Balanced Bridges Research Articles

Balanced Cantilever Construction Method in Post-Tensioned Concrete Bridges

This article gives an overview of the history of, and the research on, the balanced cantilever construction method, with a focus on post-tensioned concrete bridges. In the introduction, the method and the history of cantilever construction in steel, concrete and post-tensioned concrete bridges is presented. Structural failure of two different bridges is shown as a motivation for a more detailed understanding of the performance and force transmission of these bridges. Recent experimental and numerical research on post-tensioned concrete balanced cantilever bridges is introduced. In conclusion, most of the research is done on already completed structures. For a better overview, the need to conduct numerical and experimental research on balanced cantilever bridges during construction is highlighted.

Time-dependant effects on curved precast segmentally constructed balanced cantilever bridges

Excessive long-term deflections and diagonal cracking in the webs are two commonly reported issues in segmentally constructed balanced cantilever bridges. The design of superstructure in such bridges is rather complicated due to the staged construction, secondary restraint forces, and time-dependent effects such as shrinkage, creep, and steel relaxation. The influence of these factors significantly increases by the curvature of the bridge on plan, to the point where it can result in the failure of the bridge if special considerations are not made. In this study, stepwise numerical analyses of a curved pre-cast construction of a balanced cantilever bridge with time-dependent material properties are carried out. The results show the effects of time-dependent losses, especially creep, on deflections during cantilevering and in long-term. It is shown that the curvature of the bridge due to long-term effects can increase the transverse moments in segments that adversely affect the principal tensile stresses, which can lead to diagonal cracking in the web of the segments.

Strain Analysis on Cast-In-Place Balanced Cantilever Prestressed Concrete Bridges During Construction

This article shows the strain analysis on two cantilever cast-in-place prestressed concrete bridges during construction. Strain gauges, measuring strain based on the change in electrical resistance, were installed on both structures in order to obtain strain results during and after construction. Nonlinear numerical models were made to simulate the realistic behaviour of the structure and show the effect of creep and shrinkage during the construction phases. The numerical model taking into account creep and shrinkage is validated and shows good overlap with the measured results. Relative compressive stresses as well as the necessary precamber are shown. The effects of creep and shrinkage are analysed. Finally, the data can be used to analyse and compare other similar bridges and validate different numerical models. A recommendation for the design of future prestressed concrete balanced cantilever bridges is given.

Bridge assessment based on deflection as a measure of damage using Machine Learning-enhanced pattern identification

Bridges worldwide are failing at increasing rates as they heavily suffer from deterioration, leading to transport infrastructure system disruptions and millions of financial losses. For instance, the failure of the Polcevera bridge alone, costed €359 million in the immediate wake, while the estimated annual losses for the Italian economy are close to one billion euros. Despite the recent technological advancements in the field of structural health monitoring, involving digital measurements and remote data collection, bridge failures still occur. The reasons behind those failures are mainly due to the pertinent damages being not easily detectable and the scarcity of the available design drawings, especially for old bridges. Furthermore, the construction sequence for the asset of interest or the level of prestressing are often not known in detail, hence the as-built condition and the actual bridge properties are highly uncertain. This is a capability gap that can only be filled with meaningful data collection and application of advanced technologies in aid of decision-making. The paper aims to extend an existing methodology that was proposed before by Kazantzi et al. (2024a, 2024b) for identifying the damage state of bridges. The aforementioned methodology was initially showcased for balanced cantilever concrete bridges only. To further advance the methodology, application to other concrete bridge typologies, including beam and slab bridges, cast-in situ slabs, continuous box-girders, and arch bridges, is herein proposed. Additionally, the paper suggests validating the machine learning kNN (k-Nearest Neighbor) methodology utilizing Finite Element (FE) model updating. This process involves adjusting numerical model parameters to better match actual structural behavior, enhancing the methodology’s reliability and effectiveness for identifying damage states in concrete bridges of different types and scenarios.

