Single-span Bridge Research Articles

Determination of free vibration properties of masonry arch bridges using the dynamic stiffness method

Masonry arch bridges constitute over half of the European bridge stock. The dynamic response of these bridges to traffic loads is influenced by their free vibration properties, i.e. their natural vibration frequencies and mode shapes. However, these properties have not been systematically examined to date. This paper utilises the dynamic stiffness method (DSM) to obtain an improved fundamental understanding of the free vibration properties of idealised single and multi-span arch bridges. In this approach, the piers and arches are modelled as an assembly of linear Timoshenko beam segments, the backing and infill are represented with axial struts and the underlying soil with concentrated spring elements. These idealisations enable rapid but accurate calculations of in-plane free vibration properties. To demonstrate this, the proposed procedure is applied to a simply-supported arch structure, a small-scale single-span arch bridge model and a multi-span arch bridge, where published experimental data is available. Then, free vibration analyses of representative single and multi-span arch bridges are performed. The results obtained from DSM analyses agree with detailed 3D finite element models and reveal the critical influence of backing elements and the interactions between adjacent spans on free vibration properties. Lastly, a range of arch bridge geometries are examined to reveal the shortcomings of existing provisions for modal frequency estimation in codes of guidance.

Stability of continuous welded rail on steel bridge subjected to thermal loading

Continuous Welded Rail (CWR) forms a smooth high-speed rail track. However, its stability has been a cause of worry for being a slender structural element and its tendency to buckle about the weaker axis. Track-Bridge Interaction (TBI) phenomenon results in additional axial rail stress, creating local high-stress zones in the track. Since TBI is the main reason for rail stress and track displacements of CWR on railway bridges, more confidence needs to be developed by quantifying the stability of CWR-on-bridge. In this study, a simplified numerical model is proposed to study the effect of TBI on the stability of CWR-on-bridge due to temperature loading. Boundary elements are utilized to reduce the number of elements in the model. The model predicts the state of the stress in CWR due to thermal loading. Stability analysis of CWR on a single span bridge employing nonlinear buckling analysis reveals a significant influence of TBI on CWR stability. The two critical buckling parameters of CWR, the maximum buckling temperature (Tmax) and safe temperature increase (Tmin), are affected by TBI. Tmin drops more rapidly compared to Tmax and needs to be kept below the safe limits to ensure track safety.

Investigation on Seismic Behavior of Historical Tokatlı Bridge under Near-Fault Earthquakes

The main purpose of this study is to compare the static and dynamic behavior of a historical single-span masonry arch bridge under different near-fault earthquakes. The historical Tokatlı Bridge, built in Karabük, is chosen for this study. To investigate the behavior of near-fault earthquakes on the historical masonry bridge, first, a finite element model is built and analyzed under various near-fault earthquakes by using ANSYS and SAP2000. To build a finite element model, 162920 nodes and 47818 elements are used in ANSYS. First, finite element analysis results are compared to each other under Earth gravity. Then, ground motions near the fault are chosen to be used in this study. These earthquakes can be listed as follows: Cape Mend (1992), Kobe (1995), Superstition Hills (1987), Northridge (1994), Imperial Valley (1979), and Chi-Chi (1999). The behavior of the single-span historical bridge is obtained under these ground motions, and the results are compared with each other using contour diagrams using ANSYS. Furthermore, at the end of these analyses, it is observed that the tensile stresses have reached the permissible masonry tensile strength, especially on the upper side of the large belt, on the upper side of the belt, and on the side of the belt, and pose a risk for damage.

Humber Bridge hanger replacements and testing

The Humber Bridge is an iconic Grade 1 listed structure, which remains one of the longest single-span suspension bridges in the world. It has a main span of 1410 m and a total span length of 2220 m. The bridge deck is connected to the main suspension cables by spiral wire rope hangers with socketed end connections. In this paper, the global analysis of the bridge is discussed to identify the predicted stresses in the hangers, which was complicated by the triangulation of the hangers. The paper then covers the selection of three trial hangers to be replaced, the specification of the replacement hangers and the testing specified to determine the residual life of the original hangers. The design, fabrication and installation of the works involved in replacing the hangers is described and the paper concludes with a discussion of the results of the hanger testing and how this has informed the strategy for management of the remaining hangers.

