Shear Connection Stiffness Research Articles

Bandgap analysis of partial-interaction composite beams periodically attached vibration absorbers

Elastic metamaterials with local resonant components exhibit unique bandgap behavior that can be utilized to control the vibration and noise of mechanical structures. This study aims to introduce the bandgap characteristics into the vibroacoustic control of partial-interaction composite beams (PICBs) widely adopted in civil engineering, aviation, and marine fields. Vibration absorbers are arranged periodically on the beam to generate a bandgap in PICBs, thereby transforming a conventional PICB into a metamaterial beam. An analytical approach is proposed to establish the spectral element (SE) matrix of a metamaterial beam based on the Timoshenko–Ehrenfest beam theory. Specifically, the governing equations of motion for PICBs follow Hamilton's principle. This model considers the effects of shear slip between two-layer sub-beams, shear deformations, and rotary inertia. The SE matrix of PICBs is then constructed and applied to obtain the SE matrix of the metamaterial beam by assembling the SE matrix of the vibration absorbers. Subsequently, the wave finite element (WFE) method is employed to predict the dispersion curve of the infinite metamaterial beam and the dynamic response of the finite metamaterial beam. In a benchmark example, the complex band structure and transmission indicated by the proposed approach are validated compared to those calculated by evaluation formulas of the literature and the finite element method. Lastly, the bandgap behavior for the vibration absorber parameters, lattice constants, and shear connector stiffness is investigated based on the defined dimensionless parameters. These results are valuable for optimizing vibration and noise reduction in PICBs equipped with attached vibration absorbers.

Load introduction to composite columns revisited—Significance of force allocation and shear connection stiffness

The AISC 360-16 Specification recommends that the design shear force between parts of a composite column in the load introduction area shall be calculated based on the force allocation at ultimate limit state. Applicability of this straightforward method to the load levels that usually arise in slender composite columns is questionable, as this capacity-based force allocation is only true when the axial force is equal to the plastic resistance of the composite cross-section. Next, the number of required shear connectors is calculated as a quotient of the design shear force and the strength of a single shear connector. We demonstrate that: first, for the lower load levels, the stiffness-based force allocation gives a more accurate estimate of the shear force; second, the number of shear connectors satisfying the strength requirement can lead to insufficient force transfer between parts of the composite cross-section. To investigate the shear transfer mechanism in composite columns, we derive an analytical model with linear elastic constitutive relations both for steel and concrete and three types of shear force slip laws: elastic, elastic plastic, and rigid plastic. The case studies carried out for different shear transfer scenarios demonstrate the importance of the shear connection stiffness on the effectiveness of the load introduction. The remaining portion of the shear force is transferred outside the load introduction area, which hampers the column’s ability to withstand shearing from varying bending moments or incipient buckling. To control the shear force transfer efficiency by enhancing the shear connection stiffness, we propose an original Stiffness Method and provide design charts as an aid in the design process.

Parametric analysis of the effective flange width of mass timber composite floor panels

Mass timber composites (MTCs), where the webs are typically spaced 750–2000 mm apart, have shown potential in overcoming span limitations of conventional flat slab mass timber floors. However, fundamental research investigating the non-linear stress distribution (i.e., shear lag) in the flanges is required. While this behaviour has been simplified in design for other materials using the concept of an effective flange width (EFW), no guidance exists in international design codes for mass timber composites. In the current study, a parametric analysis was conducted on a mass timber I-beam under positive bending where the effects of web spacing, beam configuration (edge or interior placement), shear connection stiffness, concentrated versus uniform loading, web depth, web width, flange thickness, and flange modulus of elasticity on the EFW, were investigated. The reference section in the finite element model consisted of a glued-laminated timber (GLT) panel for the flanges, a glulam beam web, and a fully composite glued connection between elements.The results have shown that existing design code provisions, even those meant for light-frame wood members, over-estimate the EFW of GLT-glulam I-beams. The web spacing, shear connection stiffness, loading type, flange thickness, and web width were observed to be the most influential parameters on the EFW of GLT-glulam MTCs. Between the upper and lower boundaries of connection stiffness, a sharp increase in the EFW was observed below the point of full composite action due to the section beginning to behave as three separate elements. Although, the decrease in composite action resulted in an overall decrease in the bending stiffness of the section. For GLT-glulam MTCs, the modulus of elasticity (MOE) of the GLT flange was not observed to significantly affect the EFW for high degree of composite action configurations. A small increase in the EFW was observed when the degree of composite action was relatively low. Ultimately, the development of equations for quantifying the EFW of MTCs is key to their increased adoption but requires the expansion of the current study to include other mass timber elements, as well as experimental data investigating the most significant parameters identified herein.

