Displacement-Based and Two-Field Mixed Variational Formulations for Composite Beams with Shear Lag

Displacement-based and two-field mixed beam elements are proposed for the linear analysis of steel–concrete composite beams with shear lag and deformable shear connection. The kinematics of the shear lag relies on a parabolic shear warping function of uniform shape along the slab. These assumptions are verified by comparing a closed-form solution of the composite beam problem with the results provided by the ABAQUS code. Moreover, three displacement-based finite elements and two mixed elements where both variables, forces, and displacements are approximated within the elements are developed especially for very coarse discretizations. All models neglect uplift and consider shear connectors using distributed interface elements. Locking problems that arise in the 10 degrees-of-freedom (DOF) displacement-based element which ensures the lowest regularity required by the problem are detected. Then, a locking-free element which relies on a reduced integration and a scaling factor method is proposed and analyzed for fine mesh discretizations. Energy errors and convergence rates of the proposed elements are illustrated while numerical examples dealing with a fixed-end steel–concrete composite beam and a simply supported concrete Tee beam are considered to confirm the validity of the closed-form solution and illustrate the performance of the proposed elements, especially of the ones with 10 and 13 DOF.     

Multicomponent Model of Reinforced Concrete Joints for Cyclic Loading

Efficient simplified models are available for reinforced concrete beams and columns, with the assumption of a perfectly rigid connection. However, interior beam∕column joints have been shown to be the area of strong deformation and degradation mechanisms, involving mainly the cyclic behaviors of concrete under shear and of bond under push-pull loading. In this paper, a global component-based model is proposed for the beam∕column connections of reinforced concrete frame structures that can be directly connected to beam elements. This model incorporates explicitly the modeling of concrete, steel, and steel∕concrete bond. Thus, the key mechanisms of deformation and degradation of the connection, as well as various interactions can be taken into account naturally. In particular, the effect of push-pull-type loading on the flexural steels can be captured. On the basis of a local finite-element modeling of the connection, simplifying assumptions are proposed and implemented leading to the component-based model. Both approaches (local and component-based) are compared on an application example.     

Local Effects Induced by Longitudinal Forces in Composite Girders

Local effects on the shear connection of composite girders induced by longitudinal actions such as the anchorages of prestressing cables, concrete shrinkage, or a uniform thermal action on the slab are analyzed. Closed-form solutions are obtained by using the simple model of a composite beam with a linearly elastic shear connection. Successively, by considering the limit scheme of an infinitely long beam, very simple formulas are derived permitting evaluation of the peak value and extension of the interface shear force distribution induced by the longitudinal actions. Numerical applications are carried out to show the effectiveness of the proposed formulas for a wide range of the shear connection stiffness and for longitudinal forces applied both along the beam axis and at the beam end.     

Static Behavior and Theoretical Model of Stud Shear Connectors

Stud shear connectors are the most widely used shear connectors in steel-concrete composite beams. The composite action of steel beam and concrete slab is effected by the stud shear properties directly. Thirty push-out tests on stud shear connectors were conducted to investigate the effects of stud diameter and height, concrete strength, stud welding technique, transverse reinforcement, and steel beam type on stud failure mode, load versus slip curve, and the shear bearing capacity. Based on the push-out test results, the stud shear mechanism was analyzed, a new expression of stud load-slip relationship was put forward, and a calculation model of stud shear bearing capacity was proposed taking into account the influences of stud diameter and height, material strength, and elastic modulus. Compared with existing models, the computed shear bearing capacities of the proposed calculation model had a better match with the experimental values.     

Potential Retrofit Methods for Concrete Channel Beam Bridges Using Glass Fiber Reinforced Polymer

The structural response of deteriorated channel beam bridge girders and channel beam bridge decks with and without glass fiber reinforced polymer (GFRP) retrofit is found from design calculations, experimental load testing, and finite element analysis. Two different types of GFRP retrofit materials are investigated including a traditional fabric wrap and a new spray material. The effects of GFRP retrofit on channel beam bridge girder and channel beam bridge structural parameters are summarized and the accuracy of design calculation methods for quantifying structural response of channel beam bridge girders retrofit with GFRP is determined.     

