ACI JOURNAL TECHNICAL PAPER Title no. 79-30 A Comparative Study of Confinement Models by Shamim A. Sheikh Various analytical models available in the literature for the confine- ment of concrete by rectilinear ties are studied. These models are applied to the specimens tested by the author as well as by other investigators to predict the results. Loadings on these specimens in- clude axial and combined axial and bending, monotonic as well as cyclic. In the case of cyclic loading, only the envelope curves are determined using the analytical models. Experimental results are compared with results predicted by various models. It is concluded that in addition to the commonly acknowledged variables such as the amount of lateral reinforcement and steel strength, two other variables play important roles in determining the behavior of the confined concrete. These variables are the distribution of the lon- gitudinal steel around the core perimeter and the resulting tie con- figuration, and the spacing of ties. Better distribution of steel and closer spacing of ties along the column longitudinal axis (for the same amount of reinforcement) result in higher concrete strength and ductility. Analytical results from the model accounting for these var- iables show the best agreement with experimental results. Keywords: axial loads; bending moments; columns (supports); confined con- crete; ductility; earthquakes; models; reinforced concrete; stress-strain rela- tionships; structural analysis; structural design; tied columns; ties (reinforce- ment). Circular spirals confine concrete much more effec- tively than rectilinear ties, and the mechanism of con- finement for circular spirals is better understood than for ties. But their relative ease in detailing makes the use of ties more attractive than spirals. When reinforced concrete sections are subjected to large deformations typical of seismic motions, their ability to carry load depends primarily on the behavior of confined concrete within the core. Numerous studies'·" have been reported on the behavior of con- crete confined by rectilinear ties. Several analytical models with various degrees of sophistication have been proposed. Some models predict only the ascend- ing part of concrete's stress-strain curve, while others predict the curve up to a certain point on the descend- ing part. A few models predict only concrete strength and corresponding strain. Several variables have been considered in these models. The amount of lateral reinforcement received most attention. Some of the other variables which ap- 296 pear in these models are strength of plain concrete, steel strength, distribution of longitudinal steel and the resulting tie configuration (steel configuration), tie spacing, and section dimensions. In this paper the available analytical models'·'·''·"·"·"·'" are applied to predict the results of tests reported by various investigators."·' 6 ·"·'"·'" The tests include speci- mens subjected to axial as well as combined axial and bending loads. One set of specimens was tested under constant axial loads and reversal of moments,'" in which case the envelope moment-curvature curves were calculated and compared with the experimental results. It is generally accepted" that the envelope curve under cyclic loading is almost identical to the curve obtained from the monotic loading. SUMMARY OF MODELS Almost all the analytical models for confinement are based on experimental results. Most experimental data were obtained from small-scale tests on simple tie con- figurations. A summary of previous representative tests is given in Table 1. In most of the tests the ratio of the area of the core bounded by the center line of the perimeter tie to the gross area of the specimen was small compared with the values commonly used in practice. The models proposed by the following researchers are used in this paper: Chan,' Kent and Park,' Roy and Sozen," Sargin," Sheikh and Uzumeri," Soliman and Yu," and Vallenas, Bertero, and Popov.'" Variables considered in these models are summarized in Table 2. Direct application of these models to all tests consid- ered in this study was not possible. Therefore, a few assumptions were made to adopt models to tests wher- ever required. Brief details of these models are given below. The assumptions made for the application of Received Oct. 20, 1981, and reviewed under Institute publication policies. Copyright © 1982, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright pro- prietors. Pertinent discussion will be published in the May-June 1983 ACI JouRNAL if received by Feb. I, 1983. 002-8061/82/040296-11 $2.50. ACI JOURNAL I July-August 1982