U-shaped Girder Research Articles

Research on Temperature Distribution and Gradient Prediction of U-Shaped Girder Bridge under Solar Radiation Effect

With the development of bridge engineering, U-shaped girder bridges have been applied in numerous bridge designs due to their structural characteristics. However, the U-shaped girder bridge is sensitive to solar radiation effects, leading to uneven temperature distributions that can affect the service performance of the structure. Thus, this study proposes an analysis method for the temperature distribution of U-shaped girder bridges and develops a prediction model to estimate temperature gradients. First, an improved ASHRAE clear sky model is proposed to calculate the structural shadow areas under sunlight, which provides a basis for the numerical simulation of U-shaped girder bridges under solar radiation effect. Then, a three-dimensional finite element model of the U-shaped girder bridge is established, and its correctness is verified by comparing with the actual temperature data. The temperature distribution of the U-shaped girder bridge under solar radiation is simulated using the verified model to obtain the maximum temperature difference and temperature variation characteristics. Finally, a prediction model for the temperature gradient is developed using nonlinear fitting approaches, and its accuracy is confirmed through comparison with actual data. The results indicate that the temperature distribution of the U-shaped girder bridge has minor changes along the longitudinal direction, while there are significant changes in the transverse distribution; the temperature distribution exhibits nonlinear changes in the height direction of the two side webs and the lateral direction of the bottom slab, with the maximum temperature difference reaching 17 °C; the fitting effect of the prediction model is very good, the correlation coefficients of the fitting curve and the actual data are all greater than 88%, providing a basis for the analysis of the temperature effects on U-shaped girder bridges and its application in design specifications.

Study on Dynamic Amplification Coefficient of U-Shaped Girder Based on Vehicle-Bridge Coupling Dynamics

In this paper, a vehicle-bridge coupling dynamic model is established considering the vertical wheel-rail tight contact and the lateral simplified wheel-rail creeping. Through the site test and the numerical calculation, the dynamic deflections and the stresses of the U-shaped girder in the Nanjing S6 Urban Rail Transit in China are obtained, and the effectiveness of the established numerical model is verified. By changing the vehicle types and speeds, the dynamic amplification coefficients (DAFs) of the vertical deflections and the biaxial stresses at the girder bottom including the key points at the plate and section intersections are calculated. The research shows that the distribution of the lateral stresses is more complex than that of the deflection and the longitudinal stresses. Based on the calculation results considering various vehicle types, it is suggested that the DAFs of the vertical deflections and the longitudinal stresses are taken as 1.30, and the DAF of the lateral stresses remains at 1.40 as stipulated by the code. The research of this paper is to provide a reference for the structural design and size optimization of the U-shaped girders for urban rail transit.

Cost Optimization of Prestressed U-Shaped Simply Supported Girder Using Box Complex Method

The use of U-shaped girders has become increasingly popular in advanced projects such as metro rail systems due to their ability to provide greater vertical clearance beneath bridges. These girders, characterized by two webs and a bottom flange, contribute essential longitudinal stiffness and strength to the overall structure while effectively countering torsional forces in curved bridges. However, the design and construction of U-shaped girders present challenges, including their relatively higher self-weight compared to other girder types. Consequently, cost optimization has become a crucial focus in structural design studies. This research aims to develop an optimization model for prestressed U-shaped girders using the AASHTO LRFD bridge design specifications. The model is based on the Box complex method, with necessary modifications and improvements to achieve an optimal design. The objective is to minimize the total cost of materials, including concrete, steel reinforcement, and prestressing strands, while satisfying explicit and implicit design constraints. To facilitate the analysis, design, and optimization processes, a program is developed using Visual Studio 2010 and implemented in Visual Basic (VB.NET). The program incorporates separate subroutines for analysis, design, and optimization of the prestressed U-shaped girder, which are integrated to produce the desired results. When running the program, the optimization process required 229 iterations to converge to the optimal cost function value. The results demonstrate that the developed algorithm efficiently explores economically and structurally effective solutions, resulting in cost savings compared to the initial design. The convergence rate of the moment capacity constraint is identified as a key factor in achieving the optimal design. This research makes a significant contribution to the field of civil engineering by applying the classical Box complex method to the optimization of girders, an area where its utilization has been limited. Furthermore, this study specifically addresses the optimization of prestressed U-shaped girders in metro rail projects, where they serve as both the deck and support structure for train loading. By employing the Box complex method, this research aims to fill the research gap and provide valuable insights into the optimization of U-shaped girders. This approach offers a fresh perspective on designing these girders, considering their unique role in supporting metro rail loads. By leveraging the benefits of the Box complex method, researchers can explore new possibilities and uncover optimal design solutions for U-shaped girders in metro rail applications.

