Local Delamination Buckling of Laminated Composite Beams Using Novel Joint Deformation Models

Local delamination buckling formulas for laminated composite beams are derived based on the rigid, semirigid, and flexible joint models with respect to three bilayer beam (i.e., conventional composite, shear-deformable bilayer, and interface-deformable bilayer, respectively) theories. Two local delamination buckling modes (i.e., sublayer delamination buckling and symmetrical delamination buckling) are analyzed and their critical buckling loads based on the three joint models are obtained. A numerical finite-element simulation is carried out to validate the accuracy of the formulas, and parametric studies of delamination length ratio, the transverse shear effect, and the influence of interface compliance are conducted to demonstrate the improvement of the flexible joint model compared to the rigid and semirigid joint models. The explicit local delamination buckling solutions developed in this study facilitate the design analysis and optimization of laminated composite structures and provide simplified and improved practical design equations and guidelines for buckling analyses.     

Effect of Friction on Shear Connection in Composite Bridge Beams

In the design of new composite steel and concrete bridge beams, the shear connectors are assumed to transmit all of the longitudinal shear forces at the interface between the concrete slab and the steel beam. However, in practice, the forces on the shear connectors are modified by friction resistances at the interface. The effect of friction on the fatigue endurance of shear connectors is first illustrated through a specially developed finite-element analysis procedure. Then a simple mathematical assessment model is proposed that allows for the beneficial effect of friction on the fatigue endurance of shear connectors in composite steel and concrete bridge beams. This procedure can extend the design life of the shear connectors in existing composite bridge beams, as it can be used to estimate their remaining endurance and their remaining strength and, if necessary, to determine the effect of remedial work on increasing the endurance of the shear connectors.     

Matrix Analysis of Shear Lag and Shear Deformation in Thin-Walled Box Beams

This paper presents an initial value solution of the static equilibrium differential equations of thin-walled box beams, considering both shear lag and shear deformation. This solution was used to establish the related finite element stiffness matrix and equivalent nodal forces vector. In the procedure a special shear-lag-induced bimoment is introduced, so that the analysis of shear lag and shear deformation of thin-walled box beams is admitted into the program system of the matrix-displacement method. The present procedure can be used to analyze accurately the shear lag and shear deformation effects for thin-walled box beams, especially for some complex structures (such as continuous box girders and box beams with varying cross section, etc.). The numerical results obtained by the present procedure are consistent with the results of model tests and predictions of the finite shell element method or finite difference approach.     

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.     

Influence of Shear Deformation on Buckling of Pultruded Fiber Reinforced Plastic Profiles

Theoretical studies of the influence of shear deformation on the flexural, torsional, and lateral buckling of pultruded fiber reinforced plastic (FRP)-I-profiles are presented. Theoretical developments are based on the governing energy equations and full section member properties. The solution for flexural buckling is consistent with the established solution based on the governing differential equation. The new solutions for torsional and lateral buckling incorporate a reduction factor similar to that for flexural buckling. The solution for lateral buckling also incorporates the influence of prebuckling displacements. Closed form solutions for a series of simply supported, pultruded FRP I-profiles, based on experimentally determined full section flexural and torsional properties, indicate the following conclusions. For members subjected to axial compression, shear deformation can reduce the elastic flexural and torsional buckling loads by up to approximately 15% and 10%, respectively. For members subjected to bending, prebuckling displacements can increase the buckling moments by over 20% while shear deformation decreases the buckling moments by less than 5%.     

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis, and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the direct differentiation method. The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a nonsymmetric, two-span continuous beam subjected to monotonic loading and a frame subassemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through forward finite difference analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.     

Boundary-Layer Effect in Composite Beams with Interlayer Slip

An apparent analytical peculiarity or paradox in the bending behavior of elastic-composite beams with interlayer slip, sandwich beams, or other similar problems subjected to boundary moments exists. For a fully composite beam subjected to such end moments, the partial composite model will render a nonvanishing uniform value for the normal force in the individual subelement. This is from a formal mathematical point of view in apparent contradiction with the boundary conditions, in which the normal force in the individual subelement usually is assumed to vanish at the extremity of the beam. This mathematical paradox can be explained with the concept of boundary layer. The bending of the partially composite beam expressed in dimensionless form depends only on one structural parameter related to the stiffness of the connection between the two subelements. An asymptotic method is used to characterize the normal force and the bending moment in the individual subelement to this dimensionless connection parameter. The outer expansion that is valid away from the boundary and the inner expansion valid within the layer adjacent to the boundary (beam extremity) are analytically given. The inner and outer expansions are matched by using Prandtl’s matching condition over a region located at the edge of the boundary layer. The thickness of the boundary layer is the inverse of the dimensionless connection parameter. Finite-element results confirm the analytical results and the sensitivity of the bending solution to the mesh density, especially in the edge zone with stress gradient. Finally, composite beams with interlayer slip can be treated in the same manner as nonlocal elastic beams. The fundamental differential equation appearing in the constitutive law associated with the partial-composite action in a nonlocal elasticity framework is discussed. Such an integral formulation of the constitutive equation encompassing the behavior of the whole of the beam allows the investigation of the mechanical problem with the boundary-element method.     

