PSI - Issue 64

Ali Alraie et al. / Procedia Structural Integrity 64 (2024) 1943–1950 Ali Alraie, Saverio Spadea, Vasant Matsagar/ Structural Integrity Procedia 00 (2019) 000–000

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Fig. 2. Design details of the considered beam.

2.2.1. Results and discussions The analytical investigation has shown that the post-tensioning force improved the load-carrying capacity of the beam by 4.8% and 18.6% when using one and four NJF ropes, respectively. The same was investigated here in the finite element analysis, and the load-deflection response of the control beam (without post-tensioning) was compared with that of the post-tensioned beam with four unbonded NJF ropes. Fig. 3(a) compares the control and post tensioned beams at 80% post-tensioning ratios. It can be noted from Fig. 3(a) that the post-tensioned beam has achieved 80.1 kN load-carrying capacity as compared to 70.1 kN for the control beam, with a 14.3% improvement. The load-carrying capacity, obtained analytically, of the post-tensioned beam was 72.2 kN, which agrees with the finite element analysis result of 80.1 kN with a difference of 10.9%. The load-carrying capacity, obtained analytically, of the control beam was 60.9 kN, which agrees with the finite element analysis result of 70.1 kN with a difference of 15.1%. The difference is justified in the analytical investigation of the under-reinforced section. The tensile stress in the steel reinforcement is calculated based on the yield stress of the steel following the standard elastic-ideally plastic constitutive law. In contrast, in the finite element analysis, it is calculated based on the actual stress in the steel at failure following the elasto-plastic constitutive law in which a linear strain hardening is considered. Moreover, the compressive force in the concrete is calculated analytically based on the rectangular stress block. In contrast, it is obtained in the FE analysis based on the compressive stress at every point in the compression zone. The deflection at service load, calculated as the load-carrying capacity divided by a load factor of 1.6, has decreased from 3.1 mm for the control beam to 1.7 mm for the post-tensioned beam. This aligns with the analytical investigation and proves the efficacy of post-tensioning the beam with unbonded NJF ropes in improving the flexural strength of the beam and reducing the deflection at service load. For further investigation on the effect of post-tensioning force on the load-carrying capacity of the beam with four NJF ropes, four different post-tensioning ratios were considered in the analysis, specifically 20%, 40%, 60%, and 80% of the ultimate tensile strength of the NJF ropes. The load-carrying capacities of the post-tensioned beams, obtained analytically and from the FE analysis, with different post-tensioning ratios, are compiled in Table 1.

Table 1. Load-carrying capacity of the post-tensioned beam with different post-tensioning ratios. Post-tensioning ratio 0% 20% 40% 60% 80% Analytical (kN) 60.9 63.5 66.3 69.1 72.2 Finite element analysis (kN) 70.1 73.4 75.6 77.8 80.1 Difference (%) 15.1 15.6 14.0 12.6 10.9

The efficiency of post-tensioning of beams with NJF ropes was compared with the case of beams post-tensioned with steel strands. The post-tensioning steel strand considered in the analysis is from high-tensile steel having 1466 MPa yield stress, 1723 MPa ultimate tensile strength, and 195 GPa elastic modulus (Raju, 2012). The steel strand has a 92.9 mm 2 cross-sectional area equivalent to the 12.7 mm nominal diameter of the strand (ASTM A 416/A416M, 2006) to be accommodated within the ducts and is post-tensioned up to 30% of its ultimate tensile