## 1 Introduction  
As structures are becoming taller and larger, the development and use of high-strength materials are becoming a trend in the construction field. In the past, the application of concrete to structures such as high-rise buildings was difficult because of the disadvantages of high self-weight and large volume; however, with the fabrication of high-strength concrete, it is now widely used in structures. Reinforced concrete (RC) beams are structural members that transmit loads by flexure, but most of them exhibit a combination of flexure and shear. To ensure safety in structures, most structural design standards induce ductile failure of RC beams. To induce flexural ductile failure before brittle shear failure, accurate prediction of the flexural and shear behaviors of RC beams is required. A simple method of predicting flexural behavior using the equilibrium and compatibility conditions and the material laws was already developed, and its accuracy is significantly high. However, the prediction of the shear behavior is challenging because the shear is related to the non-homogeneity and tensile properties of concrete. High-strength concrete behaves more brittle than normal-strength concrete, and the increase of tensile strength of concrete is significantly lower than that of compressive strength. In addition, the cracks are close to straight lines and have the property of penetrating the aggregates. In RC beams, shear is transmitted by compression and tension in concrete and shear transfer at crack surfaces as well as steel reinforcement. Therefore, as the compressive strength of concrete increases, the compressive, tensile, and cracking properties of concrete have a significant effect on shear strength and shear deformation. Since the 1980s, studies on the shear of reinforced high-strength concrete beams have been actively conducted. In 1986, [PERSON] et al. [1] conducted a shear test of reinforced high-strength concrete beams with and without shear reinforcement and evaluated the applicability of the ACI building code. In the same year, [PERSON] et al. [2] experimentally evaluated the shear capacity of high-strength RC beams without shear reinforcement and proposed a shear strength equation. In 1989, [PERSON] and [PERSON] [3] conducted a study on the minimum shear reinforcement of high-strength concrete beams. In 1992, [PERSON] and [PERSON] [4] compared the accuracy of each country's design codes for high-strength beams with shear reinforcement. After that, experimental studies to evaluate the shear strength of reinforced high-strength concrete beams were continued by many researchers. Since the 2000s, more complex experimental studies such as shear strength tests of high-strength concrete beams with FRP bars instead of steel bars or various types of fibers have been conducted [5; 6; 7; 8; 9; 10]. Most of these studies focus on the shear strength prediction based on experiments. When the shear strength of RC members is estimated by using only the equilibrium condition, the shear deformation of the RC members cannot be predicted, and the accuracy is lowered if the experimental range is exceeded. The development of a shear analytical model that can consider both shear strength and deformation began with the compression field theory (CFT) developed by [PERSON] and [PERSON] [11], and the meaningful high accuracy was demonstrated by employing the modified compression field theory (MCFT) developed by [PERSON] and [PERSON] [12] and the rotating angle softened truss model (RA-STM) developed by [PERSON] et al. [13; 14]. Early compatibility-aided truss models are also called rotation angle theory because of the assumption that the principal stress and crack direction are the same. Subsequently, the fixed angle theory was developed to fix the crack angle to be closer to the actual characteristics of RC structures [15; 16]. In RC beams, the difference between the longitudinal and transverse reinforcement ratios is generally large.