Dynamic Analysis of Existing Continuous Bridge

Three dimensional finite element models are developed to deal with the bridge-vehicle interaction problem of simply supported composite multi I-girders bridge. The bridge is modeled by using ANSYS 15.0 program with solid and shell elements to represent concrete and steel members, respectively. AASHTO HL-93 truck is idealized as 3D non-linear model consisting of five lumped masses connected by rigid beams and supported by spring-dampers. The separation between the tires and road surface and surface roughness condition are simulated by Gap and actuator elements, respectively. The road surface roughness profiles are generated from power spectral density (PSD) and cross spectral functions. The models used are capable to take all bridge and vehicle responses into consideration with no limitations on the complexity of the models. The dynamic responses of the multi I-girder bridge are investigated under conditions of various loading positions, roughness classes, vehicle speeds, and bump height. The dynamic behaviors are presented in terms of Dynamic Amplification Factors (DAF). The results show the girder that itself supporting the moving vehicle has lower value of DAF because of higher static responses. A 45 km/hr vehicle speed provides higher DAF value. The bump heights have significant effect on DAFs for bridge with short span.

Dynamic amplification factors of corrugated steel plate culverts

Single Station Microtremor method, which is widely used nowadays, is an effective and easy applicable method. In this study, dynamic amplification factor distributions of the study area were obtained using scenario earthquake parameters with single station microtremor data gathered at 112 points. In addition, a surface wave active method, which is known as MASW (Multichannel Analysis of Surface Waves), was applied at 43 profiles to calculate the soil amplification values. Dynamic amplification factor (DAF), soil amplification, the predominant soil period (PSP), geology and topography data of the study area were analysed together. Dynamic amplification factor and soil amplification values were obtained 2 or higher at about sea level parts of the study area which are generally composed of alluvial units. Additionally, in high altitude regions that are composed of volcanic rocks, relatively lower dynamic amplification factor and soil amplification values were obtained. The minimum amplification value in the study area was 1.15, while the maximum amplification value was 3.05 according to the dynamic amplification results and the soil amplification values were between 1.16 and 3.85 in harmony. It is seen that the obtained DAF values and the soil amplification values calculated from the seismic velocities are very similar to each other numerically and regionally. Because of this, it is concluded that the values of the soil amplification obtained by the MASW method and the calculated DAF values in this study are in harmony with each other. Although the depths of research in these two calculation methods are different from each other, the similarity of the results allows us to arrive at the result of how effective the ground layer is on the amplification. It has a great importance to calculate the amplification values and other dynamic parameters by in situ measurements for a planned plot because geological units can vary even at very short distances in heterogeneously distributed areas.

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.

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.

Detailed laboratory datasets of the dam break-induced surge impact pressures measured by Lobovský et al. are analyzed, upon which the dynamic amplification factors (DAF) of the single degree of freedom structures with different natural periods are calculated to quantify the dynamic responses of the measured total pressure series, the decomposed impulsive and quasi-steady pressure series based on the Hilbert-Huang transform algorithm. The maximum DAFs of the measured total and decomposed impulsive pressure series increase with the decrease of structure natural periods, while those of the decomposed quasi-steady pressure series show no relation with structure natural periods. The impulsive pressure is more influential to structures with small natural periods, whereas the quasi-steady pressure plays a predominant role regarding structures with large natural periods. Due to the resonance effect, the oscillatory pressure can significantly increase the maximum DAFs and delay its occurrence time of the measured total pressure series for structures with small natural periods. Nevertheless, the damping effect can generally decrease the DAFs of structures and therefore the resonance effect. Considering the damping coefficient varies from 0 to 0.1 in reality, increase of the maximum DAF induced by resonance is non-negligible for structures with small damping and short natural period.

The development of accurate codes for the design of bridges and the evaluation of existing structures requires adequate assessment of site-specific heavy traffic loading and also the dynamic interaction that may occur as this traffic traverses the structure. Shortcomings in current design codes occur due to the relatively independent manner in which critical static loading values and the corresponding allowance for dynamic amplification factor (DAF) are obtained. It is important that an approach is adopted that allows for the reduced probability of both high static loading and high dynamic amplification occurring simultaneously. Consideration of only relevant critical loading events will allow for efficient and accurate determination of independent values for characteristic (lifetime-maximum) static and total load effects. This paper proposes a method whereby initially the critical static loading scenarios for a chosen bridge are determined, from Monte Carlo simulation using weigh-in-motion (WIM) data from a typical European route. The development of a database of 3-dimensional finite element bridge and truck models allows for the analysis of these various different combinations of vehicular loading patterns. Thus the bridge specific critical loading scenarios are modelled and analysed individually to obtain the critical total (dynamic + static) load effect. It will then be possible to obtain a correlation between critical static load effect and corresponding total load effect/DAF and to extrapolate a characteristic DAF. This approach can lead to significant savings in structural design/assessment where site-specific maximum design load effects are determined from measured traffic data and experimental bridge-truck dynamic interaction.

