Shear Lag Research Articles

Experimental and theoretical investigation of shear lag effect in twin box‐shaped composite girders of long‐span cable‐stayed bridges

AbstractSteel‐concrete composite box girders offer notable advantages such as high stiffness, excellent torsional performance, and light self‐weight, making them prevalent in large‐span bridges, particularly in cable‐stayed configurations. However, a persistent challenge arises from the shear lag effect in the concrete slab within the flanges induced by shearing interactions between the webs and flanges. Limited attention has been devoted to investigating the experimental and theoretical aspects of shear lag in long‐span cable‐stayed bridges with twin box‐shaped composite girders. This research addresses this gap by designing a segmental scale twin box‐shaped composite model specimen to simulate the cable spacing of the main girder in a cable‐stayed bridge, specifically targeting the shear‐lag effect. The study successfully captures the non‐uniform distribution of cross‐sectional strain in the top concrete slab. Subsequently, analytical strain solutions for the composite girder under mid‐span concentrated load and axial load are derived using the energy variation method. The theoretical model's applicability is then calibrated against experimental results. The investigation extends to the in‐situ testing of the Chibi Yangtze River Bridge, the world's largest steel‐concrete composite girder cable‐stayed bridge, boasting a main span of up to 720 m. An established finite element (FE) analysis model for the Chibi Yangtze River Bridge simulates the transverse stress distribution under typical construction conditions of CC6. Comparative analyses between the simulated results, calculated values from elementary beam theory, and the theoretical model against field‐measured values reveal that the FE model provides a more accurate estimation of the shear lag effect in the concrete slab. Notably, the FE model effectively reflects the bridge's characteristics and serves as a baseline for subsequent studies. This comprehensive investigation contributes significantly to the understanding and analysis of shear lag phenomena in twin box composite girders of cable‐stayed bridges. The integration of experimental, analytical, and construction site validations establishes robust tools for engineering design and the construction of safe and serviceable cable‐stayed bridges. The research augments knowledge regarding shear lag behavior and underscores the necessity to appropriately consider its effects in bridge analysis and design.

Tensile damage evolution and mechanical behaviour of SiCf/SiC mini-composites through 4D in-situ micro-CT and data-driven modelling

Damage evolution of SiCf/SiC ceramic matrix mini-composites (CMMCs) was characterised by using a 4D in-situ micro-computed tomography (CT) tensile test and digital volume correlation (DVC) technique. Additionally, a CT damage data-driven shear lag model was developed to predict its tensile stress-strain response. A 4D in-situ X-ray CT tensile test of a unidirectional SiCf/SiC mini-composite was first carried out. Then two ad-hoc deep-learning image segmentation models were developed to automatically identify its microstructure and damages induced by tension, respectively. Damage evolution was quantitively characterised by visualising the initiation and propagation of matrix cracks in three-dimensions (3D). A two-step approach was employed to evaluate its 3D internal strain distributions at various loading levels, which further revealed strain concentrations and helped establishing the tensile stress-strain response of the CMMCs. It was observed that transverse cracking is the predominant damage mode, and the average crack opening displacement increases with loading. A high-fidelity X-ray CT data-driven shear lag model was developed, incorporating inputs of transverse matrix crack spacing calculated by the 4D in-situ CT test data. The predicted stress-strain response showed a good correlation with the experimental results.

The Concrete Effective Width of a Composite I Girder with Numerous Contact Points as Shear Connectors

Due to the shear strain in the plane of the slab, the parts of the slab remote from the steel beam lag behind the part of the slab located in its proximity. This shear lag effect causes a non-uniform stress distribution across the width of the slab. As a result, several standards have introduced the concept of an effective flange width to simplify the analysis of stress distribution across the width of composite beams. Both the computed ultimate moment and serviceability limit states are directly impacted by the effective width. The effect of using a large number of contact points as shear connectors on the effective width of a steel beam flange has not been investigated. A three-dimensional finite element analysis is carried out in this paper. The ABAQUS software (version 6.14) is used for this purpose, where several variables are considered, including the surface area connecting the steel beam and concrete slab, the transverse space, and the number of shear connectors. It was discovered that the number of shear connectors on the steel beam flange has a major impact on the effective width. The many connectors work together to provide a shear surface that improves the effective width by lowering the value of the shear lag.

