DYNAMIC ANALYSIS OF COMPOSITE MULTI I-GIRDERS BRIDGE USING FINITE ELEMENT METHOD

Dynamic amplification factors of corrugated steel plate culverts

This paper presents the investigation of the effect of dynamic loads on the dynamic amplification factors (DAFs) of an existing continuous bridge. A three-dimensional analytical model to idealize the vehicle and a finite element model to analyze the bridge have been developed. Experimental testing of this existing bridge has been conducted by the Ministry of Transportation, Quebec. Two vehicle models, having seven and 11 degrees of freedom with and/or without trailers, are considered in the analysis of the interaction between the bridge and vehicles. Based on International Standards Organization specifications, the road-surface roughness of the approach roadways and bridge deck is generated from the power-spectral density function for very good, good, and average roads. The solutions obtained from the present models are compared with the experimental results for different vehicle speeds. The DAFs are computed from the present finite element model for three different types of measurements (displacements, strains, and reactions). The numerical results show that the DAFs computed with displacements are less than those estimated from strains and reactions. It is concluded that current design codes tend to underestimate dynamic amplification factors, especially for long-span continuous bridges.

This research focuses on the application of the spatial system of finite element modeling for the vehicle-bridge interaction on reinforced concrete US Girder Bridge in order to obtain the effect of surface roughness. Single vehicle and multiple vehicles on reinforced concrete T beam bridge were studied with variable surface roughness profiles. The effects of six different surface roughness profiles (very good, good, measured, average, poor, and very poor) were investigated for vehicle-bridge interaction. The values of the Dynamic Amplification Factor (DAF) were obtained for single and multiple vehicles on T Beam Bridge for different surface roughness profiles, along with the distances between the axles of heavy vehicle. It was observed that when the bridge has very good, good, measured, and average surface roughness, the DAF values for the single vehicle over the bridge were observed to be within acceptable limits specified by AASHTO. However, for the bridge with multiple vehicles only very good and measured surface roughness profiles showed a DAF and vehicle axle distances within the acceptable limits. From the current studies, it was observed that the spatial system showed reliable responses for predicting the behavior of the bridge under variable road surface roughness conditions and was reliable in vehicle axle detection, and therefore, it has a potential to be use for realistic simulations.

Recent research has shown that the dynamic amplification factor (DAF) to be applied to free-flowing traffic-induced load effect may not be as high as previously thought. Therefore, congested traffic states may govern extreme load effect at lower bridge lengths than currently assumed. Thus, there is a need for a methodology that incorporates both free-flowing and congested traffic states in the calculation of lifetime load effect. It should allow for the relative frequency of occurrence of the different forms of traffic and any form of DAF function that may arise. This paper presents such an approach and also presents a general probabilistic DAF formulation for inclusion. Using measured traffic, the approach is applied to a range of bridge lengths and load effects employing a variety of DAF approaches from the literature, in addition to the new DAF formulation. Using a critical traffic index, it is shown that the governing form of traffic is very sensitive to the dynamic amplification model used. Further, depending on this model, congested traffic can govern short spans, and for other spans, a combination of free- and congested-flow traffic states must be considered.

This work presents the results of a parametric study on the dynamic amplification or impact factor due to transit vehicles. The study was performed on a single span simply supported bridge composed of prestressed concrete bulb tee girders with a concrete deck and direct fixation track. The study varied the key parameters affecting the structural response of the bridge, viz. stiffness of the bridge, vehicle speed and axle configuration. The bridge was numerically modeled using CSI-Bridge software. Stiffness was manipulated in the models by varying the elastic modulus of the concrete. Vehicle speed varied form quasi-static speed of 0.45 m/s (1 mph) to 35.32 m/s (79 mph) in increments of 1.34 m/s (3 mph). Different axle configurations were obtained by modeling trains consisting of different numbers of cars as well as considering different light rail vehicle types. Light rail vehicles defined by transit agencies in Denver, Boston, Washington DC, Phoenix and Houston were considered, which provided a total of 22 different configurations. Vehicle lengths as well the number of axles and spacing between axles varied. The moving loads were modeled using a linear elastic time history analysis. It was assumed that the rail was connected to the bridge deck at distinct points represented by the rail clip connections at approximately 0.76 m (30 inches) on-center. The magnitude of the axle load at a point ramped up from zero to maximum as the axle traveled from the preceding rail clip to the point under consideration and then decreased to zero as the axle traveled onto the following connection point. This triangular variation with time was modeled as a time dependent ramp function which was applied to the different light rail vehicle trains. The time between the start and end of the ramp function was dependent on the speed of the vehicles and train speed was modeled by changing the time base of the ramp function. Dynamic impact was estimated from the models from the ratio of the maximum deflection at midspan under time dependent moving load to the deflection due to a static load analysis. The results showed that the dynamic impact effects on the structure vary greatly with speed and configuration of the vehicle. While the effects generally increased with vehicle speed, the change was not linear and showed in general more than one peak value within the speed range selected. The maximum computed dynamic effect did not occur at the highest speed. The dynamic effect was also dependent on vehicle configuration, with a clear difference in responses between two axle and three axle cars. The overall length of the vehicle had less of an effect. The results were compared to the impact factors typically used by transit agencies and showed that in general for normal ranges of structure stiffness the Agency criteria are conservative or extremely close for vehicle speeds under 35.3 m/s (79 mph). However, the ACI equation for dynamic impact which is the only equation that incorporates vehicle speed and structural stiffness is usually conservative at higher speeds but may be unconservative at lower and medium speeds and does not reflect effects of axle configuration.