This paper describes the dynamic response of minimum facilities with different structural configurations which are subjected to random seas. The finite element models are kept simple with the aim of focusing on the physics of the phenomena involved. The response is studied in terms of the dynamic amplification factor (DAF), representing the ratio between the dynamic and the static response. Two different formulations of the DAF under random seas are compared. The first is defined in terms of standard deviation (DAF1), the second in terms of the most probable maximum value (DAF2). Ringing is observed to be a relevant feature of the dynamic response and to affect primarily the braced monopod configurations. Ringing is detected using DAF2. The paper also addresses the importance of the kinematic representation above the still water level. Different methods of stretching the velocity field in the wave zone (delta, Wheeler and exponential stretching) are shown to have a significant impact on the dynamic response of the platforms.

Importance of ‘DAF’ in evaluating structural adequacy of gravity-load designed RC buildings

As the need for drilling and production platforms in deep waters becomes more and more pressing, several alternative structural concepts are being evaluated for potential application. One concept that has been studied for some time. and has been brought to a high level of development is the Guyed Tower Platform (GTP). This paper discusses some basic variations of the original GTP concept which might enhance its feasibility and range of application as well as its economic advantages over other deep water solutions. In particular,The spud can, foundation is replaced by a system of piles.An integrated deck and predrilling template have been included.Details in the mooring system design have been changed. The paper contains a description of the main components of the structural system and a discussion of the principal design criteria. The results of some parametric studies and a brief description of fabrication and installation procedures are also included. INTRODUCTION Over the past thirty years fixed jacket-type platforms have represented the most common structural solution for drilling and production facilities. As the need to move into deeper waters arose technological advancements, ever-growing expertise. more sophisticated analytical techniques and faster and larger computers pushed the state-of-the-art further wld further. Today the tallest jacket stands in 1050 ft. of water in the Gulf of Mexico. However, there are various indications that with the present technology, water depths beyond 1000 ft. may require an altogether different approach. One of the main problems to be faced by the designer of deep water platforms is the dynamic interaction between waves and structure. Figure I, taken from Ref. 11, shows a set of design conditions typical of the Gulf of Mexico. The main diagram shows three wave spectra, labeled as operating weather, winter storm and design storm. The curve in the frame describes how the dynamic amplification factor (D.A.F.) varies with the ratio of the structural period to the dominant wave period. It should be noted that the curve shown is valid for systems with one degree of freedom. while an offshore structure is obviously a multi-degree of freedom system. For a qualitative discussion however, the simplification is acceptable. The shallow water (300 ft.) jacket has a natural period of about 2 sec; this period is much smaller than the peak periods of the various sea states. Accordingly, the ratio of the periods is less than one. and the representative point on the dynamic amplification factor curve is on the left side of the resonance peak. As long as the periods ratio is small enough, the D.A.F. is very close to 1 and the structural response is essentially static. As the water depth increases, the structural period increases and approaches the spectral peaks while the D.A.F. becomes larger than 1 and moves closer to the resonance peak.

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.

In this paper, a finite element (FE) model for a cable-stayed bridge designed according to Australian standards is developed and analysed statically and dynamically with and without geometrical nonlinearities. The dynamic amplification factor ( DAF) and demand-to-capacity ratio ( DCR) in different structural components including cables, towers and the deck are calculated and it is shown that DCR usually remains below one (no material nonlinearity occurs) in the scenarios studied for the bridge under investigation, however, DAF can take values larger than two. Moreover, effects of location, duration and number of cable(s) loss as well as effect of damping level on the progressive collapse resistance of the bridge are studied and importance of each factor on the potential progressive collapse response of the bridgeis investigated.

Dynamic properties of the bridge superstructure vary depending on many characteristics of the bridge and the loading conditions. In this paper, maximum Dynamic Amplification Factor was calculated for six different types of typical pre-stressed concrete beam bridges. It showed that each type of bridge with similar loading has a different range of Dynamic Amplification Factor. At the same time, every recently built bridge has different geometry and design load. Hence, it is difficult to determine a characteristic value of Dynamic Amplification Factor for the similar type of structures. By using fullscale dynamic and static bridge tests, it is possible to determine the necessary characteristics which show possibly high Dynamic Amplification Factor. This factor indicates if it is necessary to make a full-scale bridge dynamic analysis. It was found that those characteristics are natural frequency (first mode), damping ratio, relative deflection, and span and depth ratio. Obtained results from tests show a range of values for each of the characteristic. These ranges were analysed for reinforced concrete slab and pre-stressed concrete slab, and girder bridges.

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.

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.