Shear Lag Effect Research Articles

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.

Integration of optical fibre sensors by material extrusion 3-D printing – The effect of bottom interlayer thickness

Thermoplastic composites are becoming the materials of choice for lightweight structures. Distributed optical fibre sensors can be valuable for structural health monitoring of thermoplastic composites, improving safety against damage and extending the operational life of composite components. However, the practical integration of optical fibres into thermoplastic composites remains still to be solved. To this end, a novel sensor integration approach by 3-D printing is proposed, and mechanical testing is conducted to test its performance. Optical fibres were placed inside thermoplastic embedding elements at controlled interlayer thicknesses (0 to 1.6 mm) from the substrate surface. Self-sensing experiments by optical fibres identified a uniform level of residual strains at −1600 µε from the 3-D printing attachment process. Furthermore, tensile creep testing (up to ca. 1% strain) revealed that distributed strain transfer coefficients for optical fibre sensors remain constant with time. A simple calculation method that accounts for the shear lag effect between the component and optical fibre strains was derived from previous analytical work. This method enables the empirical prediction of strain transfer coefficients for optical fibre surface attachments with arbitrary embedding interlayer thickness.

Shear Lag Effects on Pedestrian-Induced Vibration and TMD-Based Vibration Control of Footbridges

The shear lag effect (SLE) is one of the vital mechanical characteristics of structures with thin-walled box sections. While most existing studies of the SLE focus on the static response of footbridges, pedestrian-induced vibration deserves more attention since it represents the actual response of footbridges during their practical service process. A theoretical framework is proposed to consider the corresponding SLE. Firstly, the SLE on the natural frequencies of the structure can be considered with a reduction ratio to the corresponding case without considering the SLE. Results show it is more necessary to consider the SLE for footbridges with smaller span-width ratios, smaller section thickness-width ratios and lower height-width ratios. The SLE may result in significant reductions in the natural frequencies of the structures. These reductions in the predicted natural frequencies due to the SLE may further result in inaccuracy in the prediction of pedestrian-induced vibrations of footbridges. Furthermore, the most often applied mitigation measures may not be reliably designed. This may result in very significant reduction in the effectiveness of vibration mitigation measures. To consider the SLE on pedestrian-induced vibration and tuned-mass-damper-based vibration control of typical footbridges with thin-walled box sections, a simplified strategy is proposed.

Improving the Seismic Response of Tall Buildings: From Diagrid to Megastructures and Mega-Subcontrol Systems

Background: Diagrid structures, widely used for the tall buildings of the third millennium, are characterized by a very effective behaviour in the elastic field due to the grid triangulation. In particular, under horizontal actions, axial forces and deformations mainly arise in the structural members of the diagrid, thus resulting in the reduction of the shear lag effect and racking deformations. The response to incremental horizontal actions beyond the plastic threshold, however, shows a poor plastic redistribution capacity, with consequent low values of global ductility, in spite of a significant design overstrength. Objective: In this paper, it is proposed to exploit the high elastic efficiency of the diagrid type and use a vibration control system, based on mass damping mechanism with large mass ratios, to reduce a priori the inelastic demands due to seismic actions. Methods: Starting from the analysis of the seismic behavior of archetype diagrid buildings, a case study is selected to assess the effectiveness of the proposed motion-based design approach. For this purpose, the diagrid is first transformed into a megastructure (MS) configuration by densifying the diagonal elements at the most stressed corner areas and transfer floors, suitably chosen. Then, the exterior mega-frame is detached from interior sub-structures, thus allowing for a relative motion between the two structural portions according to a “mega-sub-structure control system” (MSCS), which activates the mass damping mechanism. Results: Time-history analyses carried out on simplified lumped-mass models confirm the effectiveness of the proposed strategy in reducing the seismic response. Conclusion: Finally, the practical feasibility of the MSCS and engineering solutions for the relevant structural organization are discussed.

Study on the Actuating Performance of an Embedded Macro Fiber Composite Considering the Shear Lag Effect.