Study on the structure-borne noise of U-shaped girder bridges with fully-enclosed sound barriers

To investigate the structure-borne noise characteristics of U-shaped girder bridges (USGBs) with fully-enclosed sound barriers (FESBs), an analysis model of the USGB-FESB coupling system was established using the fast multipole boundary element method (FMBEM). The structure-borne noise analysis model was validated using a noise field test of a 27-m-long simply-supported concrete USGB under the loading of moving trains in an urban rail transit. The structure-borne noise radiation characteristics of the USGB-FESB coupling system were studied, and the influences of sound barrier type (vertical sound barrier and fully-enclosed sound barrier) and bridge type (U-shaped girder and box girder) on these characteristics were analyzed. The results show that the noise radiated from the USGB with FESBs was higher than the noise radiated from the USGB without FESBs by 0.28 to 2.53 dB (L) in the frequency band of 20 to 100 Hz. In comparison to vertical sound barriers, the structure-borne noise generated by the FESBs contributes more to the structure-borne noise. The structure-borne noise of a box-girder bridge with FESBs is more significant than that of the USGB-FESB.

Noise contribution analysis of a U-shaped girder bridge with consideration of frequency dependent stiffness of rail fasteners

The U-shaped girder has been widely constructed in urban rail transit systems, and related investigations have been conducted to study the vibration and noise radiation. However, the constant stiffness fastener (CSF) model was used in most previous research when simulating the noise radiation of U-shaped girder bridges. Moreover, the sound radiation from piers was generally ignored in noise prediction. In this study, a numerical model of U-shaped girder bridge with piers and frequency dependent stiffness fasteners (FDSF) was developed. Then, the frequency domain method was used to simulate both the dynamic response of the bridge and the associated noise radiation. Field tests were also conducted to verify the accuracy of the proposed method. Finally, the acoustic contribution and sound pressure distribution of the pier and girder were discussed based on the FDSF model. The research shows the simulated dynamic responses agree well with the experimental results in the frequency range of interest (20 to 200 Hz). The predicted noise by using FDSF model is closer to measured results than the case using constant fastener stiffness, which indicates that the frequency dependence of rail fasteners should be considered in noise simulation. The piers have obvious influence on the vibration and noise radiation of the bridge structure, especially at the support pier section, where the noise level is larger than that at the mid span. The structure-borne noise from the pier is distributed in a narrow frequency band (50 to 80 Hz), and only affects the acoustic field in the limited space around the pier. In contrast, the sound contribution of the girder noise to the total noise level is dominant in most of the area.

Experimental background behind new AASHTO LRFD specifications for partially partially debonded strands

To develop a unified approach for the design of partially debonded strands in prestressed concrete highway bridge girders, a coordinated analytical and experimental investigation was conducted. This investigation examined amounts of partial debonding, distribution of partially debonded strands within the cross section, debonded lengths, locations and staggering of termination of debonded strands, confinement of debonded regions and their termination points, and the impact of adding nonprestressed reinforcement in the region of partial debonding. The results from testing full-scale I- and U-shaped girders indicate that partially debonding strands does not result in deleterious performance if adequate reinforcement is provided to resist the longitudinal tension due to bending and shear. Crack patterns and angles were not noticeably affected by the amount of debonding. Regardless of the debonding ratio, the maximum measured crack widths at the capacities predicted by the eighth edition of the American Association of State Highway and Transportation Officials’ AASHTO LRFD Bridge Design Specifications remained small. The requirements for debonded strands were revised significantly in the ninth edition of the AASTHO LRFD specifications based on the presented research.

Comparison of vibration and noise characteristics of urban rail transit bridges with box-girder and U-shaped sections

Rolling noise and structure-borne noise from rail transit viaducts often lead to complaints from nearby residents. Concrete box section bridges are commonly adopted for the viaducts but those with U-shaped sections have become popular recently due to their more attractive form and reduced visual impact. One question that often arises in relation to the choice of the section types is their relative noise performance. This study aims to compare the vibration and noise characteristics of concrete bridges with different sections in a systematic way by using the same noise prediction method. A coupled track-bridge model is introduced to obtain the rail vibration and the power input to the bridge through the rail fasteners. A three-dimensional vibro-acoustic finite element method is applied to obtain the noise radiated from the bridge and the rail subjected to sets of multiple forces acting on them. This is determined in terms of the radiation efficiency and sound pressure transfer functions for arbitrary forcing. The averaged mean squared vibration velocity of the coupled wheel-track-bridge model subjected to roughness excitation is used to scale the noise from the acoustic model. The method is validated by comparison with field measurements of noise from a U-shaped bridge in Shanghai. Comparative investigations are then conducted of the U-shaped bridge, a box girder bridge with single cell and a twin-box girder bridge with two cells; each is fitted with equivalent noise barriers. It is found in each case that the noise from the rail is about 10 dB(A) larger than the bridge noise at positions to the side of the bridge. The U-shaped girder generally leads to slightly lower total noise levels than the box girders, with differences of less than 1 dB(A) when they have noise barriers of the same height. In terms of the bridge noise, however, the single-box and twin-box girders produce an average of 8.6 and 11.7 dB(A) less noise than the U-shaped girder.

