Diaphragm Spacing Research Articles

Compressive behavior of an innovative double-steel-plate composite shear wall with iron tailings and recycled aggregate concrete

In this paper, a double-steel-plate composite shear wall filled with iron tailings and recycled aggregate concrete (ITRAC-CSW) is proposed. It was assembled from Z-profiled steel units with shear studs welded to the inside of the flanges. Iron tailings and recycled aggregate concrete (ITRAC) consists of recycled aggregate concrete (RAC) and iron tailings sand (ITS). All aggregates of ITRAC are 100 % solid waste. Five full-scale ITRAC-CSWs were fabricated and tested to investigate the axial compression performance. The parameters are whether to arrange shear studs, different inner diaphragm spacing, and the different height-to-thickness. The investigation revealed that setting shear studs increased the axial bearing capacity by 7 % and its initial stiffness by 29 %. Increasing the inner diaphragm spacing reduces the axial bearing capacity, initial stiffness, and ductility by approximately 5 %. Elevating the height-to-thickness significantly enhanced initial stiffness and ductility with minimal impact on bearing capacity. The finite element model of ITRAC-CSW was developed and verified considering the initial defects and material nonlinearities. Based on finite element model, the stress states of ITRAC-CSW core concrete and shear studs are analyzed. Finally, the axial bearing capacity theoretical calculation method of ITRAC-CSW was established based on the five-parameter damage principle of concrete and the post-buckling strength of steel plate. The ratio of the calculated axial bearing capacity to the tested axial bearing capacity is between 0.94 and 1.00.

Study on Fatigue Cracking of Diaphragm's Arc Opening of OSD in Steel Bridges by Using Biaxial Stress Method.

Changes in loading position have a significant impact on the stress field of each vulnerable area of an orthotropic steel deck (OSD). The arc opening area of the diaphragm and the connecting area between the U-rib and the diaphragm under the moving load are prone to fatigue cracking. By comparing the stress responses under different methods, the hot spot stress (HSS) method is used as the main stress extraction method in fatigue performance evaluation. The control stress of fatigue cracking was analyzed by comparing the direction of the principal stress field with the crack direction in this experiment. According to the stress amplitude deviation under the biaxial stress state, a set of methods for evaluating the effects of in-plane biaxial fatigue was developed. An improved luffing fatigue assessment S-N curve was applied to analyze the fatigue life of the diaphragm's arc opening area. The results show that when the moving load is exactly above the connection of the deck and the web of the U-rib on one side, it is in the most unfavorable position in the transverse direction, and the diaphragm is mainly under the in-plane stress state. The longitudinal range of the stress influence line of the arc opening is approximately twice the diaphragm spacing. Two to three stress cycles are caused by one fatigue load. Fatigue crack control stress is the principal stress tangential to the arc opening's edge in this area. The normal direction of the principal stress in the model test is roughly consistent with the crack initiation direction. The variation in the stress amplitude deviation in this area is caused by changes in the action position of the moving load. When the moving load is at a certain distance from the involved diaphragm, it is reduced to zero, implying that the in-plane fatigue effect is the greatest in this area.

Improved design of intermediate diaphragm spacing in horizontally curved steel box bridges

Eccentric live loading acting on the steel box girders induces cross-sectional distortion in the steel box sections. In particular, the distortional behavior in horizontally curved steel box bridges can be significant compared to that in straight ones; the reason is that the curvature effects of horizontally curved steel box bridges can provide additional distortional behavior due to gravity and live loads even without eccentricity of the applied loadings for every construction sequence (self-weight for non-composite and live loads for composite box sections). Therefore, to control the distortional warping normal stresses induced by the distortional behavior, it is necessary to install intermediate diaphragms in the box sections for straight and horizontally curved box bridges. This study aimed to estimate, using three-dimensional finite element analysis (FEA), the distortional bi-moments and stresses of single-cell horizontally curved rectangular steel box girder bridges with a single span, and to provide an improved design methodology to determine adequate intermediate diaphragm spacing in straight and horizontally curved steel box bridges considering various construction phases. Based on the parametric study, we considered not only various design parameters, such as design live loads, magnitude of the torsional moment, span length, spacing of intermediate diaphragms, subtended angle, and various normal stress ratios but also construction sequences with various loading conditions. Finally, the required intermediate diaphragm spacing for straight and horizontally curved steel box bridges were proposed.

