Shear Lag Effect Research Articles

Numerical modeling of the shear lag effect in GFRP as function of fiber content

Numerical modeling of the shear lag effect in GFRP as function of fiber content

Study on bending performance of prefabricated glulam-cross laminated timber composite floor

Abstract The glulam-cross laminated timber (CLT) composite floor is a type of prefabricated composite floor that integrates glulam beams and CLT slab into a unified structure using shear connectors. To investigate the bending performance of the glulam-CLT composite floor, the bending test was conducted on a full-scale composite floor under static load. The study comprehensively analyzed the failure mechanism, load–deflection behavior, interface slip and strain distribution of the glulam-CLT composite floor. The test results of the composite floor indicated that the failure mode was tensile fracture of the wood beam at the bottom. As the load increased, the deflection deformation of the mid-span beam exceeded that of the edge beam. When the load reached its ultimate limit, the deflection deformation of the mid-span beam increased by 14.4% compared to the edge beam. In the early loading phase, the strain distribution of the composite section satisfied the assumption of a plane section. However, the strain distribution deviated from this assumption with the increased load due to the relative slips between the glulam beam and CLT flange. To calculate the bending performance of the composite floor, the M-shaped section of the glulam-CLT composite floor was simplified as T-section composite beams. The linear-elastic method for determining the flexural rigidity and ultimate bearing capacity of the glulam-CLT composite floors was proved to be accurate and reliable. The findings provided valuable insights into the bending behavior of the CLT flange under load and emphasized the non-uniform stress distribution caused by shear lag effects.

Shear Lag Effect on Box Steel Beams with Wide Curved Flanges

Shear Lag Effect on Box Steel Beams with Wide Curved Flanges

Analytical prediction of temperature effects on Lamb wave response in smart plates and its experimental verification

Abstract This article examines the effectiveness of a recently developed theoretical model for the generation and sensing of Lamb waves in thin plates with surface-bonded piezoelectric transducers in predicting temperature effects on Lamb waves and their time reversibility. In particular, the analytical model provides a closed-form solution, which incorporates both the shear-lag effect of the bonding layer and the system inertia in transducer-plate interaction modeling. Temperature-dependent material properties and thermal expansion of the system constituents are considered to predict the Lamb wave signal under a thermal environment. The accuracy of the theoretical prediction is assessed in comparison with experimental results obtained using an aluminum plate with adhesively bonded lead zirconate titanate transducers to its surface at different system temperatures ranging from 20°C to 75°C. Comparison is also made with experimental data and analytical solutions presented earlier without considering the inertia effect. The study reveals that the current solution accurately predicts the change in Lamb wave signal due to temperature variation, including the frequency dependency of the peak amplitude change with temperature rise. However, the theoretical model fails to predict the experimental trends when the inertia terms are neglected. The current model is also used to study the contributions of individual system parameters to the overall temperature effect on the time reversibility of Lamb waves and its dependence on the excitation frequency.

Investigating the mechanical properties related to the vertical bending of composite I‐beams with corrugated steel webs

AbstractThe maximum angular rotation attributable to the in‐plane shear deformation of flange slabs is used as generalised displacement in the conventional analysis method for I‐beams. However, the mechanical concepts are poorly understood due to the complex nature of this analysis method. Consequently, a novel strategy for analysing vertical bending in composite I‐beams is proposed in this study. This approach uses the additional deflection of composite I‐beams induced by the shear lag effect as the generalised displacement. Furthermore, this research comprehensively considers the accordion effect, shear lag and self‐equilibrium conditions for the shear lag warping stress and bending moment. Moreover, two longitudinal warping displacement difference functions are employed to accurately describe the variation of shear lag in composite I‐beams with varying flange slab widths. The differential equations of the I‐beams with corrugated steel webs in the elastic range are established based on the energy‐variation method. A complete mechanical system of a composite I‐beam is decomposed into two parts, namely, the shear lag mechanical system and the elementary beam mechanical system, which are independent of each other. The theory presented in this paper reflects the internal mechanical mechanism of composite I‐beams. The calculation accuracy is considerably improved in this study. Therefore, this method is more unambiguous and well‐defined. It enriches and advances the current analysis theory of composite structures, which can guide the design of composite I‐beams.