考虑楼板效应的外环板式梁柱节点抗弯承载力

楼板的存在对梁柱节点的局部受力影响显著, 在梁柱节点设计中, 若仅仅把楼板与钢梁的组合效应作为安全储备, 可能会产生结构由"强柱弱梁"转变成"强梁弱柱"的颠覆性结果, 因此忽略混凝土楼板对节点承载力及刚度的影响是造成破坏的重要原因.基于已完成的带楼板的T型梁柱节点低周往复荷载试验, 建立了非线性有限元分析模型.为了更加全面地了解钢梁-楼板组合节点的工作机制, 进一步补充完善试验研究的不足, 模型考虑了楼板与钢梁之间的栓钉连接以及材料非线性等因素, 模型的计算结果与试验结果具有高吻合度.在此基础上, 通过有限元参数分析, 详细分析了构件尺寸效应、轴压比、楼板厚度、楼板强度和柱宽厚比共五个参数对考虑楼板影响的外环板式梁柱节点抗震性能的影响.结果表明尺寸效应、轴压比对梁端抗弯承载力及刚度的影响小到可以忽略, 楼板厚度、楼板强度和柱宽厚比对梁端抗弯承载力有显著影响.结合理论分析进一步提出了考虑楼板影响的外环板式梁柱节点梁端抗弯承载力计算公式, 通过对比公式计算结果与试验、有限元分析结果可得, 该计算公式可较好的计算带楼板外环板式梁柱节点梁端抗弯承载力.      

Interface Shear Connection Analysis of Ultrahigh-Performance Fiber-Reinforced Concrete Composite Girders

The purpose is to analyze the interface shear connection behavior for ultrahigh-performance fiber-reinforced concrete (UHPFRC) and normal concrete (NC) composite girders. The shape and dimension of the shear stud in the conducted tests are referenced from the traditional interface connection design and engineering experiences. The interface shear connection parameters, i.e., initial stiffness and slippage capacity of a single shear stud, are measured from three groups of lateral direct push test specimens with different numbers of studs. Based on the UHPFRC tensile failure characteristics and cracked section rotational mechanisms of the UHPFRC-NC composite structures with flexural, or flexural and shear failure, the limit state is defined as a full pullout from the bottom fiber of the UHPFRC girders. Pseudostrain hardening behavior of the UHPFRC is simplified as an equivalent rectangular stress block. From this mechanism, the interface equilibrium equations are constituted and the interface shear connection degree of the UHPFRC-NC composite girders is derived. It is recommended that the interface shear connection degree may be used as minimum design standard for UHPFRC-NC composite interface shear connection design.     

Mixed Finite Element for Three-Dimensional Nonlinear Dynamic Analysis of Rectangular Concrete-Filled Steel Tube Beam-Columns

A beam finite-element formulation following Euler-Bernoulli beam theory is presented for geometrically and materially nonlinear analysis of rectangular concrete-filled steel tube (RCFT) beam-columns. The formulation is geared for conducting transient dynamic analysis of composite steel/concrete frame structures. The element stiffness and internal forces were derived through adopting a mixed finite-element approach based on the Hellinger-Reissner variational principle. The load transfer between the steel and concrete constitutive materials was provided through steel and concrete interface via friction and interlocking. Six extra translational degrees-of-freedom (DOFs) were added to the conventional 12 DOF beam element to quantify the differential displacement between the two media. The formulation was verified for a range of geometrically nonlinear test problems and geometrically and materially nonlinear RCFT experimental test specimens from the literature. Strong correlation and convergence characteristics were achieved compared to the published results.     

C0 Zig-Zag Finite Element for Analysis of Laminated Composite Beams

A new C0 finite element for accurate analysis of laminated composite beam structures is developed. The element formulation is based on a quadratic zig-zag layerwise theory developed previously by the writers. The theory assumes a zig-zag distribution of the in-plane displacement field through the thickness and satisfies the interlaminar shear stress continuity across the layer interfaces. In developing the finite-element formulation, the shear strain fields are made field consistent, and thus the shear locking phenomenon is eliminated. A new transverse normal strain is derived by assuming the transverse normal stress to be constant through the thickness of the laminate. This assumption is shown to remove Poisson's ratio stiffening. The results obtained from the present finite element are found to be in good agreement with exact elasticity solutions available for simply supported beams. A multisublaminate approach that is simple to implement with the present element is shown to improve the predictions of the present model for complex laminated structures.     

