fasteners for a vehicle speed of 100 km/h 4.3 Force at hinge pins The time history plots of transverse shear force at hinges for varying vehicle speed are shown in Figs. 13 to 15. It was found that the maximum vertical shear force of magnitude 600 N occurs when the traveling speed is equal to 30 km/h. This causes transverse shear stress in the hinge pin equal to only 1.0 MPa (single shear plane). This value is so small as compared to the allowable shear stress of SUS316 (0.5F y = 100 MPa). Fig. 9 indicates the location and element numbering of the hinge pins. S25 Fig. 9. Location of hinges and spring fasteners Fig. 13. Vertical shear force at hinge pin for a vehicle speed of 30 km/h Fig. 10. Time history plots of tensile force at spring fasteners for a vehicle speed of 30 km/h Fig. 14. Vertical shear force at hinge pins for a vehicle speed of 60 km/h Fig. 11. Time history plots of tensile force at spring fasteners for a vehicle speed of 60 km/h
100 0.097 0.98/0.50 5. REFERENCES [1] Computers and Structures Inc. (2009), SAP 2000 Release 12 Fig. 15. Vertical shear force at hinge pins for a vehicle speed of 100 km/h 5. CONCLUSION This report has summarized the numerical analysis results for expansion joint of Rama IX bridge subjected to Thai truck loading (Gross Wt. = 130% of AASHTO HS20-44). Transient dynamic analyses have been conducted for varying vehicle speeds (30, 60 and 100 km/h). Moreover, the static solution has also been conducted as for reference. It was found that dynamic response of the joint plates is strongly dependent on vehicle traveling speed. The higher traveling speed leads to less vertical displacement amplitude at mid of plates. This rather agrees with the analytical results proposed by Clough and Penzien (1993) analyzed for a single DOF mass-spring system as shown in Fig. 16. However, neglecting transient dynamic effect will obviously lead to unconservative result as shown in Table 4. It was found that the critical traveling speed occurs at 30 km/h. At this critical speed, the dynamic response factor of 1.58 is observed. The maximum von Mises stress at the extreme fibers of joint plates is found to be significantly less than the allowable value (0.5F y = 180 MPa). Furthermore, it was found that the tensile force in spring fastener and transverse shear force at hinge pin are significantly below the material yield value, so that the overall structure is safe against local yielding. [2] IMMS Co.,Ltd. (2004), Final report: An inspection and design of the expansion joint for Rama IX bridge [3] R.W. Clough, J. Penzien (1993), Dynamics of structures, 2 nd ed., McGraw-Hill [4] O.C. Zienkiewicz, R.L. Taylor (2000), Finite Element Methods, 5 th ed., Butterworth-Heinemann Fig. 16. Displacement response spectra for three types of impulse (Clough and Penzien, 1993) Table 4. t 1 /T 1 values for different traveling speed Traveling speed (km/h) t 1 /T 1 DRF model /DRF theory (Half sine wave) 30 0.584 1.58/1.62 60 0.292 0.90/1.10