Shear Lag Effect Research Articles

Lateral constrained wrinkling of the film with partial contact

This paper establishes three analytical models, including the interface bonded type (B-type), interface sliding type (S-type) and the lateral constrained type (C-type), to reveal the effects of the partial contact and lateral constraints on the film wrinkling behaviors. Due to the geometrical and contact nonlinearities, a numerical method is applied to solving the displacement and stress fields, and the shear-lag effect caused by contact is included. The deformation of the film can be characterized by 5 processes, firstly compressing (I), secondly wrinkling (II), then the growing of wrinkled part giving rise to point contact (III), line contact (IV), and finally mode transition(V), which are verified by a demonstrative experiment. Moreover, effects of the contact parameters, including the interfacial strength, interfacial stiffness and the initial contact region length, on the deformation of the film are analyzed. Finally, the established models are applied to characterize the wrinkling behaviors of a graphene contacting to the polyethylene terephthalate (PET). The minimum pre-existing defect size for graphene wrinkling is 7 nm, less than which the interface failure precedes the film wrinkling. The critical wrinkling strain shows significant size effect when the graphene length is less than 13μm, where all the interfaces participate the load transfer. The obtained results are consistent with the experimental and the numerical data given in the references, where the differences are also discussed detailly.

Predicting failure modes and load-capacity of fiber-reinforced polymer rods in adhesively bonded anchorages based on numerical modeling

The tensile properties of fiber-reinforced polymer (FRP) rods in adhesively bonded anchorages are expected to be studied in detail. Therefore, the study aims to predict the failure modes and load-bearing capacity (load-capacity) of FRP rods subjected to direct tensile force. The cohesive zone models were employed to evaluate the interfacial bond between materials. Firstly, two representative volume element models of fibers and matrix were proposed to predict engineering constants and strengths of the FRP material in three dimensions. Then, the main simulation, including the FRP rod, filling material, and steel tube, was carried out to analyze FRP rods under the variation of cohesive zone model parameters. The load-capacity, failure modes, shear-lag effect were predicted based on the maximum stress criterion. The results revealed that the FRP material strengths enforce the failure in two modes associated with the transverse and longitudinal directions of FRP rods. In addition, diameter is a significant factor that increases the shear-lag effect and reduces the tensile strength of the FRP rods. The numerical simulation provided a new method to predict the load-capacity of FRP rods.

Mechanics of controlled fragmentation by cold drawing

Cold drawing is a mature and widely adopted technique in the shaping of metallic and polymeric materials in industry. Interestingly, cold drawing of a ductile cladding containing a brittle core wire or a ductile substrate supporting a deposited brittle film has recently emerged as a method to produce micron sized rods and ribbons through controlled fragmentation induced by local necking. While this method shows tremendous potential in providing an economic yet efficient technological platform for large-scale manufacturing of structures at the micro- and nanoscale, there is so far no theoretical guideline on how to control the size of the fragmented components. Here, we develop a theory of controlled fragmentation in cold drawing of both axisymmetric core-cladding and plane-strain film-substrate systems. The theory reveals that the process is governed by a reverse shear lag effect which gives rise to a peak tensile stress leading to controlled fragmentation near the necking zone, where the material properties of both the brittle core/film and ductile cladding/substrate play critical roles. Of particular interest is how the feature size of the fragmented components can be reduced toward the nanoscale. To this end, our theory shows that the fragmentation size mainly depends on the interfacial shear strength, geometrical dimension and stiffness of the brittle material, and can be reduced via increasing the strength of interfacial interactions and/or decreasing geometrical dimensions such as the core radius or film thickness.