In a half-through or through arch bridge, the hangers (or suspenders) are considered as critical structural components, especially for dynamic performance assessment. This paper aims to study the dynamic impact of stiff hangers in an arch bridge caused by moving vehicles. An iterative algorithm is firstly proposed to solve the three-dimensional coupling vibration between the vehicle(s) and the large-scale bridge. In addition, the uncertainty of the computed strain-based dynamic amplification factor (DAF) due to measurement noise and the relationship between the DAF and local stiffness degeneration are investigated, respectively. After that, the influences of several parameters on the strain-based DAF of the hangers are studied by parametric analyses, including vehicle speed, road surface conditions, loading lane, vehicle spacing and vehicle model. The results show that the proposed iterative algorithm can accurately solve the refined three-dimensional coupled vibration system, and that the strain-based DAF is sensitive to measurement noise and changes of local stiffness. The shortest hanger suffers a more serious impact effect and a higher dynamic fatigue risk. The analysis results of this study could provide some useful and practical recommendations for the routine maintenance and traffic management of arch bridges with stiff hangers.

Effect and its mechanism of spatial coherence of track irregularity on dynamic responses of railway vehicles

Shear failure is a common mode for bridge column collapse during a vehicle‐column collision. In current design codes, an equivalent static load value is usually employed to specify the shear capacity of bridge columns subject to vehicle collisions. But how to consider the dynamic effect on bridge columns induced by impact load needs further research. The dynamic amplification factor (DAF) is generally used in the analysis and design to include the dynamic effect, which is usually determined using the equivalent single degree of freedom (SDOF) method. However, SDOF method neglects the effect of the higher‐order modes, leading to big difference between the calculated results and the real induced forces. Therefore, a novel method to obtain dynamic response under concentrated impact load including the effect of higher‐order modes is proposed in the paper, which is based on the modified Timoshenko beam theory (MTB) and the classical Timoshenko beam theory (CTB). Finite element models are conducted to validate the proposed method. The result comparisons show that the results from the proposed method have more accuracy compared with the results from the CTB theory. Additionally, the proposed method is employed to calculate the maximum DAF of shear forces for bridge columns under impact load. Parametric studies are conducted to investigate the effect on the DAF of shear forces including slenderness ratio, boundary condition, and shape and position of impact load. Finally, a simplified formula for calculating the maximum DAF of shear force is proposed for bridge column design.

Although structural capacity seems to be the major concern of many pavement engineers, road users primarily judge the quality of a road based on its roughness or ride quality. Several parameters influence the ride quality of pavements as felt by the road users. These parameters include pavement surface characteristics, as well vehicle characteristics such as vehicle response and speed. In the present study these parameters contribute to the pavement roughness evaluation by using proper mathematical models accomplished with field data analysis information. Furthermore, an alternative roughness index is developed taking into account the above parameters. The suggested index seems to have an advantage over the international roughness index (IRI) and the power spectral density (PSD) spectrum that is often applied for evaluating pavement roughness.

고속철도상 교량의 동적응답을 보다 정밀하게 해석하기 위한 동적해석방법을 개발하였다. 고속으로 주행하는 동력차에 의한 교량의 동적거동을 면밀한 속도변수분석과 고속철, 교량 그리고 궤도구조물의 상호작용을 포함한 수치모델로 구성하였다. 40미터 단순지간의 PSC박스거더교를 3차원 유한 프레임요소로 모델링 하였다. 스펙트럼 밀도함수로 산출된 궤도불규칙값과 궤도간 상이한 거리차이를 고려하여 고속철 차량은(KTX) 38자유도로 구성하였다. 38자유도 모델은 3방향 변위와 상응하는 회전각을 고려하였다. 동적증폭계수는 다양한 궤도의 불규칙성, 켐버, 주행속도, 자갈도상과 같은 주행조건에 의해 결정된다. 이와 같은 동적증폭계수를 해석하기 위하여 Newmark-<TEX>${\beta}$</TEX> 기법과 Runge-Kutta 기법을 적용하여 비교분석하였다. A dynamic analysis procedure is developed to provide a better estimation of the dynamic responses of bridge during the passage of high speed railway vehicles. Particularly, a three dimensional numerical model including the structural interaction between high speed vehicles, bridges and railway endures to analyse accurately and evaluate with in-depth parametric studies for dynamic responses of bridge running high speed railway vehicles. Three dimensional frame element is used to model the prestressed concrete box bridge(40 m simply supported) Track irregularity employed as a stationary random process from the given spectral density functions and irregularities of both sides of the track are assumed to have high correlation. The high-speed railway vehicle (KTX) is used as 38-degree of freedom system. Three displacements (vertical, lateral, and longitudinal) as well as three rotational components (pitching, rolling, and yawing) are considered in the 38-degree of freedom model. The dynamic amplification factors are evaluated by the developed procedure under various traveling conditions, such as track irregularity camber, train speed and ballast. The dynamic analysis such as Newmark and Runge-Kutta methods which are able to analyse considering the dynamic impact factors are compared and contrasted.