Investigation of the Shear Lag Effect of an Innovative Steel Box Girder in Cable-Stayed Bridges: Experimental and Bar Simulation Method Analysis

Investigation of the Shear Lag Effect of an Innovative Steel Box Girder in Cable-Stayed Bridges: Experimental and Bar Simulation Method Analysis

Analytical modeling of stress concentration in composite box girders

In several structures/structural forms, including box beams, T-beams, U-beams, box girders, and tubular buildings, the stress concentration caused by the shear lag effect reduces their load-resisting capacity. The energy method has been proven to be more effective in analyzing the shear lag effect in these structures. Utilizing the minimum potential energy principle, this study illustrates a simplified approach to assessing stress concentration in composite box girders. Based on boundary conditions and shear loading conditions, closed form solutions are obtained for normal stresses and deflection. The present research results are verified with finite element analysis results and literature, demonstrating the robustness of the methodology. A composite box girder can be analyzed using the present approach under any support and loading conditions, taking material properties into account. To increase composite box girders’ load carrying capacity, additional layers of material are generally added to the flange. When retrofitting a box girder in this way, cross-sectional flexural rigidity is trivially improved. The additional layer of material on the flange of the box girder may reduce stress concentrations caused by the shear lag effect when it improves the shear flow capacity (SFC) of the flange. Shear flow parameter (Γ) measures flange shear flow capacity. The flange SFC increases significantly for a core/layer with a ratio of elastic modulus to shear modulus (E c /G c ) up to 1.26. When E c /G c rises even further, the flange SFC decreases. A composite box beam may have enhanced flange stiffness, with cores/layers having E c /G c ratios up to 2.86 and stress concentrations similar to that of a box beam without a core/layer. In composite box beams with a low aspect ratio, considering only flexural deformation in the core/layer augments the stress concentrations significantly. Deflection and negative shear lag are reduced significantly when the composite box beam flange has a high SFC.

Refined Analysis of Spatial Three-Curved Steel Box Girder Bridge and Temperature Stress Prediction Based on WOA-BPNN

Bridges often improve the visual appeal of urban landscapes by incorporating curve elements to create iconic forms. However, it is noteworthy that curved bridges have unique mechanical properties under loads compared to straight bridges. This study analyzes a spatial three-curved steel box girder bridge based on an actual engineering case with a complex configuration. Initially, the finite element software Midas/Civil 2021 is utilized to establish a beam element model and a plate element model to examine the structural responses under dead loads in detail. Then, two different temperature gradient distribution models are employed for the temperature effect analysis. The backpropagation neural network (BPNN) optimized by the WOA algorithm is trained as a surrogate model for finite element models based on the results of temperature stress simulation. The results reveal that the bending–torsion coupling effect in the second span of the spatial three-curved steel box girder bridge is pronounced, with the maximum torque reaching 40% of the bending moment. The uneven distribution of cross-section stress is particularly significant at the vertices, where the shear lag coefficient exceeds 3. Under the action of temperature gradients, the bridge displays a warped stress state; the stress results obtained from the exponential model exhibit a 21% increase compared to BS-5400. Optimization of the weights by the WOA algorithm results in a significant improvement in prediction accuracy, and the convergence speed is improved by 30%. The coefficient of determination (R2) for predicting temperature stress can reach as high as 0.99.