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

Analysis and Study on Bending Vibration Frequency of New Corrugated Steel Web Composite Box Girder

In order to accurately analyze the bending vibration frequency of the new composite box girder, the effects of web folding effect, shear lag, and shear deformation are comprehensively considered in this paper, and the elastic control differential equation and natural boundary conditions of the composite box girder are established by using the Hamilton principle. A one-span composite box girder with corrugated steel webs is used as a numerical example. The effects of height span ratio, width span ratio, web thickness, cantilever plate length, and fold effect on the vertical vibration frequency of the new composite box girder are analyzed. The results show that the analytical solution is in good agreement with the finite element solution. When considering the shear lag and fold effect, the vibration frequency of composite box girder decreases. With the increase in order, the influence of shear lag and fold effect on its frequency becomes stronger. The changes of height span ratio and web thickness of composite box girder have a great influence on its folding effect, while the changes of width span ratio and cantilever plate length have little influence on it. The conclusion can provide a reference for the design of medium section new composite bridge in practical engineering.

Study on pre-damage diagnosis and analysis of adhesively bonded smart PZT sensors using EMI technique

The electro-mechanical impedance technique (EMI) is one of the best methods for continuous structural health monitoring (SHM) by embedding a smart piezoelectric ceramic Lead Zirconate Titanate (PZT) sensor or pasting it over the surface of the structure. The smart PZT transducer is intensely affected by the adhesive bonding condition between the PZT patch and the host structure. The current paper studies the damage-diagnosis process of the coupled electro-mechanical behavior of an adhesively bonded smart PZT transducer. The inverse of impedance signatures is used for investigating pre-damage diagnosis and analysis of surface-mounted PZT transducer. A parametric study on the variation of adhesive property is carried out to overcome the shear lag effect. The novel contribution of this paper discusses a methodology for an early diagnosis of damage in the PZT transducer and adhesive bond layer during the SHM process. Firstly, the damage is introduced to the PZT patch and bonding layer, and the corresponding EMI signatures are obtained using numerical modeling and simulations. The damage detection using susceptance is discussed for lower frequencies from 0 to 20 kHz. It is observed that the change in susceptance signature is not large enough to detect adhesive debonding. Subsequently, the conductance signatures are utilized for the investigation. It is observed that damage in the adhesive layer and PZT patch cause upward or downward shift with no alteration along the horizontal direction. It helps to detect sensor breakage and adhesive debonding effectively. Secondly, the simulation results are verified using the theoretical analysis for the single piezo configuration by improved continuum-based impedance equations. A modified dual piezo configuration is investigated to validate the proposed method. Experimental investigation on PZT-bonded aluminum plate involving perfectly bonded, adhesive debonding, and sensor breakage conditions are conducted to verify the process. It is found that the real part of the admittance signature is reliable and critical in sensor diagnosis, and sensor faults of debonding and breakage can be identified and differentiated. It also validates the semi-analytical work results. Therefore, the proposed methodology for pre-diagnosing damage present in the smart PZT sensor and adhesive layer using the EMI technique can be utilized for effective SHM.

STUDY ON SPATIAL STRESS EFFECT OF PC CONTINUOUS THIN-WALLED BOX GIRDER BRIDGE

In order to study the influence of spatial stress effect and shear lag effect on the cracking of PC continuous thin-walled box girder bridge, a spatial model was established by using ANSYS finite element software to analyze the internal stress distribution of the bridge. The test results are compared with the analysis results of spatial model and plane link system model through the load test of real bridge. The results show that the longitudinal stress is evenly distributed along the width direction, which means that the spatial stress effect and the shear lag effect have little influence on the downdeflection of the bridge. The shear lag coefficient at the longitudinal axis of midspan bottom plate and the intersection of bottom plate and web are larger than other positions, which is most likely to produce cracks caused by stress concentration, and should be strengthened here in practical engineering. The results of load test show that the results of spatial finite element analysis are more reliable than those of plane link system calculation, and the design and construction based on the results of spatial finite element analysis is safer.

