Engineering Structures 30 (2008) 941–954 www.elsevier.com/locate/engstruct A cyclic shear stress–strain model for joints without transverse reinforcement Meredith Anderson a , Dawn Lehman b,∗ , John Stanton b a Reid Jones Christoffersen, Ltd., Vancouver, Canada b Civil and Environmental Engineering, University of Washington, Seattle, WA 98195, United States Received 11 April 2006; received in revised form 31 January 2007; accepted 2 February 2007 Available online 30 July 2007 Abstract In many older reinforced concrete frames, the joints contain no transverse reinforcement. Under seismic loading, those joints may suffer damage and deform, and thereby contribute significantly to the displacements of the frame, which significantly impacts its performance. However, engineers typically ignore joint deformations in seismic analyses, largely due to the lack of appropriate analytical models and reliable data against which to verify them. To improve the simulation of two-dimensional response of frames with joints without transverse reinforcement, a constitutive model was developed for the shear deformations of the joint. The model replicates cyclic degradation in strength and modulus, and energy dissipation of the branch curves. It was calibrated using measured data from tests on joints without transverse reinforcement that were subjected to a range of displacement histories and joint shear stress demands. The model has a general form, and is supplemented by recommendations for the values of the model parameters, which are expressed as functions of the joint geometry and material properties. An independent data set was used to validate the proposed model. c  2008 Published by Elsevier Ltd Keywords: Earthquake engineering; Performance-based seismic design; Beam–column joints; Seismic analysis; Retrofit 1. Introduction Reinforced concrete frame buildings built prior to the 1970s typically contain reinforcing details that do not lead to ductile response. Such frames are referred to as non-ductile. The lack of ductility is associated with many potential damage modes, including column shear, column axial load, slip of spliced or embedded rebar, and joint shear. The study reported here addresses only joint shear. Joints in reinforced concrete frames that are subjected to lateral loading may experience high shear stresses. In current seismic design, limits on joint shear stresses play a dominant role in determining the column size, but this was not always the case. Prior to the pioneering experiments of Hanson and Connor [11], codes did not specify limits on the joint shear stress or require joint transverse reinforcement. As a result, older joints may be subjected to shear stresses that are larger, ∗ Corresponding author. Tel.: +1 206 632 6860. E-mail address: delehman@u.washington.edu (D. Lehman). and vary more, than those in modern joints, yet they typically contain no transverse reinforcement. This combination of high demand and poor detailing increases their vulnerability. The mid-1970s saw the adoption into codes of prescriptive rules for seismic design that closely resemble those in force today. However, many existing buildings were constructed before that time and the robustness of their seismic performance is therefore open to question. Although definitive data on the numbers of non-ductile concrete buildings are lacking, some estimates exist. For example, the California Seismic Safety Commission estimates that there are 40,000 such buildings in California, which suggests that simulation models specific to this type of building are needed for their seismic evaluation. Previous experimental research has focused largely on measures to improve the seismic response of beam–column joints. As a result, almost all of the experimental specimens have included transverse reinforcement and the test results have concentrated on strength. Furthermore, the imposed displacement histories have almost all consisted of monotonically increasing drift cycles (e.g., [7,8,14,16]). 0141-0296/$ - see front matter c  2008 Published by Elsevier Ltd doi:10.1016/j.engstruct.2007.02.005