Analytical Method of the Shear Lag Effect in Thin-Walled Box Girders Based on the Shear Flow Distribution Law

This paper presents an analytical method based on the shear flow distribution law to study the shear lag effect of thin-walled single- and double-cell box girders. The first step in this method is to determine the box girder’s shear flow distribution. Subsequently, a series of novel improved longitudinal displacement functions mathematically expressed as cubic parabolas are established. The parabolic origin of these functions is located at the zero point of the shear flow corresponding to each plate; the unknown parameters used to describe the function form can be determined according to the shear flow distribution, the continuity conditions, and the axial force balance condition. Then, the variational energy method is adopted to derive the governing differential equations. The shear lag effect in thin-walled single- and double-cell box girders under several boundary conditions and load cases is studied and analytical expressions for the shear lag coefficient are derived. Finally, results obtained using the proposed method are validated via comparison with numerical results. The results show that the proposed method can provide reasonable predictions for the shear lag effect of single- and double-cell box girders, and that this method is more straightforward and practical. In addition, the shear lag coefficients at different webs are not entirely equal, which is related to the distance from the web to the zero point of the shear flow.

Effect of external prestressing on the special shear lag behavior of precast box girder bridges

The shear lag behavior exhibited by precast segmental box girders (PSBGs) under concentrated external prestressing differs significantly from that observed in box girders subjected to vertical loads. To study the special shear lag behavior of PSBGs under external prestressing, a theoretical analytical method was developed based on the classical energy variational principle. In this analysis, the effect of external prestressing was decomposed into axial compression and bending effects through the equivalent load method. For each of these effects, appropriate longitudinal warping displacement modes were assumed, and the total energy functional expressions of the system under these two effects were further established. The governing differential equations for the two effects were derived using the principle of energy variation. Analytical solutions for the normal stress of the beam section under axial compression and bending effects were deduced, and corresponding boundary conditions were obtained. Subsequently, the normal stress of the section under the two effects was superimposed to obtain the comprehensive normal stress distribution curve of the beam section under external prestressing. The reliability of the theoretical analysis method was validated through a comparison of the theoretical analysis results with experimental and numerical analysis results.

Analysis of Stud Spacing on the Mechanical Behaviour of Steel-Concrete Composite Beam under Uniform Load

The stud spacing significantly affects the bond strength and interracial slip between steel and concrete of thin-walled steel-concrete composite beams, and it interacts with shear lag and shear deformation to affect the structural deflection and sectional stresses. In this paper, a new interracial slip model considering the influence of stud spacing and stud shear stiffness is proposed first, then a potential energy equation of a simply supported steel-concrete composite beam under vertical uniform load considering the coupled effect of interracial slip, shear lag and shear deformation is obtained, and the calculation formulae for structural deflections and sectional stresses are derived, in which the parameter of stud spacing is explicitly shown. The comparison between the observed data in the completed experiment with the theoretical values using the presented formulae and the design code formulae are fulfilled, showing that the presented formulae hold agreeable calculation precise. The proposed formulae can be used to estimate the influence of stud spacing on the mechanical behaviour of steel-concrete composite beams in the preliminary design.

Health monitoring of steel structures using surface mountable and detachable PZT sensor

A lot of collapse in the infrastructure were reported in the last decades, hence the need for monitoring the health of the structures also arises. There are various techniques available to monitor the health of the structure, in which Electromechanical impedance (EMI) technique is one of them. In EMI technique, the PZT sensor is bonded to/embedded in the structure using epoxy. The thickness of epoxy layer used as an adhesive should be maintained as thin as possible, which cannot be achieved ideally, which introduces shear lag effect such that is, complete strain transfer cannot take place between PZT and host structure. The shear lag effect caused is one of the major drawbacks in the EMI technique and due to this effect, the damage detection sensitivity decreases. To overcome this drawback, in this study a new sensor named Surface Mounted PZT Sensor (SMPS) is proposed for the steel structure. Along with this, the performance of other sensor configurations such as conventionally bonded PZT with epoxy that is Surface Bonded PZT Sensor (SBPS) and Adhesive Covered Surface Bonded PZT Sensor (ACSBPS) are also been compared. The results show that, SMPS was working effectively and was more sensitive compared to SBPS and ACSBPS.