Investigation of shear lag effect in tall tube-type buildings

The dominant structural systems used for high-rise buildings are tube-type systems. Tall tube-type structures act as a cantilever box girder and become prone to the shear lag phenomenon. This phenomenon causes nonlinear stress along the side of the tubular structures, while the beam theory assumes the stress to be linear. This mechanism reduces the efficiency of tube-type structural systems to resist lateral loads. This study explains a detailed discussion of the shear lag effect and the cause of its existence in two cases, positive and negative, through simple numerical analyses. To this end, the impact of lateral deformation on the shear lag effect was investigated in three tube-type structural systems: framed tube, diagrid, and hexagrid with different heights of 50-, 80-, and 110- story buildings subjected to wind load. The lateral deformation of the model structures was compared with the planer deformation (shear and bending deformation) of the cantilever box girder as the benched mark. Analysis results illustrated that the tube type structural system configuration affected the shear and bending deformation portions and the shear lag effect. Based on the results, the direction of the shear flow was changed according to the slope direction of the tangent line of the deflection curve (first deviation) and caused two cases, positive and negative ones. From the numerical results of candidate models, when the tangent line's angle became zero, the shear lag became minimum. When the curvature of the deflection curve (second deviation) was changed (upward into inward), the shear lag became maximum.

Spatial refinement grillage model of box-girder bridges

The objective of this study was to overcome the shortcomings of the current analysis and calculation methods of the spatial bar system model, plane beam grillage model and solid element model in the design of the box-girder bridge. For example, the spatial bar system model lacks refined analysis of spatial effects, such as the shear lag effect, effective distribution width problem, and eccentric load coefficient problem. The similarity of the plane beam grillage model on the principle of equivalence cannot accurately reflect the shear stress distribution of the box-shaped composite beam and the local force on the top and bottom plates. The solid element and shell element models cannot directly calculate the internal force of the cross section. The calculation efficiency is low, and it is difficult to combine with the overall calculation. This paper proposes a spatial grid element analysis model suitable for fine analysis of box-girder bridges, which has the completeness and reliability of the analysis results and makes up for the shortcomings of the current box-girder bridge analysis methods. Firstly, the stiffness matrix of the spatial grid element is deduced, and the analysis program of the combined box girder based on the spatial grid element is written using MATLAB software. Then an actual calculation example is analyzed, and the difference between the calculation result of the spatial grid element and the result of the literature is compared and analyzed. The correctness and applicability of the spatial grid element model is verified.

Behaviour and Design of Cold‐Formed Steel Bolted Portal Frame Connections

AbstractCold‐formed steel (CFS) sections have a wide range of applications, among which portal frames take up an ever more popular place. The behaviour of CFS moment‐resisting frames depends mainly on the performance and failure mechanism of their connections (i.e. the beam‐to‐column and column‐to‐base connections). This paper aims to study the structural performance of CFS moment‐resisting connections by investigating a commonly governing failure mode consisting of local buckling of the CFS member web adjacent to the bolted connection. Experimentally validated finite element models of CFS bolted connections were developed in ABAQUS using Python scripts, taking into account material and geometric nonlinearity, geometric imperfections and realistic bolt bearing behavior. The validated models were then used to investigate the effects of the cross‐sectional shape, plate thickness, bolt configuration and bolt group length on the flexural and the axial compressive capacities of CFS bolted connections. It was concluded that, depending on the geometric characteristics of the connection, its ultimate capacity may be significantly affected by the effects of shear lag. The results were subsequently employed to develop design equations for the nominal flexural and axial compressive capacities of CFS bolted moment‐resisting connections.

