Box Cross Section Research Articles

Repair and Strengthening of Cantilever Continuous Bridges using External Prestressed Cables: The Case Study of the Tan De Bridge in Vietnam

Continuous cantilever bridges utilizing cross-sectional box girders have been widely used worldwide, as well as in Vietnam, with outstanding advantages, such as the ability to cover large spans, good torsional resistance, high stability, and low maintenance costs. The arrangement of the prestressed cables in the span can use all internal cables (cables arranged in a box cross-section) or a combination of internal wires and external cables (cables arranged in a box cavity). The arrangement of the external cables helps reduce the cross-sectional area and self-weight of the span, leading to savings in foundation costs and an increase in the ability to exceed the span. However, the external cables degrade and become damaged. Therefore, repair and strengthening solutions are required to ensure the longevity of the project. This study focused on researching solutions to restore and enhance span structures using external prestressed cables through specific projects implemented in Vietnam.

Wave Propagation in Prestressed Structures with Geometric Nonlinearities Through Carrera Unified Formulation

This paper deals with the analysis of wave propagation characteristics in various prestressed structures with geometric nonlinearities using the Carrera Unified Formulation (CUF). CUF provides a versatile platform to model a wide range of structures and nonlinearities that can take care of all wave propagation aspects. In this work, different geometric nonlinearities for which representative governing equations have been derived and numerical solutions have been obtained through a unified approach are considered. The study investigates in detail the effect of prestress and geometric nonlinearity on wave propagation behavior. The results indicate that prestress has a very influential effect on modal frequency and dispersion characteristics for wave propagation. Specifically, three CUF-modeled beams are considered herein, having a sandwich, metallic portal, and metallic box cross section, respectively. Initially, the principal cross-sectional modal shapes of the unstressed, linear, and full nonlinear (i.e., full three-dimensional Green–Lagrange strain matrix) beam with a prestress are investigated, among which torsional and flexural modes can be recognized. Afterward, the equilibrium curves of such structures for various geometrical nonlinear approximations are traced, highlighting that most types of nonlinearity induce a hardening behavior in the system, which increases with the preload, directly leading to a variation in modal frequencies. The dispersion relations of the full nonlinear structure examined as a function of the applied preload are further compared, enriching the investigation by exploiting wave finite element method capabilities. This knowledge paves the way toward the design and optimization of prestressed systems with enhanced acoustic performance, and that fosters the development of sound absorption, noise insulation, and structural isolation.

COMPARASION PLASTIC BEHAVIOR OF BOX GRIDER BRIDGE WITH MULTIPLE BOX AND CELLULAR BOX CROSS SECTIONS

This study compares plastic deformation behavior in box girder bridges with multiple boxes and cellular box cross-sections. The cross-section's shape significantly influences the girder's post-yield behavior despite being designed to have the exact yield moment. Steel's stress-strain relationship undergoes linear behavior until the yield stress is reached, followed by strain hardening. This study aims to assess the impact of strain hardening on the plastic behavior of girder box bridges.Two types of box girder sections, multiple box and cellular box, are designed with equivalent yield moments. The analysis is conducted with and without strain hardening calculations to evaluate plastic moment, inelastic area length, shape factor, and moment-curvature relationship. The design and analysis follow RSNI T-03-2005 standards using SAP 2000 v.15.Results indicate that multiple box sections exhibit more prominent plastic moments and inelastic area lengths than cellular box sections. Strain hardening calculations show significant increases in plastic moments for both section types. Graphical comparisons highlight the differences in moment-curvature relationships between models with and without strain hardening. Understanding the impact of strain hardening on plastic behavior provides valuable insights for designing and assessing box girder bridges, ensuring structural safety and performance under load conditions.

Light-weight design of an overhead crane’s girder with a non-symmetric box cross-section

The proper choice of material and geometric properties of the girder of the bridge crane can significantly reduce its weight and production cost. This research presents the weight optimization of the main girder with a non-symmetric box-like cross-section. The strength analysis in characteristic points of the critical cross-section and the local stability of plates were conducted using Eurocodes. This study aimed to prove that a proper choice of geometry for the cross-section plates and their additional design elements can have a meaningful impact on the weight. The optimization procedure was done using Water Evaporation Optimization (WEO) algorithm, with the implementation of all necessary criteria and conditions which must be fulfilled. This study revealed that the application of the light-weight design philosophy to the structure of the main girder could significantly reduce its weight, which is verified in the existing examples of double-beam bridge cranes. Achieved savings in girder weight are between 24.43% and 34.73%, dependingly on the considered example. Also, the study showed the influence of the chosen material on the steel girder’s optimum weight and geometric parameters. Depending on the studied example of the bridge crane and selected material, the WEO algorithm gave the same solution through simulations. The value of the optimum weight had a slight deviation at the second decimal place, which is neglectable. The algorithm successfully avoided the trap of getting into the local minimum during the search. In the end, it can be stated that the application of the WEO algorithm was successful in the considered engineering problem since it was the optimization of a complex steel structure with 11 variables and more than 20 constraint functions.