Experimental Study on Mechanical Performance of U-Shaped Steel-Encased Concrete Composite Beam-Girder Joints

This paper proposes a novel U-shaped steel-encased concrete composite beam-girder joint (referred to herein as the novel composite beam-girder joint), in which the U-shaped beams at two sides (L and R) are inserted into a shaped sleeve, and the U-shaped girder and two U-shaped beams are connected by the shaped sleeve through welding. Compared with the traditional beam-girder joints, the novel composite beam-girder joints take advantage of easy construction, light weight, and short construction period. The failure patterns, load-strain and load-deflection curves, and strain distributions of the novel composite beam-girder joints were investigated through the static loading tests on two full-scale specimens, denoted as GBJ1 and GBJ2. The two specimens were varied in beam section reinforcements. Specimen GBJ2 was equipped with 3Ф16 additional bars in the U-shaped beams based on Specimen GBJ1. Test results show that the two specimens failed as the through arc cracks developed at the concrete slab interfaces. The additional bars can increase the bearing capacity slightly but will also increase the stress concentration on the bottom flange of the shaped sleeve, leading to the decrease of ductility for Specimen GBJ2. The slab effect is considered in the test and can thus reflect the actual stress state of the beam-girder joints well. This study can provide a reference for the design and application of beam-girder joints.

Push-out tests of shear connectors in U-shaped steel–concrete composite girder

U-shaped steel–concrete composite girder has higher flexural resistance, more excellent fire resistance and better sound insulation due to the infilled concrete in U-shaped steel girder, compared with traditional composite beams. The existing researches indicated that U-shaped composite beams with shear connectors of headed studs and steel angles all exhibited good flexural performance. However, limited studies were conducted on shear resistance of angle-shaped connectors in U-shaped composite beams and then it is difficult to choose the more suitable shear connector for U-shaped composite beams. Therefore, push-out tests of different configuration of shear connectors were performed to determine their effectiveness in developing composite action in term of strength and load-slip behavior. In the tests, several options of shear connectors were examined including steel angle welded to webs, steel angles welded to flanges, headed studs, steel angle welded to webs working together with headed studs, and two separated steel plates welded to webs. The experimental results showed angle connectors welded to the webs of U-shaped girder possess higher shear resistance, larger slip capacity among all shear connectors. Combining with avoiding the congestion between shear connectors and longitudinal reinforcements, steel angles welded to the webs are recommended as shear connectors for U-shaped composite beams. At last, analytical formulas were proposed to describe the load-slip curves of different shear connectors and the design parameters obtained by regression analysis agreed well with the test results.

Conception and Justification of a New Test Setup for Assessment of the Fatigue Strength of Connections Between Precast Railway Bridge Girders

Important investments have been made worldwide in the modernization and construction of railway lines. Plans for new constructions have also been laid out. Recently, precast concrete has been widely employed in the construction of railway bridges and viaducts. Several precast solutions have been applied, namely: I-shaped or U-shaped precast girders and uni-cellular or bi-cellular precast box girders. Regarding the structural scheme in the longitudinal direction, either simple span or continuous decks have been used. In this context, this work aims to contribute to the knowledge about the real performance of these structures through the development of a laboratory tests setup, for the study of this type of structure, focusing on the connection between the precast beams. The setup will be implemented at the Laboratory of Earthquake and Structural Engineering (LESE), several experimental campaigns on the cyclic behaviour of reinforced concrete elements have been carried out.

Study on The Influence of Negative Temperature Gradient of U-shaped Girder of Rail Transit in Winter

To study the influence of negative temperature gradient of U-shaped girder of rail transit in winter season, a U-shaped rail transit girder was researched in Qingdao. The temperature self-stress of the mid-span section were observed for a 48-h period during the winter. The temperature stress were obtained which caused by vertical and transverse temperature gradient at maximum temperature difference time. The temperature effects caused by different temperature gradient models were analyzed and compared with actual results using a finite element model. The results show that, given the temperature effect, the compressive stress of the mid span section of the structure is small, the web and bottom slab have a greater longitudinal tensile stress which should be considered in the design.

