The influence of the web-flange junction stiffness on the mechanical behaviour of thin-walled pultruded beams

Composite thin walled members, produced by the manufacturing process of pultrusion, exhibit structural behaviour that is governed by their specific stiffness and strength properties. Although the basic knowledge about their constitutive behaviour has already been assessed in current technical literature, several relevant features are still being studied. They include the evaluation of the long term behaviour, the influence of the shear deformations, the buckling load as well as the influence of the web-flange junction stiffness. Due to the presence of unidirectional fibres along the length of the beam, the condition of a rigid connection between the flanges and web panel should be replaced by accounting for possible relative torsional rotations, which can influence the pre-buckling behaviour. In this paper, a one dimensional mechanical model with the purpose of detecting such an influence is presented. The model, which is based on many common assumptions (a linear kinematics conjugated with small strains and moderate rotations), is innovative in relation to the presence of a few additional degrees of freedom which allow to simulate the web/flange relative rotations, thus generalizing the classical assumptions concerning the generic cross-section which maintains it un-deformed. Many numerical examples obtained by using a finite element approximation with the aim of highlighting the model capabilities have been developed

FINITE ELEMENT ANALYSIS ON THE MECHANICAL BEHAVIOUR OF ADHESIVE LAP JOINTS

Adhesive lap joints for structural purposes are well known in many sectors of Engineering, above all in the Aeronautical and Mechanical fields, mainly due to the strong reduction of both time and construction cost given by their use. Other benefits are represented by the resistance to corrosion and fatigue as well as the toughness with regard to the fracture. In recent years, adhesive lap joints are going to diffuse themselves also in the field of Civil Engineering, in particular regarding the applications of FRP (Fiber Reinforced Polymer) structural members. The modern theoretical approaches in studying the mechanical behaviour of adhesive lap joints refers to Fracture Mechanics and follows two main lines: the first one is based on the classical Griffith criterion (Linear Elastic Fracture Mechanics), while the second one is based on appropriate models of interfacial laws (cohesive constitutive laws) between adherents and adhesive. The main limit of the first line is represented by the hypothesis of linear elastic behaviour required to adherents and adhesive up to the fracture. In fact, when dealing with adhesive lap joints made of FRP, the aforementioned hypothesis is certainly satisfied by the adherents, but it is certainly not appropriate for the adhesive. A theoretical and numerical analysis on the equilibrium problem of FRP adhesive lap joints, has been recently developed using cohesive interfacial laws [14-15]. In particular, bilinear interfacial laws have been considered, composed of a linear elastic branch followed by a decreasing range, linear too, which corresponds to a softening behaviour of the adhesive. No shear deformability as well as no coupling between extensional and flexure behaviour of the adherents have been taken into account. Furthermore, only a pseudo-interaction between fracture modes I and II has been considered, by using the Hutchinson and Suo fracture criterion [4]. The aim of the present paper is to extend the above mentioned analysis accounting for the shear deformability of the adherents and the coupling between extensional and flexure equilibrium problems. The numerical results, obtained via finite element simulations, are compared with those available in literature

Non-linear pre-buckling behavior of shear deformable thin-walled composite beams with open cross-section

A kinematic model is presented for thin-walled composite beams able to account for axial, bending, torsion and warping strains. Shear deformations on the mid-surface are considered and modeled by means of a polynomial approximation employing suitable shape functions on the curvilinear abscissa along the cross-section mid-line. Small strains and moderate rotations are considered over the pre-buckling range. The model allows to predict the static non-linear behavior and the critical loads of composite pultruded beams. A finite element approximation is derived from a variational approach. Some numerical results are also presented revealing the importance of shear terms on the mechanical response and their effect on the stability of pultruded composite members