Macro fiber composite (MFC), which are new ultrathin piezoelectric smart materials, are mostly applied in the fields of shell structure deformation and vibration control. Among others, the application of embedded MFCs in sandwich structures has received wide attention. Currently, its actuating force formula is primarily acquired based on the Bernoulli–Euler Model, which does not consider the shear lag effect and actuating force of MFC ends. To study the actuating performance of an MFC in a sandwich structure, according to its action characteristics, the MFC is divided into upper and lower actuating units without any interaction between to two under the condition of plane strain, and the shear lag effect is considered between the units and the top and bottom of the sandwich structure. The actuating force of the MFC ends is obtained by considering its influence on the bending deformation of the sandwich structure, which deduces the actuating force formula of the embedded MFC. In contrast to ANSYS piezoelectric simulation, the distribution of the MFC interior normal stress is similar to the result from ANSYS piezoelectric simulation, and there is a very small deviation between the MFC end and central normal stress and the result from ANSYS piezoelectric simulation. Taking the end deflection of the sandwich structure with an embedded MFC as an example, the actuating force simulation of the MFC considering the shear lag effect is compared with the ANSYS piezoelectric simulation and actuating force simulation based on the Bernoulli–Euler model. The result indicates that the actuating force simulation of the MFC considering the shear lag effect is closer to the ANSYS piezoelectric simulation, which proves the rationality and necessity of considering the shear lag effect and end actuating force of the MFC.

Study on Dynamic Characteristics of an Improved Composite Box Girder with Corrugated Steel Webs

Composite box girders with corrugated steel webs (CBGCSWs) are used worldwide owing to their light self-weight, high efficiency of prestressing application, and reasonable distribution of shear force and bending moment. An improved composite box girder with corrugated steel webs (ICBGCSWs) has been recently introduced to further reduce the dead weight and improve its durability. Because the innovative ICBGCSW has emerged as a new structure, very few studies have been conducted on its dynamic characteristics. In the present study, a theoretical analysis was first conducted. By comprehensively considering the shear lag effect and the shear deformation of CSWs, the element stiffness matrix of ICBGCSW was derived based on the principle of stationary potential energy. The natural frequencies and mode shapes in vertical bending vibration were calculated via a self-developed software program. The proposed method was verified by comparing the results with finite-element analysis and experimental results. Then, sensitivity studies were performed to investigate the influences of the shear lag and shear deformation on the natural frequencies of vertical bending vibration. Finally, vibration frequencies of the continuous ICBGCSW were calculated, and a general formula for calculating the fundamental frequency of simply supported girders, continuous girders with equal spans, and continuous girders with unequal spans was proposed. The proposed method, being able to consider both the effects of shear lag and shear deformation of the box girder, delivered very good performance in studying the dynamic characteristics of the ICBGCSW, whereas the proposed general formula of fundamental frequency could serve as a good reference for the bridge design in practice.

Evaluation of shear lag effect in HSS-UHPC composite beams with perfobond strip connectors: Experimental and numerical studies

In order to evaluate the shear lag effect of high strength steel (HSS)-Ultra high performance concrete (UHPC) composite beams with perfobond strip connectors (PBLs), this study involved the preparing and testing of six HSS-UHPC composite beams with different shear connections, deck width-to-thickness ratios, and deck width-to-span ratios. Failure mode, load-deflection curve, load-slip response, and stresses distribution of the HSS-UHPC composite beams were presented and discussed. Experimental results indicated that uniform elastic stresses in the UHPC deck cross-section were observed, and the stress distribution became uneven as the composite beam entered the plastic stage. Under a load of 0.3Mu, the bending stress at the cross-section top center of UHPC deck was 5.3% larger than that at the edges, and this stress discrepancy went up to 9.4% as load approached 0.9Mu. To gain insight into the plastic performance of the tested beams, the finite element (FE) model was further established for the composite beams. Numerical results indicated that the sectional stress hysteresis coefficient (λ) at L/4 near loading point was briefly similar to that of the mid-span in elastic stage, and the stress unevenness increased as the shear connection degree dropped. As the connection degree decreassed from 1.02 to 0.89 and 0.76, the λ of the investigated beams were magnified by 2.7% and 6.7%, respectively. Results also showed that the shear lag effects degraded as deck width-to-thickness ratio increased. The λ for the beams using width-to-thickness ratios of 4.50 and 4.09 were 13.3% and 18.6%, both smaller than that using the ratio of 5.63. Moreover, as the width-to-span ratio increased from 0.20 and 0.24, the stress hysteresis effect of HSS-UHPC composite beams barely varied.