Transverse Natural Vibration of a Beam with an Internal Joint Carrying In-Plane Flexibilities

Existing research on semirigid jointed frame includes only the rotational flexibility of the joint without consideration of the flexibility in the direction of the transverse shear force. This omission would lead to inaccuracies in the dynamic response of structures, especially in the nonlinear analysis. This paper investigates the dynamic behavior of a bolted joint which has flexibility in both the tangential and rotational directions. The joint is prestressed with axial tension in the bolt shank. It is represented as a virtual connection spring element at the intersection between the beam and the supporting member. The formulation of the hybrid beam–column element including the end springs is presented, and the dynamic behavior of a cantilever beam with this nonlinear semirigid joint is studied. The natural frequencies and mode shapes remain relatively unchanged only for a limited range of the joint stiffnesses, and the eigenpair is influenced by the instantaneous stiffness of the joint defined at a point on the hysteretic loop, particularly when the initial moment stiffness is small.     

Performance Simulation of Nuclear Containments for Security

Under blast loading, nuclear containment structures are subjected to cyclic flexural, axial, and shear forces. Less attention has been paid to modeling the cyclic behavior of reinforced concrete elements in which shear deformations are significant, such as in nuclear containments. Research has demonstrated that the strength of concrete in the principal compression direction is softened by tension in the lateral direction. This interaction has been considered for monotonic loading for many years. To consider this interaction for cyclic loading, the material laws recently derived by Mansour et al. in 2001 for the cyclic softened membrane model (CSMM) can be used. Both fire and explosion effects resulting from blast loading can also be incorporated into the constitutive models of concrete and reinforcing bars. This paper presents a method to implement the CSMM model, so that it can be used to simulate the performance of nuclear containments for security by the design communities.     

Scale Transition in Steel-Concrete Interaction. I: Model

This paper deals with the analysis of reinforced concrete (RC) structures with special emphasis on modeling of the interaction between concrete and reinforcement. A new mode for consideration of the response of the composite material at the member (structural) scale is proposed. It is obtained from extension of the fracture energy concept, originally developed for the simulation of cracking of plain concrete, to reinforced concrete. Hereby, the fracture energy related to the opening of primary cracks is increased in order to account for bond slip between steel and concrete. This increase is determined from the distribution of bond slip by means of a one-dimensional composite model introduced at the bar scale. The model consists of steel bars and the surrounding concrete. Between these two components, a nonlinear bond stress–bond slip relation is considered. The obtained results at the bar scale, such as the average crack spacing between adjacent cracks and the load-displacement response of the composite material, form the basis for determination of the increase of the fracture energy at the member scale. The performance of the proposed transition of the steel-concrete interaction from the bar scale to the member scale is assessed by means of reanalysis of experiments performed on RC bars. The application of the respective material model for reinforced concrete to real-life engineering structures is reported in Part II of this series.     

高层建筑混合结构设计

文章简要介绍了型钢混凝土混合结构构件的特性、适用范围和其它结构相比较的优缺点,以及目前高层建筑混合结构的设计要求,并从结构布置总体要求、适用高度和高宽比限值、概念设计要点、结构计算分析特点等几个方面进行论述,强调了混凝土筒体延性和钢框架柱地震剪力调整的重要性。     

Fiber Element for Cyclic Bending and Shear of RC Structures.?II: Verification

The fiber beam element with shear modeling developed in the companion paper is calibrated and verified by comparison with test data. The verification is carried out for the material constitutive behavior and for single beam and column elements using available test results from literature. A structural analysis of a shear sensitive viaduct pier subjected to ground input motion is presented. Details of the algebraic expressions used for the concrete and steel constitutive behaviors are provided.     

Bond Length of CFRP Composites Attached to Precast Concrete Walls

Carbon fiber composite connections for hollow-core precast concrete wall panels have been investigated with respect to bond behavior. A panel assembly made up of three precast concrete walls was loaded in the in-plane direction using a cyclic quasi-static load, which was transferred to the wall interface as a shear force. The application of the carbon-fiber-reinforced polymer (CFRP) composite was varied in the covered area, number and orientation of plies, and the concrete surface preparation. An expression, which compares well with the experimental findings, is presented for the effective bond length of carbon fiber composite sheets. The effective bond length of the connection depends on the peel-off shear strength of the concrete, the maximum tensile strain in the composite, the modulus of elasticity of the composite, and thickness of the composite plate.     

