## 1 Introduction  
Modern structural engineering has been moving toward more economical structures by continuously improving design methods and using higher-strength materials. This results in a smaller cross-sectional area and subsequent weight reduction. This is especially important for reinforced concrete, where dead loads represent a large amount of the load, and such advancements are vitally important. Prestressed concrete was developed to overcome the limiting features of ordinary reinforced concrete. Prestressing systems are defined as the preloading of a structure prior to the application of service loads to improve structure performance in a specific way. Prestressing concrete systems include two types of prestressing. The first type is called pre-tensioning prestressing (the tendons are stressed before the concrete is placed), and the second one is known as post-tensioning prestressing (the tendons are tensioned after the concrete is placed) [1, 2, 3]. In bridge construction, the post-tensioned concrete system is most commonly used, as it has much better advantages compared to traditional reinforced concrete. This system offers improved material utilization, enhanced deflection and crack control, increased durability, faster construction times, reduced costs, and greater design flexibility [4]. A typical post-tensioning tendon includes prestressing strands, ducts that house the strands, grout, and anchorages that transfer the forces to the concrete [5]. There are two ways to achieve post-tensioned prestressed concrete: bonded post-tensioning and unbonded post-tensioning. In bonded post-tensioning, the tendons are in direct contact with the surrounding concrete, transferring stresses through the bond at the surface. On the other hand, in unbonded post-tensioning, tendons are away from the concrete, so the stress is not transferred through the bonding of the surface. The profile of the tendon is important for decreasing the tensile stress in the concrete. Finally, the forces induced by the curvature of the tendons provide counterbalancing forces that compensate for the tensile forces induced by the applied load. In order to counteract the sagging and bending moments caused by the transverse loads, tendons are positioned with eccentricities toward the softit of the beam. When the prestressing force is applied, the prestressed beam deflects upward. The profile of the bending moment diagram is equal to the tendon profile layout because the bending moment diagram represents the product of eccentricity and prestressing force [6]. Flexural strength indicates the tensile strength or the ability of a beam or slab to resist bending moments up to the point where failure occurs [7]. In recent decades, numerous experimental and numerical studies have been conducted to examine the flexural behavior of unbonded prestressed concrete beams. Additionally, several numerical investigations have explored the impact of tendon profile configurations on the overall structural performance. In their study, [PERSON] et al. [8] examined the flexural performance of prestressed concrete bridge girders using experiments and finite element modeling, providing insights into capacity, failure mechanisms, and design recommendations for engineers. In their research, [PERSON] et al. [9] conducted a finite element simulation of unbonded prestressed concrete beams, and a convergence method utilizing the Newton-Raphson scheme was developed for this purpose. In their study, [PERSON] et al. [10] provided a long-term pretension loss analytical method, and new formulas for the long-term prestress loss were developed. In the study by [PERSON] et al. [11], 11 test specimens of post-tensioned prestressed concrete beams with different strength strands were used to evaluate flexural performance. The results showed that the increase in stress in the high-strength strands was underestimated by the ACI 318-19 [12] and AASHTO [12] design criteria [13].