Coupled Dynamics of Vehicle-Bridge Interaction System Using High Efficiency Method

Vehicle-bridge interaction is the core for a variety of applications, including vehicle vibration, bridge vibration, bridge structural health monitoring, weight-in-motion, bridge condition inspection, and load rating. These applications give rise to a great interest in pursuing a high-efficiency method that can tackle intensive computation in the context of vehicle-bridge interaction. This paper studies the accuracy and efficiency of discretizing the beam in space as lumped masses using the flexibility method and as finite elements using the stiffness method. Computational complexity analysis is carried out along with a numerical case study to compare the accuracy and efficiency of both methods against the analytical solutions. It is found that both methods result in a similar level of accuracy, but the flexibility method overperforms the stiffness method in terms of computational efficiency. This high efficiency algorithm and corresponding discretization schema are applied to study the dynamics of vehicle-bridge interaction. A system of coupled equations is solved directly for a simply supported single-span bridge and a four-degree-of-freedom vehicle modeling. Pavement roughness significantly influences dynamic load coefficient, suggesting preventative maintenance or timely maintenance of pavement surface on a bridge, to reduce pavement roughness, is of significant importance for bridge’s longevity and life-cycle cost benefit. For class A and B level pavement roughness, the dynamic load coefficient is simulated within 2.0, compatible with specifications of AASHTO standard, Australian standard, and Switzerland standard. However, the Chinese code underestimates the dynamic load coefficient for a bridge with a fundamental frequency of around 4 Hz. The proposed method is applicable to different types of bridges as well as train-bridge interaction.

Study on the additional support length requirements of single-span bridges due to skew using a simplified method

Skew bridges with seat-type abutments are frequently unseated in earthquakes due to large transverse displacements at their acute corners. It is believed these large displacements are due to in-plane rotation of the superstructure. Lack of detailed guidelines for modeling of skew bridges, many current design codes give empirical expressions rather than theoretical solutions for the additional support length required in skew bridges to prevent unseating. In this paper, a parametric study has been carried out to study the influence of skew angle, aspect ratio and fundamental periods of bridges on the additional support length requirements of single-span bridges due to skew using a shake table experiment validated Simplified Method, which is capable of simulating gap closure based on response spectrum analysis. This method is developed based on the premise that the obtuse corner of the superstructure engages the adjacent back wall during lateral loading and rotates about this corner until the loading reverses direction. A design response spectrum specified in AASHTO LRFD Specifications was employed to represent the design-level earthquakes. The results show the additional length required to prevent unseating due to skew increases with the skew angle in an approximately linear manner when the angle is less than a critical value and decreases for angles above this value. This critical skew angle increases with the aspect ratio approximately in a linear manner and shows negligible dependence on the fundamental periods of the bridges, and combination of span length and width. In addition, the critical skew angle varies between 58° and 66°, when the aspect ratio is varied from 3.0 to 5.0. The results also show that the empirical formulas for minimum support length requirements of skew bridges in current codes and specifications can not accurately reflect the influence of skew.

Real-Time Hybrid Simulation of a Single-Span Girder Bridge Using a Shake Table Coupled with an Actuator

This paper recounts a real-time hybrid simulation (RTHS) that employed a shake table coupled with an actuator to evaluate the seismic performance of a single-span girder bridge. The test specimen for this RTHS was a scaled single-span girder bridge, which was subjected to Loma Prieta excitation in the test. In the RTHS, the bridge specimen, which lacked mass on top of the bridge deck, was physically tested by a shake table and an actuator, whilst the mass on the bridge, as well as the pile foundation and the soil were modeled numerically. OpenSEES was used for numerical modeling and OpenFresco was used for the communication between the test system and numerical model. An adaptive time series (ATS) technique was employed to compensate for time delay in the RTHS. In this way, a novel bridge engineering RTHS application case composed of shake table and actuator control was presented. To validate the results of the RTHS, a shake table test (STT) of the bridge structure with full mass on the bridge deck was conducted correspondingly. Comparing the RTHS and STT results, it can be concluded that acceleration histories, bearing deformation histories, and strain histories of the selected points matched well. The application of RTHS to assess the seismic behavior of the single-span girder bridge was reasonably verified in this paper.

