PSI - Issue 64

Luigi Granata et al. / Procedia Structural Integrity 64 (2024) 1073–1080 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

1077

5

+( ) =

( , )

(6)

(Tsai-Hil); + + = (Tsai-Wu). (7) In Eqs (6) , is the tensile strength of the stirrup (dependent on the number of layers), and S is the shear strength of the stirrup, whose evaluation is described in section 2.5. In Eqn (7) parameters 1 , 11 and 66 assume the following expressions: = , + ′ ; =− , ⋅ ′ ; (= ) = . (8a-c) In Eqs (8a-c) X' is the compressive strength of the composite (CFRP layers and resin), equal to 2095 MPa, and S is the shear strength of the stirrup whose evaluation is described in section 3. 2.4. Evaluation of shear and axial stresses The tangential shear stress, , for a curved beam assumes the expression reported in Eqn (9), where T is the shear force, ∙ is the stirrup cross-section area, and is the shear factor function of the curvature radius . = ∙ (9) The expression of the shear factor is reported in Eqn (10): = ⁄( ∙ ) = − [ ( −− )−( − ) ( + )] (10) Further parameters introduced are: = ⁄ , = ∙ 3 ⁄12 , and = ( 12∙ ) 3 [ ( 1+ 2 1− 2 )− ] . The normal stresses are thus evaluated according to the following equation: = + ∙ − ; = − (11) In Eqs. (10) and (11) x is the distance of the chord considered from the neutral axes. For the evaluation of the shear strength, S , of the composite (stirrup and resin), the model proposed in [6] is adopted, producing the following expression: = ∙ [ + ( −√ ) ( − )] (12) In Eqn. (12): is the shear strength of the matrix, is a reduction coefficient (Eqn. (13)), is the volume of voids assumed equal to zero ( =1 ), is the fibre volume fraction, and are the shear modulus of the matrix and the fibres, respectively. = − √ ( − ) (13) 3. Case Study The present model is evaluated based on the experimental results available in [11]. Different types of specimens are characterised by the number of layers employed during the filament winding fabrication process, which impacts the geometric properties of the reinforcement, as shown in Table 1.