Tension-Induced Localized Wrinkling in a Patched Thin Film Supported by an Elastomer.

The wrinkling behavior of thin films has received great attention for their applications in developing various wrinkle-based novel technologies. Herein, a new wrinkling system: tension-induced wrinkling in an elastomer-supported patched thin film (TW-P&SF) is investigated by using PDMS-supported patched polyimide thin films with different thicknesses and varied length/width ratios. Different from the well-studied compression-induced wrinkling in an elastomer-supported thin film (CW-SF) and tension-induced wrinkling in an edge-clamped free-standing thin film (TW-FF), in the system of TW-P&SF, the wrinkles are localized near the edge of the film with a finite length that follows a center-symmetric distribution. It was found that the wrinkle length lmax and the wrinkle period λ scale with the film thickness h as λ ∼ h0.86 and lmax ∼ h-0.79. With the assistance of the two-dimensional shear lag model and scaling analysis, the underlying mechanism for wrinkle localization is clarified. Furthermore, the promise of the TW-P&SF-enabled wrinkle-based method as a new method for thin film mechanical characterization is demonstrated.

Effective width of steel-concrete composite box girder bridges: a review and method comparison

Steel-concrete composite girders have non-uniform stress distribution on the slab, presenting maximum stresses next to the webs of the girder. This phenomenon is known as shear lag effect. To understand this effect, there is the effective width concept, in which only a portion of the slab width is considered effective in contributing to the composite element’s resistant capacity. However, in the technical standards, there is no recommendation for calculating the effective width in steel-concrete composite box girder bridges. In view of this situation, the purpose of this paper is to carry out a systematic review on effective width and/or the shear lag effect in steel-concrete composite bridges, in order to raise the main existing recommendations and compare them. Through a bibliometric scan with carefully chosen keywords, it was found that of all research on shear lag or effective width in steel-concrete composite structures, only 31.19 are on bridges and 14.97% are on bridges with box girders. Among the papers, those that have a method for calculating the effective width of steel-concrete composite girder bridges have been compared quantitatively and qualitatively with the procedures of AASHTO and EN 1994-2-2. In these procedures were also identified that the, for the boundary conditions of the present paper, the parameters that most influencing the effective width are, in that order, the span length, the distance between girders, the concrete slab height, the longitudinal position and the type of load.

Modeling the strength of aluminum extrusion transverse welds using the film theory of solid-state welding

Reducing production scrap is vital for decarbonizing the aluminum industry. In extrusion, the greatest source of scrap stems from removing profile sections containing transverse (charge) welds that are deemed too weak for their intended purpose. However, until now, there has been no predictive transverse weld strength model. This article establishes a transverse weld strength model as a function of billet properties and extrusion parameters. It extends the film theory of solid-state welding by enhancing Cooper and Allwood's plane strain model to consider non-plane strain deformations at the billet-billet interface. These enhancements are informed by analyzing oxide fragmentation patterns through shear lag modeling and microscopy of profiles extruded from anodized billets. Model predictions are assessed through shear tests on welds from single and two-piece billets, extruded into rod, bar, and multi-hollow profiles. The experiments reveal that negative surface expansions at the weld nose cause interface buckling and weaker welds, but both surface expansions and weld strengths increase with distance from the nose. In non-axisymmetric profiles, deformation conditions and strengths vary across, as well as along, the weld. Two-piece billet welds are longer but reach bulk strength long before weld termination. The model predicts these trends and shows that die pressures are sufficient for micro-extrusion of any exposed substrate through interface oxide cracks. This underscores the significance of interface strains in exposing substrate and determining the weld strength. The model can help increase process yields by determining minimum lengths of weak profile to scrap and aiding process optimization for increased weld strength.