A numerically stable exact method for analysis of partial-interaction composite beams based on Timoshenko beam theory

The traditional direct stiffness matrix method may occur numerical instability for analysis of partial-interaction composite beams with long spans. To solve this problem, this paper proposes a numerically stable exact method called the coefficient matrix method for analysis of two-layered partial-interaction composite beams using the Timoshenko beam theory. By replacing the nodal displacements with the undetermined parameters of shape function obtained by the governing equation as primary unknown coefficients, the coefficient matrix method can avoid the inversion operation on the matrices in obtaining the direct stiffness matrix. Thus, numerical stability can be ensured. Finally, the coefficient matrix method is validated against experimental, ANSYS and other theoretical results in the literature with good agreement. And the effect of shear deformation on shear slips at the interface of the sub-beams by varying shear connector stiffness, shear-to-Young’s modulus ratios, and span-to-depth ratios are discussed.

Shear behavior of large studs and novel bolted connectors in steel-UHPC composite beams

With the gradual application of ultra-high performance concrete (UHPC), steel-UHPC composite bridges produce higher interfacial shear, which require larger diameter studs to avoid the group-stud effect of abundant small studs and accelerate the construction. Considering welding problems of larger studs, bolted connectors could be an alternative and benefit the replacement of composite bridges. The traditional bolted connector expressed early slip on the steel-UHPC interface due to the bolt-to-hole clearance, which reduced the composite action. To decrease the clearance, three novel bolted connectors involving a hinged bolt, a threaded-hole bolt, and a taper-sleeve bolt were proposed and tested along with large studs and traditional bolted connectors. The diameter of shear connectors ranged from 24 mm to 40 mm. Three failure modes were observed, in which the failure of the studs was significantly influenced by the welding quality. The shear capacities of the novel and traditional bolts with the same diameter were similar and unrelated to the bolt-to-hole clearance. The novel bolted connectors did not exhibit an early slip in load-slip curve and their stiffness was maximum 4.1 times that of the traditional bolt. The shear capacity and stiffness of shear connectors increased with their diameter. Six equations for predicting shear capacity and five equations for the shear stiffness of shear connectors were evaluated, the ductility of the studs and bolts were also assessed. The hinged bolt was evaluated to have a better comprehensive shear performance than other bolted connectors.

Dynamic Analysis of a Steel–Concrete Composite Box-Girder Bridge–Train Coupling System Considering Slip, Shear-Lag and Time-Dependent Effects

A dynamic computational program considering slip, shear-lag and time-dependent effects of composite box-girder bridge–train coupling system is firstly proposed based on the authors’ previous studies. In the program, the long-term vertical displacement of a composite bridge is firstly calculated. The calculated vertical displacement is then superimposed on the existing uneven track as the new excitation of the composite box-girder bridge–train coupling system to obtain the dynamic responses of the bridge–train coupling system. A 3 × 40 m simply supported steel–concrete composite box-girder bridge is selected to investigate the influence of its time-dependent behavior on its dynamic responses. The results showed that the time-dependent effect will amplify the dynamic characteristics of the composite box-girder bridge and the high-speed train. The maximum vertical displacement and acceleration of the composite bridge increase by 8.82% and 13.64%, and the maximum vertical acceleration of the train body increases by 144.78%. Additionally, the slip and shear-lag effects have an impact on the dynamic responses of the composite box-girder bridge–train coupling system at different operation times. The dynamic responses of the coupling system strengthen with the decrease in shear connection stiffness. The dynamic responses of the system may be underestimated when the shear-lag effect is not neglected. Therefore, these conclusions should be given sufficient attention in the design, construction and operation of high-speed railway composite bridges.

