Locking-free two-layer Timoshenko beam element with interlayer slip

A new locking-free strain-based finite element formulation for the numerical treatment of linear static analysis of two-layer planar composite beams with interlayer slip is proposed. In this formulation, the modified principle of virtual work is introduced as a basis for the finite element discretization. The linear kinematic equations are included into the principle by the procedure, similar to that of Lagrangian multipliers. A strain field vector remains the only unknown function to be interpolated in the finite element implementation of the principle. In contrast with some of the displacement-based and mixed finite element formulations of the composite beams with interlayer slip, the present formulation is completely locking-free. Hence, there are no shear and slip locking, poor convergence and stress oscillations in these finite elements. The generalization of the composite beam theory with the consideration of the Timoshenko beam theory for the individual component of a composite beam represents a substantial contribution in the field of analysis of non-slender composite beams with an interlayer slip. An extension of the present formulation to the non-linear material problems is straightforward. As only a few finite elements are needed to describe a composite beam with great precision, the new finite element formulations is perfectly suited for practical calculations. (c) 2007 Elsevier B.V. All rights reserved

Flexural–torsional behavior of thin-walled composite box beams using shear-deformable beam theory

This paper presents a flexural–torsional analysis of thin-walled composite box beams. A general analytical model applicable to thin-walled composite box beams subjected to vertical and torsional loads is developed. This model is based on the shear-deformable beam theory, and accounts for the flexural–torsional response of the thin-walled composites for an arbitrary laminate stacking sequence configuration, i.e. unsymmetric as well as symmetric. The governing equations are derived from the principle of the stationary value of total potential energy. Numerical results are obtained for thin-walled composites under vertical loading, addressing the effects of fiber angle and span-to-height ratio of the composite beam

Axial-flexural coupled vibration and buckling of composite beams using sinusoidal shear deformation theory

A finite element model based on sinusoidal shear deformation theory is developed to study vibration and buckling analysis of composite beams with arbitrary lay-ups. This theory satisfies the zero traction boundary conditions on the top and bottom surfaces of beam without using shear correction factors. Besides, it has strong similarity with Euler–Bernoulli beam theory in some aspects such as governing equations, boundary conditions, and stress resultant expressions. By using Hamilton’s principle, governing equations of motion are derived. A displacement-based one-dimensional finite element model is developed to solve the problem. Numerical results for cross-ply and angle-ply composite beams are obtained as special cases and are compared with other solutions available in the literature. A variety of parametric studies are conducted to demonstrate the effect of fiber orientation and modulus ratio on the natural frequencies, critical buckling loads, and load-frequency curves as well as corresponding mode shapes of composite beams

Reinforcement of wood with natural fibers

This paper describes an experimental programme which examines the reinforcement in flexure of timber beams with composite materials based on natural fibers in the form of fabrics made from hemp, flax, basalt and bamboo fibers. The industrial use of natural fibers has been continuously increasing since 1990s due to their advantages in terms of production costs, pollution emissions and energy consumption for production and disposal. The technique allows the reinforcement of the intrados of beams, avoiding the dismantling of the overlying part of the structure with significant savings in terms of costs and work time. The test program consists of three phases incorporating 45 beams. The bending tests on the wooden elements made it possible to measure the increase in capacity and stiffness resulting from the composite reinforcement. This was applied to beams, creating different arrangements and using different quantities (number of layers). Despite the diversity of the various tests carried out, the results obtained in some cases showed significant increases in terms of load-carrying capacity and in deflection ductility

Flexural behaviour of structural fibre composite sandwich beams in flatwise and edgewise positions

The flexural behaviour of a new generation composite sandwich beams made up of glass fibre-reinforced polymer skins and modified phenolic core material was investigated. The composite sandwich beams were subjected to 4-point static bending test to determine their strength and failure mechanisms in the flatwise and the edgewise positions. The results of the experimental investigation showed that the composite sandwich beams tested in the edgewise position failed at a higher load with less deflection compared to specimens tested in the flatwise position. Under flexural loading, the composite sandwich beams in the edgewise position failed due to progressive failure of the skin while failure in the flatwise position is in a brittle manner due to either shear failure of the core or compressive failure of the skin followed by debonding between the skin and the core. The results of the analytical predictions and numerical simulations are in good agreement with the experimental results