A Study on the Shear Lag Effects in Longitudinally Welded Connections Subject to Eccentricity

AbstractIn United States design specifications, shear lag in longitudinally welded connections is accounted for by means of a tabulated factor, which until 2010 was only applicable to plate‐type members having equal length welds on each side, subject to the further constraint of having a minimum weld length equal to the distance between the welds. This created the paradox that connections with longitudinal welds shorter than the distance between the welds were considered by the Specification to have no capacity at all. Research in extant literature based on historical experimental data developed alternative factors that augmented and replaced the previous approaches, making them applicable to longitudinally welded plates, angles, channels, tees, and wide‐flange shapes having equal or unequal weld lengths, and without any weld length‐to‐connection width limitation. This paper presents the results of an experimental study of shear lag effects in longitudinally welded tension members under both in‐plane and out‐of‐plane eccentricity. Forty specimens were tested representing twenty configurations and the experimental results were compared to three theoretical values – (a) the shear lag factor from the 2016 American Institute of Steel Construction (AISC) Specification, (b) the shear lag factor based on a bi‐planar model found in literature, and (c) the shear lag factor from the 2010 AISC Specification. It is concluded that the shear lag factor provided in the 2016 AISC Specification offers the best prediction of the capacity of longitudinally loaded welded connections subject to both in‐plane and out‐of‐plane eccentricity.

Analytical observability method for the structural system identification of wide-flange box girder bridges with the effect of shear lag

In the field of bridge structural system identification (SSI), Bernoulli beam element models are often used to solve inverse problems. More rarely, Timoshenko beam element models can be calibrated. However, these models account for only the general shear effects, whereas other shear effects, such as shear lag, are not accounted for. However, as wide-flange box girder bridges become prevalent due to design demands, neglecting shear lag may introduce significant errors in predicting the mechanical parameters of the system and, hence, reduce the accuracy. In this paper, for the first time, the shear lag's effect on the vertical deflections is taken into account in an inverse problem. A parametric SSI, the observability method (OM), is updated to address the identification of thin-walled box girder bridges with wide flanges, including the shear lag effects. The structural analytical equations are used to connect the spatial shear effects with the beam-unidimensional-element model to be applied in the inverse analysis, which is referred to as the analytical observability method (AOM-SSI). This updated version of the OM is established and validated to identify the mechanical parameters of a structural test. The identified mechanical parameters show much better agreement with the expected results than those obtained with previous methods.

Free vibration performance of curved composite box-girders with corrugated steel webs

The curved composite box girder with corrugated steel webs (CBG with CSWs) shows a more complex performance compared to a straight one due to the coupled flexural-torsional effect caused by its curvature. However, the relevant studies on it were limited. In this paper, considering the shear lag effect of the flanges, the shear deformation of the steel webs, and the coupled flexural-torsional effect, the natural frequencies of the curved CBGs with CSWs were derived using the energy variation method and Hamilton principle. Free vibration experiments were conducted on three simply-supported curved CBGs with CSWs. Numerical analysis was performed using ANSYS software. According to the parametric analysis, the torsional kinetic energy and the additional effect of the restrained torsion have little effect on the natural frequencies in the flexural-torsional vibration, while they significantly affect the flexural mode component. The natural frequencies decrease with the increase of λ (the ratio of calculation span to the radius of the curved axis). When λ ≤ 0.5, the reduction is smaller than 5%, but larger than 10% when λ > 0.7. The span presents an insignificant influence on the fundamental frequency if λ remains constant. Based on the analytical and experimental researches, a simple-to-use equation was proposed to calculate the fundamental frequency of the curved CBGs with CSWs.

Fiber reinforced polymer in civil engineering: Shear lag effect on damaged RC cantilever beams bonded by prestressed plate

This paper presents a careful theoretical investigation into interfacial stresses in damaged RC cantilever beam with bonded prestressed FRP composites, taking into account loading model, shear lag effect and the prestressed composites impact. These composites are used, in particular, for rehabilitation of structures by stopping the propagation of the cracks. They improve rigidity and resistance, and prolong their lifespan. In this paper, an original model is presented to predict and to determine the stresses concentration at the FRP end, with the new theory analysis approach. This research gives more precision related to the others studies which neglect the effect of prestressed composites coupled with the applied loads. A parametric study has been conducted to investigate the sensitivity of interface behavior to parameters such as laminate and adhesive stiffness, the thickness of the laminate and the fiber orientations where all were found to have a marked effect on the magnitude of maximum shear and normal stress in the composite member. The numerical resolution was finalized by taking into account the physical and geometric properties of materials that may play an important role in reducing the stress values. This research is helpful for the understanding on mechanical behaviour of the interface and design of the FRP-damaged RC hybrid structures.

