Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.

A comparative study on the hull strength of a ship with thin-walled box girders

Based on the Finite Element Analysis and Thin Walled-Box girder Mechanics, two design concepts of adding box girders under main deck in order to increase the hull strength of ship are presented. By comparison and analysis on the longitudinal strength, torsion strength and deck buckling between designed concepts and the original concept, it is found that by adding box girders under the main deck, the weight of hull structure is increased by lower than 10%, but the stress on the plate of the main deck is reduced by about 10%, the stress on the plating of the second deck is reduced about 20%. The shear stress on the plating of both of the main deck and second deck is reduced, but the shear stresses in several nodes are increased. Also the capability of resisting damage to ship is obviously increased by adding box girders under the main deck. The deck buckling is also increased by more than 90%. Consequently, the box girders added under the main deck are useful and effective to increase the strength of hull and ship survivability.

Powell's optimal identification of material constants of thin-walled box girders based on Fibonacci series search method

A dynamic Bayesian error function of material constants of the structure is developed for thin-walled curve box girders. Combined with the automatic search scheme with an optimal step length for the one-dimensional Fibonacci series, Powell＇s optimization theory is used to perform the stochastic identification of material constants of the thin-walled curve box. Then, the steps in the parameter identification are presented. Powell＇s identification procedure for material constants of the thin-walled curve box is compiled, in which the mechanical analysis of the thin-walled curve box is completed based on the finite curve strip element （FCSE） method. Some classical examples show that Powell＇s identification is numerically stable and convergent, indicating that the present method and the compiled procedure are correct and reliable. During the parameter iterative processes, Powell＇s theory is irrelevant with the calculation of the FCSE partial differentiation, which proves the high computation efficiency of the studied methods. The stochastic performances of the system parameters and responses axe simultaneously considered in the dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step length is solved by adopting the Fibonacci series search method without the need of determining the region, in which the optimized step length lies.

Fatigue Crack Propagation Law of Corroded Steel Box Girders in Long Span Bridges

In order to investigate the fatigue performance of orthotropic anisotropic steel bridge decks,this study realizes the simulation of the welding process through elastic-plastic finite element theory,thermal-structural sequential coupling,and the birth-death element method.The simulated welding residual stresses are introduced into the multiscale finite element model of the bridge as the initial stress.Furthermore,the study explores the impact of residual stress on crack propagation in the fatigue-vulnerable components of the corroded steel box girder.The results indicate that fatigue cracks at the weld toe of the top deck,the weld root of the top deck,and the opening of the transverse diaphragm will not propagate under the action of a standard vehicle load.However,the inclusion of residual stress leads to the propagation of these cracks.When considering residual stress,the fatigue crack propagation paths at the weld toe of the transverse diaphragm and the U-rib weld toe align with those observed in actual bridges.In the absence of residual stress,the cracks at the toe of the transverse diaphragm with a 15%mass loss rate are categorized as type I cracks.Conversely,when residual stress is considered,these cracks become I-II composite cracks.Residual stress significantly alters the cumulative energy release rate of the three fracturemodes.Therefore,incorporating the influence of residual stress is essential when assessing the fatigue performance of corroded steel box girders in long-span bridges.

Explosion resistance performance of reinforced concrete box girder coated with polyurea:Model test and numerical simulation

To study the anti-explosion protection effect of polyurea coating on reinforced concrete box girder,two segmental girder specimens were made at a scale of 1:3,numbered as G(without polyurea coating)and PCG(with polyurea coating).The failure characteristics and dynamic responses of the specimens were compared through conducting explosion tests.The reliability of the numerical simulation using LS-DYNA software was verified by the test results.The effects of different scaled distances,reinforcement ratios,concrete strengths,coating thicknesses and ranges of polyurea were studied.The results show that the polyurea coating can effectively enhance the anti-explosion performance of the girder.The top plate of middle chamber in specimen G forms an elliptical penetrating hole,while that in specimen PCG only shows a very slight local dent.The peak vertical displacement and residual displacement of PCG decrease by 74.8% and 73.7%,respectively,compared with those of specimen G.For the TNT explosion with small equivalent,the polyurea coating has a more significant protective effect on reducing the size of fracture.With the increase of TNT equivalent,the protective effect of polyurea on reducing girder displacement becomes more significant.The optimal reinforcement ratio,concrete strength,thickness and range of polyurea coating were also drawn.

