End Diaphragms Research Articles

Shake Table Testing of Bidirectional Ductile Diagraphs with Buckling‐Restrained Braces in V-shaped configuration

The Bidirectional Ductile Diaphragm concept relies on Buckling Restrained Braces (BRBs) used at ends of spans in common multi‐span bridges to provide seismic resilient damage‐free bridges at low cost, while minimizing displacement demands to levels that can be easily accommodated by conventional expansions joints. This paper reports on the results of a shake-table testing program of Bidirectional Ductile Diaphragms designed with Buckling Restrained Braces (BRBs) deployed in a V-shaped layout. A single span taken from a scaled straight bridge with no skew, simply supported on slider bearings, and BRBs end connection details was subjected to: (1) earthquakes scaled to match the design level; (2) BRB deformation demands corresponding to 75 years of cycles of bridge thermal expansions, and: (3) earthquake scaled to levels exceeding the design level such as to bring the BRB to fracture upon repeated cycles of large inelastic deformations at extreme ductility demands. Results demonstrate that bridges using the bidirectional ductile end diaphragm concept with BRBs in a V-shaped configuration can develop a stable hysteretic response, with inelastic deformations concentrated in the BRBs. These bridges would experience no loss of functionality following an earthquake, resulting in fully resilient bridges that remain in service throughout and after the earthquake.

Fast analysis and prediction approach for geometrically nonlinear bending analysis of plates and shells using artificial neural networks

For the first time, this paper introduces a Fast Analysis and Prediction (FAP) approach for geometrically nonlinear bending analysis of plates and shells. The proposed approach consists of two phases: fast analysis and prediction using artificial neural networks (ANNs) combined with the Bayesian regularization algorithm. In the first phase (fast analysis), geometrically nonlinear bending analysis of a structure is performed using only several load steps. This enables the efficient computation within a short period of time. In the second phase (prediction using ANNs), the deflections obtained in the first phase are utilized as the data for training the ANNs. The trained networks are then used to quickly predict deflections at any load step. The calculation process in the second phase is also very fast. For the analysis package in the first phase, the formulation of this paper is originated from the literature for geometrically nonlinear analysis of composite shells. High accuracy and efficiency of the FAP approach were demonstrated via solving nonlinear bending problems of plates and shells including an isotropic square plate, a composite cylinder subjected to internal pressure, a FG-CNTRC panel and a pinched cylinder with end diaphragms. The proposed approach offers significantly computational savings (up to 70%) compared to the conventional one. ANNs combined with the Bayesian regularization algorithm, which are proposed for the FAP approach in this work, possess the outstanding advantages compared to many existing neural networks. The FAP approach can be applied to simulations, observations, or experiments where nonlinear responses are present or data is limited. Applying the FAP approach to such areas can significantly save labor, time, and money.

Optimization methods for the distortion of thin-walled box girders and investigation of distortion effects

To investigate the distortion process of thin-walled box girders, three commonly used methods based on energy variational calculus and static balance analysis are optimized. A generalized analytical formula for box-girder distortion research is derived, and a fourth-order distortion control differential equation is obtained. Typical numerical examples are used to verify and compare the three methods. The results show that the value of distortional warping normal stress calculated by the optimized methods is slightly different from the literature values and that the maximum error between methods does not exceed 5.39%. The calculation results of Method 2 and Method 3 are similar. The values of the geometric distortion characteristics calculated by the three methods are related to the cross-sectional form of the box girder and the distortion analysis process, and the calculated values are not unique. The absolute value of the peak normal stress of distortion on the top plate of a thin-walled box girder with a cantilever plate is smaller than that on the bottom plate. Under a concentrated distortion load, the distribution of the distortion deformation along the length of a simply supported box girder with only end diaphragm is not consistent, and there is reverse deformation near the beam end.