Dynamic Amplification Factors of Partial-Interaction Composite Beams Acted Upon by the Moving Load

This paper focuses on the dynamic response, mainly dynamic amplification factors (DAFs), of partial-interaction composite beams (PICBs) based on the Timoshenko beam theory (TBT). By assuming that each sub-beam behaves as an independent Timoshenko beam, the governing differential equations of motion of the PICBs are derived under the action of dynamic load. The natural frequencies and modal shapes for simply supported PICBs are also extracted. For decoupling the governing differential equations of motion, the orthogonality property of two distinct vibration modes is checked and applied for further analysis. The modal superposition method is then utilized to derive the analytical expressions of transverse deflection, interfacial shear slip, and normal stresses of the PICBs subjected to the moving load. Finally, two test beams are organized to validate the proposed methodology. For this purpose, the results which are calculated by ANSYS and obtained from available methods are appropriately compared. The effects of shear connector stiffness and speed of the moving load on the DAFs of the PICB acted upon by the moving constant load are discussed.

A calculation approach for sandwich panels with facings made of UHPFRC and pre-tensioned CFRP reinforcement

Sandwich panels are widely applied in construction industry, e.g. for modern building envelopes. They show low self-weight and high load-bearing capacity as well as sufficient physical properties, but are usually limited to relatively short spans. In contrast, thin concrete shell structures show high stiffness as well as load-bearing capacity even for long spans. Combining both construction methods and applying non-corrosive high-strength materials enables multifunctional, light elements with long spans, high load-carrying capacities and additional physical properties.In this paper, sandwich panels with flat and folded plate facings made of ultra-high performance fibre reinforced concrete (UHPFRC) and carbon fibre reinforced polymer (CFRP) prestressing strands are investigated. For a reliable bond strength and to account for spatial facings, a special production method was developed. For the prediction of the flexural behaviour, a new calculation approach is derived step-by-step which accounts for non-linear behaviour. Theoretical bending moment–curvature relationships are derived for UHPFRC cross-sections with CFRP prestressing strands and incorporated in differential equations of sandwich theory to account for cracking and residual stresses in facings. As additional merit of this approach, the tensile strength of UHPFRC is derived from material samples. Spring models to consider stiffness of shear connectors and core material are applied. The non-linear calculation approach covers typical failure mechanisms. Non-linear load-deformation relationships are calculated and compared to experimental test data of prestressed sandwich panels.

Mechanical behavior of an innovative steel–concrete joint for long-span railway hybrid box girder cable-stayed bridges

This research proposes an innovative steel–concrete joint, which utilizes front and rear bearing plates and concrete filled steel cells, for long-span railway hybrid box girder cable-stayed bridges. This study investigates the mechanical behavior of the steel–concrete joint through a model test and finite element analysis, aiming to understand the stress distributions, shear lag effects, deformations, and force transfer pathway of the joint under axial and shear loads. A large-scale model (scale: 1/5) was designed following the similarity theory. The model was fabricated and tested under representative load cases. Based on the model test, a three-dimensional finite element model was established and validated using the model test results. Then, the finite element model was utilized to perform a parametric study on the effects of the length of the joint, the thickness of the bearing plates, the height of steel cells, and the stiffness of shear connectors. The results show that the proposed steel–concrete joint provides desired stress distribution and force transfer behavior, in terms of the force transfer rate and uniformity. In the composite section of the joint, the rear bearing plate transfers 57% the total axial force. This study is expected to promote the design and applications of hybrid girders.

An equivalent single-layer theory for free vibration analysis of steel-concrete composite beams

An equivalent single-layer theory (EST) is put forward for analyzing free vibrations of steel-concrete composite beams (SCCB) based on a higher-order beam theory. In the EST, the effect of partial interaction between sub-beams and the transverse shear deformation are taken into account. After using the interlaminar shear force continuity condition and the shear stress free conditions at the top and bottom surface, the displacement function of the EST does not contain the first derivatives of transverse displacement. Therefore, the C0 interpolation functions are just demanded during its finite element implementation. Finally, the EST is validated by comparing the results of two simply-supported steel-concrete composite beams which are tested in laboratory and calculated by ANSYS software. Then, the influencing factors for free vibrations of SCCB are analyzed, such as, different boundary conditions, depth to span ratio, high-order shear terms, and interfacial shear connector stiffness.