Lateral-Torsional Buckling of Stepped Beams with Continuous Bracing

Continuous span multibeam steel bridges are common along the state and interstate highways. The top flange of the beams is typically braced against lateral movement by the deck slab, and in many bridges the cross section is stepped at discrete points along the span. Design equations for lateral–torsional buckling (LTB) resistance in the American Association of State Highway and Transportation Officials “Load and resistance factor design bridge design specifications” are for prismatic beams and ignore the lateral restraint provided by the bridge deck. A new design equation is proposed that can be applied to I-shaped stepped beams with continuous top flange lateral bracing. By including the effects of the change in cross section size and the continuous top flange bracing, the calculated LTB resistance is significantly increased. Critical bending moment values from the proposed equation are compared to values from finite element method buckling analyses. The new equation is sufficiently accurate for use in design and in the evaluation of existing bridges.     

钢—混凝土组合梁抗剪承载力计算

我国GBJ17－88《钢结构设计规范》中钢与混凝土组合梁部分和欧洲钢与混凝土组合结构规范都规定,组合梁截面上的全部剪力驻由钢梁腹板承受,按下面公式计算：V≤hwtwfv,但大量试验结果表明,按上面公式计算的抗承载力普通小于其实测值,一般仅为实测值的60％－70％。因此,建议在计算组合梁抗剪切承载力时应考虑混凝土剪板的抗剪能力,并推导了考虑混凝土翼板抗剪承载力的组合截面抗剪承载力计算,计算结果与实测值吻合良好。     

Recurrent Single Delaminated Beam Model for Vibration Analysis of Multidelaminated Beams

Free vibration analysis of a through-width multidelaminated beam is performed in the present study. Multiple delaminations are assumed to spread from the top through the thickness direction of the beam. The natural frequencies of the multidelaminated beams are obtained from a recurrent single delaminated beam (RSDB) model, which is the subsingle delaminated beam from the top surface of a global beam. Each frequency equation for the RSDB with unknown boundary conditions is obtained through continuity conditions. Then this result is updated to the next one. With these sequential operations, the final frequency equation of the multidelaminated beams is obtained for both end boundary conditions of the global beam. The numerical results for the beams are compared with those of finite element analysis to give the reliance on the proposed model and to investigate the effects of the shape, number, and size of multidelaminations on the natural frequency. It was shown that the variations in the natural frequency for the multidelaminated beams were significantly affected by the delamination length.     

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.     

Maximum Shear Strength of RC Beams Retrofitted in Shear with FRP Composites

In reinforced concrete (RC) beams strengthened in shear with fiber-reinforced polymer (FRP), crushing of the web can be a potential mode of failure. The guidelines provided by codes and standards for the design of structures strengthened with externally bonded FRP recommend limiting the maximum shear strength to avoid such an undesirable failure scenario. However, these limitation provisions are not based on specific research studies performed on beams strengthened in shear with FRP. Rather, they simply duplicate provisions used in conventional concrete codes and standards. The main objective of this research study is to assess the suitability of the limits specified by the guidelines, and propose, if necessary, an alternative equation as an upper limit for shear strength against web crushing failure in such structures. To this end, an analytical approach was developed based on the static theorem of the theory of plasticity. The predictions of the equations resulting from this approach were compared with those obtained from tests reported in the literature and with those predicted by ACI Committee 440-02, Canadian Standard S6-06, and the European recommendations fib TG 9.3. The study shows that the current ACI Committee 440-02 and Canadian Standards provisions are overly conservative and therefore need to be reviewed.     

