Post-Tensioned Anchorage Zones Research Articles

General Prediction Models for Local Bearing Capacity of Concrete

The local bearing capacity is a basic mechanical property, which is crucial in the post-tensioned anchorage zone design. However, it is challenging to accurately predict local bearing capacity due to the disordered and complex stress conditions in anchorage zone. The existing prediction models have limited application scope, which are difficult to meet the application requirements of novel materials. In this study, the objective is to develop the general prediction models for evaluating concrete local bearing capacity. A reliable database was established based on the test result datasets collected from this study and previous studies. Then, the influence of concrete strength, local area aspect ratio and duct was analyzed. The calculation model was obtained based on fitting analysis (FA) and artificial neural network (ANN) technology. Besides, both the FA model and ANN model were proven to accurately predict concrete local bearing capacity, according to the prediction performance comparisons with existing typical prediction models.

Analytical approach for bursting cracking analysis of post-tensioned anchorage zone

In prestressed concrete structures, improper design and detailing of the anchorage zone frequently cause bursting cracking along the tendon path. Due to the complex stress state in the anchorage zone, it is difficult to estimate the actual cracking load, even in well-controlled experimental tests. Previous studies on anchorage zone cracking are mainly based on numerical simulation. There is still a lack of explicit approaches for practical use. This study aims to provide an analytical approach for predicting the first bursting cracking loads in the post-tensioned anchorage zone. It is found that the stress ratio of compression to tension is significantly higher in the anchorage zone than in the split cylinder. Thus, a strength correction factor is derived to compensate for the tensile-strength reduction due to the effect of biaxial stress state. Besides, a tension chord model is developed to quantify the contribution of bursting reinforcement in enhancing the tensile strength of concrete. After clarifying the effect of biaxial stress state and the contribution of bursting reinforcement, direct equations are proposed for predicting the first bursting cracking loads in the anchorage zone. The analytical approach is compared with existing test data and is applied in the cracking analysis of an actual bridge, indicating that it is accurate and convenient for application.

Numerical study of reinforced concrete in post-tensioned anchorage zones

Prestressed structures have been put into practice in construction since the beginning of this century, but the prestressed structure is concerned with the bearing capacity of anchorage ends. Applying steel reinforcement in anchorage zones can significantly improve the structure behavior and bearing capacity of post-tensioned anchorage zones. Proper reinforcing can relieve congestion and poses difficulty in pouring concrete. Based on materials test data, the nonlinear Finite Element Model (FEM) under local compression was established as part of this study. The nonlinear analysis of the load process was completed based on ABAQUS software. In addition, the model's accuracy was verified by comparing the FEM calculation results with experimental results.Furthermore, the verified FEM was adapted for a parametric study to investigate the influence of various parameters on the bearing capacity, such as the spacing, shape, length of the bearing plate, and reinforcement spacing. The results demonstrate that enhancing steel reinforcement can withstand the forces and stresses and comprehensively improve the local bearing capacity of the specimens; with the decrease of reinforcement spacing, the bearing capacity of the specimen increases, indicating that the reinforcement can dissipate the high stresses among the member from the anchorage zone. The bearing capacity increases with the increase of the bearing plate length, meaning that the bearing plate has a significant influence on bearing the prestressing force in the anchorage zone. Meanwhile, the effect of the bearing plate shape was not obvious. The relationship between the local bearing capacity and the bearing plate length is linear, which indicates that the influence of the bearing plate length on the local pressure properties belongs to the structural layer.

Bearing capacity of concentric anchorage zones in post-tensioned members: A stress field solution

The post-tensioned anchorage zones are generally subdivided into local and general zones, which are treated with semi-empirical approaches and strut-and-tie models separately in many design codes. Even with their functions that look different, the two adjacent zones are intrinsically related in terms of the compression dispersion mechanism. Holding this view, this paper intends to present a mechanical model to integrate their combined actions. Firstly, two confinement effects in anchorage zones are studied: the local confinement under the bearing plate and the passive confinement by bursting reinforcement. Then, a discontinuous stress field model for concentric anchorage zones is proposed, which allows for a triaxial state of compression stresses in the local zone and the contribution of bursting reinforcement in the general zone simultaneously. After that, an explicit bearing capacity formula for anchorage zones is derived, in which the ultimate failure can be attributed to either the yielding of the distributed tension subfield or the crushing of fan subfields. The prediction of bearing capacity is in fairly good agreement with the collected test results.

