Shear Connection Stiffness Research Articles

Composite actions within steel-FRP composite beam systems with novel blind bolt shear connections

The shear stiffness of novel blind bolts was experimentally investigated for shear connections within steel-FRP composite beam systems using steel-FRP joints loaded in tension. The number of bolt rows (either one or two bolt rows) and the effect of the pultrusion orientation of the FRP web-flange sandwich slab on joint stiffness and joint capacity were examined. It was found that joint capacity and failure modes were dependent on the pultrusion configuration of the FRP slab and the number of bolt rows. A unidirectional configuration consisting of an FRP slab with box-profiles parallel to flat panels exhibited shear-out failure, whereas a bidirectional orientation consisting of an FRP slab with box-profiles perpendicular to flat panels exhibited both shear-out and net-tension failure in the FRP component. The experimentally derived shear connector stiffness was then used in a proposed design formulation to predict the bending stiffness of modular steel-FRP composite beam systems, considering two kinds of partial composite actions. These were the composite action provided by the blind bolt shear connector and the composite action provided by transversely-oriented webs within the slab. Good agreement was observed between the experimental results and the proposed design formulation.

Serviceability performance of steel–concrete composite beams

The use of steel–concrete composite beams in which wide-flanged steel beams act compositely with a concrete or steel–concrete composite slab above is well established in building construction. However, for composite beams with low degrees of shear connection between the beam and slab, significant additional deflections can occur due to slip in the shear connectors. A design formula is presented for the effective stiffness of composite beams taking account of the stiffness of the shear connectors, which is compared to measured deflections of six symmetric composite beams and an 11 m span composite beam of asymmetric profile. It is shown that the comparison is good when using a shear connector stiffness of 70 kN/mm for single shear connectors and 100 kN/mm for pairs of shear connectors per slab rib. The results of push tests on a range of slab profiles confirmed these initial elastic stiffnesses. To ensure that the slip at the serviceability limit state does not lead to permanent deformations of the composite beam, it is proposed that the minimum degree of shear connection should not fall below 30% for unpropped beams and 40% for propped beams of symmetric cross-section.

Exact finite element formulation for an elastic hybrid beam-column in partial interaction with shear-deformable encasing component

The authors present the exact finite element formulation for partially connected shear-deformable elastic hybrid beam-columns with several embedded sections. Euler-Bernoulli’s kinematic assumptions are adopted for the embedded section whereas Timoshenko’s kinematic assumptions are considered for the encasing element. The shear connection between the encasing component and the embedded section is modeled through a continuous relationship between the interface shear flow and the corresponding slip. A set of coupled system of differential equations in which the primary variables are the slips and the shear deformation of the encasing cross-section is derived from the governing equations describing the behavior of an elastic shear-deformable hybrid beam-column in partial interaction. This coupled system has been solved in closed-form, and the “exact” stiffness matrix has been derived using the direct stiffness method. The latter has been implemented into a general displacement-based finite element code, and has been used to investigate the behavior of shear-deformable hybrid beams. Three numerical examples have been considered in order to assess the capability of the proposed formulation and to investigate the effect of the shear connection stiffness and span-to-depth ratios on mechanical responses of the beam-columns. It has been found that the transverse displacements are more affected by the shear flexibility than the slips.

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

Dynamic characteristics analysis of partial-interaction composite continuous beams

The dynamic characteristics of continuous steel-concrete composite beams considering the effect of interlayer slip were investigated based on Euler Bernoulli\'s beam theory. A simplified calculation model was presented, in which the Mode Stiffness Matrix (MSM) was developed. The natural frequencies and modes of partialinteraction composite continuous beams can be calculated accurately and easily by the use of MSM. Proceeding from the present method, the natural frequencies of two-span steel-concrete composite continuous beams with different span-ratios (0.53, 0.73, 0.85, 1) and different shear connection stiffnesses on the interface are calculated. The influence pattern of interfacial stiffness on bending vibration frequency was found. With the decrease of shear connection stiffness on the interface, the flexural vibration frequencies decrease obviously. And the influence on low order modes is more obvious while the reduction degree of high order is more sizeable. The real natural frequencies of partial-interaction continuous beams commonly used could have a 20% to 40% reduction compared with the fully-interaction ones. Furthermore, the reduction-ratios of natural frequencies for different span-ratios two-span composite beams with uniform shear connection stiffnesses are totally the same. The span-ratio mainly impacts on the mode shape. Four kinds of shear connection stiffnesses of steel-concrete composite continuous beams are calculated and compared with the experimental data and the FEM results. The calculated results using the proposed method agree well with the experimental and FEM ones on the low order modes which mainly determine the vibration properties.