Vibration Serviceability Evaluation of a Single Span Steel–Concrete Composite Foot Bridge under Dynamic Pedestrian Loadings Considering Moving Mass Effect

In this paper, we present the analysis results on the vibration serviceability of a pedestrian bridge considering the effect of pedestrian moving mass inertia. Using dynamic finite element analysis, we considered different walking scenarios, including pedestrian density, walking speed, random walking, and synchronized walking, to analyze the acceleration response of a 40m long single-span bridge with a steel composite box cross section. We showed that the equivalent fixed mass analysis method did not significantly differ from the moving mass analysis in the random walk scenario and a wider frequency excitation band may be useful to consider when evaluating vibration serviceability in a random walk scenario.

Development of Bi-hexagonal hybrid crash box subjected to axial loading for enhancement of crashworthiness

Crash box design had been developed to increase crashwortiness performance. The crash box cross section is one important parameter to increase the energy absorption as crashwortiness performance. In the previous study, hexagonal cross section provide the higher energy absorption than other cross section. One of strategy to increase cross section is using two cross section put together in one component of crash box design. Bi-tubular crash box shows higher energy absorption with easy manufacture opportunity. In other study, hybrid crash box is investigated to reduce crash box mass. In this study, development of bi-hexagonal hybrid crash box subjected to axial loading to enhance crashworthiness were investigated. Analysis of crash box design is developed by using computer simulation with ANSYS Workbench 19.2. The crash box materials used are Aluminum Alloy and carbon-epoxy woven. The material modeling in the crash box is assumed as deformable body while the impactor is a rigid body. The axial loading is modelled by setting impactor impact the crash box with a speed of 7.67 m/s. Fixed support is set on the bottom of crash box. Nine of frontal test models were simulated for the bi-hexagonal hybrid crash box with different layups orientation angle and composite hexagonal tube diameter. Energy absorption and deformation patterns were observed. The results indicated that the highest energy absorption and specific energy absorption is occured on the A60 model with layups orientation angle of [0/60/0/60] and composite hexagonal tube diameter of 41 mm are 3693.8 J and 19.121 kJ/kg. The deformation pattern in the aluminum part is diamond mode, while in the composite part, the deformation pattern produce transverse shearing, lamina bending, brittle fracturing and local buckling mode

3G-optimization of multi-cell crash box cross-section of autobody based on crashworthiness

The cross-section, thickness, and material of the autobody structure determine the crashworthiness and lightweight level. Different from the variables in traditional autobody design that are considered separately, the basic theory of 3G-optimization is to simultaneously consider geometric shape (Geometry), the thickness of structure (Gauge), and material grade (Grade) in structural optimization design, which is conducive to maximizing the lightweight potential of the structure. This paper presents a cross-section optimization method for multi-cell thin-walled structures based on 3G-optimization, which is used in the structural design of crash box. Based on full width frontal collision condition, the cross-section shape, thickness, and material variables of the multi-cell crash box are optimized simultaneously. Multiple sets of optimization schemes show obvious weight reduction effect while ensuring safety. Besides, the sub-system decoupling method and hybrid cellular automaton (HCA) method are applied to 3G-optimization process, which is beneficial to improve the calculation efficiency and provide a theoretical basis for the definition of the initial design space for 3G-optimization.

Influence of Adhesive Layer Thickness on the Effectiveness of Reinforcing Thin-Walled Steel Beams with CFRP Tapes-A Pilot Study.

When reinforcing thin-walled steel members with composite tapes, two issues often overlooked in published scientific papers should be considered, namely the correct thickness of the adhesive layer and the optimum bond length of the CFRP tape. In this article, the authors focused on the first of these issues. For this purpose, eight beams with a thin-walled box cross-section and a length of 3 m were subjected to bending in a four-point scheme. Six beams were reinforced with Sika CarboDur S512 composite tape, and two beams without reinforcement were tested as reference members. Three thicknesses of the adhesive layer (SikaDur-30) were analyzed: 0.6 mm, 1.3 mm and 1.75 mm. In addition to examining the effect of the thickness of the adhesive layer on displacements and deformations of thin-walled steel members, the load value at which the composite tape peeled off was also analyzed. Numerical analyses were then carried out in Abaqus, the outcomes of which showed good agreement with the laboratory results. Both numerical and laboratory results have shown that the thickness of the adhesive layer had a minor effect on the reduction in deformation and displacement of the tested beams. At the same time, with the increase in the thickness of the adhesive layer, the value of the load at which the CFRP tapes detached from the beam surface significantly decreased.

