Nonlinear Analysis Of Composite Beams Research Articles

Concentrated Approaches for Nonlinear Analysis of Composite Beams with Partial Interaction

AbstractTwo plane displacement‐based formulations with concentrated nonlinear effects for numerical analysis of composite beams are presented here. The effects of geometric nonlinearity, plasticity and partial shear connection are considered. In these two approaches, the co‐rotational system is defined to allow large displacements and rotations in the numerical model. The first formulation is based to Strain Compatibility Method, where the sections strains are explicitly evaluated as well as the slipping at the steel‐concrete interface. Thus, the axial and flexural stiffness of the cross section is determined in each step of the incremental‐iterative process. The second methodology considers rotational pseudo‐springs at the finite elements ends to simulate of plasticity. Furthermore, the effects of partial interaction can not be simulated by the inherently rotational behavior of the pseudo‐springs. Thus, the cracking and partial interaction effects are approached through effective moment of inertia defined by normative criteria. Four composite beams are simulated with these two formulations and compared by the load‐displacements paths. In all numerical result findings these formulations are closed and accurate to the experimental data presented in literature.

Geometrically nonlinear analysis of composite beams using Wiener-Milenković parameters

This paper presents a geometrically nonlinear analysis of composite beams including static, dynamic, and eigenvalue analyses. With the increase in size and flexibility of engineering components such as wind turbine blades, geometric nonlinearity plays an increasingly significant role in structural analysis. The Geometric Exact Beam Theory (GEBT), pioneered by Reissner and extended by Hodges, is adopted as the foundation for this work. Special emphasis is placed on the vectorial parameterization of finite rotation, which is a fundamental aspect in the geometrically nonlinear formulation. This method is introduced based on Euler's rotation theorem and the property of rotation operation: the length preservation of the rotated vector. The GEBT is then implemented with the Wiener-Milenković parameters using a mixed formulation. Several numerical examples are studied based on the derived theory, and the results are compared with analytical solutions and those available in the literature. The analysis of a realistic composite wind turbine blade is provided to show the capability of the present model for generalized composite slender structures. It concludes that the proposed model can be used as a beam tool in a multibody framework whose valid range of rotation is up to 2π.

Nonlinear analysis of composite beams with concrete-encased steel truss

Composite beams constituted by a concrete-encased steel truss welded to a continuous steel plate are analyzed using a nonlinear finite element formulation based on Newmark's classical model. The web member of the steel truss is made by deformed or structural steel rebars and behaves like a deformable shear connection. In order to avoid slip locking, finite elements based on second-order interpolation of longitudinal displacements and flexural rotations are employed. Simply supported composite beams subjected to a uniformly distributed transverse load are considered. The bending capacity is evaluated for short up to long spans, taking the nonlinear behavior of concrete, steel and shear connection into account. The effects of the shear connection ductility are put in evidence, showing that, for short spans, the interfacial stress transfer resulting from the yielding of connection may be penalizing. In fact, the high slip gradient arising in sections near the supports may lead to a premature concrete failure. In this case, the exact solution to the linear elastic problem for steel–concrete composite beams can be used for design purposes.

Non-Linear Analysis of Composite Beams

A B S T R A C T When a structure deforms, under a load its stiffness changes. Depending upon the amount of change in the stiffness, the field variables are calculated using linear or nonlinear approaches. In this paper linear and geometric non-linear analysis of a FRP composite beam is carried out using two-dimensional finite element method by simulating the problem in commercial software ANSYS. Influence of the parameters (i) span to height ratios(s) and (ii) Load on geometrical non-linear behavior of the beam for a fixed width-to-height ratio (b/h) of 0.2 is studied.

Non-linear quadrature element analysis of composite beams with partial interaction

Quadrature element formulation for material non-linear analysis of composite beams with partial interaction is derived on the basis of the Newmark kinematical model. The quadrature element method is characterised by direct evaluation of the integrals involved in the variational description of a problem. The number of integration points in a quadrature element is adjustable in accordance with convergence requirement. A representative case is studied and results are compared with finite element solutions. It is shown that high computational accuracy and efficiency are achieved using the quadrature element method.