Derivation of the exact stiffness matrix of shear-deformable multi-layered beam element in partial interaction

This paper presents the exact finite element formulation for the analysis of partially connected shear-deformable multi-layered beams. Timoshenko׳s kinematic assumptions are considered for each layer or component, and the shear connection is modeled through a continuous relationship between the interface shear flow and the corresponding slip. The effect of possible transversal separation of the two adjacent layers has not been considered. The governing equations describing the behavior of a shear-deformable multi-layered beam in partial interaction consist of a set of coupled system of differential equations in which the primary variables are the slips and the shear deformations. This coupled system has been solved in closed form, and the “exact” stiffness matrix has been derived using the direct stiffness method. The latter has been implemented in a general displacement-based finite element code, and has been used to investigate the behavior of shear-deformable multi-layered beams. Both a simply supported and two continuous beams have been considered in order to assess the capability of the proposed formulation and to investigate the influence of the shear connection stiffness and span-to-depth ratios on mechanical responses of the beams. It has been found that the transverse displacement is more affected by shear flexibility than the interlayer slips.

Generalised Beam Theory (GBT) for composite beams with partial shear interaction

This paper presents a theoretical model for the partial interaction analysis of composite steel–concrete beams within the framework of Generalised Beam Theory (GBT). The main contribution of this work relies on its ability to account for the deformability of the longitudinal shear connection between the slab and the steel beam, commonly known as partial shear interaction, in the evaluation of the cross-sectional deformation modes. This approach can handle arbitrary composite cross-sections, in which more than one shear connection can exist between the concrete and steel components, and for which the steel beam can be formed by open, closed or partially closed cross-sections. The proposed GBT approach falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses. In particular, the deformation modes are selected as the dynamic eigenmodes of an unrestrained planar frame representing the cross-section. Warping is then evaluated for the conventional modes in a post-processing stage taking account of the kinematic discontinuity at the interface, while in the evaluation of the shear modes the partial interaction behaviour is included in the out-of-plane dynamic analysis. Two numerical composite examples, one where the bottom component consists of an open steel section and one based on a partially closed one, are presented to highlight the ease of use of the proposed partial interaction formulation for different levels of shear connection stiffness. The accuracy of the numerical results is validated against those calculated with a shell finite element model developed in ABAQUS.

Dynamic analysis and model test on steel-concrete composite beams under moving loads

This paper is concerned with the dynamic analysis of simply-supported steel-concrete composite beams under moving loads. Considering the interface slip between steel girder and concrete slab, the governing motion equations are derived from the direct balanced method. By variable separation approach, the analytical solution of natural frequencies and mode shapes are obtained, as well as the orthogonal conditions. Then the dynamic responses of the composite beam under moving loads are analyzed, and compared with the experimental results. The analysis results show that the governing motion equations become more complicated when interface slip is taken into account, and the dynamic behaviors are significantly influenced by the shear connection stiffness. In the dynamic calculation of composite beams, the global stiffness should not be reduced as the same factor to all orders, but as different ones according to the dynamic stiffness reduction factor (DSRF), to which should be paid more attention in calculation, design and experiment, or else great deviation is inevitable.

Finite element analysis for buckling of two-layer composite beams using Reddy’s higher order beam theory

In this paper, a two-layer partial composite columns model is built based on Reddy׳s higher order beam theory, and two novel displacement based finite elements for this and Timoshenko composite beams are respectively formulated by means of the principle of minimum potential energy. Subsequently, the buckling analyses of pinned–pinned and clamped–guided composite columns are performed using the proposed finite elements, and the results are compared with those obtained by plane stress model, Timoshenko and Newmark composite beams model respectively. The superior quality of Reddy composite columns model over Timoshenko composite columns model and the correctness of the proposed Timoshenko composite columns model are demonstrated by the numerical comparison. Finally, the parametric study explores effects of parameters including stiffness of shear connectors, span-to-depth ratios, Young׳s modulus ratios and sub-layer׳s depth on the buckling load. The discrepancies between the performance of higher order and Timoshenko composite columns have also been numerically investigated.