Analysis of shear lag effect in the negative moment region of steel-concrete composite beams under fatigue load

Shear lag effect was a significant mechanical behavior of steel-concrete composite beams, and the effective flange width was needed to consider this effect. However, the effective flange width is mostly determined by static load test. The cyclic vehicle loading cases, which is more practical, was not well considered. This paper focuses on the study of shear lag effect of the concrete slab in the negative moment region under fatigue cyclic load. Two specimens of two-span steel-concrete composite beams were tested under fatigue load and static load respectively to compare the differences in the negative moment region. The reinforcement strain in the negative moment region was measured and the stress was also analyzed under different loads. Based on the OpenSees framework, finite element analysis model of steel-concrete composite beam is established, which is used to simulate transverse reinforcement stress distribution as well as the variation trends under fatigue cycles. With the established model, effects of fatigue stress amplitude, flange width to span ratio, concrete slab thickness and shear connector stiffness on the shear lag effect of concrete slab in negative moment area are analyzed, and the effective flange width ratio of concrete slab under different working conditions is calculated. The simulated results of effective flange width are compared with calculated results of the commonly used specifications, and it is found that the methods in the specifications can better estimate the shear lag effect in concrete slab under static load, but the effective flange width in the negative moment zone under fatigue load has a large deviation.

Finite beam element with 22 DOF for curved composite box girders considering torsion, distortion, and biaxial slip

Experimental and numerical study on the mechanical performance of curved steel–concrete composite box girders is reported in this research. First, this research establishes a theoretical model for curved composite girders with 11° of freedoms (DOFs) for each node. The DOFs include the longitudinal displacement, transverse displacement, deflection, torsion angle, warping angle, and interface biaxial slip between steel and concrete. Based on the virtual work theorem, the equilibrium function, the stiffness matrix, the node displacement matrix and the external load matrix are proposed for the curved composite girders using the FE spatial discretization. Second, the authors conduct an experimental program on three large-scale curved composite girders with various interface shear connectors and central angles. The comparison between the developed finite beam element, the elaborate FE model and the test results indicates the developed finite beam element has an adequate level of accuracy in predicting the deflection, the torsion angle and the axial strain distribution of test specimens. Third, based on the developed finite beam element model, the effect of initial curvature, number of diaphragms, and the interface connector stiffness on the curved composite girder is examined. The simulation results showed that the initial curvature significantly contributes to the displacement and stress of composite girders. Applying more diaphragms can notably reduce the distortion angle and distortion displacement. The interface shear connector stiffness has a significant influence on the curved composite girder. With the increasing shear connector stiffness, the displacement and stress of curved composite girders decrease notably. Based on the parametric analyses, it is recommended to limit the central angle of simply supported composite girder below 45°, to apply an adequate number of diaphragms, and to design curved composite girders as fully shear connection specimens.

Finite Beam Element for Curved Steel-Concrete Composite Box Beams Considering Time-Dependent Effect.

Curved steel–concrete composite box beams are widely used in urban overpasses and ramp bridges. In contrast to straight composite beams, curved composite box beams exhibit complex mechanical behavior with bending–torsion coupling, including constrained torsion, distortion, and interfacial biaxial slip. The shear-lag effect and curvature variation in the radial direction should be taken into account when the beam is sufficiently wide. Additionally, long-term deflection has been observed in curved composite box beams due to the shrinkage and creep effects of the concrete slab. In this paper, an equilibrium equation for a theoretical model of curved composite box beams is proposed according to the virtual work principle. The finite element method is adopted to obtain the element stiffness matrix and nodal load matrix. The age-adjusted effective modulus method is introduced to address the concrete creep effects. This 26-DOF finite beam element model is able to simulate the constrained torsion, distortion, interfacial biaxial slip, shear lag, and time-dependent effects of curved composite box beams and account for curvature variation in the radial direction. An elaborate finite element model of a typical curved composite box beam is established. The correctness and applicability of the proposed finite beam element model is verified by comparing the results from the proposed beam element model to those from the elaborate finite element model. The proposed beam element model is used to analyze the long-term behavior of curved composite box beams. The analysis shows that significant changes in the displacement, stress and shear-lag coefficient occur in the curved composite beams within the first year of loading, after which the variation tendency becomes gradual. Moreover, increases in the central angle and shear connection stiffness both reduce the change rates of displacement and stress with respect to time.