A Review on the Physical Parameters Affecting the Bond Behavior of FRP Bars Embedded in Concrete

The present study is a detailed literal survey on the bond behavior of FRP (Fiber Reinforced Polymer) reinforcing bars embedded in concrete. There is an urgent need for the accurate assessment of the parameters affecting the FRP–concrete bond and quantification of these effects. A significant majority of the previous studies could not derive precise and comprehensive conclusions on the effects of each of these parameters. The present study aimed at listing all of the physical parameters affecting the concrete-FRP bond, presenting the effects of each of these parameters based on the common opinions of the previous researchers and giving reasonable justifications on these effects. The studies on each of the parameters are presented in detailed tables. Among all listed parameters, the surface texture was established to have the most pronounced effect on the FRP–concrete bond strength. The bond strength values of the bars with coarse sand-coating exceeded the respective values of the fine sand-coated ones. However, increasing the concrete strength was found to result in a greater improvement in bond behavior of fine sand-coated bars due to the penetration of concrete particles into the fine sand-coating layer. The effects of fiber type, bar diameter and concrete compressive strength on the bar bond strength was shown to primarily originate from the relative slip of fibers inside the resin of the bar, also known as the shear lag effect.

An efficient assessment of the vibration behaviour of cracked steel–concrete composite beams using GBT

In this paper, a previously developed GBT-based finite element (Henriques et al., 2020) is extended to allow calculating, very efficiently, natural frequencies and vibration mode shapes of steel–concrete composite beams, accounting for cross-section deformation (including shear lag effects) and concrete cracking. This new finite element enables a straightforward characterisation of the vibration modes, due to the unique modal decomposition features of GBT. The element aims at helping structural designers assess, very easily, the vibration behaviour of such beams at the serviceability limit state. A physically non-linear analysis is first carried out, accounting for cracking and cross-section deformation. Then, the natural frequencies and vibration mode shapes are calculated from the associated eigenvalue problem, with a very small computational cost. To illustrate the accuracy and potential of the proposed approach, two numerical examples are presented and discussed. For validation and comparison purposes, shell finite element model results are provided, showing that the proposed element leads to very accurate results with much less DOFs.

Symplectic analysis of thin-walled curved box girders with torsion, distortion and shear lag warping effects

Shear lag effect and torsional and distortional warping can significantly affect the performance of thin-walled curved box girders used in modern bridge engineering. The structural behaviour of these bridges exhibits complexity due to coupled bending and torsion together with warping effects of non-uniform torsion, distortion and shear lag. A practical method of analysis, based on the symplectic approach, with the same perspective as the Higher Order Beam Theories, is presented for overcoming the difficulties of numerical approaches via the Finite Element Method. In this paper, the Hamiltonian Structural Analysis method implements the analysis of the shear lag effect together with non-uniform torsion and distortion, for curved box girder bridges. The examples given can allow engineers to evaluate the effects of the negative shear lag phenomenon and the distribution of axial stresses in box slabs and webs, due to different warping effects, which strongly influence thin-walled box sections subjected to point loads and restrained areas.

An analysis model accounting for time-dependent shear lag effects in assembled composite bridge decks

The concrete deck of steel-concrete composite bridges made via prefabricated construction consists of precast slabs and construction joints between the slabs. When the age difference between the longitudinal joint concrete and precast slab concrete (new-old concrete) across a beam section is considered, the time-dependent characteristic of the assembled deck is different from that of the whole prefabricated deck. Based on the virtual work principle, differential equations were established to analyse the influence of the time-dependent characteristics of new-old concrete across a beam section on the shear lag effect of the composite beams. The analysis of examples showed that the proposed model was more accurate than the traditional model, which ignores the concrete age difference across a beam section, especially when analysing the long-term stress of joint concrete. The long-term stress of the joint concrete obtained by the proposed model decreased faster than that obtained by the traditional model with time, which increased the non-uniformity of the distribution of stress along the concrete flange. Overall, the proposed model could reasonably forecast the long-term performance of composite beams with assembled decks, which is beneficial to the life-cycle design and service behaviour analysis of composite bridges.

Numerical simulation and simplified calculation of the effective slab width for composite cable-stayed bridges

With the advent of progressively large and complex structures, the simultaneous presence of axial forces and bending on bridge decks is emerging as a recurring and increasingly concerning phenomenon. In the design of steel–concrete composite cable-stayed bridges, the combination of the axial force, mainly induced by the inclination of the cables, and bending is being increasingly considered to realize long spans that can bear the weight of the structure while ensuring a high rigidity of the deck. Despite its importance, this aspect is not sufficiently treated in the design codes, e.g., Eurocode specifications do not consider the axial force and its shear lag effects; therefore, the design rules are specified exclusively for the case of bending. From a practical standpoint, this deficiency can entail design complications due to the use of complicated FE models (shell and brick elements), which incur significant computational loads and design effort. In this study, a simple methodology for the design and verification of a girder composite deck subjected to combined compression and bending is developed. The methodology is based on a parametric study performed using finite element (FE) models that are valid for a generic girder composite deck. The stress distribution on the composite deck can be assessed while accounting for the axial force and bending moments associated with the deck by considering the results obtained using universal beam models. The proposed methodology is applied to an existing cable-stayed bridge.