Unseating of single-span bridges with skew angles out of the limit range for free rotation

Past researches have indicated that skewed bridges can rotate around the obtuse corners upon gap closure and the bridge deck can rotate freely when the skew angle is within a limit range. Beyond this range, the rotation of the bridge deck could be locked against the abutments. For these bridges, girder unseating can be avoided either by geometric constraint of the deck or by providing adequate support length to account for seismic demands. In this paper, the unseating of single-span bridges is studied for skew angles out of the limit range for free rotation. To begin, the skew angle limit range for free rotation was derived for bridges with and without expansion gaps. It was found that the expansion gap has a slight influence on the skew angle limit range for free rotation. The minimum support length (N) of skewed bridges to reach geometric constraint (when locked against the abutments) was then derived step-by-step based on geometry. It is found that the N to reach geometric constraint increases with skew angles approximately in an exponential manner. Finally, a parametric study was performed on prototype skewed bridges using a shake table experiment-validated nonlinear model to compute the support length demands during design-level earthquakes. Nonlinear analysis was performed under seven historical near-fault records scaled to the design-level earthquakes. Comparison was made between the support length to reach geometric constraint and those from numerical analysis. The results indicate that it is very likely that a single-span bridge of any skew angle could rotate freely during the design-level earthquakes even when its geometry could allow it to be blocked by the abutments. Therefore, the minimum support length of single-span bridges should be designed based on seismic demands rather than geometric constraint when the skew angles are out of the limit range. In addition, it was also found that the Japan Road Association (JRA) is unreasonable to assume zero skew effect on the minimum support length requirements and current codes and specifications underestimate the skew factor when the skew angles fall out of the limit range.

Simplified Performance Assessment for Single-Span Masonry Arch Bridges under Live Load

Abstract A quantitative, rapid screening assessment methodology for masonry arch bridges, with minimal input parameters, is proposed. The developed mechanism-based analysis procedure is validated a...

Design of Prestressed W-Shape Beams with a Separated Prestressing Cover Plate

Prestressed steel beams with a prestressing cover plate (PBCP), which are expected to overcome the limitations of prestressed steel girders using tendons, were investigated in this study. Experiments and finite element analyses (FEA) were performed to present a design procedure. The maximum compressive force according to flange slenderness, which could be applied to steel beams subjected to bending moment due to ultimate load, was investigated for rolled W-shape beams. The flexural capacity and elastic flexural stiffness of steel beams could be significantly increased by using a cover plate attached at a fixed distance from the bottom flange of a steel beam as a prestressing member. A PBCP with W920 × 1377 could achieve a maximum span of 72 m for a two-lane, single-span composite bridge with five girders when the span-to-depth ratio is limited to around 38.0, whereas an ordinary composite beam with the same W-shape section, having a span-to-depth ratio of 36.0, could achieve a maximum span of around 50 m. The limitations of maximum bridge length, minimum steel amount and maximum span-to-depth ratio that rolled flexural members can achieve were able to be efficiently overcome by using the PBCP. The span-to-depth ratio of PBCPs was about 2.08 times larger on average than that of plate girders for bridge lengths of 50 m to 72 m. The PBCP could employ a smaller steel volume than plate girders for the same span-to-depth ratio. Therefore, it could be seen that the PBCP could be an alternative to plate girders for the limited span-to-depth ratio and even for the cost efficiency.