Flexural and eigen-buckling analysis of steel-concrete partially composite plates using weak form quadrature element method

Flexural and eigen-buckling analyses for rectangular steel-concrete partially composite plates (PCPs) with interlayer slip under simply supported and clamped boundary conditions are conducted using the weak form quadrature element method (QEM). Both of the derivatives and integrals in the variational description of a problem to be solved are directly evaluated by the aid of identical numerical interpolation points in the weak form QEM. The effectiveness of the presented numerical model is validated by comparing numerical results of the weak form QEM with those from FEM or analytic solution. It can be observed that only one quadrature element is fully competent for flexural and eigen-buckling analysis of a rectangular partially composite plate with shear connection stiffness commonly used. The numerical integration order of quadrature element can be adjusted neatly to meet the convergence requirement. The quadrature element model presented here is an effective and promising tool for further analysis of steel-concrete PCPs under more general circumstances. Parametric studies on the shear connection stiffness and length-width ratio of the plate are also presented. It is shown that the flexural deflections and the critical buckling loads of PCPs are significantly affected by the shear connection stiffness when its value is within a certain range.

Theoretical analysis on long-term deflection of GFRP-concrete hybrid structures with partial interaction

The creep and shrinkage of concrete and the creep of glass-fiber reinforced polymer (GFRP) may lead to the increase of long-term deflection of GFRP-concrete hybrid structures under service loading, due to the change of internal forces and stresses. This paper presents a calculation model to consider the influence of the aforementioned changes in analyzing the long-term deflection of GFRP-concrete hybrid structures with partial interaction under service loading, based on the age-adjusted effective modulus method (AEMM). The calculated results from the proposed calculation model agree well with the available experimental results. A further discussion is also made about the effects of the concrete creep and shrinkage and the GFRP creep, as well as the shear stiffness of shear connectors on long-term behavior of GFRP-concrete hybrid structures. Especially, the significant influence of concrete shrinkage on long-term interface slip, interface shear and long-term deflection is found. What’s more, the long-term deflection may increase with the augment of horizontal shear stiffness of shear connectors.

Numerical analysis of the effect of partial interaction in the evaluation of the effective width of composite beams

Abstract Most of the engineering problems involving structural elements of steel-concrete composite beam type are approximations of the structural problem involving concrete plates connected by connectors to steel beams. Technical standards allow the replacement of the concrete plate element by a beam element by adopting a reduction in the width of the plate element known as effective width. The effective width is obtained, in most technical norms, taking into account only the parameters of beam span length and distance between adjacent beams. Numerical and experimental works found in the literature show that this effective width depends on several other parameters, such as the width and thickness of the concrete slab, and the type of loading. The objective of this work is to verify the influence of the partial interaction in the evaluation of the effective width of composite beams formed by a concrete slab connected to a steel beam with deformable connection, being used in numerical simulation three types of finite elements: a plate element for nonlinear analysis of the concrete slab; a bar element for non-linear analysis of beams with cross-section defined by a polygon; and an interface element which connects the plate and beam elements, simulating the deformation effect of the shear connectors. In the studied examples, it was found that the reduction of the shear connection stiffness at the interface between the concrete slab and the steel beam leads to a decrease in the shear lag effect and, consequently, makes the effective width of the concrete slab closer to the its real width. In another example, curves are constructed to define the effective width of a composite beam with medium stiffness. Considering maximum stresses and maximum displacements, these curves are obtained by forcing the equivalence of the approximate model with the model closest to the real problem.