Coupled bending-torsion behaviour of single-box multi-cell curved composite box-girders with corrugated-steel-webs

Due to initial curvature, curved composite box-girder with corrugated steel webs (CCBG-CSWs) exhibits complex behaviour. This study develops an analytical solution for describing coupled bending-torsion behaviour of CCBG-CSWs with arbitrary single-box multi-cell cross-section in elastic stage under arbitrary loads. First, governing differential equations are deduced with energy-variational principle and solved by Galerkin-method. Next, experimental studies and finite element analysis are performed, which validates the analytical solution. It also identifies governing parameters. Discussion of analytical solution's calculated items shows steel webs' shear deformation has significant effects on flexural deflection, but no effects on torsional angle and normal stress at section corner. The additional restrained torsion has little impact on flexural deflection and torsional angle while non-negligible influence on normal stress. Shear lag effect of flanges has larger effects on the normal stress than that of on the flexural deflection and torsional angle. Furthermore, parametric study presents span-radius ratio and bending-torsion stiffness ratio have substantial impacts on bending-torsion behaviour. The corrugated steel web thickness and the eccentricity between torsional centre and centroid have relatively less effects. Diaphragm spacing effects are the least. The study may provide new insights to understand the coupled bending-torsion behaviour of CCBG-CSWs and finally guide better design.

Experimental investigation and design optimization on flexural behavior of new UHPC deck panel with longitudinal ribs reinforced by steel plates

Due to high strength and superior durability, ultra-high performance concrete (UHPC) is usually used in bridge deck panels to reduce self-weight and improve the anti-cracking capacity. In this study, two schemes of the UHPC deck panel with longitudinal ribs reinforced by steel plates were investigated basing on the Binzhou Yellow River Bridge, including the design considerations and advantages. The experiments were conducted to investigate the flexural behavior of this UHPC deck panel. The experimental results showed that the steel plate can improve the anti-cracking performance and stiffness of the deck more effectively compared to conventional measures of using steel bars. Cracks developed at the position where headed studs were placed due to the weakening of cross-section by high studs. Specimens failed with the appearance of the slightly compressive crack. In addition, the experimental test was simulated by finite element (FE) model in software ABAQUS. The cracking position, load-displacement relationship and strain response of testing specimens were verified by the FE model. For the design purpose, a numerical method was established to analyze flexural behavior including the stiffness, ultimate capacity and strain. The prediction results agreed well with the test results. Further, a parameter analysis was performed and it was clear that the narrow and high rib scheme provided superior flexural properties. Compared with UHPC tensile strength, the steel plate thickness had a more significant effect on the stiffness and ultimate capacity for the specimens. Finally, the segmental FE models were developed for the Binzhou Yellow River Bridge to obtain the actual stress state of the new UHPC deck. The calculation results indicated that the maximum longitudinal nominal stress in the UHPC deck was 7.6 MPa. In addition, when the diaphragm spacing was between 3.0 m and 5.0 m, the longitudinal stress would increase by about 12% with the diaphragm spacing increasing by 0.5 m. The comparisons between the actual stress and experimental results ensured the feasibility of the design.

Multi-tube energy-absorbing structures with different matching patterns of heights and diaphragm spacings

There are defects including peak stacking and large load fluctuations in existing multi-tube combined structures. To overcome these defects, a differentiated combination design based on the idea of peak load dislocation superposition is undertaken for the height configuration and diaphragm spacing configuration of each tube. The influence of time to peak load is revealed by combining experiment, theory, and simulation. The results show that the height difference only induces a difference in the time to initial peak loads of tubes, while the subsequent peak loads remain stacked, which cannot reduce the load fluctuations. The variations of the diaphragm spacing can prolong or shorten the duration of deformation of folds in a designated area, thus changing the formation timings of subsequent peak loads, which is a feasible method for controlling the time to formation of the peaks. By optimally setting heights and distributing diaphragm spacings of tubes, peak loads of multi-tube structures can be fully separated, thus reducing the initial peak and load fluctuations. The initial peak load and the fluctuations of the 6-4GT-ΔJ-ΔH 2-Adj combined tube constructed based on the configuration differentiated design idea are reduced by 45.33% and 76.62% respectively, while maintaining the high energy absorption of the system.