End diaphragm and interior cross frame modeling in steel tub girder superstructures

Composite steel tub girders are proven to be an economical choice for long span bridges. However, detailed analysis of such superstructures requires extensive Finite Element (FE) modeling that includes many internal and external diaphragms. This paper is an attempt to study diaphragms and interior cross frames in tub girders and present simplified FE modeling details for the tub girder superstructures under gravity and seismic loadings incorporating accurate end diaphragm and interior cross frame stiffness equations. The simplified model is applicable to design of new tub girder bridges as well as load rating, health monitoring and retrofitting of existing bridges which require more sophisticated models. To this end, first a parametric study using 18 different FE models was carried out to better understand the behavior of tub girder superstructure and its components such as end diaphragms, the composite concrete deck and interior cross frames. Second, the stiffness equations for the end diaphragms and interior cross frames were derived analytically. These were associated with equivalent beam elements, which were used in combination with girder/deck elements to arrive at the simplified model. The resultant FE modeling was validated against detailed 3D FE models under gravity and seismic loads as well as the fundamental modes of vibration. Results indicated that the modeling approach is able to efficiently simulate different component behaviors and estimate the static and dynamic demands on the girders with remarkable accuracy.

Environment-Induced Performance of End Concrete Diaphragm in Skewed Semi-Integral Bridges

Past research has shown that as skewed bridges change temperature, additional lateral movement or forces will occur along with the elongation of the bridge. Even though past research has documented this behavior, lateral movements of semi-integral bridge superstructure associated with temperature effects on bridge skewness have not been well predicted. In this study, the seasonal movements of a 24-year-old semi-integral bridge caused by temperature effects with skewed abutment have been investigated by conducting a series of field measurements on bridges subjected to various environmental climates. The measured data showed that as the bridge heated up, the superstructure tended to move toward the acute corner of the bridge, and the bridge would contract towards its obtuse corner with a negative temperature change. During warm weather, the cracks on the end diaphragm tended to open with a positive temperature change and close with a negative temperature change, which was much more predictable than the cold weather behavior. This behavior confirms that even though the bridge moves linearly with temperature, the end diaphragm response to the temperature depends on the season. Movement of the bridge superstructure from temperature change has caused cracks in the end diaphragm, which are now propagating to the deck. These cracks could damage the bridge enough that it would require repair work in the future. The evidence in this study will help provide a complete picture of seasonal jointless bridge behavior so future semi-integral bridges can be made safer and more efficient.

Seismic response of regular multi-span bridges having buckling-restrained braces in their longitudinal direction

Buckling Restrained Braces (BRBs) have been used widely in building seismic resisting systems, and have much potential for applications in bridges. One such application is in ductile end diaphragms, a design concept that aims to protect bridge substructures and limit displacement demands by the use of fuse elements, and that can achieve these goals using BRBs. Here, regular, straight, simply-supported, multi-span bridges with BRBs in bidirectional ductile end diaphragms are studied in the longitudinal direction to better understand the behavior of such bridges and correspondingly provide design recommendations (to complement the existing AASHTO design provisions that already address response in the transverse direction for that structural system). Two different layouts of implementation were studied, and designed using the multimode spectral method to identify their respective benefits. A parametric study was conducted on the preferred configuration in which BRBs were used to connect spans to piers, using nonlinear response history analysis to understand the influence of pier stiffness, BRB yield displacement, target BRB ductility demand, and other factors on overall inelastic response. Overall, the use of BRBs was found to effectively limit the displacement demands in columns and expansion joint opening, achieving the structural fuse objective. These dynamic analyses allowed to understand the impact of many parameters on longitudinal response and behavior of the type of bridges considered, which led to a proposed design procedure for BRBs used in this configuration.

Parametric Study of the Intermediate External Bracing System of Composite Steel Box Girder Bridges

During the pouring of concrete deck, the installation of external bracing between the inner and outer girders may be necessary when the bridge has sharp curve in order to control the deflection and rotation of the girders. However, it is important to minimize the number of external bracing members, as they have expensive cost and they also have opposite effects for the fatigue features of the steel tub girders. The analysis of curved box girder bridges is carried out numerically by the use of finite element method through (ANSYS 19.2) software. The curved box girder with the intermediate external diaphragms was modeled and the analysis was carried out for many parameters like external bracing sections, girders with or without concrete deck, girders with end diaphragms or without them. The study concluded that ANSYS program has a good ability in evaluating the external bracing force comparing with code equations.