Simulating creep induced moment redistribution in prestressed concrete bridges constructed by the balanced cantilever method: ad hoc traditional formulae versus real time-dependent analysis

Assessing available numerical techniques adopted to determine the design time-dependent moment for prestressed concrete segmental bridges constructed by the balanced cantilever method is of utmost importance to the bridge design community. In essence, despite some apparent diversity, there are basically two key conventional approaches to compute the design time-dependent moment accounting for creep effects for this type of bridges. The first is a family of varied simplified methods typically known to practicing designers and with pre-consensus on their reliability and effectiveness. Time-dependent moments retrieved from these classical methods always reside in an intermediate state falling between the results from “two” time-independent analysis cases, namely, (a) sequentially adding all partial permanent loads and prestressing pertaining to various construction steps using the part-bridge structural system corresponding to each step, and (b) assuming all loads and prestressing forces to be applied at-once to the final completed bridge. The second approach is through performing real sophisticated step-by-step time-dependent analysis using a specialized software. The research primary objective is to assess the validity/reliability of commonly used ad-hoc approaches that evolved over the years relying on simplified analyses/formulae to cater for time-dependent creep effects for this type of bridges. Aiming at realistic conclusions, three case-study real-world segmental balanced cantilever bridges over the Nile River in Egypt are elected. Midas Civil commercial package is used to perform time-dependent finite element analyses for the three bridges. Main parameters considered are, inter alia, time-dependent effects of creep and shrinkage of concrete, relaxation of prestressed steel, losses due to friction and anchor setting of prestressing tendons, sequence of construction, and construction-driven temporary change of support conditions (where applicable). The study concludes that creep-induced moment redistribution from simplified traditional formulae typically adopted in the literature may lead to a considerable error in estimating the design time-dependent moment in balanced cantilever bridges.

INVESTIGATING THE MEASUREMENT ERRORS OF THE COMPONENTS OF THE COMPLEX RESISTANCE OF MUTUAL INDUCTION BY THE PHASE METHOD

A microcontroller measurer of the complex resistance components of mutual induction (MI) of magnetically coupled coils is considered for the case when, due to the effects of “capacitance” and “eddy currents”, an active component arises in the EMF of the secondary coil, the 90° phase shift angle between this electromotive force and the current of the primary coil is violated (“phase defect”). At the same time, corrective terms ("admixture" and "frequency correction") appear in the resistance MI. These phenomena increase with an increase in the frequency and value of the supply current of the coils, when using ferromagnetic cores. Balanced AC bridges are used in well-known resistance component MI measurers; their disadvantages are listed. The developed measurer uses the phase method using a temporary separation of the measurement channel. The measuring circuit (MC) is powered by the current of a controlled generator of sinusoidal signals. In the MC, the measured parameters are converted into the phase shift angle between the two output voltages. These voltages are supplied to the analog inputs of a programmable microcontroller (MCC), in which angle is measured by the discrete counting method. During the measurement process, the MCC sets the frequency of the MC power generator, controls the position of the electronic switch of the measurement channel, measures angle and determines the values of the components of the MI complex resistance according to the specified algorithms. A method of theoretical investigation of measurement errors has been developed. The errors are caused by the inaccuracy and instability of the parameters of the MC and MCC elements appearing in the algorithms for determining the measured values. The method of error calculation is accompanied by a numerical example. The results of calculation of measurement errors are presented.

Comparative Study of Balance Cantilever Bridge and Extradosed Bridge

Abstract: Now a days, in India Balance Cantilever bridges are widely used in hilly region were supporting from the bottom is difficult. The name Balance Cantilever Bridge is arrived due to the application of construction methodology which balances out the cantilever portion. It is one of the most effective methods of building bridges without the need of false work. Balanced cantilever bridges are used for special requirements like construction over traffic, short lead time compared to steel and use local labour and materials. Extradosed bridge is a unique idea bridge between Girder Bridge and cable-stayed bridge. A balanced cantilever bridge with construction stage analysis consideration a model is prepared in the Midas Civil software and analysed, we can see how it considers construction stage analysis with creep & shrinkage effect. The construction stage analysis in the Midas Civil considers shrinkage and creep during construction stages to simulate the construction process of a incremental stage. As most of the literature covers either balance cantilever bridge or extradosed bridge, this paper introduces and attempt to summaries comparative study of balance cantilever and extra dose bridge with its span arrangement, span by depth ratio, prestressing steel etc. Keywords: Construction stage, balance cantilever , extradosed, prestress