Investigation of Bursting Force In I-Section Post-Tensioned Anchorage Zone

In post tensioned concrete beam the high transverse tensile stress is generated and if proper reinforcement is not given, bursting may occur. To study the effect of these stresses and to find bursting stress in end region the analytical study was carried out. In present work the end block of post-tensioned prestressed concrete beam is modelled in finite element based software with eccentric tendons. The bursting zone of beam is evaluated and parametric study was carried out by varying eccentricity, anchorage ratio and web thickness of girder. The 3D modelling was done and results are compared in terms of bursting force. The results are compared with Indian Standard 1343:2012 and inferences are drawn towards the usability of IS code equation of bursting force for I-section.

Investigation of Bursting Stress and Spalling Stress in Post-tensioned Anchorage Zones

Over the past decades, considerable efforts have been made to quantify the bursting forces in the post-tensioned anchorage zones based on the simplified model or fitting formulas, however reproducing the transverse stress distribution is still a challenging topic, which is also important to detail the reinforcing details in the anchorage zones, especially for cracking control. To address this issue, this paper is devoted to seeking an elasticity solution for transverse stresses in the anchorage zones, and providing a more rational equation for transverse distribution in anchorage zones. The sum function of normal stresses is employed to solve the stresses filed in the anchorage zones with concentric load and two eccentric loads. The bursting stresses in the concentric anchorage zones and spalling stresses in the eccentric anchorage zones are verified by the photoelastic tests. The transverse stresses along the symmetry axis of the eccentric anchorage zones can be handled as a concentric single anchorage zone with equivalent bearing plate width. Moreover, according to the concept of force stream tube, the profiles of isostatic line of compression (ILCs) are determined and validated, which confirms the existence of ILCs.

Full-range nonlinear analysis of post-tensioned anchorage zones based on modified strut-and-tie model

The strut-and-tie model (STM) has been adopted as a preferred methodology for the design of the post tensioned concentric anchorage zones. However, the STM is just a design model at ultimate limit state developed based on the elastic stress trajectory without the consideration of stress redistribution after cracking, which can not be used to predict the serviceability behavior of anchorage zones. To address this issue, this paper is devoted to developing a modified strut-and-tie model (MSTM) to predict the behavior of concentric anchorage zones throughout loading process. The compatibility condition was introduced into MSTM based on the principle of stationary complementary energy at each load step. According to MSTM, the elastic and inelastic behavior of concentric anchorage zones, including load-strain response, load-deformation response and crack width, can be estimated from loading to failure. Moreover, simplified formulas have been proposed to calculate the first cracking load, ultimate load and the maximum crack width. Finally, the proposed MSTM was validated by the testing results.

Performance Assessment of the Post-Tensioned Anchorage Zone Using High-Strength Concrete Considering Confinement Effect.

Post-tensioned anchorage zones need enough strength to resist large forces from jacking forces from prestress and need spiral reinforcement to give confinement effect. High-strength concrete (HSC) has high-strength and brings the advantage of reducing material using and simplifying reinforcing. We tested strain stabilization, load–displacement, and strain of lateral reinforcements. Specimens that used one and two lateral reinforcements without spiral reinforcement did not satisfy the strain stabilization. Load capacity also did not satisfy the condition of 1.1 times the nominal tensile strength of PS strands presented in ETAG 013. On the other hand, specimens that used three and four lateral reinforcements without spiral reinforcement satisfied the strain stabilization but did not satisfy 1.1 times the nominal tensile strength of PS strands. However, the secondary confinement effect could be confirmed from strain stabilization. In addition, the affection of HSC characteristics could be confirmed from a reinforcing level comparing other studies. The main confinement effect could be confirmed from the reinforcement strain results; there was a considerable difference between with and without spiral reinforcement at least 393 MPa. Comprehensively, main and secondary confinement effects are essential in post-tensioned anchorage zones. In addition, the performance of the anchorage zone could be increased by using HSC that the combination of high-strength and confinement effect.

An Improved Equation for Predicting Compressive Stress in Posttensioned Anchorage Zone

Validity of the approximate equation for predicting compressive stress in the posttensioned anchorage zone presented in the AASHTO LRFD Bridge Design Specifications was investigated in this study. Numerical analysis based on the finite element method (FEM) and theoretical analysis showed that the AASHTO formula gives relatively accurate stress values when the effect of duct holes is neglected. However, it was found that the formula can significantly overestimate the stresses in the actual prestressed concrete member with spaces occupied by ducts. Therefore, an improved equation was proposed for the existing AASHTO equation to consider the effect of the duct holes on the stress distribution. This resulted in relatively accurate prediction of the distribution and magnitude of the compressive stresses even with the presence of the duct holes. The proposed equation was also validated by comparing with the stresses measured in the test of a posttensioned full‐scale specimen. This study is expected to contribute to the design of the anchorage zone in prestressed concrete structures by suggesting a more reasonable way to assess the appropriateness of anchorage devices.