Cohesive Zone Model Based Numerical Analysis of Steel-Concrete Composite Structure Push-Out Tests

Push-out tests were widely used to determine the shear bearing capacity and shear stiffness of shear connectors in steel-concrete composite structures. The finite element method was one efficient alternative to push-out testing. This paper focused on a simulation analysis of the interface between concrete slabs and steel girder flanges as well as the interface of the shear connectors and the surrounding concrete. A cohesive zone model was used to simulate the tangential sliding and normal separation of the interfaces. Then, a zero-thickness cohesive element was implemented via the user-defined element subroutine UEL in the software ABAQUS, and a multiple broken line mode was used to define the constitutive relations of the cohesive zone. A three-dimensional numerical analysis model was established for push-out testing to analyze the load-displacement curves of the push-out test process, interface relative displacement, and interface stress distribution. This method was found to accurately calculate the shear capacity and shear stiffness of shear connectors. The numerical results showed that the multiple broken lines mode cohesive zone model could describe the nonlinear mechanical behavior of the interface between steel and concrete and that a discontinuous deformation numerical simulation could be implemented.

Behaviour of partially connected composite plate girders containing web openings

This paper is concerned with an approximate method to predict the bending behaviour and ultimate strength of partially connected composite plate girders. Based on curvature compatibility, analytical solution incorporating post-buckling effect in the webs and different degree of shear connection is presented herein. Slender girders with centrally placed square or circular web openings of various proportions are considered in the analysis. The obtained results are verified against the corresponding ones using the established finite element method. A satisfactory correlation between the findings establishes the accuracy of the proposed method to a certain extent. Results are presented in the form of ultimate strength and load-deflection response for girders with variations in shear connection stiffness.

Approximate analysis method for composite beams with partial interaction using Fourier series

This paper presents an alternate analysis method for calculating the deflection and internal forces for arbitrary boundary and loading conditions of composite beams with partial interaction. The internal axial force was approximated by the Fourier series to solve the governing equation of composite beam. Then, the coefficients of the Fourier series were determined using the Euler-Lagrange equation of minimizing a definite integral. An evaluation of the convergence and the accuracy for the proposed method in the determination of the deflection for four types of boundary conditions with four types of loading cases was made. The results were agreed with those obtained by other analytical methods. The displacement of the partial composite beam depends on the stiffness of shear connectors, boundary conditions and loading conditions.

Elastic Seismic Response of Steel-Concrete Composite Frames with Partial Interaction

The finite element formulations of steel-concrete composite (SCC) beams considering interlayer slip with end shear restraint is established. Elastic seismic response of SCC frame structures under different shear connection stiffness and slip boundary conditions are examined. The influences of the shear connection stiffness and the slip boundary condition on elastic seismic response are analyzed. With the shear connection stiffness increasing, the free vibration frequencies increase and the seismic responses decrease. The natural vibration properties of SCC frame structures and seismic responses are also significantly affected by the slip boundary condition, and it should be properly imposed on all composite beams in seismic response analysis.

Dynamic Analysis of Steel-Concrete Composite Frames with Partial Interaction

The finite element formulations of steel-concrete composite (SCC) beams considering interlayer slip with end shear restraint were established. Free vibrations of SCC beams and frame structures under different slip boundary conditions were examined. The influences of the shear connection stiffness and the slip boundary condition on dynamic characteristics were analyzed. It is shown that the low order 8-DOF element may exhibit slip locking phenomenon in free vibration analysis for very stiff connection. The free vibration frequencies of composite beams and frame structures increase with the shear connection stiffness increasing. Besides, it is found that the natural vibration properties of SCC frame structures are significantly affected by the slip boundary condition, and it should be suitably imposed on all composite beams in dynamic analysis.

Dynamic analysis and shear connector damage identification of steel-concrete composite beams

With the advantages of large span, light deadweight and convenient construction, the steel- concrete composite beam (SCCB) has been rapidly developed as a medium span bridge. Compared with common beams, the global stiffness of SCCB is discontinuous and in a staged distribution. In this paper, the analysis model for the simply-supported SCCB is established and the vibration equations are derived. The natural vibration characteristics of a simply-supported SCCB are analyzed, and are compared with the theoretical and experimental results. A curvature mode measurement method is proposed to identify the shear connector damage of SCCB, with the stiffness reduction factor to describe the variation of shear connection stiffness. By analysis on the 1 st to 3 rd vertical modes, the distribution of shear connectors between the steel girder and the concrete slab are well identified, and the damage locations and failure degrees are detected. The results show that the curvature modes can be used for identification of the damage location.