Research on spatial corrosion behavior and durability protection technology of concrete box girder bridge in cold regions

In order to study the corrosion behavior of concrete box girder in deicing salt environment, a series scaled model of concrete box girders were made to study the deterioration mode of concrete box girder under load, chloride corrosion, freeze-thaw cycle and their combined action. Combined with silane impregnation, the durability protection technology of concrete box girder bridges in cold regions was proposed. The experimental results show that under freezing-thawing action, the top plate of the box girder has the most serious deterioration, and the performance of the web is better. The surface erosion of the top plate is 65.38 % and 80.77 % different from that of the bottom plate and web plate, respectively. The freezing-thawing erosion of the concrete box girder has a significant spatial multi-dimension. The chloride ion erosion law of the top plate and bottom plate of concrete box girder is similar to the distribution law of shear lag effect under load. The inhibition effect of compressive stress on chloride ion is 9.67 %, and the overall inhibition effect is not large. The maximum difference of chloride ion concentration at each measuring point on the bottom plate is 30.14 %. Silane can be used as a protective coating for concrete bridges in cold areas, and the coating thickness of 2 mm can meet the requirements of anti-freezing. With the increase of freeze-thaw time, the silane protection ability began to decline. The maximum silane protection effect of 0–1 cm from the surface at 90d and 180d decreased by 40.8 % and 71.7 %, respectively. After the silane coating was applied, the chloride ion erosion rate of the bottom plate still showed a faster trend. When the freeze-thaw cycle exceeded 30 times, the silane protection ability decreased almost at a linear rate with the freeze-thaw time. Regardless of whether the silane coating protection technology is adopted, the chloride ion concentration of the bottom plate of concrete box girders is at least 10 % more than that of the top plate for freeze-thawing 90d and 180d, and the maximum can reach 32.1 %. The deterioration behavior of concrete box girders in cold regions has significant spatial multi-dimension. The existing single-parameter durability design methods, which mainly focus on solid section, are no longer suitable for box girder structures.

A NUMERICAL MODEL FOR ANALYZING CROSS LAMINATED TIMBER UNDER OUT OF PLANE LOADING

This paper targets the validity of a novel numerical model for analyzing CLT under out of plane loading. This numerical model was initially developed for determining the shear lag effect that appears in laminated thin walled composite beams. A parametric study was conducted in order to determine the influence of orientation of layers in CLT panels on bending strength and deflection. For confirming the accuracy of the proposed model, the results from the numerical model are compared with the external results of the computer software Ansys. The differences in bending stress vary from 0.27% to 1.69% depending on the orientation of layers and for deflection the differences are ranged from 2.25% to 7.42%. A numerical study was conducted and obtained data corresponds to results obtained from experimental study. It was concluded that the proposed numerical method can enough precisely predict the behavior of CLT under out of plane loading.

Experimental and Analytical Study on Shear Lag Effect of T-Shaped Reinforced Concrete Shear Walls

Because of the flanges on T-shaped shear walls (TSSWs), the shear force acting on such walls results in a shear lag effect, making it impossible to forecast with accuracy the normal stresses of the flanges using the Bernoulli–Euler assumption. Shear lag (SL) in flanged walls has, however, received less attention from researchers, particularly in experimental studies. Understanding the SL in T-shaped reinforced concrete shear walls under shear and axial force is the main goal of this work. First, a SL model is suggested for TSSWs. In this model, the SL deflection is considered to be the generalized displacement and the SL warping deformation, and it is assumed to be a quadratic nonlinear function. Then, experimental and numerical simulation studies are, respectively, conducted to investigate SL effect of TSSWs, and also to evaluate the accuracy of the SL method. Finally, the parameter analysis is conducted to investigate the influence of axial load, shear force, and flange length on the SL effect of TSSWs. The results show that the SL of the TSSW is significant, the normal stress distribution (NSD) of the flange is uneven, and the normal stresses near the web are higher, according to the results of the analytical, simulated, and experimental results. The SL model can accurately predict the normal stresses of the flange of TSSWs, and the quadratic parabola assumption of the SL warp displacement of TSSWs is reasonable. Parameter analysis shows that axial force has little effect on the SL effect of TSSWs. The TSSWs under larger shear force have the more obvious SL effect. A more obvious SL effect occurs in the TSSWs with longer flanges.

Shear Lag Effect and Its Additional Deflection Contribution of Composite Beam Bridges

The composite beam structure is widely used in the engineering field because it benefits from the advantages of two materials, presenting outstanding advantages for construction purposes. However, at present, there are issues with the analysis and solution of the composite beam structure, such as the difficulty in developing a suitable analytical theory and the low degree of refinement achieved by simulation analysis. To accurately grasp the mechanical behavior of the composite beam structure and achieve its refined analysis, this paper proposes a refined spatial grid element analysis method that can simultaneously obtain the internal forces, displacements, and stresses of various parts of a composite beam. Based on the above new method, the effects of geometrical structural factors such as wide-span ratio, high-span ratio, and web thickness with respect to the shear lag effect are analyzed. The distribution law of the shear lag coefficient and its additional deflection are analyzed. The results demonstrate that using this analysis method to calculate and analyze steel-concrete duplex type composite beams can directly obtain the internal forces and displacements of the joints of the composite beam roof, floor, and web. The spatial grid element analysis method provides both the theoretical and practical means to achieve both the overall and local refinement analysis of the composite beam structure.