Evaluation of time-dependent deflections on balanced cantilever bridges

The use of prestressed concrete box girder bridges built by segmentally balanced cantilevers has bloomed in the last decades due to its significant structural and construction advantages in complex topographies. In Colombia, this typology is the most common solution for structures with spans ranging of 80-200 m. Despite its popularity, excessive deflections in bridges worldwide evidenced that time-dependent effects were underestimated. This problem has led to the constant updating of the creep and shrinkage models in international code standards. Differences observed between design processes of box girder bridges of the Colombian code and Eurocode, led to the need for a validation of in-service status of these structures. This study analyzes the long-term behavior of the Tablazo bridge with data scarcity. The measured leveling of this structure is compared with a finite-element model that consider the most widely used creep and shrinkage models in the literature. Finally, an adjusted model evidence excessive deflection on the bridge after six years. Monitoring of this bridge typology in Colombia and updating of the current design code is recommended.

Resistances of Infinite Electrical Networks

It is interesting to find the equivalent resistance between two nodes of an infinite electrical network. In this paper, we consider an infinite electrical network that can be described as a series of squares whose edges are resistors with resistance $R$ and whose corresponding vertices are joined successively by resistors with resistance $R$ as well. Our major work is to find the equivalent resistance between the diagonal vertices of the base square of this infinite network. First, we apply the techniques of balanced bridges and symmetry of voltages to convert each iteration of the network to a parallel circuit that includes the previous iteration. Then, we evaluate the equivalent resistance of each iteration of the network and derive a recursive sequence of equivalent resistances with iterations. After that, we prove that the recursive sequence is convergent using the contraction theorem in real analysis. Finally, we claim that the limit of the recursive sequence is the equivalent resistance of the infinite network.

Time-Dependent Analysis of Precast Segmental Bridges

Prestressed segmentally constructed balanced cantilever bridges are often subjected to larger deflections than those predicted by calculations, especially for long-term effects. In this paper, the case of modular balanced cantilever bridges, which are prestressed segmental bridges obtained through a repetition of the same double cantilever, is investigated. The considered bridges are two typical cases of modular balanced cantilever both subjected to large deformations during their lifetime. In this case, due to the unusual employed static scheme, creep deflections indefinitely evolve over time particularly at the end of the cantilevers and in correspondence with the central joint. These remarkable deflections cause discomfort for vehicular traffic and in certain cases can lead to the bridge collapse. Important extraordinary maintenance interventions were necessary to restore the viability of the bridges and to replace the viaduct design configuration. To this aim, the static schemes of the structures were varied, introducing new constraints, new tendons, and carbon fiber reinforcements. In the present work, time analysis was performed to compare the time-dependent behavior of the bridge according to two different creep models, the CEB-FIP Model Code 2010 and the RILEM Model B3, with the real-time-dependent behavior of the bridge observed during its lifetime. The two different employed models exhibit different behaviors in terms of displacements and bending moments acting on the bridge. Interesting considerations are made on their reliability in simulating the long-term creep effects that evolve indefinitely over time. Moreover, retrofitting techniques have been proposed and modeled to predict their effectiveness in reducing time-dependent deflections.

Near-fault vertical ground motion effects on the response of balanced cantilever bridges

Post-tensioned balanced cantilever reinforced concrete (RC) bridges allow the economic spanning of wide spans using fewer columns than in more traditional bridges. More and more post-tensioned balanced cantilever bridges are constructed every year all round the world. The aim of this study was to investigate numerically the effects of near-fault vertical ground motions (VGMs) on the seismic behaviour of segmentally constructed, balanced cantilever RC bridges. Two long bridges constructed in Artvin, Turkey – the three-span Budan Bridge and the two-span Sengan Bridge – were selected for the application. Three-dimensional finite-element models (FEMs) of the bridges were created to obtain their dynamic characteristics such as natural frequencies and mode shapes numerically. The frequencies calculated from the FEMs of the bridges were then verified using experimental frequencies measured from ambient vibration tests. Acceleration records of near-fault earthquakes (1992 Erzincan (M = 6·69), 1999 Kocaeli (M = 7·51), 1999 Düzce (M = 7·14) and 1989 Loma Prieta (M = 6·93)) were selected for the seismic analyses. The seismic behaviours of the verified FEMs of the bridges with two and three spans were determined by considering horizontal, vertical and combined horizontal and vertical components of the earthquakes. It was found that near-fault VGM significantly affects the seismic response of segmentally constructed, balanced cantilever bridges.

