Ultimate Strain Criteria and Plastic Hinge Length for RC Members in Monotonic Or Cyclic Flexure With Axial Load

Abstract eng:
A large volume of measured curvatures in plastic hinges of RC members are used as input to analytical moment-curvature relations to back-estimate strains in rebars and at the extreme concrete fibers of a RC section or its confined core at ultimate conditions due to flexure with axial load. The measurements come from tests on circular or rectangular columns, walls or beams. The ultimate strains derived for rebars and confined or unconfined concrete are not local material properties, as they depend on geometric characteristics of the section and of the immediate neighborhood of its most critical point. The "ultimate" strains show clear size effects: a) the ultimate strain of concrete increases when the size of the compression zone decreases; b) the ultimate strain of tension bars in monotonic loading increases when the number of bars in the tension zone decreases; c) the ultimate strain of steel bars in cyclic loading increases if the number of rebars in the compression zone increases; d) the ultimate strain of confined concrete is larger at a corner of a section subjected to biaxial flexure than along the full side of a rectangular compression zone in uniaxial flexure (along the perimeter of a circular section the ultimate concrete strain is between those of a rectangular section in uniaxial and biaxial bending). For cyclic loading the ultimate strain of bars in tension increases with increasing ratio of bar diameter to stirrup spacing, because the potential for bar buckling in previous compression half-cycles is reduced. The derived ultimate strains apply both as mean values in a plastic hinge and as maximum values at the end section of a prismatic member. Ultimate curvatures computed from the proposed ultimate strains do not have bias and exhibit much less scatter with respect to measured values than those obtained from arbitrary ultimate strains specified in some modern codes; these code predictions are generally unsafe. A much larger volume of experimental measurements, of several hundred cyclic or monotonic tests on rectangular or non-rectangular concrete beams or walls, and circular, rectangular or hollow rectangular columns, is used then to develop expressions for the plastic hinge length of such elements under cyclic or monotonic loading. The expression for circular members is a linear combination of the section's depth and the member's shear span length, times a factor which decreases with increasing axial load level; that for all other types of prismatic concrete members involves an additional factor which depends on the aspect ratio of the section. The so-determined plastic hinge length is to be used in a three-component formula for the ultimate drift capacity of concrete members under monotonic or cyclic loading: the drift ratio at flexural yielding, the fixed-end-rotation of the yielding end due to slippage of the tension bars from their development zone beyond that end and the drift ratio due to the rotation of the plastic hinge. The second and third components are in terms of ultimate curvatures. The expressions for plastic hinge length do not apply, unless the values as ultimate curvatures are those of the paper.

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