Comparison of Stresses for Circular and Rectangular Pre-stressing Plates in Post-Tensioned Anchorage Zone

Comparison of Stresses for Circular and Rectangular Pre-stressing Plates in Post-Tensioned Anchorage Zone

Design equation to evaluate bursting forces at the end zone of post-tensioned members

Design equations to evaluate the bursting force in a post-tensioned anchorage zone have been introduced in many design codes, and one equation in AASHTO LRFD is widely used. However, this equation may not determine the bursting force exactly because it was designed on the basis of two-dimensional numerical analyses without considering various design parameters such as the duct hole and shape of the bearing plate. To improve the design equation, modification of the AASHTO LRFD design equation was considered. The behavior of the anchorage zone was investigated using three-dimensional linear elastic finite element analysis with design parameters such as bearing plate size and diameter of sheath hole. Upon the suggestion of a modified design equation for evaluating the bursting force in an anchorage block with a rectangular anchorage plate (Kim and Kwak 2018), additional influences of design parameters that could affect the evaluation of bursting force were investigated. An improved equation was introduced for determining the bursting force in an anchorage block with a circular anchorage plate, using the same procedure introduced in the design equation for an anchorage block with a rectangular anchorage plate. The validity of the introduced design equation was confirmed by comparison with AASHTO LRFD.

Investigation and Improvement of Bursting Force Equations in Posttensioned Anchorage Zone

In posttensioned concrete members, the high local stress under the anchorage causes transverse tensile stress. Therefore, it is very important to predict the bursting force to determine appropriate reinforcement details. In the present work, the existing equations of the bursting force for the anchorage zone were evaluated and an equation for the bursting force based on finite element analysis was proposed to improve the model’s accuracy. Parametric analysis was performed considering the anchorage shape, tendon angle, and eccentric distance. The analytical results indicate that the existing equations underestimate or overestimate the bursting force. The proposed equation is able to predict the bursting force reasonably well for an anchorage zone with rectangular bearing plate, cavity, and eccentric distance.

Finite element analyses and design of post-tensioned anchorage zone in ultra-high-performance concrete beams

This article presents analyses and the design of a post-tensioned anchorage zone made of ultra-high-performance concretes with three-dimensional finite element analyses. The structural behavior was investigated through the failure modes and cracking patterns to show the anchorage zone resistance enhancement with an increase of the strength in concrete. Since the anchorage failure is usually initiated from the local zone in the case of ultra-high-performance concrete beams that have compressive strength of more than 80 MPa, the placement of reinforcements can effectively be used to enhance the strength and ductility for the local zone. However, ultra-high-performance concrete requires a smaller amount of reinforcement than normal-strength concrete. Parametric analyses are carried out to show the effect of the spiral reinforcement on the strength of the anchorage zone, and comparison with the design guidelines in NCHRP Report 356 is made. Finally, improved guidelines are suggested to cover the design of ultra-high-performance concrete.

Investigation of crack propagation of the concentric anchorage zones based on linear elastic fracture mechanics

In the past decades, significant progress has been made in prediction of the structural behavior of the posttensioned anchorage zones, an aspect which has not yet been sufficiently clear up, however, is the serviceability behavior of posttensioned anchorage zones, especially with regard to the crack formation. To address this problem, a numerical method based on linear elastic fracture mechanics is proposed to investigate the crack propagation in posttensioned anchorage zones, and predict the structural behavior in the serviceability state. Following Irwin's approach, an effective crack length is proposed for I‐II mixed‐mode crack growth. The numerical analyses of the tested anchorage zone specimens show that the proposed procedure is able to accurately describe the crack propagation behavior, including crack length, crack width, and crack trace. Parameter analysis is performed to study the effects of the layout of the reinforcement on crack width in the service state. The results show that the proper bursting rebar diameters and rebar spacing can lead to the significant decrease of the crack width, while the longitudinal rebar makes little contribution to cracking control.

