The anchorage zone is defined as the portion of structure in which the concentrated post-tensioning forces are transferred from the anchorage device to the structure. In post-tensioned anchorage zones, the spread of the concentrated forces will produce transverse tensile stresses, usually referred to as bursting stresses, along the tendon path. The resultant of the bursting stresses is called bursting forces. Practically, both the bursting forces and the bursting stresses are used to detail the reinforcing details in the anchorage zone.
To date, a large number of studies of the prediction of bursting stresses and bursting forces in anchorage zone have been conducted, including linear elastic studies, finite element analysis, experimental studies and the strut-and-tie models.
Based on the theory of elasticity, Guyon (
1953) studied the behavior of a concentric load applied over a rectangular body, and then provided a formulation to determine the bursting stress distribution ahead of a concentric end anchor for different bearing plate ratios. This relation was very influential in the design of anchorage zones. Yettram and Robbins (
1970,
1971) reported that the location of uniform stress and the effect of Poisson’s ratio were insignificant to the stress distribution based on elastic finite element analysis. Moreover, the extension of bursting stresses of I-sections was further than in rectangular sections and the flanges played an important role in reducing the spalling stresses. Sanders and Breen (
1997) conducted experimental studies of anchorage zones with 36 specimens tested. By assuming that the resulting force at the end of the specimen would be shifted in the direction of the crack, the dispersion angle of the compressive strut should be reduced, then a modified strut-and-tie model was proposed to predict the ultimate load of the anchorage zones. Wollmann (
1991) conducted three experimental tests of concentric anchorage zones to study the influence of reaction forces on bursting stresses. For small tendon eccentricity, the influence of reaction forces on linear-elastic bursting forces and the resulting bursting force is conservative and can be neglected. Besides, the reaction forces have little influence on the failure mode of anchorage zones. Based on the results of those tests and finite element analyses, a fitting formula was proposed for calculating the bursting forces for typical anchorage zones (Breen et al.,
1994), which had been adopted in the AASHTO-LRFD Bridge Design Specifications (
2014) since 1994. Foster and Rogowsky (
1997) studied the bursting stress distributions in the case of service load behavior, and distributions in the case of ultimate load behavior of anchorage zones by using rotating crack finite element model. They stated that the bursting stress distribution was flatter than that of the linear analysis due to the stress redistribution after cracking, which led to a conservative estimation of the bursting forces, and then a modified equation was proposed to estimate the load capacity of the anchorage zones. After analyzing the stress magnitudes and distributions of rectangular post-tensioned anchorage zones using ultra-high performance concrete (UHPC), Kim and Kim (
2017) concluded that the use of UHPC gives significant reduction of anchorage zone size and no reinforcements are required. Yun (
2005) proposed the nonlinear strut-and-tie model approach to predict the behavior of structural concrete, and then extended this study to the ultimate strengths of post-tensioned anchorages by checking the occurrence of a nodal zone failure mechanism, geometric compatibility condition, and the structural instability of the model struts and ties. Following the concept of isostatic line of compression (ILCs) initialed by Guyon (
1953), Sahoo et al. (
2009) presented an analytical equation for estimating the bursting stress and bursting forces by introducing certain boundary conditions of ILCs. However, this model was imperfect due to some questionable assumptions on the boundary conditions (Windisch,
2010). He and Liu (
2011) proposed the compression dispersion model (CDM) by excluding the unreasonable assumptions in Sahoo's model. Nevertheless, the CDM failed to reproduce the bursting stresses along the tendon path due to insufficient boundary conditions. Based on the equilibrium condition at the far-end of the anchorage zones, Zhou et al. (
2015) updated the CDM by incorporating two more boundary conditions, and verified by finite element analysis. However, in this updated model, the location of interface section of compressive and tensile stress was assumed to be constant, what is in contradiction with reality.
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 zone. To address this issue, this paper is devoted to seeking an analytical solution for transverse stresses in the anchorage zones, and providing a more rational equation for transverse distribution in anchorage zones.