تعیین ضریب تاثیر برای پل های فلزی راه آهن با توجه به اثر همزمان سرعت خودرو و فاصله محور به نسبت طول دهانه

In common bridge analysis method, traffic load is considered as a static load increased by an impact factor. Impact factor is just a function of span length or the first vibration frequency of the bridge according to the present codes. In this paper the effects of various parameters including velocity, train axle distance, the number of axles and span lengths on dynamic responses of railway steel bridges and also impact factor values are studied. In this regard dynamic responses and impact factors for four bridges with 10, 15, 20 and 25 m span lengths under trains with 100–400 km/h velocity and axle distance between 13 to 24 m have been calculated. Dynamic analysis results show that in most cases the calculated impact factor values are higher than that recommended by the relevant codes and so the offered rations for impact factor are underestimated. It has also been shown that the train velocity affects the impact factor, so that the value of impact factor rises incredibly with the train velocity. Another effective element for impact factor is the ratio of train axle distance to bridge span length so that the impact factor value varies for the ratio below and above unity. The train number of axles just affects the impact factor under resonance conditions. In this paper some relations are offered for the impact factor considering parameters: velocity, train axle distance and the bridge span length.

Bridges’ response to dynamic loads is one of the most important factors in safety and durability of bridges. Since dynamic loads are imposed on the bridge structure in various forms, the study of these loads, their specifications and their effects on bridges, improves the methods of design and increases the safety and efficiency. One of important points in bridge dynamics is the way traffic loads affect various bridge elements’ responses. Normally when a low-speed load is exerted on a structure, it is assumed that the acceleration on the mass of all elements and parts is equal to zero and there is sufficient time so that the equilibrium between external loads and internal elastic forces happens. In this case, static analysis is adequate for these structures. However, some loads create dynamic reactions in structure because of their rapid exertion, and common static analysis methods no longer acquire design requirements. Today high speed railway lines are developed in many countries. This fact has brought about some structural problems which relate to the design of bridges along the railways. Researchers face a new debate which is the effects of moving loads caused by the train movement on the bridges. Bridges Responses to moving loads have been considered as one of the design requirements since the early stages of railway transportation. In studies carried out by Timoshenko, Fryba and others, the main emphasis has been on the dynamic response of a simple beam to a single moving load. Based on these studies, a variety of standards such as Euro code and AREMA for railway bridge design, considered the dynamic effect of a moving load by introduction of the impact factor, which indicates the difference between dynamic and static responses of bridges to the moving load [1]. Recently some, studies have been carried out for verification of impact factor relations introduced in design codes, and comparison with empirical and numerical results. Some of the studies reveal the insufficiency of these relations. Yang et al. [2] studied Impact Factor for vehicles moving over simple and continuous beams and showed impact factors for different bridge responses (moment, support reactions and deflections) are not the same and suggested different formulas for the Impact Factor. Zhang [3] conducted research to determine the impact factor for concrete–steel composite bridges. He analyzed 120 various bridges considering different parameters including span length, the number of main beams and the number of traffic lines in ABAQUS environment. To stimulate traffic load, some concentrated moving loads were implemented. As the vehicle mass was not very relative to bridge mass, the vehicle bridge interaction was disregarded. According to this research the Impact Factor for composite bridges based on AASHTO formula is over-estimated for moment and deflection and is under-estimated for support reaction. Fryba [4] studied the resonance condition caused by the train movement on bridges and introduced two parameters as the main causes of resonance vibration: the first is the exerting of consecutive loads due to train axles and the other is the high speed of modern trains. In this research, simple equations for impact factor are proposed. He also showed that the magnitude of vibration amplitude in a resonance condition is in direct relation with bridge span length and squared value of velocity and adversely relates to damping, train length and bridge stiffness. Cheng [5] studied railway bridge vibration, considering the rail’s conditions and showed that the rail’s conditions do not have a noticeable effect on bridge vibrations. He also studied dynamic magnification coefficients for the different conditions of rails. Lin [6] studied the resonance condition in the dynamic response of railway bridges to train movement and showed that the bridge vibration frequencies must be different from train frequency. Lou [7] evaluated railway bridge and train responses with the finite element model, and studied the effect of rail smoothness on the reduction of bridge dynamic response. In this research, train, rail and bridge were modeled as an integrated model, to study the bridge and train interactions. Equations of motion are directly derived from the Hamilton principle. The resulting equations are solved by direct integration. The results have shown that the rail conditions have serious effects on vertical displacement and acceleration of the train but not on train body rotation and vertical displacement and acceleration of the bridge. Therefore, the rail condition is only important for passengers’ comfort. Goicolea [1], considering the resonance phenomenon in bridges as a result of consecutive moving loads exerted by train passage, emphasized the inadequacy of the European design manual’s methods. According to his research, dynamic response of bridges designed based on European Rail Research Institute (ERRI) recommended specifications are more than expected values in some velocities and specific axle distances. Yang et al. [8] studied the dynamic response of bridge girders with elastic bearings to moving train loads. The results indicate that the insertion of elastic bearings at the supports of the beam for the purpose of isolating the earthquake forces may adversely amplify the dynamic response of the beam to moving train loads.

In this research a parametric study has been conducted to specify the effects of various parameters including velocity, train axle distance, the number of axles and span length, on railway bridge responses and impact factor. Dynamic responses and impact factor have been calculated for four bridges with different span length and 34 various velocities and 12 different train axles. Considering the research results and comparing them to bridge design codes shows that in many cases the impact factor values proposed by current bridge design codes are underestimated and insecure. Impact factor relations offered in current design codes have been defined just based on span length, where there is a decrease with an increase in span length. But the results of the research show that in some conditions impact factors for bridges with a longer span length are greater than those for shorter ones. The research also shows that train velocity and the ratio of axle distance to span length are also effective parameters in impact factor. Another finding of the research is that the numbers of wagons have no important effect on maximum responses. According to achieved results, conditions for impact factor are different in three different velocity ranges (i.e. under 180 km/h, 180–300 km/h and over 300 km/h). The results show that an increase in train speed causes an increase in impact factor values. On the other hand, greater axle distance to span length ratios lead to smaller impact factor values. In this research, according to dynamic analysis results, some formulas are proposed for impact factor in velocity ranges under 180 km/h and 180–300 km/h, based on axle distance to span length ratio. So in addition to considering velocity effect, the simultaneous effects of train axle distance and bridge span length are observed in proposed impact factor equations. In velocities higher than 300 km/h, results show there are great differences between dynamic and static responses; therefore design based on impact factor method in this range may lead to a non-cost effective design. More studies are suggested for this velocity range and the way of reducing bridge dynamic responses.