Experimental Study of Ultra Shallow Floor Beams (USFB) with Perforated Steel Sections

ABSTRACT: In modern building construction design, floor spans are becoming longer. Hence, steel framed structures have become more competitive when compared with traditional reinforced concrete framed buildings. In order to minimise the structural section of the composite sections, and for economic reasons, steel perforated beams are designed to act compositely with the floor slab. When the concrete slab lies within the steel flanges, as in the Ultra Shallow Floor Beam (USFB), there is an additional benefit when considering fire resistance. The aim of this study is to investigate the contribution of the concrete in composite cellular beams in the case where the concrete slab lies between the beam flanges of a steel section, when resisting vertical shear forces. The concrete between the flanges enhances the load-carrying capacity by providing a load path to transfer the shear force. Four specimens of steel-concrete composite beams with web openings in the steel section were tested in this study. One bare steel section with web openings was also tested as a comparison. This is the first such investigation of the failure mode under shear resistance (Vierendeel action) of the Ultra Shallow Floor Beam. In the test specimens, the web opening diameter is 76% of the beam depth, which is the largest currently available. This represents the worst case in terms of Vierendeel bending forces generated in the vicinity of the web openings. The smaller the hole is, the easier it is for the trapped concrete between the flanges to transfer shear across the opening. The results from the composite beam tests show a significant increase in shear resistance. The percentage of the shear capacity improvement of the particular case is presented herein as well as the failure mode of the composite beams. The shear enhancement demonstrated in this study has been utilised software that is used in design practice

On sixfold coupled buckling of thin-walled composite beams

A general analytical model based on shear-deformable beam theory has been developed to study the flexural–torsional coupled buckling of thin-walled composite beams with arbitrary lay-ups under axial load. This model accounts for all the structural coupling coming from the material anisotropy. The seven governing differential equations for coupled flexural–torsional–shearing buckling are derived. The resulting coupling is referred to as sixfold coupled buckling. Numerical results are obtained for thin-walled composite beams to investigate effects of shear deformation, fiber orientation and modulus ratio on the critical buckling loads and corresponding mode shapes

Vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under axial loads and end moments

A finite element model with seven degrees of freedom per node is developed to study vibration and buckling of thin-walled composite I-beams with arbitrary lay-ups under constant axial loads and equal end moments. This model is based on the classical lamination theory, and accounts for all the structural coupling coming from material anisotropy. The governing differential equations are derived from the Hamilton’s principle. Numerical results are obtained for thin-walled composite I-beams to investigate the effects of axial force, bending moment and fiber orientation on the buckling moments, natural frequencies, and corresponding vibration mode shapes as well as axial-moment-frequency interaction curves

On sixfold coupled vibrations of thin-walled composite box beams

This paper presents a general analytical model for free vibration of thin-walled composite beams with arbitrary laminate stacking sequences and studies the effects of shear deformation over the natural frequencies. This model is based on the first-order shear-deformable beam theory and accounts for all the structural coupling coming from the material anisotropy. The seven governing differential equations for coupled flexural–torsional–shearing vibration are derived from the Hamilton’s principle. The resulting coupling is referred to as sixfold coupled vibration. Numerical results are obtained to investigate the effects of fiber angle, span-to-height ratio, modulus ratio, and boundary conditions on the natural frequencies as well as corresponding mode shapes of thin-walled composite box beams

Geometrically nonlinear theory of thin-walled composite box beams using shear-deformable beam theory

A general geometrically nonlinear model for thin-walled composite space beams with arbitrary lay-ups under various types of loadings is presented. This model is based on the first-order shear deformable beam theory, and accounts for all the structural coupling coming from both material anisotropy and geometric nonlinearity. The nonlinear governing equations are derived and solved by means of an incremental Newton–Raphson method. A displacement-based one-dimensional finite element model that accounts for the geometric nonlinearity in the von Kármán sense is developed. Numerical results are obtained for thin-walled composite box beams under vertical load to investigate the effects of shear deformation, geometric nonlinearity and fiber orientation on axial–flexural–torsional response