A theoretical model for investigating shear lag in composite cable-stayed bridges

A theoretical model for investigating shear lag in composite cable-stayed bridges

How to select discrete or continuous interfaces in biological materials to achieve a strength-toughness tradeoff

Many biological materials, such as nacre, bone and turtle shell cuticle, can successfully achieve a tradeoff between strength and toughness, which is attributed to the stacked microstructure formed by soft and hard phases. However, among these biological materials, the soft phase-formed interfaces of some biological materials are continuous, while those of some are discrete. In this paper, a shear lag model considering an elasto-plastic discrete interface is established to reveal the selection mechanism of two kinds of interfaces in different biological materials, thus solving the tradeoff between strength and toughness. Based on the shear lag model, theoretical solutions of the stress and displacement in the hard phase and the shear stress in the soft interfacial phase are obtained for a general case with any number of interfacial bonding segments. The relationship between the effective stress and effective strain of the representative volume element (RVE) is further achieved, with the help of which the strength and toughness of staggered bio-composites can be analyzed. Corresponding experiments based on 3D-printed samples are further performed to verify the theoretical predictions. It is found that, when the hard phase and soft phase have comparable mechanical properties, like those in turtle shell cuticle, the interface guarantees a high load transfer efficiency to generate the ultimate stress in the platelet, while its discrete distribution leads to a higher interfacial shear stress level than that in a continuously bonded interface. Such a material-structure co-action induces a hybrid damage mode of hard phase fracture and soft phase failure, consequently leading to an excellent strength-toughness tradeoff. However, if the mechanical properties of two phases differ significantly, like those in nacreous materials or bone, a discrete interface should result in a unique damage mode of interface failure and a low utilization efficiency of hard phase. Instead, a continuous interface in this case is more conducive to obtain a tradeoff between strength and toughness. All the results demonstrate that biological materials choose different interface structures to meet the requirements of strength and toughness matching, based on the differences in the mechanical properties of soft and hard phases. Such a selection mechanism provides a direct reference for the optimal design of artificial composites with an excellent strength-toughness match.

Design and Performance Evaluation of the Curved Hengjiang Avenue Pedestrian Bridge: Y-shaped Piers and Mixed Decks

Urban pedestrian bridges should contribute to the improvement of the overall image and function of the place where the footbridge is located. In order to establish a complete pedestrian access area of a Green Belt Park, an elegant pedestrian landscape bridge with Y-shaped piers and mixed decks was designed and built, providing an open and diverse viewing experience. Accelerated bridge construction technologies were adopted to build the footbridge. Finite-element models, including the full bridge model and local model, were established and a continuous rigid frame and continuous girder composite bridge system was proposed after scheme comparison. Preliminary statics and dynamics analysis, as well as detailed calculations for the local stresses of Y-shaped piers and the shear lag effect of the deck, were carried out aiming to demonstrate its safety and suitability.

Contribution of the Fe-rich phase particles to the high temperature mechanical behaviour of an Al-Cu-Fe alloy

The high temperature strengthening mechanisms in Al-Cu-Fe aluminium alloy was analysed basis on a comprehensive microstructural study of the as-cast alloy and mechanical testing results. An approach which extracts the specific contribution of solid solution atoms, precipitates, and Fe-rich particles to the creep strengthening was utilized. Additionally, the Shear Lag model, was employed to account for the contribution to strengthening of the Fe-rich intermetallic particles through a load transfer mechanism. For this study, an as-cast Al-Cu alloy, which does not contain Fe impurities, has been also used for comparative purposes. The findings suggest that the large and 3D interconnected Fe-rich phase particles (Al6(MnFe) and α-Fe) generate the main strengthening effect at high temperature through a load transfer mechanism, whereas the contribution of the nanometric Al2CuMg precipitates were very limited.