Discussion on Detection and Evaluation of Simply Supported Prestressed Concrete Small Box Girder Bridge After a Fire

The article takes a simply supported prestressed concrete small box girder bridge project as an example for inspection and evaluation after a fire incident.This includes appearance detection,concrete color hardness detection,concrete strength detection,concrete surface damage layer detection,reinforcement protective layer detection,and concrete carbonation detection.It is hoped that this analysis can be used as a reference for the detection and evaluation of future bridge projects with fire incidents to smoothen its subsequent repair and maintenance.

Lateral static and dynamic characteristics of thin-walled box girder

To analyze the static and dynamic behaviors of the thin-walled box girder in its lateral webs in consideration of shear lag effect and shear deformation, an approach based on the minimum potential principle is introduced in this paper. Both static and dynamic response equations as well as the corresponding natural boundary conditions of the box girder are deduced. Meanwhile, three generalized displacement functions： w （x） , U（x） and O（x） are employed and their differences in the calculus of variation are quantitatively investigated. The comparison of finite shell element results with analytical results of calculation examples validates the feasibility of the proposed approach.

Finite element failure analysis of continuous prestressed concrete box girders

In order to analyze the load carrying capacity of prestressed concrete box girders, failure behaviors of in-situ deteriorated continuous prestressed concrete box girders under loading are experimentally observed and a finite failure analysis method for predicting behaviors of box girders is developed. A degenerated solid shell element is used to simulate box girders and material nonlinearity is considered. Since pre-stressed concrete box girders usually have a large number of curve prestressed tendons, a type of combined element is presented to simulate the prestressed tendons of box girders, and then the number of elements can be significantly reduced. The analytical results are compared with full-scale failure test results. The comparison shows that the presented method can be effectively applied to the failure analysis of in-situ continuous prestressed concrete box girders, and it also shows that the studied old bridge still has enough load carrying capacity.

SIMPLIFIED ANALYSIS METHOD FOR ULTIMATE LOAD CAPACITY OF WEB PLATES OF BOX GIRDERS

The prosperous post buckling load capacity of web plates of box girders can be used.In this article,the post buckling behaviour of web plates of box girders under different loading conditions is theoretically analyzed and on the basis of domestic and overseas design codes of steel structures,the corresponding simplified analysis methods are put forward for the engineering design or code revision.It is proved that the simplified methods are safe,efficient and practicable through the comparison between several results.

Improved concept models for straight thin-walled columns with box cross section

This paper focuses on developing improved concept models for straight thin-walled box sectional columns which can better predict the peak crushing force that occurs during crashworthiness analyses. We develop a nonlinear translational spring based on previous research and apply such a spring element to build the enhanced concept models. The work presented in this article is developed on the basis of the publication of the author (Liu and Day, 2006b) and has been applied in a crashworthiness design issue, which is presented by the author in another paper (Liu, 2008).

Temperature distributions in concrete box girders due to heat of concrete hydration

Based on heat transfer theory,a two-dimensional complex exponential function was used to compute heat of concrete hydration.A concrete box girder consisting of a single box with two cells used on Harbin Songpu Bridge was measured on site.The two coefficients in the complex exponential function were determined to best fit the field measured data.ABAQUS program was used to simulate the heat transfer and determine the temperature distribution in the concrete box girders during concrete setting.The calculated temperature distribution in the box girders were compared with the field measured data and good agreement was observed.The temperature distribution and gradient in the entire box section,webs and bottom slab were analyzed using the measured and calculated results during the course of concrete hydration.

