# Prediction of Post-Yield Performance of Hybrid Precast Beams Based on Strength Degradation
## 1 Introduction  
Steel-reinforced precast concrete frames (SRCs) have been widely used in the construction industry due to their favorable characteristics, which include high load-bearing capacity, energy dissipation, stiffness, and ductility [1; 2; 3]. However, the use of cast-in-place steel-concrete members has been limited in conventional residential buildings because of the complexity of the construction process. The use of precast steel-concrete components has increased recently for various reasons, including the efficiency and high quality of these structural members and the reduction in wasted resources for on-site activities [4]. In addition, the use of precast frames offers significant advantages, such as reduction of on-site labor cost and quality control. A significant number of analytical and numerical investigations have been undertaken to assess the flexural behavior of steel-concrete composite beams under various types of loading [5; 6; 7]. [PERSON] et al. [5] presented an analytical method for predicting the ductility and post-yield deflection of four steel-concrete precast beams based on the stiffness degradation obtained from hysteretic load-displacement relationships. In their paper, the stiffness degradation was analytically derived as a function of normalized mid-span deflection for limited specimens. It was found that the proposed analytical method accurately predicted the post-yield behavior of the tested specimens. [PERSON] et al. [8] performed an analytical investigation on the stiffness and capacity of steel-concrete composite beams. In their analytical method, a formula for the ultimate flexural capacity of steel-concrete beams was developed and verified by experimental investigations of five test specimens. Later, [9] studied the bending resistance of composite beams with openings, and their analytical calculations included a reduced rigidity method that was used in calculating the first yield limit state of the composite beam. The calculated deflections agreed well with the test results, and their proposed method contributed to the design practice of steel-concrete composite members. The deflection of composite beams based on numerical simulations has also been investigated elsewhere [6; 10]. Experimental investigations have also been performed to uncover the failure modes of steel-concrete beams, [11; 12; 13; 14] studied the flexural load capacity of composite beams. In their work, the effects of steel flanges on beam stiffness, ultimate load, and the associated failure mechanism of the concrete slab were also investigated. Four groups of pre-stressed steel-concrete composite beams were tested with external tendons in the negative moment regions. The aim of the experiment was to analyze the cracking behavior and the ultimate negative moment resistance of the specimens [15]. [PERSON] et al. [16] conducted an experimental study to verify the values that were predicted by the analytical investigation of a pre-stressed beam subjected to a negative bending moment. It was shown in [17] that pre-stressing composite beams with external tendons can significantly increase the ultimate resistance capacity of the beams. Other investigations regarding the structural performance of pre-stressed composite beams have also been conducted [18; 19; 20]. Although several investigations have been conducted on the structural behavior of composite beams, understanding of the overall post-yield structural behavior of different types of steel-concrete beams loaded under various boundary conditions has been limited. This study provided a simplified, but accurate strength degradation-based inelastic structural behavior analysis of steel-concrete composite beams loaded under various boundary conditions. This study sought to predict the post-yield hysteretic behavior of the precast steel-concrete composite beams listed in Table 1 based on stiffness degradation, which was calculated by normalizing effective stiffness with respect to stiffness at the yield limit.