Contribution of Different Elements of Inclined Trash Racks to Head Losses Modeling

Low bar spacing trash racks have been widely investigated in order to guide fish toward bypasses. In addition to this biological function, the formulae to predict head losses, for hydropower plants, are still being discussed. This paper investigates and models the global head losses generated by inclined trash racks with six different bar shapes and two different supports, in an open channel for six angles and two low bar spacings. The girders that supported the trash racks were U-shaped and different profile shapes. In addition to the previously studied rectangular and “hydrodynamic” bars, four new bar shapes, combining different leading and trailing edges, were investigated. Water depths were measured upstream and downstream of the rack for each configuration, and head loss coefficients were characterized and modeled. Three of these new bar shapes generated lower head losses than the hydrodynamic bar shape. The most efficient bar profile reduced the shape coefficient by 40% compared to the hydrodynamic profile and by 67% compared to the conventional rectangular profile. Concerning the supports, the use of a profiled girder to replace a conventional U-shaped girder also significantly reduced the head losses. The addition of the girder effect in a global formula increased its accuracy in predicting head losses of inclined trash racks upstream of hydropower plants.

Experimental analysis of gradient of negative temperature for polypropylene fiber concrete U-shaped girder

To study the negative temperature gradient models of a rail transit U-shaped girder during the winter season, a U-shaped rail transit girder was researched in Qingdao. The temperature field of the midspan section was observed for a 48-h period during the winter. The maximum vertical and horizontal temperature difference distributions were obtained, and the negative temperature gradient models for the winter were established. The results show that the vertical temperature gradient models of the web and bottom slab should be considered. The vertical temperature gradient model of the web is a piecewise function composed of exponential and linear functions. The vertical temperature gradient model of the bottom slab is an exponential function. The transverse temperature gradient of the web is obvious, whereas the transverse temperature gradient of the bottom slab is slight.

Experimental and Numerical Investigation on the Ultimate Vertical Bearing Capacity of U-Shaped Girder with Damaged Web

U-shaped girder has been extensively used for its excellent adaptability in the urban railway transit system. As an open thin-walled structure, significant difference of working mechanism exists between U-shaped girder and conventional section girder (e.g., T section or box section). The thin-walled web plays significant role in the flexural performance of U type girder particularly. Moreover, severe collision may occur between the moving train and the girder, and subsequently results in the decrease of the structural bearing capacity. In this paper, a full-scale test was carried out to examine the ultimate bearing capacity and the failure mechanism of the U-shaped girder, and a refined numerical model was developed to simulate the damage evolution and the failure process. It was shown that the flexural failure occurred on the U-shaped girder under vertical loads. In addition, the ultimate bearing capacity of the structure under different web damage conditions (e.g., web damaged region or damaged range) was studied by applying the displacement based lateral load on the flange of the U-shaped girder to simulate the damage caused by accidental train collision. The numerical results have shown that the damaged web greatly affects the ultimate bearing capacity of U-shaped girder, more severe bearing capacity descending occurs around the middle span rather than the beam ends. The damaged range (length) of the web has less influence on the falling amplitude of bearing capacity. It can be concluded that the major reason accounting for the bearing capacity decrease is that the original section is weakened by the web damage, and consequently results in the buckling of the damaged web and lead to the total failure of the structure. It is recommended that the lateral resistant design for the web should be taken into consideration to ensure the operation safety of the urban railway transportation.

Reconstruction of low-frequency bridge noise using an inverse modal acoustic transfer vector method

Low-frequency noise emitted by elevated viaducts in light rail transit lines has considerable adverse effects on inhabitants living nearby. Reliable prediction of the acoustic field radiating from the viaduct using forward numerical models is challenging because the model parameters that influence viaduct vibration are difficult to obtain. To avoid directly quantifying these parameters, such as wheel–rail combined roughness, an inverse method is presented to reconstruct the acoustic field using modal acoustic transfer vectors and the sound pressures at a small number of measurement points. First, a forward numerical method based on the train–track–bridge interaction analysis is performed to predict the structure-borne noise of a concrete box girder viaduct. Then, the calculated sound pressures are treated as virtual measurement results to illustrate the inverse method procedure. Both QR decomposition and singular value decomposition with Tikhonov regularisation are used in the inverse analysis. Third, the proposed inverse method is validated by comparing the sound pressure levels computed using the inverse method with the results simulated using the forward prediction method. Finally, the reliability of the inverse procedure is further validated through field tests of two U-shaped girder viaducts.