An Improved Model for the Analysis of Plates Stiffened by Parallel Beams Including Creep and Shrinkage Effects: Application to Concrete or to Composite Steel-Concrete Structures

In this paper, an improved model for the static analysis of reinforced concrete plates stiffened by arbitrarily placed parallel reinforced concrete or steel beams with deformable connection taking into account the influence of creep and shrinkage effects relative with the time of the casting and the time of the loading of the plate and the beams is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation (i.e. uplift neglected) and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces taking into account their relation with the interface slip through the shear connector stiffness. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account describing better in this way the actual response of the plate - beams system. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. Six boundary value problems are formulated and solved using the Analog Equation Method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model describes better the actual response of the plate - beams system and permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The evaluated lateral deflections of the plate - beams system are found to exhibit considerable discrepancy from those of other models, which neglect inplane and axial forces and deformations. Numerical examples with great practical interest are presented.

Load Transfer Mechanism of Hybrid Pylon Joint with Cells and Bearing Plates

To investigate the load transfer mechanism of the steel‐concrete hybrid pylon joint with cells and bearing plates, a theoretical model based on the continuous elastic interlayer method was established. Both the slip effect at the steel‐concrete interface and the local compression effect of the bearing plate were considered in the proposed theoretical model. A segment model test with a 1 : 3 scale was carried out to obtain the strain distribution of the hybrid joint and the relative slip between steel and concrete components. Finite element analysis was implemented on the tested segment model, and the structural performance of the tested hybrid joint was compared with the FEA results. The test and analysis results show that the stress of steel and concrete components is at a lower level, and the relative slip between steel and concrete components is extremely limited. The bearing plates and shear connectors are the two load‐transferring components and could transfer 40% and 60% of the vertical force into the lower concrete pylon, respectively. The vertical force of shear connectors is at a much lower magnitude within 0.6 times the length of the hybrid joint from the bearing plate and will increase gradually within 0.6 to 1.0 times the length of the hybrid joint. The FEA results are in good agreement with the model test results, and the maximum shear force difference between the theoretical analysis results and the FEA results is less than 10%, proving that the proposed theoretical model can reasonably predict the shear force distribution at the steel‐concrete interface of the hybrid joint. In addition, the stiffness of shear connectors has limited effect on the shear force distribution at the steel‐concrete interface.

Deflection calculation method on GFRP-concrete-steel composite beam

A calculation method was presented to calculate the deflection of GFRP-concrete-steel beams with full or partial shear connections. First, the sectional analysis method was improved by considering concrete nonlinearity and shear connection stiffness variation along the beam direction. Then the equivalent slip strain was used to take into consideration of variable crosssections. Experiments and nonlinear finite element analysis were performed to validate the calculation method. The experimental results showed the deflection of composite beams could be accurately predicted by using the theoretical model or the finite element simulation. Furthermore, more finite element models were established to verify the accuracy of the theoretical model, which included different GFRP plates and different numbers of shear connectors. The theoretical results agreed well with the numerical results. In addition, parametric studies using theoretical method were also performed to find out the effect of parameters on the deflection. Based on the parametric studies, a simplified calculation formula of GFRP-concrete-steel composite beam was exhibited. In general, the calculation method could provide a more accurate theoretical result without complex finite element simulation, and serve for the further study of continuous GFRP-concrete-steel composite beams.

Residual stiffness and strength of shear connectors in steel-concrete composite beams after being subjected to a pull-out pre-damaging: An experimental investigation

Horizontal stability of the medium rise steel frame structures is usually ensured by vertical bracings and diaphragm action of composite floors. Load transfer within the composite floor system is made through shear connectors, e.g. headed studs. In an event of explosion, such connectors must reserve sufficient residual stiffness and strength in order to avoid a sudden or delayed collapse of the building. These remaining capacities have not been experimentally studied yet in the literature. This paper presents large scale horizontal push out tests to determine the residual stiffness of the shear connectors after being initially damaged by explosion. The initial damaging is reproduced by a pull-out test using a quasi-static loading. Two types of numerical simulation have also been developed using ABAQUS/CAE software to provide a better understanding of the experimental results.