MECHANICAL BEHAVIOUR OF ADHESIVE JOINTS: THE INFLUENCE OF CURVATURE RADIUS

Over the last few years, adhesive lap joints have been used in Civil Engineering in conjunction with the structural application of Fiber Reinforced Polymers (FRP). Such applications mainly include the restoration of existing structures, usually made of concrete or masonry, while a minor part concern the field of new structures made from FRP. The behaviour of adhesive joints depends on many factors, such as the physical and mechanical properties of adherents and adhesive, as well as the joint configuration (the thickness of the adhesive layer, the length of the overlapping area, the curvature radius, etc.). A literature review of the most recent contributions given in this research field is summarized in [1], where, in addition to classical stress analysis approaches, is presented the modelling of the adherents/adhesive interfaces by cohesive laws. Such laws can be expressed by two uncoupled relations: the normal interaction, , versus the transverse relative displacement, , and the tangential interaction, , versus the axial relative displacement, , evaluated at the interface. The fracture energies relative to mode I (opening) and mode II (sliding) are activated by the displacements and , respectively. Current literature includes several significant papers which have mainly focused on mode II fracture [2-3]. The interest in mode II fracture is due to the fact that joints are designed to essentially transfer axial forces. Nevertheless, the additional presence of shear and flexural stresses, also mobilised by the curvature radius, even if less relevant in respect to the axial stresses, justifies the interest towards more refined approaches accounting for mixed mode I/II fracture [4-11]. The present paper aims at developing a wide analysis of the mixed fracture mode I/II applied to curved adhesive joints. The numerical results are presented as function of many parameters relative to: the mode I/II fracture energies ratio, the curvature radius, the stiffness of the reinforcement in comparison to that one of the support. The numerical results are compared with some others available in literature

FRP adhesive lap-joints: a micro-scale mechanical approach

As it is well-known, when dealing with thin films the size effect (i.e. the thinner, the stiffer) is often observed [1-2]. Such an effect also occurs in the case of adhesive interfaces between FRP profiles, where the glue layer can be few μm thick. Due to the lack of internal material length scale parameters, classical models cannot be able to capture the microstructure dependent size effect and, therefore, need to be extended by using high order non-local continuum theories. Both the classical couple stress elasticity theory elaborated by Koiter [3] and some other higher-order elasticity theories available in literature [4-8] include four material constants: two classical and two additional. In particular, the two additional parameters, related to the symmetric and antisymmetric part of the curvature tensor, cannot be determined from single experiments as the twisting of a thin cylinder or the pure bending test of a thin film. Combinations of both types of test are required. In order to overcome the difficulties related to the evaluation of two microstructure length scale parameters [9-10], a modified couple stress theory has been recently developed by means of restricting the couple stress tensor to be symmetric [11]. As a consequence, the strain energy does not depend on the antisymmetric part of the curvature tensor and, therefore, only one additional material length scale parameter is required. Based on this modified couple stress theory, some one-dimensional models have been very recently proposed for studying both the Bernulli-Euler [12-13] and Timoshenko [14] beam problems. The aim of this paper is to apply the modified couple stress theory [11] for investigating the behavior of FRP adhesive lap-joints under generic external loads. Two-dimensional elasticity fields are utilized for simulating both the response of the adherents (plane stress) and that one of the adhesive films (plane strain); in the last case, the mechanical model takes into consideration the internal material length scale parameter too. The mechanical model proposed by the authors also accounts for the most common interfacial cohesive laws [15-18]: elastic moduli of the thin adhesive layers, in fact, are step-by-step modified in such a way so that the value of the strain energy density is equal to that one corresponding to the cohesive mixed-mode fracture law considered. The goal is to extend the numerical investigation already developed by the authors -without considering the scale effect- for predicting the ultimate behavior of FRP adhesive lap-joints [19-20

The influence of the shear deformations on the local stress state of pultruded composite profiles

Due to the relevance of shear deformability, the practical use of composite profiles still conflicts with the serviceability requirements related to the stiffness demand for civil applications. Moreover, when dealing with shear deformable beams, it is also well recognized that displacement-based 1-D models can lead to inaccurate stress predictions. Hence, a relatively simple beam model allowing to evaluate both strains and stresses accurately may represent a useful tool. The main motivation of the present paper is precisely to investigate these features by presenting relevant numerical results dealing with the mechanical response of pultruded composite profiles with thin-walled open cross-section made of both Glass (GFRP) and Carbon Fiber Reinforced Plastic (CFRP). Comparisons with solutions given via classical 1-D / 2-D mechanical models are also provided, which highlight the accuracy of the proposed kinematics, especially with the aim of an accurate stress evaluation