ASSESSING SHEAR-LAG EFFECT ON PULTRUDED FRP RODS BASED ON A NUMERICAL SIMULATION

Fiber reinforced polymer rods fabricated from unidirectional fibers and a polymer matrix strengthen effectively reinforced concrete structures, such as the use in near-surface mounted systems. This study focused on aramid fiber reinforced polymer (AFRP) and analytically assessed the shear-lag effect that significantly affects the tensile capacity of the rod. A representative volume element model was employed for predicting the transversely isotropic properties of AFRP rods. In addition, a finite element simulation for the tension test model was performed to assess the shear-lag effect of an AFRP rod with various diameters. The study proposed a procedure for calculating the stress distribution in any cross-section of a fiber reinforced polymer rod. The simulation results agreed well with the previous experimental study. The findings clearly indicated the position of the failure section and the unequal tensile stress distribution in it. The study revealed that the shear-lag effect varied by the rod diameter affects the stress distribution at the failure section and the tensile capacity. The paper shows that the ultimate tensile capacity of any pultruded FRP rod can be predicted by the proposed method.

A numerical and theoretical analysis of the structural performance for a new type of steel-concrete composite aqueduct

A new type of steel-concrete composite aqueduct, made of steel trough and concrete cover connected by shear studs, is proposed. The composite aqueduct has better fluid tightness, lighter weight, higher capacity and faster construction speed compared with traditional prestressed concrete aqueducts; therefore, it has a broad potential to be applied in water transfer projects. To study the structural performance of the composite aqueduct, a fine finite element model is established by using ABAQUS, whose results are representative of the typical spatial deformations experienced by the aqueduct. Parametric analyses are carried out in the longitudinal and transverse directions. The results indicate that the longitudinal stress is higher than the transverse stress, and a significant shear lag is found on the steel bottom plate. Thus, design parameters are dictated by the longitudinal stress of the steel bottom plate. In order to facilitate the estimation of the longitudinal stress, a fiber model that considers the shear lag effect is developed. The formula of the effective width is fitted based on the results of a series of finite element-based parametric analyses. The fitted formula is more accurate and simpler compared to several national codes, and the error of the stress is usually less than 10%.

Understanding Impedance Response Characteristics of a Piezoelectric-Based Smart Interface Subjected to Functional Degradations

The functionality of piezoelectric devices is of significant importance in the electromechanical impedance (EMI)-based structural health monitoring (SHM) and damage detection. Despite the previous work, the EMI response characteristics of a degraded piezoelectric-based smart interface have not been sufficiently investigated due to the difficulty in making realistic functional defects via the experiment. To overcome this issue, we present a predictive simulation strategy to comprehensively investigate the EMI response characteristics of a smart interface subjected typical functional degradations. For that, a bolted steel girder connection is selected as a host structure to experimentally conduct EMI response measurement via the smart interface. Then, a finite element (FE) model corresponding to the experimental model is established and updated to reproduce the measured EMI response. By using the updated FE model, four common degradation types, including shear lag effect, transducer debonding, transducer breakage, and interface detaching are simulated and their effects on the EMI response are comprehensively analyzed. It is found that the interface detaching defect has significant impacts on the primary resonances of the EMI response and generates additional peaks with complex modal shapes. Also, the functional defects can result in distinctive EMI response characteristics, which are promising for assessing the functional condition of the smart interface.