Bond behavior and modeling of steel-FRP composite bars in engineered cementitious composites

The combination of the steel-FRP composite bar (SFCB) and engineered cementitious composite (ECC) holds favorable applications in terms of durable resilient structures. However, a clear understanding of the interfacial bond performance of this novel combination is currently lacking. Therefore, the bond behavior and mechanism of the SFCB-ECC interface were investigated through direct pullout tests. A total of 48 cube specimens were fabricated, with the test variables including bar type, bar diameter, embedment length, and matrix type. The experimental results indicated that the bond failure mode of SFCBs and FRP bars differed from that of deformed steel bars, attributed to the damage of resin-rich ribs in relatively high-strength ECC. The bond-slip curves revealed both the fundamental differences and similarities among steel bars, SFCBs, and FRP bars. The Poisson effect and shear lag effect increased with a decrease in bar stiffness and an increase in diameter. The combined impact of the interaction between the bar stiffness and diameter resulted in varying bond strengths for steel bars, SFCBs, and GFRP bars, despite their similar surface geometries. A theoretical model for the bond strength at the SFCB-ECC interface was derived using the thick-walled cylinder principle and subsequently validated with test data. Finally, a unified empirical model framework for predicting the bond strength of various bar-matrix combinations was proposed based on the theoretical model. The accuracy of this method was evaluated using a collected database.

Experimental Study on Shear Lag Effect of Long-Span Wide Prestressed Concrete Cable-Stayed Bridge Box Girder under Eccentric Load

Based on the engineering background of the wide-width single cable-stayed bridge, the shear lag effects of the cross-section of these bridge box girders under the action of the eccentric load were experimentally studied. The behavior of shear lag effects in the horizontal and longitudinal bridge directions under eccentric load in the operational stage of a single cable-stayed bridge was analyzed by a model testing method and a finite element (FE) analytical method. The results showed that the plane stress calculation under unidirectional live load was similar to the results from spatial FE analysis and structural calculations performed according to the effective flange width described in the design specification. At the position of the main beam near the cable force point of action, the positive stress at its upper wing edge was greatest. At a distance from the cable tension point, the maximum positive stress position trend showed that from the center of the top flange to the junction of the top flange and the middle web to the junction of the top flange and the middle web and the side web. Under eccentric load, the positive and negative shear lag effects on the end fulcrum existed at the same time, and the shear lag coefficient on the web plate was larger than the shear lag coefficient on the unforced side. Due to the influence of constraint at the middle fulcrum near the middle pivot point, positive and negative shear lag effects were significant, and the coefficient variation range was large, resulting in large tensile stress on the roof plate in this area. According to FE analytical results, stress and shear forces of a single box three-chamber box girder under eccentric load were theoretically analyzed, the bending load decomposed into the accumulation of bending moment and axial force, using the bar simulation method, and the overall shear lag effect coefficient λ was obtained and verified.

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.

On the Use of the Effective Width for Simply Supported Generally Loaded Box-Girders

A new method for evaluating the effective flange width of simply supported rectangular box-girders in bending is illustrated. It aims to overcome the lack in the literature of a general method able to supply the effective flange width for a general distribution of loads along the beam axis, not restricted, i.e., to the few cases reported in standard codes. The method consists of finding an analytical expression for the effective width under sinusoidal loads of arbitrary wavelength and combining the results in the framework of a Fourier analysis. The model allows investigating the shear-lag effects on displacements and stresses. The analytical formulation proposed is validated against numerical results supplied by refined Finite Element analyses.

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.

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.

Superior strength-ductility combination in TiC/TC4 composites via In situ construction Ti2Cu nanoparticles

Synergistic improvement of strength and ductility is challenging in the engineering applications of titanium matrix composites (TMCs). Herein, we fabricated the TC4 composites reinforced with grain boundary micron-TiC and intragranular nano-Ti2Cu using spark plasma sintering (SPS) and hot rolling (HR) to achieve a good balance between strength and ductility. An interfacial reaction between Ti and C forms the grain boundary TiC, and the vast majority of intragranular nano-Ti2Cu precipitates to accommodate the severe lattice distortion caused by the solid solution of Cu in β-Ti phase. Benefiting from Ti2Cu nanoprecipitates and their ability to effectively suppress dislocation motion, precipitation strengthening, and dislocation strengthening are the main factors, in addition to grain refinement strengthening due to deformation processing, that contribute to the realization of the superior yield strength (YS) of 1360 MPa and ultimate tensile strength (UTS) of 1504 MPa in composites than TC4 matrix (YS = 986 MPa, UTS = 1160 MPa). Meanwhile, the interfacial strain-delocalization effect of TiC/Ti2Cu with Ti matrix, the shear-lag effect of TiC, and the sustained strain-hardening effect provided by TiC/Ti2Cu empower the composites with an outstanding ductility (fracture elongation of 8.4 %). This study highlights the untapped potential for improving the mechanical properties of Ti matrix composites.

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.