Effect of cross-sectional rigidity on intermediate diaphragm spacing of steel-box girder bridges

To control the distortion of box girder bridges and minimize the distortional stresses due to the torsional behavior when eccentric live loads are applied, it is necessary to install intermediate diaphragms in the box sections in the design of box girder bridges. This study estimated the distortional bi-moments and stresses of single-span rectangular steel box girder bridges by conducting a three-dimensional finite element analysis (FEA) considering various cross-sectional rigidities of the box girder sections. Based on the FEA, improved design equations for determining the distortional stresses and the appropriate intermediate diaphragm spacing were established considering various design parameters, such as cross-sectional rigidity, live load combination, normal stress ratios, and magnitude of the torsional moment. Finally, design recommendations were presented for the intermediate diaphragm spacing based on various design parameters.

Effect of Load Combinations on Distortional Behaviors of Simple-Span Steel Box Girder Bridges

When eccentric live loads are applied on the deck overhang of steel-box girder bridges, torsional moments, comprising pure torsional and distortional moments are generated on the box sections. The torsional moment on the bridge girders distorts the box girder cross-sections, inducing additional normal stress components and causing instability of the box girder sections in severe cases. Hence, it is essential to install intermediate diaphragms in the box sections to minimize distortional behaviors. Although the applied live loads are critical parameters that influence intermediate diaphragm spacings, the effects of live load combinations have rarely been addressed in the design of intermediate diaphragm spacings. Thus, load combinations should be evaluated to design the intermediate diaphragm spacing of the box girder bridges more thoroughly. In this study, the load combination effects on the distortional behavior and adequate intermediate diaphragm spacing were evaluated through a finite element analysis (FEA). Composite rectangular box girder bridges with different cross-sectional aspect ratios (H/B) and spans (L) were analyzed in the parametric study. It was found that the truck load, which represents the concentrated load, significantly influences the distortional warping normal stress, normal stress ratio, and intermediate diaphragm spacing. In addition, the FEA results showed that the controlling load combinations could be varied with the span.

Mechanical Performance Analysis and Parametric Study of a Self-Anchored Suspension Bridge with Ultra-Wide Double-Sided Steel Box Girder

A sufficient understanding of mechanical performance of self-anchored suspension bridge with double-sided steel box girder is essential for design and normal use as such bridges are widely built in urban bridge. Using the Yunlongwan Bridge which is a suspension bridge with ultra-wide double-sided steel box girder as an example, this paper investigates its deformation and mechanical performance under vehicle load. Firstly, based on the field test results, the deformation performance of the bridge and the stress distribution of the main girder are analysed, with emphasis on the shear lag effect of double-sided steel box girder. Then, a multiscale model of the bridge was built, and the accuracy of the model was verified by comparison with the test data. Finally, the influence of design parameters on the mechanical behaviour of double-sided steel box girder is studied by numerical simulation. The results show that the deformation of the bridge has good symmetry, there is obvious shear lag effect on the main girder, and the U-rib thickness, diaphragm spacing, and vehicle load could significantly affect the stress of the main girder top plate. The obtained analytical results lead to a better understanding of the mechanical performance and provide reference for the design of self-anchored suspension bridge with double-sided steel box girder.