Probabilistic Analysis on Aerostatic Displacement-dependent Wind Loads on a Stream-lined Box Girder

Due to the limitations of the bridge deck modeling and wind tunnel installations, the parametric uncertainties of aerostatic displacement-dependent wind loads have become an urgent problem for reliability analysis in bridge engineering. Computational fluid dynamic (CFD) simulations were conducted to investigate the distribution model of aerostatic coefficients. The Monte Carlo simulation (MCS) was used to generate random samples of stream-lined box cross-sections. Among these samples, wind attack angles of −8°–8° were considered, and the sample size of each angle group was set as 30. Then, the statistical properties for the variation and distribution of aerostatic coefficients were discussed. In addition, sub-samples with sizes of 5–20 were randomly sampled from the initial sample group to evaluate the influence of the sample scale. The coefficient of variation (COV) of aerostatic coefficients with respect to geometric uncertainties increased up to 0.217, which occurred at −7° wind attack angle. Lognormal distribution models obtained by hypothesis tests maintained a low deviation for estimating the distribution of aerostatic coefficients. The sample size had a significant effect on quantifying the error between empirical and theoretical distribution models. Simulation method proposed in this paper provides a systematic approach for probabilistic problems involving fluid-structure interaction and parametric uncertainties.

Multi-objective optimization of a sandwich structure with a hybrid composite grid core

This study evaluated two multi-objective optimization problems of a hybrid composite grid core sandwich structure, aiming at maximizing the critical buckling load while minimizing the structural weight or the costs of raw materials. The sandwich structure had a core with a composite isogrid pattern covered by two composite skins, and design variables included the space between core ribs, the core rotation angle, and the dimensions and materials of ribs. The stiffeners of the core were considered with I and box cross sections to investigate the cross section effect of ribs. The results showed that materials with high density and low mechanical properties are not suitable for reducing cost and weight. Geometrically, the use of cross-section and box has a significant effect on the buckling load capacity of the structure. Although two different criteria have been used to design the structure, the end results are almost the same. Moreover, the First-order Shear Deformation Plate Theory and the Ritz method were utilized to obtain the buckling load. Finally, the optimal alternative was found among the existing ones using the continuous genetic algorithm approach.

Calculation method for the torsional bearing capacity of composite girders with CSW-CFST truss chords

Torsional behavior tests and a theoretical analysis were conducted on the composite girders with corrugated steel webs and concrete-filled steel tubular (CSW-CFST) truss chords. Their performance was compared with that of composite girders with circular hollow section (CSW-CHS) truss chords and composite box girders with CSW-CFST chords. The study revealed the influence of the concrete in the chord and the sectional form of the composite girders on their twist failure mode and torsional behavior. The test results showed that the sectional form of composite girders with CSW-CFST truss chords can perform as well as closed box cross-sections. The point of twist failure was found to be when the concrete roof obliquely cracked with an angle of 45° between the crack and the girder axis and the rebar had already yielded. The concrete in the chord contributes to the torsional stiffness and bearing capacity of composite girders. The paper puts forward a method for calculating the compound stiffness of CFST specimens by superposing their linear stiffness. Then, on the basis of the four types of twist failure that can affect composite girders with CSW-CFST truss chords, a method for calculating their torsional bearing capacity is proposed. The deviation between the results acquired using the proposed method and the results from the tests and a finite element analysis is less than 8.5%.