Vibrations of a Girder on Rigid Supports of Finite Mass Interacting With Soil under Seismic Loads

Transverse vibrations of a single-span girder bridge are considered in the article; the pile part of the bridge interacts with the surrounding soil under seismic action. We assume that the strain of the structure does not go beyond the elastic limit, and the vibrations are linear. The bridge supports are assumed to be immersed in soil and interact with a rigid body under the impact of unsteady dynamic influences. We consider the case when the right and left supports have equal masses and interact with the surrounding soil. Here the symmetry condition is applied, so it is sufficient to consider the equation for the right half of the girder. The problems are solved by the analytical Fourier method under given boundary conditions. The results obtained are analyzed and presented in the form of the distribution of displacements and stresses over the time and length of the bridge structures.

Strength, Flexural Rigidity and Aerodynamic Stability of Fiberglass Spans in Pedestrian Suspension Bridge

At present, it is highly relevant to improve the safety of transport and pedestrians by crossing their paths at different levels. At the same time, to cross wide highways, it is rational to design pedestrian bridges without intermediate supports, namely suspension and cable-stayed bridges. In addition, numerous studies have confirmed the feasibility of using fiber-reinforced plastic (FRP) as a material for load-bearing structures. However, in order to massively introduce FRP suspension bridge designs into production, it is necessary to improve the method of designing suspension bridges, which has been used mainly on steel and reinforced concrete bridges for decades. Therefore, the paper describes theoretical and experimental studies of strength, flexural stiffness (calculations are made taking into account geometric nonlinearity), as well as the aerodynamic stability of structures of single-span suspension bridges with main beams made of polymer composite materials. As a result of the research, the feasibility of designing FRP bridge structures within the framework of the adaptation concept was confirmed. The obtained conclusions will serve to improve the method of calculating suspension bridges with main beams made of polymer composites.

Design of Haunched Single Span Bridges

A novel method for the design of variable depth single span bridges having maximum depth at the ends and minimum depth at midspan is presented. These bridges are intended to be used for long span river crossings or highway overpasses, where only a single span is required, and the vertical clearance below needs to be maximized, and/or an aesthetically pleasing graceful shape is desired. The design is made possible by “fixing” the ends to “lock-in” negative moments, so that the positive moments at midspan are greatly reduced, and a shallow section may to be used. The method is developed and presented in two parts. The first part discusses and unifies the behavior of three very famous bridges (the Luzancy Bridge in France designed by Eugène Freyssinet, the Gänstor Bridge in Germany designed by Ulrich Finsterwalder, and the Pinzano Bridge in Italy designed by Silvano Zorzi). The second part describes the method in detail by virtue of a complete design example. Application of the method to other bridges is included, and abutment treatments to enhance the visual qualities are presented. This innovative bridge type will be of interest to those looking for a practical and elegant new bridge solution for long span bridges.

Evaluation of the vertical load capacity of masonry arch bridges strengthened with FRCM or SFRM by limit analysis

The large number of existing masonry bridges still in service in the world roadway and railway networks requires that transportation system managers carry out ordinary and extraordinary maintenance. In many of these networks, the need for increasing the speed and/or weight of the traffic loads also entails the design of strengthening interventions aimed at enhancing the load-carrying capacity of masonry bridges. Among the available techniques for the strengthening of these structures, the use of fiber reinforced cementitious matrix (FRCM) composites has gained popularity due to their advantages with respect to more traditional techniques. More recently, the use of steel fiber reinforced mortars (SFRM), has also been investigated for the strengthening of masonry bridges, with promising results. In this paper, a limit analysis for assessing the vertical load-carrying capacity of single-span bridges strengthened with FRCM or SFRM, applied at the intrados, is described, and calibrated using available experimental results. The document highlights the variables that should be considered in such procedure and also discusses the similarities and differences between the two strengthening techniques. A subsequent parametrical analysis shows that both techniques produce comparable increments in the load carrying capacity of the masonry bridges when compared to unstrengthened conditions. In addition, it was seen that if the finite friction between blocks is not considered when performing the limit analysis of masonry bridges, the ultimate load capacity of the arches can be overestimated as the failure mode can be attained due to shear sliding of the masonry blocks, a hinge mechanism or a combination of both.

