# Validity of Anchorage Zone Design for Post-Tensioned Concrete Members with High-Strength Strands
## 1 Introduction  
In post-tensioned concrete members, the pre-stressing force is transferred to the concrete through an anchorage device at the end of the member as a compression force. The high stresses caused by compression force, such as the bearing force and bursting force, are generated in the anchorage zone, as shown in Figure 1. If the stress in the anchorage zone exceeds the compressive strength of the concrete, cracks and failures may occur in the anchorage zone, which can cause corrosion of the strands and reduce the structural performance of the members. Therefore, it is important to accurately predict the bearing and bursting stresses generated in the anchorage zone; appropriate reinforcements are required to allow the anchorage zone to resist these concentrated stresses. Design codes such as American Concrete Institute (ACI) Building Code, ACI 318-19 [1] and Association of State Highway and Transportation Officials (AASHTO) [2] suggest methods for calculating stress and design of anchorage zones. However, many researchers have pointed out the inaccuracy of these design criteria and have focused on methods to predict stress accurately and prevent failures in the anchorage zones using experiments and nonlinear finite element analysis. [PERSON] [3] conducted a nonlinear analysis based on a strut-and-tie model to investigate the validity of the AASHTO approximate stress analysis and design method for bursting and bearing stresses. [PERSON] and [PERSON] [4] proposed a bursting force equation thatconsidered concentricity, eccentricity, and tendon inclination using compression-dispersion models. The proposed equation was verified in a comparison with the AASHTO design codes using finite element analysis and experimental results. [PERSON] et al. [5] proposed an equation for transverse stresses and bursting forces based on an updated model using an infinite number of isostatic lines of compression; the authors evaluated the proposed equation by comparing it with the results of a finite element analysis, equations from previous research [4; 6], and AASHTO specifications. [PERSON] [7] investigated thirty-two lightweight concrete specimens with different bearing plate sizes, amounts of reinforcing bar, and forms of reinforcing bar in the anchorage zone. The experimental results were used to determine the reinforcement details for the post-tensioned anchorage zone in lightweight concrete by considering the ratio of the area of the supporting concrete to the bearing area and the lateral confining reinforcement. [PERSON] and [PERSON] [8] conducted a case study of numerical simulations of anchorage tests using nonlinear finite element analysis. The results showed that the basic rules for designing ETAG 013 anchorage zones of post-tensioned concrete structures have limitations related to the shape of anchorage devices and the size of members, and investigation revealed that spiral confinement reinforcement effectively resisted stress in the anchorage zone. Recently, high-strength strands of Grade 2400 MPa have been developed to provide a 29% increase in tensile strength compared to conventional strands of Grade 1860 MPa. In the high-strength strands, a higher concentrated load is applied to the anchorage device. In addition, the magnitude of pre-stress force in pre-stressed concrete member may change the natural vibration frequencies [9]; therefore, the current design methods for post-tensioned anchorage zone need to be verified. This study assessed the applicability of the design method specified in the design standards [1; 2] for the anchorage zone of post-tensioned concrete members with high-strength strands, considering the shape of the anchorage, number of strands, and reinforcement details.