Intermediate diaphragm spacing for single-cell rectangular steel box girder bridges considering aspect-ratio

Eccentric vertical loads acting on bridge girders induce distortion of the cross-section of the steel box girder, which causes distortional warping normal stress at the flange and web of the box section in a longitudinal direction. Recent design standards specify that intermediate diaphragms, which prevent deformation of the box section, need to be installed to control these distortional warping normal stresses. In addition, the maximum ratio requirements between distortional warping normal stress and bending normal stress should not exceed 5 and 10%, respectively. However, the design standards do not provide specific formulae for use in determining the appropriate intermediate diaphragm spacing; therefore, an accurate structural analysis is required from the design stage and the iterative structural analysis time-consuming. In this study, to simplify the structural analysis steps required in the design phase, a parametric study was conducted using 3D finite element analysis (FEA) to estimate the intermediate diaphragm spacing required for composite simple span single-cell box girder bridges. In the parametric study, the box girder bridges were modeled using actual bridge data relating to the cross-sectional aspect ratio, span length, and flange thickness. The FEA results show that the coupling effects of the cross-sectional aspect ratio, the ratio of the distortional warping constant to the moment of inertia, span length, and eccentricity, have a significant effect on the diaphragm spacing and normal stress ratio. Based on these FEA results, efficient intermediate diaphragm spacing was determined in consideration of the cross-sectional aspect ratio, span length, and flange thickness.

Fatigue cracking investigation on diaphragm cutout in a self-anchored suspension bridge with orthotropic steel deck

To investigate the mechanism of base-metal cracking on diaphragm cutout in a self-anchored suspension bridge with orthotropic steel deck (OSD), multi-scale finite element models were established to obtain stress response at cutout detail under the passage of wheel loads. Fatigue life was evaluated based on nominal stress method and hot-spot stress method. The results indicated that the length of the longitudinal influence line for detail stress to wheel loads approximately equalled to twice the diaphragm spacing. The wheel loading location of maximum stress was the front wheel of middle-axle group 0.3 m from the diaphragm, and the stress was dominated by in-plane stress. The nominal stress was hard to define at cutout detail for high stress concentration, and the hot-spot stress was preferred to fatigue assessment based on S-N curve of FAT125, also nominal stress should be extracted at the location 5.0 mm from cutout edge. Cutout shape of Highway Bridge in Eurocode was suggested, and diaphragm thickness should not be below 12 mm. The cutout cracking was caused by poor cutout shape, thin diaphragm, high truck traffic volume and overloaded wheel loads, while undesirable fabrication control and large residual stress might also contribute to the cracking.

Distortion analysis of non-prismatic composite box girders with corrugated steel webs

In this study, the distortion effect of non-prismatic composite box girders with corrugated steel webs (CBGCSWs) is theoretically analysed under eccentric loads during the elastic stage. Considering the mechanical properties of corrugated steel web, a governing differential equation for distortion is derived for non-prismatic CBGCSWs. The differential equation is solved using the Newmark method to obtain the distortional warping normal stresses of angular points. The feasibility of the proposed theoretical method is validated by the finite element (FE) method. The proposed method is then applied to examine the effects of the number of diaphragms (N), girder length (L), girder width (b), shortest girder height (hmin) and girder height ratio (ξ) on the maximum ratio of distortional warping normal stress to longitudinal bending normal stress (distortion-to-bending stress ratio, ζ) of non-prismatic CBGCSWs. Based on the results of the parametric study, a diaphragm spacing equation is developed for determining the diaphragm spacing of non-prismatic CBGCSW bridges to reach the desired distortion-to-bending stress ratio. The presented equation can be further used as a reference to design the diaphragm spacing of this type of bridge.

Effect of Inconsistent Diaphragms on Exterior Girder Rotation During Overhang Deck Construction

The construction of bridge deck overhangs results in unbalanced eccentric loads acting on exterior girders which can cause rotation and increased stresses not accounted for during design. Permanent diaphragms and temporary bracing in bridge exterior girder lines or panels are used to resist these loads and subsequent transverse rotation of the exterior girders. The addition of extra diaphragms in the exterior panels is one potential alternative to temporary bracing which is not always effective. In this paper, a unique steel plate girder bridge in the state of Illinois with extra diaphragms in one exterior bay was instrumented with tilt sensors and strain gages to monitor transverse rotations and strains due to unbalanced loads occurring during construction. Two types of rotations were recorded; maximum and residual rotations. The extra diaphragms were included in the design of this bridge on only one side of the bridge to carry utility lines. The full bridge was modeled using the commercial finite element analysis software ABAQUS and the model was validated using field data. As expected, diaphragm spacing was found to have a high impact on exterior girder rotations that occur during bridge deck construction. The maximum obtained finite element rotation was 0.47° which occurred at mid span and on the bridge deck side that does not have extra diaphragms. Field residual rotations were found higher (approximate 50% on average) than rotation determined from the finite element analysis. These extra stable rotations were seen in the exterior girders and was a result of permanent deformation occurring when the finishing screed passed by the section under consideration.

