Eliminating Shrinkage Effect from Moment Curvature and Tension Stiffening Relationships of Reinforced Concrete Members

Abstract

Experimental results on cracking and deformation behavior of RC members subjected to short-term loading are frequently misinterpreted because shrinkage effect is not taken into account. Even at first loading, free shrinkage strain of concrete may well exceed the cracking strain. The shrinkage strain, restrained by reinforcement, significantly affects the cracking resistance and short-term deformations of RC members. Despite this, most known constitutive laws were derived by using the test data of shrunk RC members under the influence of tension stiffening coupled with shrinkage effect. In this paper, a numerical procedure has been proposed for eliminating shrinkage from moment-curvature and tension-stiffening relationships. The procedure is on the basis of the smeared crack approach and layer section model. It combines direct and inverse techniques of analysis of RC members. The inverse technique, earlier proposed by the first writer, aims at deriving tension-stiffening stress-strain relationships from experimental moment-curvature diagrams. The shrinkage effect was eliminated by assuming in the direct technique a positive (expansion) free shrinkage strain. On the basis of the proposed procedure, free-of-shrinkage tension-stiffening and moment-curvature relationships were derived by using test data of shrunk RC beams obtained by the writers and reported by other investigators. It was shown that negative portions of the tension-stiffening curves disappear after eliminating shrinkage.