Stress Evaluation for Segmental Concrete Box Girder Diaphragm

Engineering Structures, 2017

In this paper, the distortion of simply supported girders with inner diaphragms subjected to concentrated eccentric loads is investigated using initial parameter method (IPM), in which the in-plane shear deformation of diaphragms is fully considered. A statically indeterminate structure was modeled with inner redundant forces, where the interactions between the girder and diaphragms were indicated by a distortional moment. Considering the compatibility condition between the girder and diaphragms, solutions for the distortional angle, warping displacements and stresses were derived and further simplified by establishing a matrix equation system. The validity of IPM was intensively verified by a finite element analysis and distortional experiments. Parametric studies were then performed to examine the effect of the diaphragm number on the distortional angle, warping displacements and stresses under various ratios of height to span of the girder and the diaphragm thicknesses. Besides, stabilities of the local web plate and mid-span diaphragm were analyzed based on IPM for box girders with symmetrical three inner diaphragms. Results show that the local web plate will buckle before overall yielding with the increment of the eccentric loads Pj, and the mid-span diaphragm is constantly stable in the whole deformation process. It shows that more attentions should be paid on the stability of the local web plate than overall yielding for girders subjected to eccentric loads. Keywords: simply supported girder; diaphragm; eccentric load; shear deformation; distortion; initial parameter method; finite element analysis; experiment; local stability the local plate, but also the resistance to the warping deformations and stresses [2,3,4]. Researches on the distortion of girders with inner diaphragms have been performed for many decades. The distortion of box girder was initially studied by Dabrowski [5] who first formulated the distortion of box girders with a symmetrical cross section. Li [6,7] proposed that the shear strain of the cross section cannot be ignored when the distortional shear rigidity is significant compared to the distortional warping one for box girders. Wright [8] proposed the Beam on Elastic Foundation (BEF) analogy for the distortion of girders with inner diaphragms, where the diaphragms are analogous to inner supports. Based on BEF, Hsu [9,10] proposed the Equivalent Beam on Elastic Foundation (EBEF) analogy considering the shear strain of the cross section, and found that the EBEF analogy is more versatile than BEF due to its simplicity in analyzing more complex problems such as non-uniform sections and multi-span beams. Interactions between the girder and diaphragms is the key issue for the distortion of girders with inner diaphragms. A statically indeterminate structure [11] was modeled with redundant forces acting along the junctions between the girder and diaphragms. Moreover, the force method was applied to calculate redundant forces, where elements in the stiffness matrix were obtained from the finite strip method [12]. The numerical results were then extended to multi-span bridges [13] and long-span curved bridges [14]. An outstanding contribution was made by Suetake [15], where the girder was regarded as an assembly of thin plates, and the extended trigonometric series method (ETS) was applied to analyze the stresses and deformations for box girders. Comparisons with FEM results show that ETS has a high accuracy. However, it is inconvenient to apply since there are many simultaneous nonlinear equations to solve even for girders with few diaphragms, e.g. there are up to 720 equations for a girder with two diaphragms. The wall thickness of diaphragms and the number of diaphragms in a girder will make a significant influence on the displacements and stresses. Park [16,17] proposed a new beam element with nine degrees of freedom per node for girders. Studies showed that the distortional warping and transversal bending stresses were reduced by increasing the diaphragm number. Similar conclusions can be drawn for straight multi-cell box girders with diaphragms [18,19]. For horizontally curved bridges, the rational spacing between adjacent diaphragms was provided [20] according to the ratio between the distortional warping stress and the bending stress. Using FEM, Zhang [21] found that the rational number for diaphragms is 3 to 5 when the ratio of width to height of the cross section is 1.5 and the rational number is 9 when the ratio is 4.5. Li [22] proposed a new finite element solution, and found that the distortional warping stress for cantilever girders can be ignored when the spacing between adjacent diaphragms is less than one fifth of the span; while for simply supported and fixed girders, the spacing is less than one eighth of the span. Initial parameter method (IPM) was proposed first by Vlasov [23] to analyze the non-uniform torsion of beams. Analogous to IPM in non-uniform torsion, IPM can be extended to analyze distortions of girders. Considering the effect of shear strains of the cross section, Xu [24,25] developed an equation with the variable distortional angle, and established two categories of IPMs of the fourth order, classified by the ratio of the distortional stiffness. Harashima [26] proposed a distortional equation with a distortional warping function, and established the fifth-order IPM. Both IPMs in distortion have a high efficiency compared with FEM. However, IPMs has not been extended into the distortion for girders with inner diaphragms. For distortions of a girder with inner diaphragms, an assumption of infinite-rigidity diaphragm was generally made in most studies [16, 20, 27], where the in-plane deformation of diaphragms was totally restrained and warping was free. Similar assumptions can be found in 86 distortion of curved box beams [28], where the distortional angle at the location of diaphragms is 87 set as zero. However, the infinite-rigidity assumption is just an approximation, which is not 88 applicable to thin flexible diaphragms. The main objective of this work is to investigate the 89 distortion of simply supported girders with inner flexible diaphragms under concentrated eccentric 90 loads, where the in-plane shear deformation of diaphragms is fully considered. Interactions 91 between the girder and diaphragms are indicated by a distortional moment. Based on the 92 compatibility condition between the girder and diaphragms, solutions for both the distortional 93 angle and warping function are obtained from the IPM. Taking a simply supported girder with 2, 5 94 and 9 diaphragms, respectively, as an example, the distortional solutions from IPM were obtained, 95 then verified by a FE analysis and experiments. This was followed by a parametric study, in which 96 distortional deformations and stresses were investigated in terms of the diaphragm number and 97 thickness and the height to span ratio of the girder. Based on the proposed IPM, stabilities of both 98 the local web plate and mid-span diaphragm were examined for girders with three symmetrical 99 inner diaphragms. A series of curves were obtained for the relations between the critical buckling load and the position of diaphragms under various height to width ratios of the cross section.

