## 1 Introduction
They tested four prestressed beams with compressive strengths from 40 MPa to 160 MPa, a reinforcement ratio of 0.00465, and an effective depth-to-width (d/b) ratio of 1.536. The results showed that an increasing compressive strength improved the ultimate load by approximately 46%. Load-deflection curves remained linear up to the yield load, similar to those of normal concrete. A failure occurred due to tensile fiber debonding and pull-out, which was attributed to the random distribution of fibers. Furthermore, strains in unbounded tendons were found to be incompatible with the adjacent concrete. [PERSON] [22] provided a finite element model to study creep, shrinkage, and tensile stiffness between cracks in partially prestressed continuous composite beams with deformable shear connections. This versatile algorithm accommodates any viscous law and load history. Numerical comparisons demonstrate its potential, and its simplicity allows for easy implementation in analytical programs. [PERSON] et al. [23] stated that the profile determination of prestressed tendons stands as a vital component in post-tensioned concrete structure design. They stated that using the load-balancing method provides substantial capabilities to obtain tendon profiles directly. They provided detailed explanations about method applications through two specific examples, which showed step-by-step procedures in different conditions. The method proves easy to execute for complex structural elements, including curved continuous bridges, according to the examples presented. The tests demonstrate that the load-balancing technique surpasses traditional approaches in efficiency, so standard procedures should be implemented according to the research findings. [PERSON] et al. [24] utilized finite elements to propose a tendon layout design for one-way prestressed concrete slabs. In their approach, they considered B-Spline for the tendon layout design for slabs. The stresses of the structural body were calculated with the finite element method. They represented the tendons as parabolas and increased their eccentricities to minimize the tensile stresses despite the fact that the use of parabolas in the design of cables is complicated, particularly for continuous structures in which tendons are nominally not parabolic. The ordinates of the B-Spline were modified in such a way that the overall shape of the tendons fitted the intended profile. As they designed the tendon layout, they verified that the stress in the structural components would not exceed the allowable maximum tensile stress. The tendon profile was then iteratively optimized according to the stress results from the finite element analysis. [PERSON] et al. (2015) applied a genetic algorithm-based optimization method for the design of simply supported prestressed concrete beams subjected to live and dead loads. In order to minimize the cost, they considered a tendon-to-concrete-cost ratio of 8. Their study examined various factors, including the beam length, tendon profile, sizing of the population in the algorithm, and live load intensity, which are effective in optimizing costs. The results demonstrated an increase of 21.7% in the optimum cost when the beam's length is increased from 14 m to 15 m and a 16.8% increase when the live load is increased from 50 kN/m to 60 kN/m. Parabolic tendon profiles increase the optimum cost over straight profiles by 4.22% for beam lengths of 14 m and 15 m. [PERSON] et al. (2016) explained the design procedures for prestressed beams made from prestressed concrete. They provided the optimal layout for standard reinforcement in prestressed concrete beams that are subjected to bending moments and shear forces. [PERSON] et al. (2017) investigated the effects of eccentricity, prestress load, and the tendon profile using a three-dimensional finite element model of a post-tensioned concrete beam under concentrated point loading. Analyses were conducted using the ANSYS 14.0 program.