Mesoscale analysis of multi-span masonry arch bridges

Masonry arch bridges often include multiple spans, where adjacent arches and piers interact with each other giving rise to a complex response under traffic loading. Thus, the assumption commonly used in practical assessment that multi-span masonry viaducts behave as a series of independent single-span structures, may not be realistic for many configurations. While several experimental and numerical studies have been conducted to investigate single-span masonry arches and bridges, only limited research has been devoted to the analysis of the response of multi-span masonry bridges. This study investigates numerically masonry arch bridges with multiple spans subjected to vertical loading. For this purpose, an advanced finite element description, which is based upon a mesoscale representation for masonry and accounts for both material and geometric nonlinearities, is employed to shed some light on the actual behaviour of these structural systems. A validation study is first carried out to confirm that the adopted modelling strategy is capable to accurately simulate previous experimental results. Then, the influence of some critical geometrical and mechanical parameters that affect the bridge response is evaluated through a parametric study. The effects of pier settlements and brickwork defects are also investigated, as well as the interaction between adjacent spans through comparisons against the response of single-span counterparts.

Fast and easy dimensioning of robust and sustainable filler beam bridges

Filler beam bridge constructions with hot-rolled steel sections at close centres and filled with concrete meet all the requirements of small- and medium-span railway bridges. Filler beam bridges have thus been used for many years with considerable success, in particular where construction depth restrictions are relevant for the design. Moreover, they are perfectly suitable for use with high-speed railway lines. Since the late 1970s, various railway companies have established standard designs with guidelines, supplemented with calculation tables that correspond to their own rules. Some of these guidelines have become outdated with introduction of the Eurocodes. However, since on one hand there is growing interest in this type of construction and, on the other, a desire to evaluate large amounts of design data economically, there is a need for a calculation tool that enables quick, efficient and reliable designs. For this reason, new design tables for filler beam bridges in the German high-speed railway network up to 350 km/h have been developed, which enable a quick and direct evaluation of all relevant cross-sectional data of single-track single-span bridges in the span range 5–35 m without costly statics. The tables and the software, with which the tables were generated, are shown in this article.

TARİHİ YIĞMA BİR KÖPRÜNÜN DEPREM DAVRANIŞININ DEĞERLENDİRİLMESİ

Tarihi yığma kemerli köprüler eski dönemlerden beri geçmiş uygarlıkların kültürel mirasını günümüze aktaran en önemli yapılardan biridir. Tarihi yığma kemerli köprüler geçmişte ulaşım, ticaret ve mimarinin en önemli unsurlarından biridir. Ancak yeni yapı malzemelerinin ve yapım yöntemlerinin gelişmesiyle günümüzde artık yığma kemerli köprüler inşa edilmemektedir. Bu yapılar deprem, sel, yangın ve savaşlar gibi dış etkenlerle zarar görebilmektedir. Ülkemizde de tarihi köprüler gibi geçmişi günümüze bağlayan önemli mühendislik yapılarının mevcut durumlarının tespit edilerek geleceğe güvenle devredilmesi amacıyla çeşitli çalışmalar yapılmaktadır. Bu çalışmanın temel hedefi tarihi yığma kemerli bir köprünün lineer dinamik analizlerini gerçekleştirerek köprünün deprem etkisi altındaki davranışını incelemektir. Bu amaçla tek açıklıklı yığma kemerli bir köprü sayısal örnek olarak ele alınmıştır. Köprünün 3 boyutlu sonlu elemanlar modeli ANSYS sonlu elemanlar programı ile makro modelleme yaklaşımı dikkate alınarak oluşturulmuştur. Lineer dinamik analizlerde köprünün bulunduğu konum da göz önünde bulundurularak 2011 Simav ve 2002 Sultandağı depremlerine ait ivme kayıtları sismik etki olarak kullanılmıştır. Yapılan analizlerden köprüye ait yer değiştirmeler ve maksimum-minimum asal gerilmeler elde edilmiş ve köprünün sismik tepkileri değerlendirilmiştir.