Sources, mitigation and implications of skew-related concrete deck cracks in girder bridges

Characteristic cracks in skewed bridges, detrimental to service performance, form in deck acute corners and run diagonally across deck span. This paper presents the relationship between skew and deck cracks, investigates crack mitigation strategies and documents changes in live load distribution caused by cracks. Finite element analyses of in-service steel and concrete girder bridges were performed and qualitatively validated. The analyses were used to study the influence of skew angle, deck reinforcement amount and orientation, end diaphragm and girder restraint on deck strains and on live load distribution for shear (i.e., live load distribution to girders as vertical shear forces) from cracked decks to girders. The results showed that high skew induces stresses high enough to cause typical diagonal deck cracking on skewed bridges due to deck shrinkage. Restraint provided by end diaphragms, particularly by full depth concrete diaphragms and diaphragms connected to deck, magnify deck stresses. Orienting transverse deck reinforcement perpendicular to bridge centreline is more effective than parallel to substructure. Larger deck reinforcement cross-sectional areas increased deck restraint and likelihood of cracking. Shear live load reaction in exterior girders of the bridges studied increased by 35% due to deck cracks, although it remained smaller than interior girder reaction.

The relationship between moisture content and shrinkage strain in the process of bamboo air seasoning and cracking

The industrial utilization of natural bamboo has been plagued by cracking that are closely related to the relationship between the moisture content (MC) and drying shrinkage. To reveal the cracking mechanism, three relationships between environmental factors and drying rate (DR), MC and shrinkage strain, strain variation and cracking were investigated during the air seasoning (AS) of the 6-meter-long bamboo in free state. The DR decreased significantly affected by hygroscopicity, and a model considering hygroscopicity and environmental factors was proposed for estimating the DR. Natural bamboos were prone to cracking between 42% and 12% MC. The top cracking was earlier and more than other parts, which is caused by initial lower MC and absence of end diaphragm. There were significant differences in shrinkage strain between different tissues and sites. This work reveals the drying characteristics, the law of strain variation, and cracking mechanism in bamboo AS process, which is vital to the prevention and control of drying defects.

Ductile steel plate external end diaphragms for steel tub girder straight highway bridges

The end diaphragm of bridges are normally designed to resist lateral seismic forces imposed on the superstructure in earthquake prone regions. Using ductile diaphragms with high deformation capacity could reduce the seismic demands on the substructure and prevent costly damage under strong ground motions. The end diaphragms of steel tub girder bridges with high lateral stiffness and dominant shear behavior have a potential to be used as ductile fuse elements. In this study, a steel plate shear diaphragm (SPSD) is introduced as an external end diaphragm of tub girder steel bridges to reduce the seismic demands imposed on the substructure. Quasi static nonlinear analyses were conducted to evaluate responses of sixteen SPSDs with different boundary conditions, aspect ratios and diaphragm plate thicknesses. Moreover, nonlinear time history analyses were performed using three different ground motions corresponding to DBE and MCE level spectrums. Cyclic and time history analyses proved the proper behavior of SPSD and its efficiency to reduce seismic demands by more than 25%.

Cracking of the End Diaphragm of a Post-tensioned Beam Bridge

Abstract In concrete beam bridges, the end diaphragm at the end of the bridge is a common structural component that connects the main beams and transfers the beam loads to the bridge bearings. In integral bridges the end diaphragm also retains the soil of embankments due to the absence of abutments. Cracking of the front surface on the end diaphragm has been detected in post-tensioned beam bridges in Finland and Sweden. Presumably the post-tensioning of the bridge and the shaping and detailing of the connection of the end diaphragm and main beam have an effect on cracking tendency. The aim of this study is to examine the structural behaviour and the cracking potential of end diaphragms using linear analysis of the post-tensioned bridge and to find measures to prevent the cracking. The observations collected through field surveys are compared to results of linear FE analysis to clarify the cause of the cracking. The verification of model is performed by comparison of patterns of cracking observed in field surveys and the distribution of maximum tensile stresses in the FE model. With model variations, the effectiveness of measures for the prevention of cracking are observed.