Discrete Shear Connection for a Portable Composite Bridge

To enable a portable composite bridge, a shear connection between steel plate girders and precast concrete deck panels, which would allow these two components to be fastened and unfastened, proposed. In the system, points of shear connection would be spaced at 3 m on center along the length of the girder. Finite element analysis was employed to compare the performance of the proposed composite system to a conventional composite girder with ductile shear studs. A nonlinear analysis was performed, and the proposed composite system was seen to demonstrate a response comparable to that of a composite girder with conventional shear studs. The model was verified for its capability to capture the possible effects of flange buckling, web buckling, and lateral torsional buckling of the steel plate girder. It was then confirmed that these failure modes did not influence the performance of the proposed portable composite bridge system for the investigated bridge configuration. A parametric study also was performed: the effects of shear connection stiffness and spacing on the behavior of the composite girder were investigated. In general, the investigated variations of these parameters had a significant influence on the girder stiffness but only a limited impact on the ultimate strength.

Static and Vibrational Analysis of Partially Composite Beams Using the Weak‐Form Quadrature Element Method

Deformation of partially composite beams under distributed loading and free vibrations of partially composite beams under various boundary conditions are examined in this paper. The weak‐form quadrature element method, which is characterized by direct evaluation of the integrals involved in the variational description of a problem, is used. One quadrature element is normally sufficient for a partially composite beam regardless of the magnitude of the shear connection stiffness. The number of integration points in a quadrature element is adjustable in accordance with convergence requirement. Results are compared with those of various finite element formulations. It is shown that the weak form quadrature element solution for partially composite beams is free of slip locking, and high computational accuracy is achieved with smaller number of degrees of freedom. Besides, it is found that longitudinal inertia of motion cannot be simply neglected in assessment of dynamic behavior of partially composite beams.

Probabilistic Analysis about Shrinkage and Creep Effect of Continuous Steel-Concrete Composite Beams with LHS

Steel-concrete composite girder is consisted of concrete slab and steel girder connected through shear connectors. Owing to shrinkage and creep of concrete, redistribution of structural internal force and stress should be caused. It is widely accepted that shrinkage and creep models of concrete possess large randomness. The influences of stochastic variation of creep and shrinkage model, compressive strength of concrete, elastic modulus model of concrete, ambient humidity, load and shear connector stiffness on structural responses of continuous steel-concrete composite beam are investigated in the present study. Through Latin Hypercube Sampling (LHS) approach, the time variant probabilistic responses of deflection, interface slip, and stress of concrete slab and steel girder of continuous steel-concrete composite beam are studied.

Behaviour of Stiffened Composite Beams with Partial Shear Interaction Accounting for Time Effects

This paper describes an analytical model to account for the effects of creep and shrinkage on the response of composite steel-concrete beams with partial shear connection stiffened by means of longitudinal plates bolted to the bottom flange of the steel member. The particularity of this model is that the partial interaction behaviour is assumed to exist between the top slab and the joist as well as between the joist and the bolted longitudinal stiffening plate, leading to a three-layered structural representation. The weak formulation of the problem is obtained and used to derive a 13 degrees-of-freedom element whose freedoms include the axial displacements of each layer, the rotations and vertical displacements at the end nodes. A parametric study has then been carried out for the case of a simply supported beam to investigate the effects of the time-dependent behaviour of the concrete for different levels of shear connection stiffness.

Exact dynamic analysis of composite beams with partial interaction

The partial differential equations and general solutions for the deflection and internal actions and the pertaining consistent boundary conditions are presented for composite Euler–Bernoulli members with interlayer slip subjected to general dynamic loading. Both free and forced vibrations are treated. The solutions are shown to be unique and complete under certain conditions, and valid for all so-called restricted admissible boundary conditions. Specifically, the exact eigenmode length coefficients are derived for the four Euler BC. They differ from those valid for ordinary, fully composite (solid) beams, except for the pinned–pinned case. The maximum deviation for beams with the other three Euler BC is shown to be less than 2–6% with respect to the eigenmode length coefficient and 3–10% with respect to the eigenfrequency, respectively, depending on the two non-dimensional parameters, composite action or shear connector stiffness and relative bending stiffness parameters. However, these deviations occur in a rather narrow range of the determining parameters, so for most practical cases the eigenmode length coefficients given for solid (fully composite) beams can approximately be used also for partially composite beams. The procedures of analysing beam vibrations are applied to a specific case. These solutions illustrate the effect of interlayer connection on the peak velocity of the beam vibrations. The proposed analytical theory is verified by tests and finite element calculations.