Intermediate Diaphragm and Temporary Bracing Practice for Precast Concrete Girder Bridges

AbstractIntermediate diaphragms are used in precast concrete girder bridges for three primary reasons: (1) to prevent torsional girder rotations during girder erection and deck placement operations, (2) to increase vertical load distribution between girders, and (3) to transfer and spread horizontal impact loads from an overheight vehicle to adjacent girders. Significant variation currently exists in intermediate diaphragm specifications between states. The importance of bracing girders after erection and during construction is widely accepted as essential. Although it is clear that intermediate diaphragms have some effect on bridge performance, the benefit is considered by some to be negligible. Increasing numbers of states have adopted permanent steel or temporary intermediate diaphragm alternatives in place of traditional cast-in-place concrete. Wide variations are found between states regarding the configuration, spacing, and transverse alignment of diaphragms. This article presents a detailed survey ...

곡선 강박스 거더의 휨-뒤틀림 응력비에 따른 중간 다이아프램 간격

Although distortions of horizontally curved box girder are more susceptible than which of the straight girder due to curvature effect, current domestic design standards does not present spacing of intermediate diaphragms for the curved box girder. In this study, parametric studies for straight and curved box girder considering distortional warping normal stresses based on linear finite element analysis were carried out. Single span curved girders were chosen for analysis based on current domestic bridge data with 1-6 of solid intermediate diaphragms, 0-30 degree of subtended angle, 30m and 60m of span length and 2-3m of flange width and web height. The adequate spacing of diaphragms for the box girder were suggested considering subtended angles and bending and distortional warping normal stress ratios with 5%, 10%, 15% and 20%. The analysis results were also compared to a current design standard and suggested spacing of diaphragm were evaluated.

Torsional behaviour of curved composite beams in construction stage and diaphragm effects

During the concrete-casting process of curved steel–concrete composite beams in construction stage, all loads including the wet concrete weight are carried by the curved open thin-walled steel girder. In order to determine the required diaphragm spacing, firstly the curved girder is simplified to straight one by using the M/r method, and its torsional behaviour is subsequently derived by solving the restrained torsional differential equation with the initial parameter method, where the discrete diaphragms are treated to be equivalent to a continuous elastic thin plate. Taking the maximum stress ratio of the warping normal stress to the bending normal stress as the control index, effects of the number of diaphragms, the span of the curved girder, the span-to-radius ratio, the girder height and the flange width on the stress ratio are studied. The parametric analysis results indicate that with the increase of the number of diaphragms, the stress ratio decreases exponentially; and with the increase of the span-to-radius ratio, the warping stress ratio increases linearly; additionally, longer span leads to reduced stress ratios, but the variation of the girder height and the flange width has little influence on the stress ratio. Calculation formulae for determining the required diaphragm spacing are obtained eventually by regression analyses. Based on the research outcomes herein, given the limit value of the warping stress ratio in the practical design of curved composite beams under construction, the maximum diaphragm spacing of the open thin-walled steel girder can be determined by using the formulae proposed in this paper.

Effects of overheight truck impacts on intermediate diaphragms in prestressed concrete bridge girders

