ACI STRUCTURAL JOURNAL TECHNICAL PAPER Title no. 87-536 Concrete Strength in Tied Columns by Shamim A. Sheikh, C. C. Yeh, and Shafik Khoury Stress-strain curve of concrete in compression depends on several factors including the size and shape of compressed concrete, types and intensity of stresses acting in different directions on concrete ele- ments, and the presence of strain gradient. The strength of concrete has little effect on the behavior of sections under pure flexure and under flexure and low-axial load levels. For sections subjected to flexure and large axial loads, when concrete strength significantly in- fluences section behavior, it is believed that strength of concrete in the specimens is reduced with an increase in axial load level. Results from five 12 in. (305 mm) square and 9ft (2. 74 m) long column specimens are reported in this paper. Based on this and the results from pre- vious research, a simple relationship is suggested in which the con- crete strength is reduced from r: at the balanced load to 0.85f; for concentric compression. A second-degree parabolic stress-strain curve with strain at peak stress equal to 0.002 can be used for reasonably accurate and conservative prediction of section capacity. Keywords: axial loads; columns (supports); compression; flexural strength; moments; reinforced concrete; strength; stress block; stress-strain relation- ships; tied columns. In assessing the behavior of concrete sections, one of the basic assumptions is that the stress-strain curve for concrete defining the magnitude and distribution of compressive stress is known. Under pure flexure, the strength of concrete does not have a significant influ- ence on the flexural capacity and deformation of a sec- tion. Under combined flexure and axial load, strength of concrete plays an important role in the determina- tion of the section capacity, particularly when the axial load is large. The ACI Building Code 1 allows the use of any concrete stress-strain relationship in compression that predicts section strength in substantial agreement with the results of comprehensive tests. In lieu of a more accurate curve, a rectangular stress block of 0.85j; over an equivalent compression zone is permit- ted by the code. The depth of this compression zone is {3c where c is the depth of the neutral axis. Up to 1: = 4000 psi (27 .6 MPa), {3 is assumed to be 0.85. For higher strength, {3 is reduced at a rate of .05 for each 1000 psi (6.9 MPa) in excess of 4000 psi (27 .6 MPa). The lower limit on {3 is 0.65. The maximum extreme fi- ber concrete compressive strain is suggested to be 0.003. To accurately represent a parabolic stress-strain curve for concrete with J: and 0.002 as the coordinates of the ACI Structural Journal I July-August 1990 peak point, the dimensions of the rectangular stress block are 0.9/; and 0.833c for the extreme fiber strain of 0.003. The moment of the area about the baseline of the stress block calculated by using these dimensions is only slightly higher than the moment calculated from the stress block suggested by the ACI Building Code. For the entire axial load-moment interaction curve, the concrete strength in the member is taken as 1: ex- cept for the point corresponding to the pure axial load P for which the concrete strength is assumed to be to 0.85/;. The change in the strength of concrete from J: to 0.85/; is rather sudden and lacks logic. Sev- eral reasons behind the lower strength of concrete in the column compared with J: have been advanced. Among these are the difference in specimen shape and size, sedimentation due to vertical casting of a column, and water gain at the top of the column. However, these reasons should not be applicable only to the case of concentric compression. There are several test results reported in the literature that deal with the members subjected to pure compression or tested under low ax- ial load and flexure. 2 ' 5 Results from the tests on speci- mens subjected to high axial load and flexure, how- ever, are limitedY Since a part of the P-M interaction curve corresponding to high axial load is not used di- rectly in the design due to the minimum eccentricity re- quirements of the code, this part of the curve has not received due attention. In the seismic design of struc- tures where the members are subjected to extreme loads, the accurate prediction of their capacities in the high axial load regions becomes important. In addi- tion, for the nonseismic design of members, the factor of safety against failure will also be affected if member capacities are not accurately known. ACI Structural Journal, V. 87, No.4, July-August 1990. Received May 22, 1989, and reviewed under publication. polici_es. Copyright © 1990, American Concrete Institute. All nghts reserved, mcludm_g the making of copies unless permission is obtained from the copyright propn- etors. Pertinent discussion will be published in the May-June 1991 ACI Struc- tural Journal if received by Jan. I, 1991. 379