Advances in Structural Engineering, 2019

Toward estimating accurately the distortional response of box girders, in this article, distortion of steel box girders strengthened with intermediate solid diaphragms under eccentric loads is analyzed by employing the so-called initial parameter method. A new model of high-order statically indeterminate structure was established with three orthogonal redundant forces acting at the junction between the girder and diaphragms. Emphasis is put onto the interaction between the girder and diaphragms, where a hypothetical bi-moment B pi indicating all longitudinal redundant force components for diaphragm was proposed besides the moment Mpi for in-plane shear component. Simplified initial parameter method solutions for distortional angle and distortional warping stresses and displacements were derived based on the in-plane and out-of-plane compatibilities between the girder and diaphragms. Taking box girders with three and five intermediate diaphragms as an example, the proposed initial pa...

Engineering Structures, 2012

Research into the effect of local stress on the carrying capacity and optimum design of box girders was performed in this paper. A mathematical model of the girder was created for the purpose of defining the stress-strain state of local character. Mathematical dependence which defines the length of the influential zone in box girders was established. The segment length relevant for the analysis of local stress is functionally dependent on geometrical parameters of the girder cross section, area of action and size of load. The methodology carried out in this paper showed that the identification of local stress can be performed only on a segment of the girder. The procedure of calculation and experimental determination of the local stress state in carrying structures was thus considerably simplified, without reducing accuracy. The influential parameters were identified and the guidelines for optimum design of quadrilateral shape of the girder cross section were given from the aspect of local stress. The comparative analysis was used to establish, under the same conditions of global carrying capacity, a more favourable stress state in trapezoidal shape in comparison with the traditional rectangular cross section of the girder. Application of the results of this paper is a contribution to the process of optimal design of supporting structures, especially those that are used for construction of transport equipment and rack structures in storage systems, where the effect of reducing the weight affects on the efficiency of transport in supply chains.

PolyTechnic, 2019

Post-tensioning tendons in segmental box girder bridges are usually anchored in very massive diaphragms. This paper presents an analytical investigation of the anchorage zone stresses for an interior pier diaphragm and a rectangular block model (model of diaphragm anchorage zone). The failure load and load-displacement relation for the two cases were compared, a typical diaphragm for a segmental box girder bridge with external prestressing tendons and rectangular block model were analyzed by finite element program (ABAQUS). The anchorage devices were subjected to a prestressing design load which was based on the ultimate strength of the tendons. The magnitude and distribution of stresses were plotted through different paths for both the diaphragm and the block model; also the contours of stress distribution for the diaphragm and block model were compared. The results showed that the stresses and failure load for the diaphragm and rectangular block model were very close.

Journal of the Computational Structural Engineering Institute of Korea

The study presents a three-dimensional approach to simulate the nonlinear behavior of a 72 m long Ultra High Performance Fiber Reinforced Concrete (UHPFRC) pre-stressed box girder for a pedestrian bridge in Busan, South Korea. The concrete damage plasticity (CDP) model is adopted to model the non-linear behavior of the UHPFRC material, in which the material properties are obtained from uniaxial compressive and tensile tests. The simulation model based on the proposed stress-strain curve is validated by the results of four-point bending model tests of a 50 m UHPFRC pre-stressed box girder. The results from the simulation models agree with the experimental observations and predict the flexural behavior of the 50 m UHPFRC pre-stressed box girder accurately. Afterward, the validated model is utilized to investigate the flexural behavior of the 72 m UHPFRC pre-stressed box girder. Here, the load-deflection curve, stress status of the girder at various load levels, and connection details is analyzed. The load-deflection curve is also compared with design load to demonstrate the great benefit of the slender UHPFRC box girder. The obtained results demonstrate the applicability of the nonlinear finite element method as an appropriate option to analyze the flexural behavior of pre-stressed long-span girders.