This paper studies the capacity of prestressed concrete bridge girders to withstand overheight truck impacts. The numerical model of the bridge was validated with the existing experimental data in the literature. The elastic-plastic modeling of concrete damage and quasi-static impact simulation of the bridge were considered. Parametric studies were then conducted with respect to the spacing and depth of intermediate diaphragms as well as girder types from which the role of intermediate diaphragms in protection and enhancement of prestressed concrete bridge girders from truck impacts is obtained. From the simulation results, it was concluded that the optimum spacing of intermediate diaphragms (that is, 25.0 ft [7.62 m]) is consistent with the results reported for previous studies. The depth of intermediate diaphragms should be extended to the top edge of the bottom flange of girders to provide maximum impact protection. Wide flanges in girders increase the bending stiffness and reduce the horizontal deflection and correspondingly decrease damage areas. However, deep webs in girders introduce a large rotation with respect to the deck, and thus increase the deflection under the truck impact. Design guidelines for typical parameters for intermediate diaphragms in prestressed concrete bridges are provided. The numerical finite-element parametric study provides a better understanding of placement and size of intermediate diaphragms in prestressed concrete bridges and their role in protecting girders from overheight truck impacts.

Spacing of intermediate diaphragms in horizontally curved steel box girder bridges

Horizontally curved box girder bridges inherently exhibit complex torsional and distortional behavior as well as bending due to the initial curvature. Distortional warping and transverse bending normal stresses, two major stress components resulting from distortion, are generally limited to a specific level for efficient use of the cross section by installing adequate intermediate diaphragms. The objectives of the present study are to develop a curved box beam finite element and to propose tentative design charts for adequate maximum spacing of intermediate diaphragms. The validity of the developed box beam element having nine degrees of freedom per node including two distortional degrees of freedom is verified from a series of thorough comparative studies using conventional shell element models. Extensive parametric studies using the box beam elements are performed and the design charts for the maximum spacing of the intermediate diaphragms are presented. Bridges taken into account are single-span, two-span, and three-span continuous horizontally curved box girder bridges. The design parameters considered are the central angle, the number of spans, the span length, the aspect ratio of the box section, the spacing of the intermediate diaphragms, and the desired ratio of the distortional warping normal stress to the bending normal stress. Unlike the current practice where the ratio of the distortional warping normal stress to the bending stress is fixed to a specific value, the proposed design charts facilitate the determination of the maximum spacing of intermediate diaphragm for various desired stress ratios.

A consideration on intermediate diaphragm spacing in steel box girder bridges with a doubly symmetric section

Diaphragms in box girder bridges are implemented primarily to prevent premature excessive distortional deformation under torsional loading condition. Distortional warping and transverse bending stresses, which are the major stress components resulting from distortion, should be appropriately limited to a specific level for efficient use of the cross-section by installing adequate intermediate diaphragms. The objectives of the present study are to develop a thin-walled box beam finite element and to propose tentative design charts for adequate spacing of intermediate diaphragms. The developed beam element possesses nine degrees of freedom per node and the validity was intensively verified from a series of comparative studies using a conventional shell element. Also, performed herein are extensive parametric studies for continuous box girder bridges of doubly symmetric steel box section. The design parameters taken into account were the desired ratio of the distortional warping normal stress to the bending normal stress, the number of spans, the span length, the aspect ratio of the box section, and the spacing of the intermediate diaphragms. The results were summarized into tentative design charts indicating efficient spacing of intermediate diaphragms for the various stress ratios.

Effects of Distortion on Strength of Curved I-Shaped Bridge Girders

The curved I-shaped plate girders used in bridges with curved alignment are subjected to forces that cause significant distortion of the cross section during construction and during application of live loads after the deck has hardened. Furthermore, the addition of curvature reduces the vertical bending stiffness, increases deflection nonlinearities, and changes stability characteristics of behavior. Although the design equations of the AASHTO Guide Specifications for Horizontally Curved Highway Bridges are formulated to address these behavioral issues, design and construction engineers often are not familiar with the difficulties curvature introduces and do not understand the relationship between distortion and deflection amplification with the design equations. Analytical research conducted as part of the FHWA Curved Steel Bridge Research Project was used to highlight and describe the effects of curvature on the strength and stability of curved I-girder bridge superstructures. Issues described include the following: ( a) effects of cross-frame and diaphragm spacing on system behavior, ( b) effects of curvature on the lateral-torsional stability of curved I-shaped beams, ( c) effects of warping stresses on flange buckling, ( d) effects of curvature on web behavior, and ( e) effects of curvature on initiation and propagation of yield stresses in the girders of curved I-girder frames.