Fully composite beams with U-shaped steel girders: Full-scale tests, computer simulations, and simplified analysis models

This paper focuses on the fully composite beam consisting of the U-shaped steel girder and angle connectors. Through the four-point bending tests of six full-scale specimens, the authors experimentally evaluated the flexural behavior of the fully composite beams. The specimens were intentionally varied to have different shear transfer capacities along the interfaces between the concrete slabs and the U-shaped girders and different geometries of the U-shaped girders. Test results show that all the specimens were fully composite and exhibited the favorable ductile flexural behavior. Computer models were then developed for the experimental specimens. It was found that the computer models were able to replicate the nonlinear behavior of the experimental specimens observed during the tests. Based on the computer models, parametric analyses were performed to investigate the influences of the residual stresses in the U-shaped girder, the strengths of construction materials, the geometries of the U-shaped girder and concrete slab on the strength of the fully composite beam. Beyond the computer models, simplified analysis models that are based on the assumed strain and stress diagrams and can be implemented through hand calculations were developed to capture the nonlinear moment-curvature responses of the composite beams. It is found that the results from the simplified analysis models agree well with the computer models. The simplified analysis models are thus recommended for future practice.

Numerical and experimental study on noise reduction of concrete LRT bridges

Rolling noise and structure-borne noise radiating from the bridge are two major sources of noise in light rapid transit (LRT) bridges. To control the noise radiation from LRT bridges, an efficient numerical method for noise prediction is needed. In this study, a combined three-dimensional dynamic model and 2.5-dimensional acoustic model were used to investigate noise reduction in a rail and in a U-shaped girder bridge. The effects of three noise mitigation measures on noise control were then compared: installation of a noise barrier, use of a rail pad with a lower stiffness, and use of a floating ladder track. The corresponding noise reduction was investigated using the numerical method. A field test was conducted to validate the noise reduction effects. It was found that the noise barrier was more effective in reducing the rail noise, and the soft rail pad is more effective to control the bridge noise. The floating ladder track can significantly reduce bridge vibration, but the excessive vibration of the ladder track itself became another major noise source. The findings should guide the selection of appropriate mitigation measures for noise reduction in LRT bridges.

Structural behaviour of an all-composite road bridge

Fibre reinforced polymer composites have become an integral part of the bridge industry because of their versatility, high strength-to-weight ratio and enhanced durability. The novel idea of an all-composite structural system for road bridges has been proposed for the first time in Poland. The FRP bridge is a simply supported structure with 10.0 m long span and 7.66 m wide deck. The superstructure consists of four U-shaped girders bonded with sandwich deck slab, fabricated by means of a vacuum infusion. The bridge configuration, a finite element model developed for design and the proof test results are described in this paper. The test has shown that an all-composite bridge can meet the relevant strength and deflection design criteria. To develop an understanding of the long-term performance of the FRP bridge, a monitoring scheme utilizing distributed fibre-optic sensors was implemented to assess any changes in the bridge structural behaviour.

Analysis on running safety of train on the bridge considering sudden change of wind load caused by wind barriers

The calculation formulae for change of wind load acting on the car-body are derived when a train moves into or out of the wind barrier structure, the dynamic analysis model of wind-vehicle-bridge system with wind barrier is established, and the influence of sudden change of wind load on the running safety of the train is analyzed. For a 10-span simply-supported U-shaped girder bridge with 100 m long double-side 3.5 m barrier, the response and the running safety indices of the train are calculated. The results are compared with those of the case with wind barrier on the whole bridge. It is shown that the sudden change of wind load caused by wind barrier has significant influence on the lateral acceleration of the car-body, but no distinct on the vertical acceleration. The running safety indices of train vehicle with sectional wind barriers are worse than those with full wind barriers, and the difference increases rapidly with wind velocity.

Experimental and analytical behavior of a prestressed U-shaped girder bridge

This paper presents an experimental and analytical investigation on the behavior of a U-shaped girder subjected to operation, cracking and ultimate loads. A full-scale destructive test was conducted on a U-shaped girder to study the cracking process, load-carrying capacity, failure mechanism and load-deformation relationships. Accordingly, the tested U-shaped girder was modeled using ANSYS and a non-linear element analysis was conducted. The investigation shows that the U-shaped girder meets the specified requirements of vertical stiffness, cracking and ultimate load capacity. Unfavorable torsional effect is tolerable during operation. However, compared with box girders, the U-shaped girder has a more transverse mechanical effect and longitudinal cracks are apt to occur in the bottom slab.