36 MAY 2019 | Ci | www.concreteinternational.com Shear in Discontinuity Regions Changes for the ACI 318 Building Code by Gary J. Klein, Nazanin Rezaei, David Garber, and A. Koray Tureyen T he strut-and-tie method was introduced into “Building Code Requirements for Structural Concrete” (ACI 318) in 2002, 1 although its origins date to the end of the nineteenth century. 1 The ACI 318-02 version of the strut-and- tie method is largely based on a 1987 report by Schlaich et al. 2 that describes procedures for designing structural elements using a system of struts and ties connected at nodes. The method is primarily intended for regions of the structure where the stress flow is influenced by concentrated loads, corners, openings, or other discontinuities. Such regions are referred to as discontinuity regions or D-regions. Strain distribution in D-regions is highly nonlinear, and the assumption of plane sections remaining plane does not apply. The strut-and-tie method is especially useful in D-regions because it allows for designing and detailing of the concrete section and reinforcement in accordance with a clearly visualized force field that is in static equilibrium, rather than relying on past practices or restrictive empirical guidelines. However, as will be explained in this article, there are several concerns and inconsistencies in the current Code (ACI 318-14 3 ) related to shear strength in D-regions: • Except for members qualifying as deep beams, minimum distributed reinforcement is not required in a D-region designed by the strut-and-tie method; • Interior struts (struts not located along a boundary of a D-region) are not weaker than boundary struts because they are “bottle-shaped”; rather, the apparent weakness arises because interior struts cross a diagonal tension field; • The strut efficiency factor β s for interior struts is unconservative because D-regions can fail in shear, which is not considered in the strut-and-tie method; • According to the Code Commentary, the shear stress in deep beams is limited to control cracking. The limiting stress is 10 c cv A f ′ , where f c ′ is the specified compressive strength of the concrete in psi ( psi units are used herein; 1 psi 0.083 MPa = ). This limit does not apply to members or D-regions that do not “qualify” as deep beams, which is inconsistent at best. Furthermore, this limit is unnecessarily restrictive for D-regions with steeply inclined interior struts; • Size effect λ s is not considered; and • The lightweight concrete factor λ is used as a multiplier on f c ′ rather than on c f ′ , as it is elsewhere in the Code. This article describes the rationale for Code changes that will be in ACI 318-19 (scheduled for publication in June 2019) that address these concerns and inconsistencies while maintaining the essential characteristics of design according to the strut-and-tie method. The Code changes relate to the strength of struts and requirements for minimum distributed reinforcement. The changes are based on review of relevant literature, analysis of published test data, and an experimental program designed to evaluate the influence of diagonal tension on the strength of struts. Strength of Struts Bottle-shaped struts ACI 318-14 defines a bottle-shaped strut as a strut that is wider at mid-length than at its ends. The Code also specifies a strut efficiency factor β s of 0.6 for unreinforced bottle-shaped struts and β s = 0.75 for reinforced bottle-shaped struts. However, research and testing by Laughery and Pujol 4 shows that bottle- shaped struts are no weaker than prismatic struts. Referring to Fig. 1, prismatic (a) and two-dimensional (2-D) bottle-shaped struts (b) exhibited approximately equal strength, both averaging about 0.85 f c ′, which is equivalent to a β s of 1.0. Prismatic and 2-D bottle-shaped struts were less than half as strong as three-dimensional (3-D) bottle-shaped struts (Fig. 1(c)). In an element like that shown in Fig. 1(b), stresses spread laterally between the concentrated load or reaction areas and mid-length of the strut without the presence of a diagonal tension field. However, in deep beams and other D-regions, the stress flow is much more complex. As illustrated in Fig. 2,