Three-dimensional shear-flexure interaction model for analysis of non-planar reinforced concrete walls

This paper presents theoretical formulation and results of experimental validation studies of a novel three-dimensional macroscopic nonlinear model that captures the interaction between axial-flexural and shear behavior in reinforced concrete (RC) walls. The original Shear-Flexure-Interaction Multiple-Vertical-Line-Element-Model (SFI-MVLEM) developed previously by the authors, which is essentially a two-dimensional line element for rectangular walls subjected to in-plane loading, is extended in this study to a three-dimensional model formulation (SFI-MVLEM-3D) by applying geometric transformation of the element degrees of freedom that convert it into a four-node element, as well as by incorporating linear elastic out-of-plane behavior based on Kirchhoff plate theory. The proposed three-dimensional, four-node model element is implemented in the official version of open-source analysis software OpenSees and validated against experimental data obtained for four well-instrumented U-shaped wall specimens tested under complex multidirectional loading protocols. Comprehensive and detailed comparisons were conducted between various experimentally-measured and analytically-predicted wall responses including the load-displacement behavior of the wall specimens in various loading directions, contributions of nonlinear flexural and shear deformations to wall displacements, vertical and horizontal profiles of flexural strains, and crack patterns. Results presented demonstrate that the proposed analytical model captures, with good accuracy, most of the experimentally-measured responses of non-rectangular walls subjected to multidirectional loading. Model predictions of the wall lateral load capacity and local responses (strains) are, although reasonable, relatively less accurate when the walls are subjected to diagonal loading conditions, due to the plane-sections-remain-plane assumption implemented in the proposed model formulation that disregards the experimentally-observed shear lag effect.

Role of transducer inertia in generation, sensing, and time-reversal process of Lamb waves in thin plates with surface-bonded piezoelectric transducers

An analytical model is presented for the generation, sensing, and time-reversible process of Lamb waves in thin isotropic plates with surface-bonded piezoelectric wafer transducers, incorporating the shear-lag effect of the bonding layer and inertia effects of the system in transducer modeling. A one-dimensional dynamic shear-lag model for the actuator-plate interaction is used to obtain the shear stress distribution at the actuator-plate interface. The Lamb wave solution for the plate under this shear traction excitation is obtained using the two-dimensional (2D) elasticity equations. A consistent sensor-plate interaction model incorporating the shear-lag and inertia effects is developed to determine the induced sensor voltage from the Lamb strain at the plate surface. The model is validated by comparing it with the 2D coupled piezoelasticity-based finite element simulation and experimental data. Detailed parametric studies are conducted to illustrate the effect of inclusion of inertia of actuator, sensor, adhesive, and plate in the transducer modeling on the Lamb wave generation, sensing, time reversibility, and the system’s best reconstruction frequency, and to ascertain how various geometrical and material parameters of the system influence the same. The developed closed-form solution will be immensely useful for the design of Lamb wave based structural health monitoring systems.

Deep learning-based functional assessment of piezoelectric-based smart interface under various degradations

The piezoelectric-based smart interface technique has shown promising prospects for electro-mechanical impedance (EMI)-based damage detection with various successful applications. During the process of EMI monitoring and damage identification, the operational functionality of the smart interface device is a major concern. In this study, common functional degradations that occurred in the smart interface are diagnosed using a deep learning-based method. Firstly, the effect of functional degradations on the EMI responses is analytically discussed. Secondly, a critical structural joint is selected as the test structure from which EM measurement using the smart interface is conducted. Thirdly, a numerical model corresponding to the experimental model is established and updated to reproduce the measured EMI responses. By using the updated numerical model, the EMI responses of the smart interface under the common functional degradations, such as the shear lag effect, the adhesive debonding, the sensor breakage, and the interface detaching, are simulated; then, the functional degradation-induced EMI changes are characterized. Finally, a convolutional neural network (CNN)-based functional assessment method is newly proposed for the smart interface. The CNN can automatically extract and directly learn optimal features from the raw EMI signals without preprocessing. The CNN is trained and tested using the datasets obtained from the updated numerical model. The obtained results show that the proposed method was successful to classify four types of common defects in the smart interface, even under the effect of noises.