Experimental analysis of shear-lag effect in reinforced concrete T-beams

The non-uniform distribution of normal stresses within wide flanges of beam sections is typically referred to as shear-lag effect. Shear lag is a result of the interaction of normal and tangential stresses or correspondingly by the influence of shear strains on longitudinal strains. In structural engineering, the shear-lag effect has been a concern in the flanges of thin-walled metallic structures or the slab of composite steel–concrete elements, among others. Though existing codes of practice provide a simplified way to address shear lag by means of the effective width concept, such provisions can be insufficient for concrete structures, for which a deeper knowledge on the real influence of shear lag is necessary due to the current trend to design wide concrete bridge girders, with geometric configurations of the cross-sections which can be sensitive to shear lag (i.e. box- or T-sections). Moreover, the influence of the behaviour of structural concrete (cracking, rheology, yielding of reinforcement) has not been dealt with in detail so far. In the present paper, an experimental campaign on two reinforced concrete T-beams is presented. The beams have been subjected to two types of tests: firstly, to time-dependent effects governed by concrete shrinkage and creep; secondly, to the application of increasing direct loads to cover the whole concrete behaviour (uncracked, cracked and ultimate stage). The strain distribution at the top slab of the T-sections has been studied with extensive strain measurements at different cross-sections. The experiments have shown a distinct intensity of shear-lag effect depending on the load type. Moreover, the shear-lag impact varies longitudinally for each cross-section. In case of direct load tests, it has been also found that the strain distribution on the top slab changes as a function of the load level, which indicates that the different behavioural stages of concrete affect the shear lag, especially cracking. The experimental results have been analyzed with the help of analytical and numerical models, which have allowed understanding the progressive modification of the strain distribution within the top slab and the shear-lag intensity.

Crack Growth and Delamination Analysis in GFRP Composite Materials

The modeling of the structural behavior of composite materials is an interesting but complex task since the response of the material to loading structural may be difficult to predict, and the failure may be manifested in different forms. In cross-ply fiber-reinforced composites, the major failure mechanisms include: (i) the failure of the matrix material (transverse cracking), (ii) delamination and (iii) the breakage of the fibers. The process of the transverse cracking is a well studied damage mechanism and can be used in numerical simulations, in order to study the effects of various parameters on the crack density. In this paper, the finite element modeling of a cross-ply composite under uniaxial loading in tension is performed using ABAQUS software, considering all the potential damage mechanisms. The model takes into account shear-lag effect for the determination of the stress transfer and furthermore it adopts a homogenization procedure for the calculation of elastic and viscoelastic material properties. Stochasticity is introduced by assigning various interfacial strengths that follow a Gaussian distribution, so as to predict the cracking sequence up to saturation in the transverse to the 0∘ layers. The results are directly compared with available experimental measurements showing reasonable agreement. Finally, a cross-ply RVE model was created and loaded in uniaxial tension and crack propagation is modelled with the Extended Finite Element Method (XFEM). The stress concentration calculations around the crack tips are in agreement with the mesoscale model.

Correction of shear lag warping function of steel bottom – Corrugated steel web box girder

To clarify the shear lag effect of the cross-section of steel bottom – corrugated steel web box girder, this study investigated the effect of replacing the concrete floor with a steel bottom on the additional warping displacement of the steel-concrete cross-section based on the energy variation principles of the cosine function method. Two methods are used to derive the maximum shear angle difference function of each member. Firstly, considering the influence of different material modulus and geometric size on the composite section of box girder, the warpage function is modified. On the other hand, the maximum angle difference function of each member on the composite section is assumed, and its expression is derived by using the matrix eigenvalue method. Refer to bridges under construction, a 6 m scale model beam is made and designed as the single box double chamber steel bottom - corrugated steel web box girder. By comparing the General beam theory, finite element method (FEM), Model beam test value and the correction method in this paper, the validity of this theory is verified.

