PSI - Issue 64

Emanuele Gandelli et al. / Procedia Structural Integrity 64 (2024) 685–692 Emanuele Gandelli / Structural Integrity Procedia 00 (2019) 000 – 000 3 pretension load = 1130 (equivalent to = 1360 and = 6.8 / ). Beam 2, on the other hand, has 7 x S15 unbonded strands located in a steel duct. Tests were performed 28 days after casting, the residual internal action of beam-1 is determined as = 960 (or = 1150 ), taking into account these short and long-term prestress losses: (i) 1.5% due to initial slip between barrels and wedges at the strand anchors; (ii) 3.6 % attributable to initial elastic deformations of the beam; (iii) 1.2% due to strand relaxation; (iv) 0.6% and 8.2% resulting from concrete shrinkage and creep, respectively. In addition, beam-1 and beam-2 are reinforced with longitudinal rebars made of steel B450C: beam-1 has 20 x Φ8 , while beam-2 has 16 x Φ8 and 4 x Φ12 . Two- leg stirrups (Φ8/30 cm) were placed along both beams and additional shear reinforcements (Φ12/5 cm) we re distributed for about 1.5 m from the beam heads. The elastic modulus of concrete ( , ) is a crucial parameter to accurately assess the dynamic response of the structural system and was determined experimentally for each beam according to EN12390-13 (CEN, 2021) by averaging three specimens tested just before the OMA tests were performed. Tensile tests on B450C steel bars (mild reinforcement) are conducted according to ISO 6892-1 (ISO, 2019-a) , using a minimum of six specimens for both Φ8 and Φ12 d iameters. The mechanical properties of S15 strands are obtained from the manufacturer's certificate according to ISO 15630-3 (ISO, 2019-b). Table 1 presents the mechanical properties of the materials and other relevant parameters, such as mass per unit length (m), moment of inertia (J, calculated assuming fully-reacting sections) and prestressing internal action ( ). The moment-bending responses of beam-1 and beam-2, calculated by the FEM program VecTor2 (Wong et al., 2013) at the same prestress value ( = 960 ), are very similar. The elastic bending stiffness of beam-1, denoted as = ∙ , ⁄ , is 8.4% higher than that of beam-2 (0.688 ∙ 4 vs. 0.630 ∙ 4 , see Table 1). However, considering that the fundamental frequency of simply supported beams is directly related to the factor √( , ∙ )⁄ , (Eq. (1)), the dynamics of beam-1 and beam-2 remain almost identical, differing only by about 2.3%. More details can be found in (Gandelli et al., 2024). To investigate the influence of the prestressing level on the dynamic response of the beam, in beam-2 the strand tension is varied from 0 kN to 1130 kN. For this purpose, a hydraulic jack has been installed at one beam head to monitor the actual strain level of the strands ( ), while at the opposite head, the strands are restrained by a steel plate equipped with a load cell (model: nbc TOR 1600 kN) to monitor the instantaneous tensile load (see Fig. 2). (a) beam-1 (b) beam-2 687

Fig. 1. Cross-sections of the case-study beams: (a) beam-1; (b) beam-2. Note: lengths in [cm]; reinforcements ’ diameter in [mm].

Fig. 2. Longitudinal view of beam-2 with details of hydraulic prestressing system (left) and of strand’s anchoring plate with load cell (right).