Vibro-acoustic performance of steel–concrete composite and prestressed concrete box girders subjected to train excitations

Owning to good mechanical properties,steel–concrete composite(SCC)and prestressed concrete(PC)box girders are the types of elevated structures used most in urban rail transit.However,their vibro-acoustic differences are yet to be explored in depth,while structure-radiated noise is becoming a main concern in noise-sensitive environments.In this work,numerical simulation is used to investigate the vibration and noise characteristics of both types of box girders induced by running trains,and the numerical procedure is verified with data measured from a PC box girder.The mechanism of vibration transmission and vibro-acoustic comparisons between SCC and PC box girders are investigated in detail,revealing that more vibration and noise arise from SCC box girders.The vibration differences between them are around 7.7 dB(A)at the bottom plate,19.3 dB(A)at the web,and 6.7 dB(A)at the flange,while for structure-radiated noise,the difference is around 5.9 dB(A).Then,potential vibroacoustic control strategies for SCC box girders are discussed.As the vibro-acoustic responses of two types of girders are dominated by the force transmitted to the bridge deck,track isolation is better than structural enhancement.It is shown that using a floating track slab can make the vibration and noise of an SCC box girder lower than those of a PC box girder.However,structural enhancement for the SCC box girder is extremely limited in effects.The six proposed structural enhancement measures reduce vibration by only 1.1–3.6 dB(A) and noise by up to1.5 dB(A).

Flexural failure experiment on cracked PC simply supported box girders

Long-term load and flexural failure experiments are carried out on two prestressed concrete(PC) simply supported box girders. In the long-term load experiment, girder-1(G1) is in an elastic state, while girder-2(G2) is in a cracking state. To investigate the influence of cracking on the flexural behaviors of PC simply supported box beams, the experiment results are analyzed from many aspects, such as load–deflection, load–strain, and failure mode. Experiment results show the following: 1) the shrinkage and creep of concrete have considerable influences on the long-term deflection and strain of the two girders; 2) in the flexural failure experiment, the cracks and ultimate loads of the two girders are close. The rigidity degeneration of G2 is significantly faster than that of G1, and thus G2 shows nonlinear characteristics earlier; 3) to prove the validity and rationality of the current code, the cracking load and ultimate load of the two girders are calculated according to the current code.

Full-scale model tests and nonlinear analysis of prestressed concrete simply supported box girders

Full-scale model tests were carried out on a 30 m span prestressed concrete box girder and a 20 m span prestressed concrete hollow slab. Failure models were prestressed reinforcement tensile failure and crashing of roof concrete, respectively. The ductility indexes of the box girder and hollow slab were 1.99 and 1.23, respectively, according to the energy viewpoint. Based on the horizontal section hypothesis, the nonlinear computation procedure was established using the limited banding law, and it could carry out the entire performance analysis including the unloading, mainly focusing on the ways to achieve the unloading curves computation through stress-strain, moment-curvature and load-displacement curves. Through the procedure, parameters that influence on the bearing capacity, deformation performance and ductility of the structures were analyzed. Those parameters were quantity of prestressed reinforcement and tension coefficients of prestressed reinforcement. From the analysis, some useful conclusions can be obtained.

Stress and noises of steel box girders in Sutong Bridge

Sutong Bridge is a cable-stayed bridge with a main span of 1 088 m. 370 high-precision stress monitoring measured data show that in the process of hoisting the steel box girders,the stress of the main girders is in the fluctuant and complex state and many meteorological factors,such as sunshine radiation,temperature and wind,have important influence on the change of stress of the steel box girders. According to the real-time weather data,the stress data after the process of wavelet denoising from representative measuring points in different weather conditions is picked to establish the stress response brought by meteorological factors with Layered Separation method,thereby basically eliminating the influence of meteorological factors on the stress of main girders,so that accurate and reliable stress data can be got for steel box girders adjustment and cable-tensioned construction control.

THE APPROXIMATE ANALYTICAL SOLUTION FOR THE BUCKLING LOADS OF A THIN-WALLED BOX COLUMN WITH VARIABLE CROSS-SECTION

For a thin-walled box column with variable cross-section, the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients, so it is very difficult to solve them by means of an analytic method. In this paper, polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations. Based on the energy principle and the Galerkin's method, the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively, and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section. This paper is of practical value.

