Ultimate Strain Criteria for RC Members in Monotonic or Cyclic Flexure

Abstract

A large number of experimental curvatures in plastic hinges of concrete members are used alongside analytical moment-curvature relations to backestimate strains in the bars, the extreme concrete fibers of a section, or its confined core at the ultimate conditions of concrete sections in flexure with axial loads. Strain limits derived from these ultimate strains can support fiber models for prismatic members or models with finite-length plastic hinges at the ends. The measurements come from circular or rectangular columns (some tested diagonally), walls, or beams. The ultimate strains derived for steel bars and concrete are not local material properties (especially for cyclic loading): they depend on the geometric features of the section as a whole and of the immediate vicinity of the most critical point in the section. The size effects are clear: (1) concrete ultimate strains increase in a small compression zone, (2) the monotonic ultimate strain of tension bars increases with decreasing number of bars in the tension zone, (3) the ultimate strain of steel in cyclic tests increases with the increasing number of bars in the compression zone, and (4) the ultimate strain of confined concrete is larger at a section corner in biaxial bending than along the full side of a rectangular compression zone in uniaxial flexure, while at the perimeter of a circular section, it is in between these two extremes. The cyclic ultimate strain of steel in tension increases as the bar diameter–to–stirrup spacing ratio increases, thanks to the delay of bar buckling in previous compression half-cycles. The ultimate strains derived apply both as mean values in a plastic hinge and at the end section of prismatic members. Compared to experimental ultimate curvatures, those computed from the proposed ultimate strains do not have bias and exhibit much less scatter than those obtained from arbitrary ultimate strains specified in some codes. These code predictions are, in general, unsafe.