Nonlinear analysis of composite beams subjected to combined flexure and torsion

There are situations in which a composite steel–concrete beam is subjected to torsion, such as members that are curved in plan or straight edge beams in buildings or bridges. The composite action of the steel beam and concrete slab in torsion is usually ignored in design codes of practice. Therefore, a three-dimensional (3D) finite element model is introduced in this paper to simulate composite steel–concrete beams subjected to combined flexure and torsion with the influence of partial shear connection using a commercial software ABAQUS. Brick and truss elements were used with the incorporation of nonlinear material characteristics and geometric behaviour in the model. This is coupled with an extensive parametric study using the validated finite element model using different parameters such as the span length and the level of shear connection. From the analytical study, a new phenomenon has been uncovered, which was validated by the test observation. This phenomenon called torsion induced vertical slip is an important issue, which would make the assumption plane sections remain plane invalid. In addition, difference in span length greatly affected the flexure–torsion interaction relationship of the composite steel–concrete beams, whilst the partial shear connection did not affect the relationship. Design models for readers to take away at the end of this paper are also proposed.

Nonlinear Analysis of Composite Beams with Partial Interaction in Steel Frame Structures at Elevated Temperature

Flooring systems containing steel-concrete composite beams are common in steel frame structures and it is widely recognized that their behavior under fire loading is profoundly different to that of simply supported composite beams under fire loading. This difference in behavior is due to the presence of restraints provided by cooler members in a compartment fire in a composite frame structure and there is extensive evidence from fire tests that composite beams with unprotected steel components in steel frames perform much better than simply supported composite beams with unprotected steel components. In order to model the structural response of a composite beam restrained in this way at elevated temperature, recourse is needed to a geometric nonlinear formulation, since the transverse beam deflections are large and interact with the substantial axial compressive force in the member at the early stages of the fire. This paper presents such a formulation, which incorporates partial interaction between the concrete slab and steel component, as well as the degradation of the stiffnesses of the components of the composite beam prior to yield at elevated temperature. The generic technique that is developed is shown to agree with solutions reported elsewhere and provides a structural model for the response of a composite beam in fire with the potential for inclusion in prescriptive code rules for rational fire engineering based designs.

Nonlinear analysis of composite beams with partial shear interaction by means of the direct stiffness method

This paper presents a modelling technique for the nonlinear analysis of composite steel-concrete beams with partial shear interaction. It extends the applicability of two stiffness elements previously derived by the authors using the direct stiffness method, i.e. the 6DOF and the 8DOF elements, to account for material nonlinearities. The freedoms are the vertical displacement, the rotation and the slip at both ends for the 6DOF stiffness element, as well as the axial displacement at the level of the reference axis for the 8DOF stiffness element. The solution iterative scheme is based on the secant method, with the convergence criteria relying on the ratios of the Euclidean norms of both forces and displacements. The advantage of the approach is that the displacement and force fields of the stiffness elements are extremely rich as they correspond to those required by the analytical solution of the elastic partial interaction problem, thereby producing a robust numerical technique. Experimental results available in the literature are used to validate the finite element proposed in the paper. For this purpose, those reported by Chapman and Balakrishnan (1964), Fabbrocino et al. (1998, 1999) and Ansourian (1981) are utilised; these consist of six simply supported beams with a point load applied at mid-span inducing positive bending moment in the beams, three simply supported beams with a point load applied at mid-span inducing negative bending moment in the beams, and six two-span continuous composite beams respectively. Based on these comparisons, a preferred degree of discretisation suitable for the proposed modelling technique expressed as a function of the ratio between the element length and depth is proposed, as is the number of Gauss stations needed. This allows for accurate prediction of the nonlinear response of composite beams.

Shear deformation effect in non-linear analysis of composite beams of variable cross section

In this paper the non-linear analysis of a composite Timoshenko beam with arbitrary variable cross section undergoing moderate large deflections under general boundary conditions is presented employing the analog equation method (AEM), a BEM-based method. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson's ratio and are firmly bonded together. The beam is subjected in an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, the axial displacement and to two stress functions and solved using the AEM. Application of the boundary element technique yields a system of non-linear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples are worked out to illustrate the efficiency, the accuracy, the range of applications of the developed method and the influence of the shear deformation effect.

Assessment of the refined sinus model for the non-linear analysis of composite beams

The objective of this paper is to evaluate a new three-noded mechanical beam finite element for the non-linear analysis of laminated beams. It is based on a sinus distribution with layer refinement. The transverse shear strain is obtained by using a cosine function avoid-ing the use of shear correction factors. This kinematic accounts for the interlaminar continuity conditions on the interfaces between lay-ers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent from the number of layers. Buckling, post-buckling, and non-linear bending tests are presented in order to compare with the ones available in the literature or based on a 2D analysis. The influence of mesh, boundary conditions, length-to-thickness ratios and lay-ups is studied to show the accu-racy and the efficiency of this finite element.