Topology optimization of horizontally curved box girder diaphragms

Curved girders are widely used in bridge construction to overcome geographical obstacles. In such cases, girders with a box cross-section are preferred due to their large flexural and torsional rigidity. Internal diaphragms are used to limit cross-section distortion and the distortional warping stress induced in the box girders. However, the use of such diaphragms hinders girder maintenance. To facilitate the maintenance process, typical cross frames such as X- or V-shape truss members are used. Alternatively, access holes are provided in the solid plate diaphragms. In this paper, finite element models for horizontally curved box girders were constructed and topology optimization method was used to obtain the optimal shapes for the internal and external diaphragms. In this analysis the optimization objective was set to reduce the diaphragm mass while maximizing its rigidity. The mass retained percentage was assigned to various values from 20% to 40%. The deformations and distortional stresses induced in the girders were compared between girders having solid plate diaphragms and girders with optimized cross-frame diaphragms. The parametric study included the cross-section aspect ratio and curved girder central angle as they have large effect on distortional warping stresses. The results showed that the increase in distortional warping normal stress was less than 4% and the increase in the cross-section distortion angle was less than 37% between optimized diaphragms and solid plate diaphragms. The optimized diaphragms were then simplified into more practical configurations that differed depending on the girder aspect ratio. The simplified diaphragms were then tested against the optimized diaphragms for girders with different numbers of internal diaphragms to check its practicality.

Effect of Device Positions on the Vibration Damping Characteristics of Bead Panels Using a New Vibration Damping Device Consisting of a Constraint Frame and a Viscoelastic Layer

This paper describes numerical simulation of the dynamic characteristics of a bead panel equipped with a new vibration control device. The device includes two blocks of viscoelastic gels and a constraint layer having a box cross section. The gel blocks are sandwiched between the constraint layer and the test structure. The modal analysis is carried out numerically using the finite element method with modal strain energy method. Effects of device positions on the vibration damping characteristics of the bead panel were evaluated using eigenmodes, modal loss factors and resonance frequencies.

Analiza i optimizacija glavnog nosača mosne dizalice sa asimetričnim kutijastim poprečnim presekom

The presented research deals with the optimal design of the main girder with an asymmetric box cross-section of the double-beam bridge crane. The Moth-Flame Optimization algorithm (MFO) is used for solving this multicriteria optimization problem. This algorithm is a relatively new population-based metaheuristic method. The paper takes the following criteria as the constraint functions: strength, local stability of the girder plates (webs and top flange), local stability of the longitudinal stiffeners, global stability of the main girder, deflections, and period of oscillation. The justification of the proposed procedure is shown in one example of a real solution of the double-beam bridge crane. Significant savings in material were achieved in this research, within the range of 19.42 to 25.49%. The use of this algorithm enables the application of a very large number of variables and constraint functions, whereby the optimal values are obtained in a relatively short period.

Shear Assessment of Existing Prestressed Box Girder Bridge

The paper deals with the shear assessment of existing prestressed concrete box-girder bridges. Mainly focuses on the historical development of technical standards used in the design of prestressed concrete road bridges in the Slovak Republic. The standards for bridge design have been amended several times. A parametric study was performed on a model post-tensioned concrete bridge with a box-girder cross-section, which compares the internal forces along the length of the bridge using various standards and technical regulations., The differences in design principles and shear capacity were investigated while the amount and geometry of the longitudinal prestressing of the bridge were the same for all cases. Case of study is a road three-span post-tensioned concrete bridge with a main span of 50 m and end spans of 40 m. The single box-girder cross section height is constant of 2.5 m. The bridge is straight without any curvature in the horizontal plane. The thickness of the bottom slab is variable near the inner supports. The prestressing is formed by 19-strands tendons with a strand diameter of 15.7 mm with a polygonal cable geometry. The numerical model is considered as a beam element with neglecting of the torsional effects of the load. The parametric study points out the differences in the internal forces with use of different design regulations and standards. It also focuses on the shear resistance of the walls of the box-girder cross-section of the bridge. Differences in design methods are presented by the required area of shear reinforcement in the wall of box cross-section. The aim of the study is to point out the historical development of design from the point of view of shear resistance of prestressed bridges. When assessing existing older bridges and trying to achieve reliability according to the current Eurocodes, there is subsequently a requirement for additional shear reinforcement.

Numerical Investigation of the Geometrical Effect on Flow-Induced Vibration Performance of Pivoted Bodies

In this study, the Flow-Induced Vibration (FIV) of pivoted cylinders (at a distance) is numerically investigated as a potential source of energy harvesting. In particular, we investigate the effect of pivot point placement, arm length, and natural frequency on the FIV performance of six different cross sections in the Reynolds number of around 1000. All sections have similar mass, area, and moment of inertia to eliminate non-geometrical effects on the performance. Classical studies show that the synchronization phenomenon (lock-in) occurs when the vortex formation frequency is close enough to the body’s natural frequency. Due to the configuration of the cylinder in this research (pivoted eccentrically), the natural frequency is also a function of the flow velocity as well as the geometrical specifications of the system. The simulation is done for the arm lengths between −3D and +3D for all cross sections. Results show that maximum output power is principally influenced more by the pivot location than the arm length. Although the box cross section has a higher amplitude of vibration, the circular cross section has the highest efficiency followed by the egg shape.