Mapping complete eigensolution space for the analysis of stress transfer in and around the broken fiber: A variational principle based approach

One of the critical reasons for the failure of the Fiber Reinforced Composite (FRC) is fiber breakage. The stress transfer in and around this breakage has remained the topic of research for the last couple of decades. The two-phase composite model is generally considered standard to gain insight into the mechanics. Most of the literature simplifies the problem by considering the shear lag approximations or some other a-prior and/or ad hoc assumptions on various field variables. Moreover, the majority of the study in the literature considers both matrix and fiber to be isotropic. On the contrary, most of the fibers in FRC are transversely isotropic. In the present manuscript, an attempt has been made to provide a solution for this problem with an anisotropic fiber satisfying all the boundary conditions and continuity requirements in an exact sense. The solution strategy adopts the derivation of the solution for individual phases under axial traction and then imposes the boundary and the continuity conditions. The formulation of the problem for the individual phase is based on the variational principle and the solution is based on the method of separation of the variables and the Frobenius method. To validate the solution the numerical results for the various stresses have been compared against the results from the Finite Element Analysis (FEA). The comparison shows a good agreement between them. Further, the effect of the volume fraction and the fiber-matrix stiffness ratio on the Ineffective length, maximum shear stress at the interface, and the far-field stresses in the fiber has been studied.

Experimental Study on the Flexural Performance of Composite Beams with Corrugated Steel Webs under the Coupled Effect of Chloride Ion Erosion and Sustained Load

The steel corrosion of composite beams with corrugated steel webs (CBCSWs) is prone to occur in a chloride environment, and the load can change the rate of steel corrosion, thereby affecting the degradation of the mechanical properties of CBCSWs. In this paper, the flexural behavior of CBCSWs under the coupled effect of chloride ion erosion and sustained load was studied through an accelerated corrosion test and bending failure test. The results showed that, during the accelerated corrosion test, the deflection at the mid-span of the corroded CBCSWs increased more and faster than that of the uncorroded CBCSWs, and the stress of the externally prestressed tendons of the CBCSWs did not change significantly. During the loading failure process, the relative slip between the web and the concrete plates of the corroded CBCSWs had not been fully developed. The ultimate load and ultimate deflection of the corroded CBCSWs were decreased by 41.1% and 17.9%, respectively, compared to those of the CBCSWs before corrosion. The quasi-plane section assumption was still approximately applicable to the corroded CBCSWs. Compared with the uncorroded CBCSWs, the shear lag effect of the top plate of the corroded CBCSWs was more obvious. The externally prestressed tendons of the corroded CBCSWs could not give full play to their performance during the process of loading failure.

Research on the influence of an adhesive layer on the monitoring signal of piezoelectric sensors

Electromechanical impedance (EMI) technology, as one of the important methods for analyzing and studying the interaction between sensors and structures, has the characteristics of clear physical meaning and high computational efficiency. However, for complex structures, it is difficult to quantitatively combine the measured impedance signal with the physical parameters of the tested structure. Therefore, establishing an appropriate EMI model is crucial to facilitate the quantitative analysis of structural health monitoring. The impedance models developed so far assume perfect adhesion between PZT and the structure, with displacement compatibility, and ignore the shear lag effect of the adhesive layer. Therefore, this research focuses on analyzing how surface-bonded PZT couples with the structure through the adhesives and conducting a shear layer analysis on two-dimensional (2-D) circular PZT to derive a closed-form solution for shear lag distribution. The shear lag effect is integrated into the 2D impedance formula. The influence of the adhesive layer on bolt loosening monitoring is studied, and it is proven that the modified EMI model can effectively predict the shear lag effect of the adhesive layer. The result of relative error analysis proves that conventional adhesive PZT also exhibits the shear lag phenomenon. The influence of different thicknesses of adhesive layers on sensor sensitivity is studied. The experimental results show that as the thickness of the adhesive layer decreases, the monitoring sensitivity of the sensor increases. Moreover, for slight bolt loosening, the thickness of the adhesive layer can affect the monitoring frequency.