Contents lists available at ScienceDirect Engineering Structures journal homepage: www.elsevier.com/locate/engstruct Review article Reinforcement anchored in tension by heads. Review of capacity formulation and applicability limits Luisa María Gil-Martín, Enrique Hernández-Montes ⁎ Department of Structural Mechanics, University of Granada, Spain ABSTRACT Longitudinal reinforcement anchored using heads is becoming more common because it avoids congestion of bars and improves the durability of the anchorage. This paper tries to facilitate its use showing that the specification of the applicability limits is not needed. This work studies the application domains of the different failure modes of the anchorage of headed bars under tension. Each one of the failure modes has its own formulation to calculate the capacity of the headed bar, that it is valid only in a specified domain. This work proposes that the limits of the domain associated with each failure mode can be considered to be implicit in the formulation itself because the domains can be associated to the intersection of the formulations of the failures modes. Due to this assumption no additional information is needed in regard to the definition of the domains which facilitates the calculation of the headed bars anchorage. Furthermore, this work shows that this hypothesis is in accordance with the available experimental campaigns. Some examples are presented. 1. Introduction A headed bar is a reinforcing steel bar used in reinforced concrete structures having a small head attached at the end, which acts as an anchor device (Fig. 1a). Designing with headed reinforcement has several advantages: speed of installation, anchorage less dependent on the spalling of the concrete cover (Fig. 1b), increase durability, avoid congestions of bars, etc. As a consequence of its use the behavior of headed bars is an active area of research [1–3]. The use of headed bars is admitted by most design codes (e.g. the ACI-318 [4] and Eurocode 2 Part 4-1 [5]). In case of Eurocode 2 [6], no direct provision is given for the headed bars; however, provisions for fasteners can be adopted (i.e. Eurocode 2 Part 4-1 [5]). These codes provide a formulation based on mechanical models adjusted with ex- perimental campaigns [7,8]. Based on the observations given by re- searchers [7,8], the ACI-318 [4] fixes domains of applicability for these formulations. This work will show that the specification of these do- mains of applicability is unnecessary because they are implicit in the formulation itself. Moreover, in this paper we will show that the shift between modes of failure are well established by the intersection of the formulations proposed by professional standards, being in accordance with the experimental observations. 2. Development length of a headed bar Headed bars in reinforced concrete structures are used for two purposes: as a way to reduce the development length of reinforcing bars in tension or as anchors to concrete. In the former case, a minimum area for the head is required, according to ACI-318 (§25.4.4) [4]. Cast-in headed elements anchor to concrete by means of tension, shear or a combination of both, however, this paper will only consider the failure modes associated with tensile forces (ACI-318§17). Fig. 2 shows the development length of a deformed bar with and without a head according ACI-318 [4]. The characteristic concrete strength is 30 MPa and steel yield strength is 400 MPa. The only re- quirement that the ACI-318 [4] imposes on the design of the head is that the net bearing area of the head, A brg , must have at least four times the area of the bar, A b . It can be observed that if a headed bar is used, the development length decreases considerably. As can be seen in Fig. 2, the use of headed bars roughly reduces the development length by half. In all that follows, dimensions will be given in mm, stresses in N/ mm 2 (or MPa, 1 N/mm 2 = 1 MPa) and forces and loads in N. 3. Headed anchorage according to the ACI-318 In the design of headed anchors such as studs or bolts, chapter 17 of the ACI-318 [4] is applicable. In order to study the capacity of a headed anchor in tension, the following failure modes have to be studied: steel failure, concrete breakout, side-face blowout and pullout. See Fig. 3. The pullout failure (Fig. 3d) is possible only if the size of the head is very small. The minimum area of the head to avoid pullout failure can be calculated equating the pullout strength of the headed bar in tension (Eq. 17.4.3 of ACI-318) with the capacity of the bar in tension (A b f y ). In https://doi.org/10.1016/j.engstruct.2019.01.063 Received 8 October 2018; Received in revised form 24 December 2018; Accepted 14 January 2019 ⁎ Corresponding author at: ETSI de Caminos, Campus Universitario de Fuentenueva, 18071 Granada, Spain. E-mail addresses: mlgil@ugr.es (L.M. Gil-Martín), emontes@ugr.es (E. Hernández-Montes). Engineering Structures 184 (2019) 186–193 0141-0296/ © 2019 Elsevier Ltd. All rights reserved. T