Analiza glavnog nosača dvogredne mosne dizalice sa dva vitla

In this research, the problem of calculating the necessary static quantities of the main girder with the box crosssection of the double-beam bridge crane with two trolleys were analyzed. The aim is to determine the critical position on the girder due to the action of all loads in the vertical plane, as a function of input parameters, and to obtain expressions for calculating deflections in the vertical and horizontal planes, as well as bending moments in these planes, ie maximum (total) stress in the girder. Verification of the results was carried out in the SAP2000 software package, with proved a quite good correlation between the results obtained, for the proposed method of the calculation model of the box-girder, in the mentioned software package. The goal of this research is primarily to show how the application of the SAP2000 software package in an easy, fast and simple way can perform the dimensioning and design of this type of carrying structures, taking into account important static conditions that must be satisfied. By applying the proposed modelling method and using a certain module in the mentioned software package, the designer easily achieves the preliminary geometric values of the girder in the initial design phase, where he can completely rely on the obtained results. Also, all geometric quantities necessary for further phases in the design and calculation are obtained. Guidelines are given on how to prepare a calculation model in this software package for these types of carrying structures, as well as recommendations related to the design of these types of carrying structures made of S355 material.

Optimization of bridges with short gap streamlined twin-box decks considering structural, flutter and buffeting performance

While it is well known that the gap between twin-box decks is a key design variable that impacts the onset flutter velocity of a bridge, further research is required to ascertain how modifications in several bridge design variables affect other aeroelastic responses. This paper utilizes aero-structural optimization techniques for the design of long-span bridges with short gap twin-box decks considering simultaneously structural, flutter and buffeting constraints. The optimization helps to reduce the material volume of the structure while maintaining all the performance and safety requirements below the imposed thresholds. It has been found that the geometry of the individual box cross-section is an important feature for the control of the buffeting response, particularly the vertical acceleration. On the other hand, flutter and torsional buffeting constraints require designs with larger gap distance and alternative box geometries, leading to a trade-off between conflicting design demands. Hence, depending on the expected wind load conditions and the specific requirements of a particular project, an optimum aero-structural bridge design with a particular deck shape can be identified. The framework presented in this study is an effective tool to achieve sustainable and safe bridge designs that seeks a most efficient balance between all the design constraints.

An Intelligent Analysis Method for Human-Induced Vibration of Concrete Footbridges

It is essential to reliably predict the human-induced vibrations in serviceability design of footbridges to ensure the vibration levels to be within the acceptable comfort limits. The human-induced structural responses are dependent on the dynamic properties of structures and human-induced excitations. For concrete footbridges, the elastic modulus of concrete is a vital parameter for determining the dynamic structural properties. To this end, a two-stage machine learning (ML)-based method is first proposed for modeling the elastic modulus of concrete. At the first stage, the ensemble algorithm, i.e. the gradient boosting regression tree (GBRT), is used to predict the compressive strength by selecting eight parameters, including concrete ingredients and curing time, as the inputs. At the second stage, the elastic modulus of concrete is modeled by using the GBRT method with the compressive strength as the input. Pedestrian crowd-induced load is the most common and crucial design load for footbridges. To consider the inter- and intra-subject variability in walking parameters and induced forces among persons in a crowd, a load model is developed by associating a modified social force model with a walking force model. By integrating the two submodels of structure and excitation, an intelligent analysis method for human-induced vibration is finally developed. A concrete footbridge with typical box cross-section subjected to human-induced excitation is analysed to illustrate the application of the proposed method.

USING CARBON FIBER STRIPS IN JOINTS STRENGTHING OF BOX SEGMENTAL SELF-COMPACTING CONCRETE BEAMS

The main objective of this research is to study the effect of carbon fibers used to strengthen the joints of the box segmental beams. For this research, four beams were produced and tested. One of these beams, monolithically, was cast as a reference beam and the three others were segmental beams. All beams were produced with Self-Compact Concrete (SCC) and box cross section. Each segmental beam consisted of three precast concrete segments were connected by post tensioning tendons. The three segmental beams have same characteristics, but different in joint types between the segments. The types of joints used were (dried, epoxied and dried strengthen by CFRP sheets). All beams were tested under static two point loads up to failure. For each test, deflections at mid-span location were recorded for each (5kN). Also, first cracking, mode of failure and ultimate loads values were recorded as well as the concrete surface strains at the specified locations for both loadings.