PSI - Issue 64

Luigi Granata et al. / Procedia Structural Integrity 64 (2024) 1073–1080 Luigi Granata, Francesco Ascione, Saverio Spadea / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction The ambition of modern civil engineering is to ensure, on the one hand, more and more durability, aimed at containing management costs and guaranteeing the continuous functionality of the structures, and on the other hand, building sustainably. However, the need to build optimised elements generates practical and technical problems associated with the assembling of formworks. Classical steel formworks are difficult to implement in non-prismatic forms due to the huge amount of manpower required and the associated elevated costs. It has been demonstrated that a filament winding process operated through high mechanical strength fibres impregnated with polymer resins (polymer-reinforced fibres, FRP) can represent a valid method for producing particular formworks called W-FRP [1 3]. The above-mentioned technique is based on the winding process of carbon fibre filaments to fabricate stirrups. The flexibility of the impregnated fibres before the resin polymerisation allows the generation of complex, geometrically optimised elements. In addition, FRP materials have several physical and mechanical advantages compared to steel, such as electromagnetic transparency, a very high strength/weight ratio, and no susceptibility to corrosion. On the contrary, FRP materials' biggest drawbacks lie in their linear elastic behaviour up to failure and their anisotropy properties [4-5]. Being the curved portions characterised by not negligible concentration of stresses, a reduction of the material efficiency in terms of strength is expected. In the curve zone, the FRP material is subjected to both shear stresses due to contact with the concrete and tensile stresses in the longitudinal direction, parallel to the fibre direction. Shear stresses are responsible for cracks in the stirrups for low stress levels due to the low resistance provided by the matrix alone [6]. Fibre buckling is another aspect that can reduce the strength of corners. During the bending process, fibres whose initial length is equal have to cover a shorter length, becoming unstable. Generally, the strength of pultruded FRP stirrups is estimated at 30-40% of the tensile strength in the direction of the fibres [7-8]. Experimental studies have shown that reducing the resistance of the curved portions compared to that of the straight portion can be limited where a rectangular cross-section is used [9-10] instead of a circular one. FRP stirrups with rectangular cross-sections are characterised by lower fibre instability due to the lower difference, concerning the case of circular stirrups, between the internal and external curvature radius. The results of a recent experimental study relative to the filament winding technique to produce stirrups in concrete elements showed a better resistance of the W-FRP near the curved portions concerning the stirrups obtained by pultrusion technique using either circular or rectangular cross-section with the same curvature (up to + 53%) [11]. Several predictive methods in the literature to evaluate the strength at corners for FRP pultruded elements, mostly empirical [9, 12-15], are based on the analysis of experimental data obtained for both circular and rectangular cross-sections. As shown by Spadea et al. [3], the applicability of this formulation to the case of elements produced by the filament winding technique is inadequate. In this context, the present research program aims to identify a simple mechanical model for predicting the bent strength of FRP stirrups realised by the filament winding technique. 2. Mechanical Model The paper aims to formulate a simple mechanical model to evaluate the strength of stirrups obtained by the filament winding technique. The generic cross-section of an FRP-RC beam, taken into consideration, is characterised by two axes of symmetry, as indicated in Fig. 1a, with lines a and b . The study is focused on a quarter of the original section, whose 3D representation is depicted in Fig. 1b. In Fig. 1c, the front and top views of the cross-section are reported where the main geometrical parameters were introduced: the diameter of the longitudinal CFRP bar,  , the curvature radius,  , the width of the stirrup, w, and the thickness of the stirrup, t. The above-mentioned curvature radius is evaluated as the sum of the radius of the CFRP longitudinal bar and half of the thickness of the carbon stirrups ( =  ⁄2+ ⁄2 ).