On a Moderate Rotation Theory of Thin-Walled Composite Beams

A small strain and moderate rotation theory of laminated composite thin-walled beams is formulated by generalizing the classical Vlasov theory of sectorial areas. The proposed beam model accounts for axial, bending, torsion and warping deformations and allows one to predict critical loads and initial post-buckling behaviour. A finite element approximation of the theory is also carried out and several numerical applications are developed with reference to lateral buckling of composite thin-walled members. The sensitivity of critical load to secondorder effects in the pre-buckling range is pointed out

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

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

On Bending of Bernoulli-Euler Nanobeams for Nonlocal Composite Materials

Evaluation of size effects in functionally graded elastic nanobeams is carried out by making recourse to the nonlocal continuum mechanics. The Bernoulli-Euler kinematic assumption and the Eringen nonlocal constitutive law are assumed in the formulation of the elastic equilibrium problem. An innovative methodology, characterized by a lowering in the order of governing differential equation, is adopted in the present manuscript in order to solve the boundary value problem of a nanobeam under flexure. Unlike standard treatments, a second-order differential equation of nonlocal equilibrium elastic is integrated in terms of transverse displacements and equilibrated bending moments. Benchmark examples are developed, thus providing the nonlocality effect in nanocantilever and clampled-simply supported nanobeams for selected values of the Eringen scale parameter

a note on torsion of nonlocal composite nanobeams

The ERINGENelastic constitutive relation is used in this paper in order to assess small-scale effects in nanobeams. Structural behavior is studied for functionally graded materials in the cross-sectional plane and torsional loading conditions. The governing boundary value problem has been formulated in a mixed framework. Torsional rotations and equilibrated moments are evaluated by solving a first-order differential equation of elastic equilibrium with boundary conditions of kinematic-type. Benchmarks examples are briefly discussed, enlightening thus effectiveness of the proposed methodology

Masonry arches strengthened with composite unbonded tendons

In this paper an analytical model to evaluate the structural behavior of masonry arches and vaults strengthened with composite unbonded tendons placed at the extrados is presented. The tendons are fixed at the imposts. The model is formulated under the assumption of finite displacements. The displaced equilibrium configurations are identified by the stationariety of the potential of the acting forces. It is shown that when the tendon is not pretensioned an increase of the arch collapse load can be achieved only if the axial stiffness of the tendon is sufficiently large. Instead if the tendon is pretensioned an increase of the load that induces the first displacement of the arch is always achieved. If the stiffness of the tendon is sufficiently large the collapse load will be greater than the load that produces the first displacement of the arch

Masonry arches strengthened with composite unbonded tendons

In this paper an analytical model to evaluate the structural behavior of masonry arches and vaults strengthened with composite unbonded tendons placed at the extrados is presented. The tendons are fixed at the imposts. The model is formulated under the assumption of finite displacements. The displaced equilibrium configurations are identified by the stationariety of the potential of the acting forces. It is shown that when the tendon is not pretensioned an increase of the arch collapse load can be achieved only if the axial stiffness of the tendon is sufficiently large. Instead if the tendon is pretensioned an increase of the load that induces the first displacement of the arch is always achieved. If the stiffness of the tendon is sufficiently large the collapse load will be greater than the load that produces the first displacement of the arch

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

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