A simplified frequency formula for post-tensioned balanced cantilever bridges

The aim of this study is to develop a simplified natural fundamental frequency formula for the post-tensioned balanced cantilever bridges using the Operational Modal and Finite Element Analyses results. For this purpose, experimental and numerical studies were carried out on the five post-tensioned balanced cantilever bridges constructed in the city of Artvin, Turkey. First, the experimental and theoretical dynamic characteristics of the selected five bridges were determined using the ambient vibration-based Operational Modal Analysis and Finite Element Method, respectively. Then, the bridge model, which is given the highest correlation between the experimental and theoretical frequencies, was selected to determine the most important parameters that affected the modal behavior of the bridges. The most important parameters were determined as bridge length and pier height. Theoretical modal analyses were carried out for a series of bridge models with different lengths and heights. Finally, a simplified fundamental frequency formula was developed for the post-tensioned balanced cantilever bridges using the method of least squares considering the frequency values obtained from the theoretical modal analyses of the bridge models. The developed formula was checked with the experimentally obtained values, and it was observed that both sets of results were close to each other.

Assessing structural efficiency: a study of gravity balanced cable-stay bridges

The past few decades have witnessed a rapid increase in the role of the architect in the design of the once sacrosanct area of engineering – bridge design. Reasons for this relative decline in the engineer's role are many and varied, but must include the overemphasis on detailed analysis at the expense of understanding and creative design in engineering courses and the alarming reduction in structural education from engineering courses. With software now readily available to perform detailed structural analysis there is an opportunity to rebalance engineering courses towards much greater emphasis on understanding and design involving new approaches to analysis that can directly assist rational decision making. This paper demonstrates how simple, physically based, analyses can aid rational decision making in bridge design and suggests that such approaches could play a wider role in engineering courses. By way of illustration, these approaches are applied to the iconic, much copied, gravity balanced cable-stay Alamillo Bridge designed by Calatrava. This example also demonstrates the inefficiency of this bridge form and shows how such approaches, applied at an early design stage, could help bring rational engineering judgement back into bridge design at a time when the planet can ill afford such unsustainable solutions.

Shear strength of RC slabs under concentrated loads near clamped linear supports

Reinforced concrete slabs without shear reinforcement subjected to concentrated loads near linear supports are usually designed or assessed in shear using design provisions that have been calibrated on the basis of tests on one-way slabs or beams with rectangular cross-section (slabs loaded over their full width). This approach may however be inconsistent, as the actual behavior of slabs under concentrated loads reflects a two-way slab response, with the shear forces not developing in a parallel manner in the failure region and with potential redistribution of the internal forces for increasing levels of load.In this research, a series of 12 tests on 6 full scale slabs (3.00m×3.00m×0.18m) is presented. The slabs were centrally supported on an aluminum profile and were subjected to two concentrated symmetrical loads. The support profile was equipped with vertical strain gauges, allowing to trace the distribution of reactions at the supported line and its redistributions as the value of the concentrated loads increased. Significant redistributions of the reactions were actually measured prior to failure, which are presented and discussed within the paper. The aim of these measurements was to improve the understanding of the mechanical behavior of such members and the role of shear cracking on the distribution of internal forces. A number of parameters was investigated, such as the location of the concentrated loads and the presence of ducts in the slab. This latter case (typical of prestressed concrete balanced cantilever bridges and residential buildings) has not been investigated in the past, despite its potential influence on the shear strength.The performance of these specimens is finally investigated and compared to the prediction of the fib-Model Code 2010 and the Critical Shear Crack Theory. This analysis shows that accurate predictions of the strength can be obtained if the influence of direct load strutting (for loads acting near supports) and redistribution of internal forces is accounted.