Stability of the World Trade Center Twin Towers Structural Frame in Multiple Floor Fires

This technical note presents the results from a nonlinear finite element analysis of a very simple two dimensional model of the World Trade Center Twin-Towers structural frame subjected to fire. The analysis was carried out for a large range of fire scenarios and was reported in detail in a recently published paper. The paper further investigates the results of this analysis to obtain the details of the collapse mechanism found. An interesting series of events leading progressively to overall collapse are discovered and described in detail. The main reason for the failure is found to be the low membrane capacity in compression of the composite steel truss and concrete deck slab floor system.     

Handling of Constraints in Finite-Element Response Sensitivity Analysis

In this paper, the direct differentiation method (DDM) for finite-element (FE) response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints (MPCs). The analytical developments are provided for three different constraint handling methods, namely: (1) the transformation equation method; (2) the Lagrange multiplier method; and (3) the penalty function method. Two nonlinear benchmark applications are presented: (1) a two-dimensional soil-foundation-structure interaction system and (2) a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDM-based response sensitivity results are compared with corresponding forward finite difference analysis results, thus validating the formulation presented and its computer implementation. The developments presented in this paper close an important gap between FE response-only analysis and FE response sensitivity analysis through the DDM, extending the latter to applications requiring response sensitivities of FE models with MPCs. These applications include structural optimization, structural reliability analysis, and finite-element model updating.     

Time-Dependent Analysis of Shear-Lag Effect in Composite Beams

Taking into account the long-term behavior of the concrete, a model for analyzing the shear-lag effect in composite beams with flexible shear connection is proposed. By assuming the slab loss of planarity described by a fixed warping function, the linear kinematics of the composite beam is expressed by means of four unknown functions: the vertical displacement of the whole cross section; the axial displacements of the concrete slab and of the steel beam; and the intensity of the warping (shear-lag function). A variational balance condition is imposed by the virtual work theorem for three-dimensional bodies, from which the local formulation of the problem, which involves four equilibrium equations with the relevant boundary conditions, is achieved. The assumptions of linear elastic behavior for the steel beam and the shear connection and of linear viscoelastic behavior for the concrete slab lead to an integral-differential type system, which is numerically integrated. The numerical procedure, based on the step-by-step general method and the finite-difference method, is illustrated and applied to an example of practical interest.     

CFRP Rehabilitation of Concrete Frame Joints with Inadequate Shear and Anchorage Details

The research presented in this study involves full-scale experimental evaluation of carbon fiber-reinforced polymer (CFRP) rehabilitation for existing beam-column joints designed for gravity load with common pre-1970s deficient reinforcement details when subjected to cyclic loading. Numerous studies have demonstrated effectiveness of externally bonded fiber-reinforced polymer (FRP) materials for retrofitting the deteriorating RC structures. Although these materials are widely used in bridges, their applications in buildings have been somewhat limited. In particular, the experimental investigations on external FRP retrofit of deficient beam-column joints have not thoroughly been investigated and they are mainly on scaled-down specimens. The failure of these subassemblies, which possess lack of shear reinforcement within the joint core and shortly embedded positive beam reinforcement, would possibly result in catastrophic collapse of reinforced concrete frame structure during an earthquake event. Recognizing the urgent need to upgrade these structural subassemblies, the current investigation uses CFRP retrofit techniques to enhance the performance of such deficient joints. Experimental variables studied entail the developed CFRP retrofit configurations, and magnitude of the applied column axial load. Comparative analysis of the lateral loads versus drift hysteresis loops, stiffness degradation, and total dissipated energy curves of three as-built and three corresponding CFRP-retrofitted RC joints revealed that significant improvement in the shear capacity of the upgraded joints occurred. More importantly, the slippage of short embedded beam positive reinforcement into the joint was substantially controlled due to the developed CFRP retrofit. The results demonstrate the effectiveness of CFRP retrofit configurations in enhancing the structural performance of actual size connections.