An indirect bridge frequency identification method using dynamic responses of high-speed railway vehicles

Developed herein is a spectral approach for evaluating the dynamic vehicle load due to the passage of a vehicle moving at constant speed along a rough bridge surface. Based on the approach, a simple closed‐form solution for predicting the variation of dynamic vehicle load on a bridge deck is derived. Numerical examples of the application of the solution to a simply‐supported bridge are presented. Four different classes of pavement roughness (including: very good, good, average, and poor pavements) and three different vehicle speeds (speeds of 60, 100, and 140 km/h) are used in numerical analysis. The Dynamic Load Coefficient (DLC), a parameter used to characterize the magnitude of dynamic vehicle load, is estimated. The effects of vehicle speed and pavement roughness on the variation of dynamic vehicle load are investigated. It is concluded that if the effect of engine motion on vehicle vibration is disregarded, both the DLC and standard deviation of dynamic vehicle load are proportional to the square root of the pavement roughness coefficient S(n 0) for a specified vehicle speed.

Monitoring vehicle axle loads is very important for preventing infrastructure degradation and traffic accidents. However, developing an accurate, cost-effective, and easy-to-implement axle load identification technology still remains challenging. In this study, a vehicle axle load identification method based on visual measurement is proposed. The principle of the method is that each axle load of the vehicle is determined based on the vehicle unsprung masses, the ratio of vehicular sprung mass to unsprung mass, and the centroid position of the sprung mass. While the vehicle unsprung masses can be treated as a known with the vehicle model identified, the mass ratio can be predicted from the visually captured free damped vibrations of the vehicle as it passes over a speed bump. To be more specific, the vibration responses of a vehicle passing over a speed bump are firstly measured by a camera, and the vehicle system matrix, which is composed of the mass matrix, stiffness matrix, and damping matrix, can be obtained from the vehicle responses. The axle load can then be determined based on the element ratios in the system matrix of the vehicle whose unsprung masses are known. The performance of the proposed method was evaluated by numerical simulations and field tests. The results show that the errors of the simulation results are all less than 1% under ideal conditions. In the field test, the average error in identifying axle loads at different vehicle speeds was 7.01% when the vehicle speed was below 20 m s−1, which proved the accuracy and effectiveness of the proposed method. This study has demonstrated a novel application of computer vision technology to identify the axle loads of moving vehicles. The proposed method does not require installation of sensors on the roadway or the vehicle, making it a promising alternative for traditional weigh-in-motion systems.

IRI (International Roughness Index): An Indicator Of Vehicle Response

Ride comfort, safety, wear and vehicle speed are the most important factors in evaluating the efficiency of railway transportation. In order to decrease the track access charges it is often desirable to run the vehicle at maximum allowed speed, while keeping an admissible amount of wear in system. This usually deteriorates the ride comfort and safety level during the operation. Therefore, an optimization problem to find a tradeoff value for vehicle speed and design parameters is inevitable. Since, ride comfort, safety and wear values are sensitive to primary and secondary suspensions’ damping parameters it is desirable to find the optimum values of such design variables. In this regard, the multiobjective optimization of railway vehicle dampers is considered to increase the cost-efficiency of railway operation. One car vehicle model with 26 degrees of freedom (DOF) along with a set of initial states, design parameters and operational conditions is explored here. All bodies are assumed to be rigid. Vehicle carbody and bogie frames supposed to have the full set of DOF in space. While, only lateral and yaw motions are considered for each wheelset. It is also assumed that wheelset roll angle is a function of the lateral displacement. Primary and secondary suspensions compromised of parallel linear springs and dampers in longitudinal, vertical and lateral directions which connect wheelsets to bogie frames, and bogie frames to carbody, respectively. Lagrange formalism is employed to obtain the system’s equations of motion. The nonlinear heuristic theory is chosen to relate creepages and the corresponding creep contact forces. The dynamic response of the system is obtained for different operational scenarios including ideal and imperfect tangent and curved tracks. Series-based functions are chosen to approximate the harmonic lateral track irregularities. Accelerations at carbody level, shift forces and wear number are used to evaluate the ride comfort, safety and wear, respectively. MATLAB genetic algorithm optimization routine is applied to perform the optimization. The Pareto sets and Pareto fronts obtained from this study provide the vectors of optimal design parameters corresponding to maximum admissible vehicle speed and guarantee the best tradeoff values for safety and comfort with threshold on wear for each operational scenario. Analysis of the obtained results gives insight into multiobjective optimized dynamic response of a railway vehicle and useful hints for designing adaptive bogie systems with the possibility to switch between optimal damping parameters value and provide the best operational efficiency.