Launching Gantries for Building Pre-cast Segmental Balanced Cantilever Bridges

Which bridge spans and types are suitable for construction by the precast segmental balanced cantilever bridge method? The reasons for the selected range of bridge will be described and the cost, quality and programme advantages will be described in this paper. The generic forms of such machines will be explained. This will include the effect that they have on the permanent structure, and thus the way in which the availability of existing machinery may affect the design of the bridge. The principal components of the machines will be highlighted, with consideration of the effect of the variety of equipment on cost and productivity. The overriding concerns on safety of the operation of the machine will be discussed. Aspects of design of the machine and its interaction with the permanent bridge structure will be discussed. The importance of the input of the main contractor will be discussed. The advantages of separating machine design from supply compared with the design / supply route will also be considered in this paper.

Time-dependent analyses of segmentally constructed balanced cantilever bridges

Segmentally constructed concrete cantilever bridges often exhibit larger deflections than those predicted by the design calculations. The slender and long spans in combination with the fact that permanent loads are only partially compensated for by prestressing are reasons for the large deflections that increase during the life time of the bridge, although at a decreasing rate. The rate of drying shrinkage may be one reason for the accelerating displacement of cast-in-place bridges. The construction of continuous spans instead of introducing joints has both comfort and durability advantages. The continuous span is however more complicated to design, and secondary restraint moments due to creep, shrinkage and thermal effects develop at the connection. The results of analyses of the stepwise cast-in-place construction of a balanced cantilever bridge with time-dependent material properties show both higher deflection than those originally assumed in the design calculations and high stresses in the webs due to stressing of the tendons in the bottom flange. The analyses show significant effects of creep during cantilevering and of a non-uniform drying shrinkage rate on the continuous bridge.

Special-Purpose Simulation Model for Balanced Cantilever Bridges

Construction of bridges’ decks involves different types of resources that interact in a cyclic manner. Further, the construction operation inherits uncertainties and a variety of demands. Contractors have to select the construction method that suits project constraints including: project conditions, technical, financial, and time constraints. There are several construction methods that can be used to construct bridges’ decks. This paper presents a special-purpose simulation model that aids government agencies and/or their representative in planning the construction of bridges’ decks using cast-in-place and precast balanced cantilever techniques. The pouring of concrete in cast-in-place balanced cantilever techniques can be executed either by using pump station and pump line, or truck mixers, whereas, the precast balanced cantilever technique is carried out using two methods: (1) placement by an independent lifting apparatus; and (2) placement with the help of a beam and winch carried by the bridge deck it...

Use of the diagonals of auxiliary balanced bridges as connecting wires in the arms of main bridges

Use of the diagonals of auxiliary balanced bridges as connecting wires in the arms of main bridges

Analogue circuits for luminescence polarization measurements

Very simple instrumentation, using the properties of balanced resistance bridges, can be used to measure directly the polarization of luminescence, emission anisotropy and other parameters. The incorporation of these circuits into a simple manually operated polarization photometer suitable for routine measurements or teaching purposes, and also into a more elaborate automated instrument for research use, is outlined.

Field Emission Ultramicrometer

A simple, contact free, ultrasensitive distance and displacement measuring instrument has been investigated. Experiments demonstrate that the instrument is capable of operating at spacings as small as a few hundred angstroms. Calculations indicate that distances of 10−3 to 10−6 cm and less can be reproduced to within about one part in 105. With suitable calibration, distance measurements in the 10−3 to 10−6 cm range can be expected to have accuracies limited only by available calibration techniques. The instrument would be most useful as a null or differential distance measuring device. It has the unusual property that resolution improves over several orders of magnitude as the null or measurement point is approached. Since the instrument contains no optical or mechanical lever systems, or delicately balanced bridges, it has inherent long term stability. Proposed applications include: (1) measurement of ball and hole diameters (contact free), (2) differential thermal expansion cell, (3) mechanical vibration sensor, (4) surface profile delineator (contact free), and (5) surface contour delineator (contact free).