Numerical Investigation of Distribution Laws of Shear Force in Box Girder Webs

To study the shear force distribution laws of a box girder with a single-box multichamber (SB-MC) configuration for different supporting conditions, numbers of webs, stiffness of end diaphragm, and web thickness values, a box girder with SB-MC was numerically simulated using three-dimensional finite element model. According to the comparison results of web shear force, the concept of η, a shear-increased coefficient for webs, was introduced. The results show that supporting conditions and chambers have a significant impact on the shear-increased coefficient η, and end diaphragm must be set up in the 3D finite element model when calculating η. Nonlinear analysis shows that in the elastic phase, the shear-increased coefficient η basically does not change, but in the cracking stage, the coefficient η of each web changes with the degree of web cracking, and side-webs (S-Webs) reach the ultimate load first. The variation of the web thickness hardly affects the distribution of the shear force, so the method to adjust the web thickness of S-Web was proposed according to the result of shear-increased coefficient η to improve the shear resistance of the box girder.

Low-Cycle Fatigue of Buckling Restrained Braces in Bidirectional Ductile End Diaphragms Due to Temperature-Change Effect on Bridge Superstructure

Low-Cycle Fatigue of Buckling Restrained Braces in Bidirectional Ductile End Diaphragms Due to Temperature-Change Effect on Bridge Superstructure

Destructive testing and computer modeling of a scale prestressed concrete I-girder bridge

Currently, there is a limited amount of published information on failures of prestressed concrete bridges subjected to shear and moment. A scale prestressed concrete bridge was constructed to investigate the ultimate behavior of the bridge with particular focus on load distribution after cracking and on contribution of full-depth diaphragms to structural capacity. A point load was applied at the quarter-span point of the bridge over an interior girder. As the loaded girder failed, the diaphragm-girder connection cracked. Torsion was observed to cause cracking in the exterior girder and the end diaphragm rotated away from the bridge as the deck deformed. A punching shear failure ended the test, however damage indicative of two-way slab behavior was observed in the deck. This failure suggests that post girder failure, the diaphragms provide an important means of load transfer, allowing moment redistribution in the deck and potentially increasing capacity. Testing in the elastic range compared favorably with respect to deflections and shear distribution factors from a grillage model, a 2-D finite element model and a 3-D finite element model.

Ductile behavior of existing internal end diaphragms in steel tub girder bridges

In steel tub girder bridges, end diaphragms transmit vertical and lateral loads to the substructure. Vulnerable response of steel diaphragms in recent strong ground motions has encouraged the researchers to work on their application as seismic force reducing devices for design and retrofitting of bridges. This study is an attempt to achieve a ductile diaphragm behavior under seismic actions by using existing internal end plate diaphragm of steel tub girder bridges. Considerable elastic stiffness and dominant shear behavior of the end diaphragm has made it a suitable choice for such behavior under seismic actions. Nonlinear quasi-static analyses using nineteen different finite element models were conducted to evaluate the internal end diaphragm behavior with different configurations and boundary elements. Moreover, plastic analyses using tension strips theory were used to derive formulations for design base shear and tension field inclination of different models. The calculated values were in agreement with the results of finite element models. As a result, remarkable response modification factor was derived for the proposed ductile system. In addition, nonlinear time history analyses were used to prove the ductile behavior of the selected models under real moderate and strong ground motions.

Experimental Investigation of Buckling Restrained Braces for Bridge Bidirectional Ductile End Diaphragms

AbstractQuasi-static experiments were conducted to subject buckling restrained braces (BRBs) to a regime of relative end displacements demands to investigate if the BRBs’ end connections could be a...