Comparative Study of Bursting Force Equations for Post-Tensioned Anchorage Zones

Comparative Study of Bursting Force Equations for Post-Tensioned Anchorage Zones

Crack Propagation and Control in Concentric Posttensioned Anchorage Zones

Crack Propagation and Control in Concentric Posttensioned Anchorage Zones

A Stress Analysis of the Post-Tensioned Anchorage Zones Using UHPC

Researches on Ultra High Performance Concrete (UHPC) have been conducted worldwide owing to its outstanding durability and strength performances compared to those of normal concrete. The application of UHPC to prestressed concrete structures, which may seem to be the most appropriate and beneficial, may result significant improvement in the design of anchorage zones due to its high compressive and tensile strength. The size of anchorage blocks and amounts of reinforcements may be reduced drastically. This paper examines the stress magnitudes and distributions of post-tensioned anchorage zones using UHPC which have nominal compressive strength levels of 120, 150 and 180 MPa respectively, by FE analysis. The analytic results are verified with the existing experimental work of 180MPa UHPC. It can be concluded that the use of UHPC to post-tensioned members gives significant reduction of anchorage zone size and no reinforcements are required.

Load Transfer Test of Post-Tensioned Anchorage Zone in Ultra High Performance Concrete

Researches on ultra-high performance concrete (UHPC) have been conducted worldwide owing to its outstanding durability and strength performances. The exploitation of the mechanical properties of UHPC will render it possible to achieve economic design through substantial reduction in the cross sectional dimensions and simplification in the reinforcement arrangement. This paper investigates experimentally the load transfer in the prestressed concrete anchorage zone. To provide distinctive features of UHPC compared to ordinary concrete, the cross sectional dimensions of the member were reduced and the stress distribution, deformation and cracking pattern of the PS anchorage zone were examined experimentally according to the degree of reinforcement of the members chosen. The distributions of the bursting stress, spalling stress and longitudinal edge stress in the specimens were observed according to the various types of reinforcement. All the specimens satisfied the load-bearing capacity criterion specified by the European ETAG-013 guidelines and their stress distributions were similar to those in the PS anchorages of post-tensioned members applying ordinary concrete. The cracks propagated longitudinally with lengths up to twice the cross sectional dimensions and their width was smaller than when applying ordinary concrete owing to the bridging effect of the steel fibers in UHPC. Accordingly, the exploitation of the high strength of UHPC enabled us to secure the resistance of the anchorage with no need for particular reinforcing devices.

Bearing capacity of steel fiber reinforced reactive powder concrete confined by spirals

Based on two basic considerations, (1) the enhancement of bearing capacity by the inclusion of confining spirals and (2) the crack-bridging and energy-absorbing improvements gained by adding steel fibers to the mixture, steel fiber-reinforced reactive powder concrete (SFR-RPC) reinforced by steel spirals can be applied to post-tensioned anchorage zones. Twelve SFR-RPC prisms containing steel spirals and a longitudinal duct hole were loaded at high concentration over a limited circular area. The tests indicated that all specimens retained integrity at failure and exhibited no less than four radial cracks, the entire depression occurred on the loading-end surface, and the splitting tendency generally developed below the first turn of the spiral if the wedge cone formed ahead of the bearing plate. Three major factors related to the geometry of the zone directly influence the bearing capacity: (1) the local aspect ratio of the net area of the concrete supporting the plate to the area of the bearing plate, (2) the core aspect ratio of the area of the bearing plate to the area of the core surrounded by the steel spirals, and (3) the steel ratio of the spirals. An expression of the bearing load capacity is proposed on the basis of the testing results.

Bearing capacity of reactive powder concrete reinforced by steel fibers

Steel fiber-reinforced reactive powder concrete (SFR-RPC) improves the behavior of steel fiber post-tensioned anchorage zones by enhancing the fiber’s tensile strength. As part of this study, nine SFR-RPC prismatic blocks, each with a central longitudinal duct, were subjected to pressure testing to simulate the anchorage zone. The pressure testing results indicate that cracking loads are close to failure loads. Although expansion occurred in the middle of the blocks at failure, integrity was maintained for all of specimens. A local SFR-RPC wedge zone, ahead of the bearing plate, was weakened by a duct. A comparison of the SFR-RPC samples, with and without ducts, shows a weakening effect indicating there was a change in the cracking load and a decrease of bearing capacity for SFR-RPC without a duct. As part of this paper, a simple expression to determine SFR-RPC bearing capacity is proposed. The expression is verified by experimental results and considers the steel fiber enhancement and weakening effect.