The objective of this study is to analyze the temperature and shrinkage stresses of the mid-span cross-section of a 20 meters box girder to find the reasons which cause the longitudinal cracks in the web and bottom of box girder. According to the results of damage inspeation, there are many longitudinal cracks in the web and bottom slab of box girders, especially the web of the edger beam, the crack is very clear. Ansys ver.10 software is used to analyze two dimensional finite element model of a typical cross section of a real bridge to calculate the temperature stresses caused by temperature difference between inside and out side of the box and the shrinkage stresses based on moisture diffusion. The results of analysis show that the outer surface of the web and bottom slab of the fabricated box girder will produce tensile stress at the effect of negative temperature difference. If the concrete reaches a certain age, the tensile stress does not cause creaks in the cross-section. The shrinkage stress changes with the moisture gradient in the box section. It will reach the maximum in 15 days and then decreases with the growth of the age. Shrinkage stress may cause cracking of the concrete surface because of the tensile strength is low in the early age.

The horizontally curved bridges are becoming the norm of highway interchanges and urban expressways as a result of complicated geometrics, limited rights of way, and traffic mitigation. This type of superstructure has gained popularity because it addresses the needs of transportation engineering. A study of box girder curved in plan with rectangular cross-section has been carried out in the present investigation. The finite element software ABAQUS is used to carryout analysis of these box girders. The analysis is carried out for the dead load, super imposed dead load and live load of IRC Class A loading. The paper presents a parametric study of curved box girders by varying span and radius of curvature and by keeping the span to depth ratio constant. The parametric investigations performed on curved box girders helps to evaluate the effects of different parameters on the behavior of the girder. This study would enable bridge engineers to better understand the behavior of curved concrete box girders.

Thin-Walled Structures, 2017

In this paper, the distortion of cantilever box girders with inner flexible thin diaphragms is investigated under concentrated eccentric loads using initial parameter method (IPM), in which the in-plane shear strain of diaphragms is fully considered. A high-order statically indeterminate structure was established with redundant forces, where the interactions between the girder and diaphragms were indicated by a uniform distortional moment. Based on the compatibility condition between the girder and diaphragms, solutions for the distortional angle and the warping function were obtained by using IPM. The accuracy of IPM was well verified by finite element analysis for the distortion of cantilever box girders with 2, 5 and 9 diaphragms under three diaphragm thicknesses. Taking a lifting mechanism as an example, parametric studies were then performed to examine the effects of the diaphragm number and thickness, the ratio of height to span of the girder, the hook's location and the wheels' positions on the distortion of cantilever box girders. Numerical results were summarized into a series of curves indicating the distribution of distortional warping stresses and displacements for various cross sections and loading cases.

IRJET, 2021

A bridges are the backbone of our nation from where we divert the traffic easily and many types of bridges are constructed now a days, as traffic problems are increasing day by day ,to control the traffic we need to underpass and overpass the traffic and control the traffic in areas through bridges, and box girders are the elements which are used in various kinds of bridges, box girder type bridges are gaining popularity in bridge engineering fraternity because of its better stability, serviceability, economy, aesthetic appearance, structural efficiency and rigidity in torsion. In this study, two different box girders bridge cross sections, rectangular and trapezoidal, are analyzed, designed and compared. The purpose of this study is to find out the efficient cross-section of box Girder Bridge. A comparative study is done on concrete two cell and three cell rectangular and two and three cells trapezoidal box girder using SAP2000 software. for three cell and two cell rectangular and trapezoidal girders the various parameters like torsion, bending moment , shear force, deflection, about different axis, and modal frequencies of entire girder span is studied. It is observed from the study that two cell box girders are more effective than three cell girders as rectangular and trapezoidal. the shear force and moment of three cell rectangular and trapezoidal girders is more than two cell rectangular and trapezoidal girders and the two cell rectangular and trapezoidal box girders have less frequency and stiffness than three cell rectangular and trapezoidal box girders

Journal of Constructional Steel Research, 1982

Abstract The results of two large-scale tests on stiffened load bearing box-girder diaphragms which were designed to collapse in different modes are described in detail. A comparison is made between the experimental behaviour up to collapse and that predicted by a recently developed large-deflection elasto-plastic finite element analysis. It is shown that it is now possible to predict accurately the complex interaction between stiffeners and plate panels in such a diaphragm. Attention is drawn to the important effect the stiffness of the flanges and webs of the box has on the overall response and ultimate load of the diaphragm. It is concluded that the powerful computer programs which are now available have been validated by test results and provide suitable bases on which sound design rules may be formulated. Comments on the new British design rules for diaphragms are made in the light of the results of this study.