Seismic retrofit of slab-on-girder steel bridges

Thin steel infill plate has been proposed in the past as a ductile end diaphragm to reduce the transverse seismic demand in slab-on-girder steel bridges. However, a simplified method is required to promote the use of steel infill plate end diaphragms as a retrofit strategy. In this paper, the retrofitting strategy is based on the ductility reduction factor (Rμ) provided by the addition of steel infill plate. A step-by-step procedure is developed to calculate the ductility reduction factor which reduces the force demand on vulnerable substructure elements. In addition, this procedure is shown to give results that compare well with numerical data from finite-element analysis.

Analytical investigation of Buckling Restrained Braces’ applications in bidirectional ductile end diaphragms for seismic performance of slab-on-girder bridge

The AASHTO Guide Specifications for Seismic Bridge Design includes provisions for the design of ductile diaphragms as Permissible Earthquake-Resisting Elements (EREs) to resist seismic loads applied in the transverse direction of bridges. However, two major limitations for this system are that: (1) other lateral-load resisting strategies have to be combined with the transverse ductile diaphragms to address seismic excitations acting along the bridge’s longitudinal axis; (2) the existing AASHTO provisions (reflecting the limits of existing research) only apply to straight bridges and provide no guidance on how to implement ductile diaphragms in skew bridges. This paper investigates ductile end diaphragm systems (EDSs) inserted in the slab-on-girder bridge superstructure, with Buckling Restrained Braces (BRBs) arrayed in two different bidirectional configurations so as to provide bi-directional resistance. Benchmark skew and straight bridge models were designed with both EDSs and analyzed using nonlinear time history analysis method to examine their seismic performance. Variations in skew, fundamental period of vibration, and earthquake excitation characteristics were considered. These dynamic analyses allowed investigating the impact of these parameters on global behavior, as well as understanding the magnitude of local demands and the extent of bidirectional displacements that the BRBs must be able to accommodate while delivering their ductile response. The long-term service life of BRBs installed across expansion joints and subjected to bridge thermal expansion histories was also studied and a minimum ratio of the BRB core length over the whole bridge length was recommended. For BRBs’ design and implementation in EDSs, these analytical results can help predict a regime of relative end-displacements representative of the BRB’s demands, when the bridge is subjected to both earthquake and temperature change in the superstructure.

Numerical study of steel box girder bridge diaphragms

Steel box girders have two webs and two flanges on top that are usually connected with shear connectors to the concrete deck and are also known as tub girders. The end diaphragms of such bridges comprise of a stiffened steel plate welded to the inside of the girder at each end. The diaphragms play a major role in transferring vertical and lateral loads to the bearings and substructure. A review of literature shows that the cyclic behavior of diaphragms under earthquake loading has not been studied previously. This paper uses a nonlinear finite element model to study the behavior of the end diaphragms under gravity and seismic loads. Different bearing device and stiffener configurations have been considered. Affected areas of the diaphragm are distinguished.

Influence of end Contsrains on the Global Behaviour of a Box Girder

Abstract This study aims to presents the importance of end constrains, boundary conditions and position of the applied forces regarding the design of precast/prestressed concrete box girders. The study is based on a destructive test which was performed on a 37.1 m span single-cell prestressed concrete box girder. The scope of the test was to certify the usage of such girders for the new Transylvania motorway bridges. The test is numerically reproduced through a full 3D FEM model implemented in SAP2000. The influence of the end diaphragms is considered by analysing the beam’s behaviour to six loading conditions: one of which is replicating the loadings during the test, while the others are conceived as real vertical and horizontally loading scenarios. The results obtained for the girders with and without end constrains are compared. The performances of both design solutions in the presence of prestressing are highlighted where applicable. It is considered that the results of this study may provide very important data if considering that Romania has an urgent need to realize a modern and an adequate transport infrastructure.