A preliminary numerical and experimental investigation on the shear stress distribution on multi-row bolted FRP joints

The first results of a numerical and experimental investigation on the shear forces distribution in a bolted joint made entirely from FRP materials are presented. It is also proposed an experimental equipment for investigating the strains and stresses distributions around the holes of the connection as well as the bearing stresses at the interface between plate and steel bolt. A good agreement between numerical and experimental results allows to use the proposed testing set-up for analysing the bearing failure of several joint configuration with different lamination scheme, geometry and type of load

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

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

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

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

Mean field sparse optimal control of systems with additive white noise

We analyze the problem of controlling a multi-agent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with a SDE constraint, we introduce a rigorous limit process towards an infinite dimensional optimal control problem constrained by the coupling of a system of ODE for the leaders with a McKean-Vlasov-type SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the $\Gamma$-limit of the cost functionals for the finite dimensional problems

LATERAL BUCKLING PROBLEM: MODIFICATIONS OF STANDARD GFRP SECTIONS SHAPE AND PROPORTIONS

In this paper the first results of a comprehensive numerical investigation regarding the flexural–torsional response of pultruded slender beams is presented. The goal of the research is to propose GFRP standard cross-sections of such proportions and shapes that would possess improved strength, stability and deformational characteristics compared to the corresponding existing sections whose proportions are generally based on standard steel sections. As GFRP sections are thin-walled but are significantly less stiff than similar steel sections, the study focuses on enhancing their appropriate stiffness and buckling strength. The novel and efficient numerical model used in this investigation was developed by the writers and can be used to trace the complete pre-buckling geometrically nonlinear response of any GFRP or steel thin-walled member with open or closed cross-section. The bucking load is computed by the asymptotic value of the load-displacement curve. It is demonstrated that due to their unsuitable proportions, available standard GFRP sections do not have adequate stiffness and buckling strength. Consequently, relative to T-cross section only recommendations are made for new sectional proportions and modified shape. The superiority of the proposed section is quantified by an efficiency factor, defined in terms of ratio of strength gain to material volume increase

A COMPARISON BETWEEN COMPOSITE AND STEEL BEAMS IN THE FLEXURAL-TORSIONAL EQUILIBRIUM PROBLEM

In this paper the first results of a comprehensive numerical investigation regarding the flexural–torsional response of pultruded slender beams is presented. The goal of the re-search is to propose GFRP standard cross-sections of such proportions and shapes that would possess improved strength, stability and deformational characteristics compared to the corresponding existing sections whose proportions are generally based on stan-dard steel sections. As GFRP sections are thin-walled but are significantly less stiff than similar steel sections, the study focuses on enhancing their appropriate stiffness and buckling strength. The novel and efficient numerical model used in this investigation was developed by the writers and can be used to trace the complete pre-buckling geo-metrically nonlinear response of any GFRP or steel thin-walled member with open or closed cross-section. The bucking load is computed by the asymptotic value of the load-displacement curve. It is demonstrated that due to their unsuitable proportions, available standard GFRP sections do not have adequate stiffness and buckling strength. Consequently, relative to I- cross section only recommendations are made for new sectional proportions and modified shape. The superiority of the proposed section is quantified by an efficiency factor, defined in terms of ratio of strength gain to material volume increase

Civil structures made entirely from FRP pultruded beams

The aim of this paper is to present the main problems connected to the design of a civil structures made from composite materials, starting from the initial choice of the material up to the choice of the opportune procedure for designing and verifying the FRP elements. Finally, the authors carried out an example of rehabilitation of a roofing structure consisting in replace totally the latter with a new one made entirely from FRP pultruded profiles. The new roofing structure is truss-frame type with a length equal to twelve meter whose connections are realized with steel bolts. The material used consist of glass FRP and the geometrical and mechanical properties are given by technical data sheets edited by the manufacturer

INFLUENCE OF BOLT DIAMETER ON THE BEARING FAILURE LOAD OF GFRP BOLTED LAMINATES

Many theoretical as well as experimental studies have been recently carried out by researchers working in the field of civil engineering on the design and verification problem of structural bolted joints for structures realized with Fibre Reinforced Polymers (FRP). It worth taking into account the results obtained by Camanho and Matthews [2], Ekh, Schön and Melin [3, 4], Hassan, Mohamedien and Rizkalla [5], Ireman [6], Kelly and Hallström [7], Li, Kelly and Crosky [8], Lie, Yu and Zhao [9], Starikov and Schön [10], Vangrimde and Boukhili [11, 12], Xiao and Ishikawa [13], Yan, Wen, Chang and Shyprykevich [14]. The results of these studies have highlighted the influence on typical failure modes of FRP bolted joints of some main factors as being: 1) stacking sequence of the laminates; 2) joint geometry: bolt diameter, plate width, end distance and thickness of the composite member; 3) matrix type and fibre nature. In this context, the aim of the research carried out by the authors is to investigate on the bearing failure mode of a laminate bolted joint and, in particular, to underline the effects of the fibre inclination angle, the laminate stacking sequence and the bolt diameter on the aforementioned failure mode. For the experimental tests circular specimens have been used, with 300mm in diameter, built-in at the edge with a central hole. Some results, in terms of fiber inclination angle and laminate stacking sequence, have been just published by the authors in [15, 16]. The experimental results, showing the influence of bolt diameter on the bearing strength, represent the subject of the present paper. In order to perform the experimental investigation, two types of GFRP laminates were tested: unidirectional and cross-ply. In particular the stacking sequence of the unidirectional laminates (10mm thick) was [CSM/08/CSM], while for the cross-ply laminates were used two different stacking sequence . These latter were: [(CSM/06/906)s] and [(CSM/03/903)2]s, where the number of plies and the thickness (12mm) was constant. On both types of laminates three different values of the bolt diameter have been considered: 20mm, 19mm and 18mm. All of them are relative to the same value of the hole diameter, equal to 21mm. The experimental results have shown that the bearing strength depends significantly on the bolt diameter for both types of laminates considered. In particular, in the case of unidirectional laminates the experimental analysis carried out put in evidence a reduction of the bearing strength, passing from the maximum diameter considered of 20mm to the minimum one of 18mm, equal to 13%. For what concerns the cross-ply laminates the analysis also shows a reduction of the bearing strength equal to 24%, replacing the bolt of 20mm in diameter with one of 18mm, as in the case of unidirectional laminates. For both types of laminates considered, the analysis shows that the bearing strength reduction, varying the bolt diameter, is independent from the fiber inclination angle as well as from stacking sequence. Finally, the authors give a new design formula for the bearing failure load, which takes into account, near the fiber inclination angle and the stacking sequence, the bolt diameter also