2-D periodic structures. A numerical study

Purpose Within the context of 2D square lattices, searching for the existence of band gaps assumes a great interest owing to many possible fields of application: from energy absorption devices to noise and vibration controllers, as well as advanced strategies for the seismic isolation. Design/methodology/approach The underlying microstructure may influence the mechanical response of 2D square lattices according to a complex interplay between different factors. A first one is related to the so-called "size-effect". A second one relates, instead, to the mass density distribution. Findings It has been observed that lumped masses may induce additional band gaps to appear and may magnify their width. Finally, an additional factor deals with the inner damping characteristics of the constituent materials, which usually are polymer-based. Originality/value This study focuses on the first factor from a specific perspective: to investigate the influence of the size effect on the existence and properties of frequency band gaps

Time-Dependent Behavior of Reinforced Polymer Concrete Columns under Eccentric Axial Loading

Polymer concretes (PCs) represent a promising alternative to traditional cementitious materials in the field of new construction. In fact, PCs exhibit high compressive strength and ultimate compressive strain values, as well as good chemical resistance. Within the context of these benefits, this paper presents a study on the time-dependent behavior of polymer concrete columns reinforced with different bar types using a mechanical model recently developed by the authors. Balanced internal reinforcements are considered (i.e., two bars at both the top and bottom of the cross-section). The investigation highlights relevant stress and strain variations over time and, consequently, the emergence of a significant decrease in concrete’s stiffness and strength over time. Therefore, the results indicate that deferred effects due to viscous flow may significantly affect the reliability of reinforced polymer concrete elements over time

Pre-buckling behavior of composite beams: an innovative approach

Fiber-reinforced composite materials have been used over the past years in several different civil structures, acquiring a leading role as structural elements [1-4]. In particular, FRP profiles are manufactured by so-called automated process of pultrusion. From a mechanical point of view, they can be considered as linear elastic, homogeneous and transversely isotropic, with the plane of isotropy being normal to the longitudinal axis (i.e. the axis of pultrusion). It is generally asserted that their mechanical behavior is highly affected by warping strains due to their small thickness. In addition, low shear moduli, more or less the same as those of the polymeric resin, can provoke a non-negligible increase in lateral deflections, thus affecting both the local and global buckling loads. Consequently, FRPs members exhibit significant non classical effects such as transverse shear, warping displacements and non-uniform torsional rigidity that make deformability and stability requirements more relevant than the strength limits in the design process. Recently, experimental studies by Mosallam [5] and Feo et al. [6] showed that the condition of a rigid connection should be replaced by a more appropriate assumption due to the presence of a higher local resin concentration in the connection region between the flange and web. Furthermore, taking into account that pultrusion guarantees very high strength and stiffness along the longitudinal direction of the beam, a deeper investigation of this topic is required. In this paper, which is a continuation of previous ones [7-8], a geometrically nonlinear model for studying the lateral global buckling problem of a generic open/closed composite beam is presented. The model is based on a full second-order deformable beam theory and accounts for both the warping effects and possible displacement discontinuities at the web/flange interface. Equilibrium nonlinear equations are derived from the Principle of Virtual Displacements. A displacement-based one-dimensional finite element model is also developed. Numerical results are obtained for thin-walled composite beams with open and closed section under flexural/torsional loads. The main aim is to investigate the lateral buckling behavior taking into account the effects of shear and web/flange junction deformability as well as the initial geometric imperfections. The reliability of the mechanical model is assured by comparisons with other numerical and experimental results available in literature. Preliminary results show that deformability and stability requirements are fundamental in the safety analysis of such members

GIUNTI ADESIVI DI GFRP: UN APPROCCIO ALLA MICROSCALA

Il comportamento meccanico di giunti incollati tra aderendi di FRP può essere influenzato dal cosiddetto "effetto-scala" in considerazione degli spessori generalmente sottili degli adesivi. La rigidezza esibita dal collegamento può risultare, in sostanza, più elevata di quella prevedibile sulle base di una analisi indifferente rispetto a tale parametro. L'effetto scala diviene rilevante a misura che lo spessore dell'interfaccia adesiva assume valori prossimi alla lunghezza caratteristica (micro scale length) della resina (20 µm) di cui essa è generalmente composta. Ne consegue un evidente interesse ad approfondire l’influenza del suddetto parametro di scala sul comportamento meccanico di giunti adesivi. A tal riguardo, alcuni risultati numerici conseguiti in precedenza dagli autori in ambito lineare sono, nel presente lavoro, ottenuti nel caso più generale di comportamento non lineare dell'interfaccia