Analysis of stress-strain State of the Local Bearing area caused by a Prestressed Cable Anchor in Reinforced Concrete beams according to the Nonlinear Model

The paper presents the results of stress and strain state of the local bearing area caused by a prestressed cable anchor in reinforced concrete beams. Ansys software was used to model and analyze the structure. The analysis process was carried out in 3 types: linear elastic analysis, nonlinear elastic analysis, and nonlinear analysis considering the destruction of concrete. The results of the analyses were also compared with each other. Keywords— Prestressed, reinforced concrete beams, nonlinear analysis, crack.


I. INTRODUCTION
The introduction of the paper should explain the nature of the problem, previous work, purpose, and the contribution of the paper. The contents of each section may be provided to understand easily about the paper. The reinforced concrete structures have been used very popular in construction and transportation works. The reasonable design for reinforced concrete components (RC) is essential to ensure the economic and technical requirements for the works [1], [2]. To achieve that, design engineers need to analyze and evaluate the behavior of load-bearing structural components [3]. According to the currently popular methods, the structural analysis is usually divided into two cases: general analysis and local analysis (or detailed analysis). The general analysis examines the overall working of the structural system with the concern of interaction behavior between structural components together. In contrast, a local analysis focused on the behavior of some small areas considered to be disadvantageous in the structure for the purpose of evaluating results or instructing to design or find solutions to limit or overcome the disadvantage of the structural parts. When analyzing the overall demand in the transport sector, there are many assumptions used to simplify and thereby reduce the amount and time of calculation. Therefore, the general analysis has been done quite completely and comprehensively in current designs. Meanwhile, the analysis and design of structures for local bearing areas faces many difficulties, especially for reinforced concrete structures although it is a very important step that affects the safety of construction parts. According to statistics of many countries around the world, damage in reinforced concrete structures usually starts from local bearing areas, connecting areas, etc [4], [5]. So, local analysis is based on adequate and consistent consideration in suitable areas in concrete structures is a great concern today. For this purpose, the study focused on solving the problem of analyzing and calculating the local bearing area caused by a prestressed cable anchor in concrete beams according to the nonlinear model.

II. STRUCTURE MODELING
Consider the local bearing area caused by a prestressed cable anchor in reinforced concrete beams under the effect of prestressing cable load as shown in Figure 1. Local bearing area (anchor head area) includes a prestressed cable, anchor, concrete reinforced area.

Types of elements Purpose Solid65
For concrete elements Solid45 For block elements that describe anchors Link8 For reinforcing elements

IV. LINKS AND LOADS
Links: nodes at the end of the anchor area will be assigned links to control the displacements in three directions. Loads: the load of the prestressed cable is transferred to the concentrated load at the anchor nodes. According to the given data, the load is divided into 5 levels and organized according to 5 data files of the corresponding load file.   As the load continues to increase, cracks spread to the breaking zone and start appearing on the outside of the concrete.

Fig.14: Development of sprung cracks at phase 3-30
Differences in stress and strain distribution in each type of analysis show: to analyze the anchor area with the cable tension load to 0.75fu, it cannot be based on elastic analysis and must consider the effect of local vandalism in concrete. Investigation of crack formation according to the stages shows: Splitting cracks will spread to the concrete surface at the adjacent area between the overall and local areas. Cracking damage has occurred since the small load. The earliest cracks occur in the concrete area behind the anchor and around the genotype. The arrangement of twisted steel to control concrete must be calculated on the basis of these cracks.

VII. CONCLUSIONS
At the local bearing areas, the stress state is usually the multi-axial stress state and there is a large and sudden change in distribution. There, concentrated stress is very large while concrete is a material that only works linearly when stress is small (concrete begins to work nonlinearly at stresses of about 40% intensity). In addition, concrete is an anisotropic material (totally different compressive and tensile behavior) and cracks in the structure can appear at the time of fabrication as well as when the load is first started. Another difficulty is that reinforced concrete is a composite material consisting of two components, concrete and reinforced with work. In the general analysis, with simple stress state and small stress values, due to the co-deformation of concrete and reinforcement as well as limiting cracking problems, it can be simplified by considering reinforced concrete is a homogeneous material (through the calculation between concrete and reinforcement). For locally stressed areas, due to the complex stress state as well as the great concentration stress, the deformation between concrete and reinforcement is not guaranteed, especially when the concrete has been cracked. So describing the work of concrete and reinforcement is not easy. In this study, the authors used nonlinear theory and finite element method with the support of Ansys software to fully and comprehensively consider the behavior of the local bearing area in phases with different load segments of post-tensioning cable anchors. The results are the initial foundation for the authors to develop other local bearing areas in reinforced concrete structures such as the position of the bearing of the abutment or local bearing area of other structural materials such as composite materials.