PSI - Issue 84

Antonella Ranaldo et al. / Procedia Structural Integrity 84 (2026) 821–828

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Hence, the load-carrying capacity can be estimated (Eq. 2), where the ties capacity N Ti are expressed in kN. = 0.455√2 1 + 0.339√2 2 + 0.212√2 3 (2) 6. STM definition In this case it is not possible to adopt a STM having the geometry commonly suggested in the literature (e.g. Desnerck et al., 2018), because the only reinforcement capable of carrying the applied load consists of the 45° inclined bars, as depicted in Fig. 4a. Therefore, the struts inclination is determined by minimizing the elastic potential energy of the STM (Fig. 5a). a b

Fig. 5. (a) Proposed STM (dimensions in mm); (b) total elastic potential energy as function of the strut inclination angle 2 . In particular, only the elastic energy contributions associated with struts S2 and S3 , and the ties T1 and T2 (see Fig. 5a) are considered, since the geometry of the remaining members is fixed. Moreover, for a given reaction force R , the unknowns, namely, the tensile forces in ties T1 and T2 , as well as the compressive forces and inclinations of struts S2 and S3 , can be expressed as functions of the inclination angle of strut S2 ( ₂ ) by means of equilibrium equations. The total elastic potential energy ( U e1 ) as a function of ₂ is shown in Fig. 5b. As illustrated in the figure, the minimum value of U e1 is attained for ₂ ≈ 71°. Therefore, this angle is adopted to define the final STM geometry (see Fig. 5a). 7. Struts and ties capacity Referring to the struts , the thickness of the half-joint section is 45 cm, of which 6 cm correspond to the concrete cover. Therefore, the effective struts thickness ( t s ) is assumed to be 39 cm. Conversely, the S1 strut width ( w 1 ) is assumed to be equal to the support width, i.e., w 1 = 17 cm. As a consequence, the S2 strut width ( w 2 ) can be evaluated as w 2 = w 1 / cos (19°) . Finally, the S3 strut width ( w 3 ) can be evaluated as w 3 = w 2 / cos (27°) . According to EN 1992 1-1:2023, the strut capacity ( N Si ) can be calculated by using the following equation (Eq. 3): = ∙ ∙ ∙ =0.85 ∙ ∙ ∙ (3) where f ck is the concrete characteristic compressive strength, w i is the width of the i-th strut, t s is the strut thickness, and γ C = 1.5 is the concrete partial safety factor. The concrete compressive strength f ck is assumed equal to 20 MPa, based on the original design documentation and on Silvestri et al. (2008). As for the ties , the reinforcements have a diameter φ = 30 mm, and each tie is composed of two reinforcements (Fig. 3). Therefore, according to EN 1992-1-1:2023, the tie capacity ( N Ti ) can be evaluated as Eq. 1.