Static Characteristics of Improved Composite Box Girder with Corrugated Steel Webs

In order to accurately calculate the cross‐sectional stresses and deflections of the improved composite box girder with corrugated steel webs, the control differential equations and boundary conditions are established based on the energy variational principle, taking into account the effects of corrugated steel web properties, shear lag, and shear deformation. A cantilever composite box girder is used as a numerical example. The influence of width span ratio and corrugated steel web bending angle on the shear lag and fold effect is analyzed. The results show that the analytical solution is in good agreement with the finite element solution. A shear lag effect and a negative shear lag effect exist in the cantilever composite box girder under uniform load. The fold effect under concentrated load has a greater influence on the mechanical properties of the wing plate than under uniform load. With the increase of the width span ratio, the effects of both shear lag and fold effect increases. With the increase of the corrugated steel web bending angle, the fold effect is obviously enhanced, but the change of the bending angle has little effect on the shear lag effect.

Prediction of Effective Width of Varying Depth Box‐Girder Bridges Using Convolutional Neural Networks

Effective flange width is widely used in bridge design to consider the effect of shear lag. The simplified formula for the effective flange width of box girder bridges of variable depth in existing codes and studies may not be conservative, and accurate methods, such as the finite element method, are time‐consuming. The purpose of this research is to develop a method that uses a convolutional neural network (CNN) to predict the effective width of box girder bridges of varying depths. These models have been trained, validated, and tested on datasets generated from thousands of finite element models. The lower error in the test set indicates that the CNN model can be used to predict the effective width. In addition, the impact of different architectures is also studied. The proposed method makes real‐time analysis possible and has a wide range of applications in the analysis and design of box‐girder bridges at different depths.

Research on shear lag effect of cantilever concrete box beam with double chambers

In this paper, the authors used finite element method to investigate the longitudinal and transverse shear lag effects and the effect of aspect ratio on the shear lag of double-chamber cantilever concrete box girder under uniform distributed load. The results show that the root section is positive shear lag, and the mid-span section is negative shear lag. In the longitudinal direction, positive and negative shear lag changes appear in box girder. The effect of shear lag at fixed end is significantly affected by aspect ratio, and the effect degree is different in different parts. The positive and negative values of shear lag must be determined by the stress curve.

Research on Shear Lag Warping Displacement Modes of Frame-Tube Structures Based on the Hamiltonian Mechanics

Based on the equivalent continuity method, the accuracy of the shear lag warping displacement functions for frame-tube structures was studied under the Hamiltonian mechanics. Different types of functions were selected to describe the shear lag warping displacement of the flange plate, and the shear deformation and longitudinal warping of the equivalent plate were considered. The total potential energy of the structure and the corresponding Lagrangian function under different displacement modes were obtained. Not with the traditional variational methods, the problem was studied under the Hamiltonian mechanics system. The Hamiltonian canonical equation for the frame-tube structure was derived and solved with the precise integration method, then the column axial force was calculated and the accuracy was analyzed. The verification results of the calculation examples show that, this method is simple and feasible to analyze the shear lag effects of the frame-tube structures. The choice of different warping displacement functions has little effect on the lateral displacement calculation results, but has great influence on the axial force solution, and the quadratic parabola can best reflect the actual warping displacement distribution of the flange. Comparison of the stress distributions in the equivalent flange under different types of loads indicate that, with the increase of the position of the external load resultant force, the negative shear-lag effect on the top gradually weakens to disappear.

Numerical evaluation for the effective slab width of continuous composite beams

Basic beam bending theory and the effective width concept are commonly used in the design and analysis of steel–concrete composite beams to evaluate deflections, stresses, and strengths. The shear-lag effect is partially accountedfor by adopting a reduced “effective” slab width rather than the actual slab width. Besides the precise numerical values obtained via numerical analysis of a composite beam, Code provisions should provide a simplified practical techniquefor calculating effective slab width that is both simple and precise. Current design codes propose effective width values that are essentially a function of the beam span, ignoring the effects of other essential factors. Finite element analysis of continuous composite beams is a complex task, as large numbers of contacts and meshing elements are required to catch all the physical phenomena; this leads to potential convergence difficulties using a general static analysis. In this paper, several 3D numerical simulations of a composite continuous beam are conducted using the RIKS method available in ABAQUS. Comparisons to available experimental results are used to validate the proposed FE model. Then, the so-validated numerical model is utilized to perform a parametrical study to assess the effect of the longitudinal reinforcement at the hogging moment region and the influence of the concrete slab width on the effective width evaluation. Finally, the proposed finite element model and EC4 specification results are compared to draft a useable design guide.