Bending of Delaminated Composite Conoidal Shells under Uniformly Distributed Load

Conoidal shells are very popular roofing units owing to their aesthetic elegance and stiffness. Many parts of the globe, which were earlier assumed to be seismologically stable, are now being considered as earthquake prone. Hence the necessity to build light structures using composites has become very important. In this paper an eight-noded isoparametric shell element is applied for analyzing the bending behavior of delaminated composite conoidal shells under a uniformly distributed load with different practical boundary conditions. To ensure compatibility of deformation and equilibrium of forces and moments at the delamination crack front, a multipoint constraint algorithm is incorporated, which leads to an unsymmetrical stiffness matrix. This formulation is validated through the solution of benchmark problems. Lamination, curvature, and extent of delamination area are varied to compare the performances of delaminated conoidal shells against those with no damage. The results are carefully observed, and a set of conclusions is presented at the end of the paper.     

Effect of Fiber Waviness on Buckling Strength of Composite Plates

This paper explores the idea of tailoring the profile of reinforcing fibers to improve the buckling strength of composite plates. This paper analyzes the uniaxial buckling behavior of composite laminates in which fibers are placed along parallel sinusoidal curves, instead of the conventional straight line pattern. The sinusoidal fiber orientation results in variable elastic stiffness and nonuniform prebuckling stress fields, which are shown to have a pronounced influence on the buckling strength. For example, changing the fiber orientation from straight line to a sinusoidal pattern can increase the buckling load of a simply supported laminate by more than 80%. For the analysis, a computerized Rayleigh-Ritz procedure is developed that exploits an analogy between bending and stretching formulations to model a variety of boundary conditions.     

Transverse Shear Effect on Flutter of Composite Panels

The effect of transverse shear deformation on the supersonic flutter of composite panels has been investigated using the finite element method. First‐order shear‐deformation laminated‐plate theory and quasi‐steady aerodynamic theory are employed for the analysis. The total displacement of the plate is expressed as the sum of the displacement due to bending and the displacement due to shear deformation. Thus, the aerodynamic pressure induced by the plate motion is also the sum of the pressure induced by bending deformation and the pressure induced by shear deformation. Numerical results show that the transverse shear deformation may have a significant effect on the flutter boundary if aerodynamic damping were small or neglected in the determination of flutter boundary.     

Inelastic Cyclic Buckling of Aluminum Shear Panels

Cyclic load tests on shear panels of low-yield alloy of aluminum (3003-O) were performed to determine the onset and effect of inelastic web buckling on load-deformation behavior. Yielding of shear panels of aluminum can be used as a means to dissipate energy through hysteresis provided strength deterioration due to inelastic buckling is controlled. Gerard’s formulation for inelastic buckling, as reported in 1948, was found to be in excellent agreement with experimental results and can be used to predict the onset of inelastic shear buckling and to design shear panels so that inelastic buckling does not occur at strains below the design requirements.     

Nonclassical Modes of Unrestrained Shear Beams

This paper considers the effect that a rotational motion has on the normal modes of a shear beam that is free to rotate, either because it is free in space or it is pivoted at one end. It is shown that the classical solutions for these two cases violate the principle of conservation of angular momentum, and that this is true even when the rotational inertia of the beam vanishes or is neglected.     

Mechanisms of Shear Resistance of Concrete Beams Strengthened in Shear with Externally Bonded FRP

In recent years, numerous investigations have addressed the shear strengthening of reinforced concrete (RC) beams with externally bonded fiber-reinforced polymer (FRP) composites. Despite this research effort, the mechanisms of shear resistance that are developed in such a strengthening system have not yet been fully documented and explained. This clearly inhibits the development of rational and reliable code specifications. This paper aims to contribute to the understanding of the shear resistance mechanisms involved in RC beams strengthened in shear with externally bonded FRP. It is based on results obtained from an experimental program, involving 17 tests, performed on full size T beams, and using a comprehensive and carefully optimized measuring device. The resistance mechanisms are studied by observing the evolution of the behavior of the strengthened beams as the applied loads are increased. The local behavior of the FRP and the transverse steel, in particular in the failure zones, are thoroughly examined. The operative resistance mechanisms are also studied through the load sharing among the concrete, the FRP, and the transverse steel, at increasing levels of applied load.     

Shear Buckling Resistance of GFRP Plate Girders

Thin webs of glass-fiber-reinforced polymer (GFRP) girders are sensitive to shear buckling, which can be considered an in-plane biaxial compression-tension buckling problem, according to the rotated stress field theory. An extensive experimental study was performed, which shows that an increasing transverse tension load significantly increases the buckling and ultimate loads caused by a decrease in the initial imperfections and additional stabilizing effects. The stacking sequence also greatly influenced the buckling behavior. Higher bending stiffness in the compression direction increased the buckling and ultimate loads, while higher bending stiffness in the tension direction changed the buckling mode shape. The general solution obtained using the Fok model accurately modeled the experimental results, while the simplified solution (modified Southwell method) provided accurate results only at higher tension loads.