Shear deformation effect in nonlinear analysis of spatial composite beams subjected to variable axial loading by bem

In this paper a boundary element method is developed for the nonlinear analysis of composite beams of arbitrary doubly symmetric constant cross section, taking into account the shear deformation effect. The composite beam consists of materials in contact, each of which can surround a finite number of inclusions. The materials have different elasticity and shear moduli with same Poisson's ratio and are firmly bonded together. The beam is subjected in an arbitrarily concentrated or distributed variable axial loading, while the shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. To account for shear deformations, the concept of shear deformation coefficients is used. Five boundary value problems are formulated with respect to the transverse displacements, the axial displacement and to two stress functions and solved using the Analog Equation Method, a BEM based method. Application of the boundary element technique yields a system of nonlinear equations from which the transverse and axial displacements are computed by an iterative process. The evaluation of the shear deformation coefficients is accomplished from the aforementioned stress functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency and the range of applications of the developed method. The influence of both the shear deformation effect and the variableness of the axial loading are remarkable.

Comparison and validation of displacement and mixed elements for the non-linear analysis of continuous composite beams

A new three-field mixed beam element and two previously introduced displacement-based beam elements are adopted for the non-linear analysis of composite beams with deformable shear connection. The formulation considers the non-linear behaviour of materials and shear connection. Numerical applications are performed using as working examples steel–concrete two-span continuous beams, a problem of practical interest in structural engineering and a difficult test for composite beam elements. The results are discussed and comparisons are made between the mixed and displacement-based elements. Comparisons with experimental tests are also discussed in order to validate the numerical model and provide indications for reliable non-linear analyses.

Three-field mixed formulation for the non-linear analysis of composite beams with deformable shear connection

A three-field mixed finite element is proposed for the non-linear analysis of composite beam with deformable shear connection. The formulation considers the non-linear behaviour of materials and shear connectors. The established mixed element is compared to the locking-free displacement element from which it derives and to a refined locking-free displacement element previously tested by the authors. In order to evaluate the way to better improve the solution in the non-linear range (three-field mixed formulation or refined displacement formulation), numerical applications are performed using, as working example, a steel-concrete cantilever, representing a difficult test for composite beam elements.

Non-linear analysis of composite beams by a displacement approach

The non-linear analysis of composite steel–concrete beams by the finite elements method permits obtaining useful information on collapse modalities but the convergence of the solution must be carefully controlled. Using the displacement formulation of the finite elements technique, the authors illustrate some aspects related to the convergence of the method by comparing solutions deriving from finite elements with 8, 10 and 16DOF. Some pathologies of the 8DOF element are posed in evidence.

Non-linear analysis of composite beams under positive bending

The structural behaviour of steel–concrete composite beams depends on the interaction between the steel beam and the concrete slab. Therefore, the connection largely influences the global behaviour of the beam and its modelling is a key issue in the analysis of these structures. An effective model requires the introduction of an explicit relationship between slip and interaction force given by each connector, which is strongly non-linear. In this paper, a numerical procedure that allows a reliable analysis of the structural behaviour of composite beams subjected to sagging moment due to short term loads, both in serviceability and ultimate state, is proposed.

Nonlinear Analysis of Composite Beams with Deformable Shear Connectors

Composite floor systems, consisting of reinforced concrete slabs and steel girders, are common in buildings and bridges. Partial restraints at the interface of the concrete slab and the steel girder have significant effects on the response of the composite beam. A few analytical models capable of accounting for these effects are available; however, none can be efficiently used for the nonlinear analysis of composite beams. In this paper, the basic governing equations are presented for a composite beam with deformable shear connectors under small displacements. Based on these equations, a new composite beam element is developed using the force method of analysis. The performance of this new element is compared with that of a previously developed displacement-based composite beam element. Both elements consist of two beam components connected through a deformable interface. A distributed spring model is used to account for the shear deformation at the interface. Two numerical examples on the nonlinear behavior of composite beams are solved using both displacement- and force-based elements. Comparison of the numerical results shows the superior performance of the newly developed force-based element over the displacement-based element.

Linear and geometrically non-linear analysis of composite beams under transverse loading

The flexural analysis of fiber-reinforced composite beams based on a higher-order shear deformation theory is studied. The geometric non-linearity is incorporated in the formulation by considering the von Karman strains. The finite element method is used to solve the non-linear governing equations by direct iteration. Unlike conventional beam models, the present beam model accounts for y direction strains. It is observed that the solution obtained from the two approaches differ slightly in the case of cross-ply laminates, but there exists a considerable difference in the case of angle-ply laminates. The influence of boundary conditions, beam geometries, and ply orientations on the deflections and stresses of laminated beams is shown both in tabular and graphical form.