Seismic performance of bridge with unbonded posttensioned self-centering segmented concrete-filled steel-tube columns: An underwater shaking table test

As one of the prefabricated structures, precast segmented bridges can be used to shorten construction time, reduce traffic delays, improve quality control, and minimize environmental impact. Despite the numerous advantages of segmented pre-fabricated rapid assembly technology, it is not widely used in high seismic hazard zones nor applied to complex water-abundant situations because of the lack of knowledge on its seismic performance. Through experimental and numerical studies, researchers have studied the seismic performance of such type of column under quasi-static testing. The behaviors of the column or bridge under desired strong ground motions (GMs) have been rarely investigated. This paper presents the major findings of an underwater shaking table testing program conducted on a 1/4 scaled single-span bridge with novel self-centering segmented concrete-filled steel tube columns. This study focuses on the performance of the bridge subjected to different GMs under 4 water conditions, which are with water at a height of 1.2 m, 1.5 m, 1.8 m, and without water. The bridge model incorporated two post-tensioned precast self-centering segmented concrete-filled steel tube (PSCFST) single columns with fixed and sliding supports connected to a single span steel box-girder superstructure. The internal unbonded PT tendons are installed at the center of the segment section, and external energy dissipation (ED) bars are installed on the outside of the bottom segment. The bridge model was then subjected to a sequence of natural and artificial GMs with different amplitudes. The well-designed PSCFST bridge demonstrated a desirable seismic performance, and no significant damage was observed. Concerning the overall response of the structure, the maximum drift ratio reached 2.14%. Moreover, a maximum residual drift of 0.09% was observed after the tests, which indicates that the test model demonstrated a desirable self-centering capability after a sequence of GMs. The cumulative energy dissipation and equivalent viscous damping ratio of the bridge were calculated. A comparison is made for the seismic performance of the bridge especially in terms of the displacement and acceleration of the whole structure under the cases of with and without water.

Using bridge weigh-in-motion systems to monitor single-span bridge influence lines

Bridge weigh-in-motion systems use instrumented bridges or culverts to weigh vehicles as they pass over the structures. They also provide data to allow the calculation of several bridge performance indicators. The article starts with the basics of a bridge weigh-in-motion system and briefly describes two key bridge performance indicators, girder distribution factor and dynamic amplification factor, which are also derived from B-WIM measurements. The central part of the article focuses on monitoring of influence lines, the third key parameter that characterises the bridge performance under traffic loads. First, the method of calculating the bending moment influence lines from random heavy traffic is described. A coefficient of rotational stiffness is introduced, which defines the shape of influence lines around the supports as a linear combination of the ideal simply supported and fixed supported influence lines, to allow quantifying the influence line changes. Then the long-term monitoring of influence lines is investigated on four different single-span test bridges. The initial focus is given on the examination of the effect of temperature on the shape of influence lines. Finally, two sets of influence lines are compared on one test bridge, one from before and the other from after replacing the expansion joints and bearings. The work done so far confirms that calculating of influence lines from random vehicles with a B-WIM system is entirely feasible and that differences in their shape can be detected on single-span bridges. What remains to be investigated is the comparison of these differences to the actual damages and under which circumstances the proposed procedure can compete with or better the routine bridge inspection and the conventional monitoring techniques.

Effect of skew on the minimum support length requirements of single-span bridges with seat-type abutments

Skew bridges are known to be susceptible to girder unseating during earthquakes, and empirical equations for minimum support length are used in their design. To determine the degree of conservatism or un-conservatism in these equations, a rigorous model of a skewed bridge was developed in OpenSees and validated against a comprehensive dataset from shake table experiments. The validated model was then used to perform a parameter study on a series of single-span, simply supported, prototype bridges with seat-type abutments. Nonlinear response history analyses were performed that included impact and friction effects at the abutments and were repeated for both far-field and near-field motions. It was found that the additional support length required to prevent unseating is a linear function of skew angle over the range 0°–60° for both types of motions. This is contrary to common practice, which uses a quadratic function (American Association of State Highway and Transportation Officials, AASHTO) or the inverse of cosine of angle of skew (Federal Highway Administration (FHWA)). Consequently, common practice appears to be underestimating support length requirements by up to 50% at midrange skew angles of 30°–40°.