Influence of aerodynamic configuration of a streamline box girder on bridge flutter and vortex-induced vibration

Streamline box girders are widely applied in the design and construction of long-span bridges all over the world. In order to study the influence of modifications of aerodynamic configuration and accessory components on flutter and vortex-induced vibration （VIV）, more than 60 cases were tested through a 1：50 scale section model. The test results indicates that the aerodynamic configuration and accessory components of streamline box girders can signifi- cantly affect the wind-induced vibration of bridge, which is in good agreement with the experience of past researchers. From the tests carried out, it is observed that if the horizontal angle of the inclined web of the streamline box girder is below 16°, the critical flutter wind speed of bridge will increase remarkably, and the VIV will diminish. The test results also show that the 15° inclined web can restrain the formation of vortex near the tail, and consequently improve the performance of aerodynamic stability of long-span bridges. Finally, a new streamline box girder with 15° inclined web was presented and strongly recommended in the aerodynamic configuration design of long-span bridges.

Estimating extreme temperature differences in steel box girder using long-term measurement data

The extreme temperature differences in fiat steel box girder of a cable-stayed bridge were studied.Firstly,by using the long-term measurement data collected by the structural health monitoring system installed on the Runyang Cable-stayed Bridge,the daily variations as well as seasonal ones of measured temperature differences in the box girder cross-section area were summarized.The probability distribution models of temperature differences were further established and the extreme temperature differences were estimated with a return period of 100 years.Finally,the temperature difference models in cross-section area were proposed for bridge thermal design.The results show that horizontal temperature differences in top plate and vertical temperature differences between top plate and bottom plate are considerable.All the positive and negative temperature differences can be described by the weighted sum of two Weibull distributions.The maximum positive and negative horizontal temperature differences in top plate are 10.30 ℃ and -13.80 ℃,respectively.And the maximum positive and negative vertical temperature differences between top plate and bottom plate are 17.30 ℃ and-3.70 ℃,respectively.For bridge thermal design,there are two vertical temperature difference models between top plate and bottom plate,and six horizontal temperature difference models in top plate.

Temperature gradients in concrete box girder bridge under effect of cold wave

The temperature distributions of a prestressed concrete box girder bridge under the effect of cold wave processes were analyzed. The distributions were found different from those under the effect of solar radiation or nighttime radiation cooling and should not be simplified as one dimensional. A temperature predicting model that can accurately predict temperatures over the cross section of the concrete box girder was developed. On the basis of the analytical model, a two-dimensional temperature gradient model was proposed and a parametric study that considered meteorological factors was performed. The results of sensitivity analysis show that the cold wave with shorter duration and more severe temperature drop may cause more unfavorable influences on the concrete box girder bridge. Finally, the unrestrained linear curvatures, self-equilibrating stresses and bending stresses when considering the frame action of the cross section, were derived from the proposed temperature gradient model and current code provisions, respectively. Then, a comparison was made between the value calculated against proposed model and several current specifications. The results show that the cold wave may cause more unfavorable effect on the concrete box girder bridge, especially on the large concrete box girder bridge. Therefore, it is necessary to consider the thermal effect caused by cold wave during the design stage.

Wind tunnel measurement of aerodynamic characteristics of trains passing each other on a simply supported box girder bridge

The aerodynamic performance of high-speed trains passing each other was investigated on a simply supported box girder bridge,with a span of 32 m,under crosswinds.The bridge and train models,modeled at a geometric scale ratio of 1:30,were used to test the aerodynamic forces of the train,with the help of a designed moving test rig in the XNJD-3 wind tunnel.The effects of wind speed,train speed,and yaw angle on the aerodynamic coefficients of the train were analyzed.The static and moving model tests were compared to demonstrate how the movement of the train influences its aerodynamic characteristics.The results show that the sheltering effect introduced by trains passing each other can cause a sudden change in force on the leeward train,which is further influenced by the wind and running speeds.Detailed analyses related to the effect of wind and train speeds on the aerodynamic coefficients were conducted.The relationship between the change in aerodynamic coefficients and yaw angle was finally described by a series of proposed fitting formulas.