Inverse technique for deformational analysis of concrete beams with ordinary reinforcement and steel fibers

Abstract

The smeared crack model, extensively applied in numerical analysis of reinforced concrete structures, is based on use of average stress-average strain constitutive relationships. This model is very effective for deformation analysis of steel fiber reinforced concrete (SFRC) members as cracking deformations of such members are restrained by fibers. One of the most critical points in the theory of SFRC is quantifying residual tension stresses for a cracked section. The purpose of the present study is to apply the inverse technique for determining residual stresses of SFRC in tension. The proposed method aims at deriving average stress-average strain relationships of cracked tensile concrete using test data of SFRC flexural members reinforced with steel bars. The paper reports results of the experimental program consisting of five beams reinforced in the tension zone with three 10 mm bars in diameter. The beams had different contents of fibers, i.e. 0, 0.3, 0.5, 1.0 and 1.5% by volume. The proposed inverse technique has been applied to the test data and average stress-strain relationships in tension were derived for each beam. It has been shown that residual stresses increase with growing amount of fiber until the content reaches 1% of the element volume. Under this limit, the efficiency of fiber increases proportionally to its content, whereas, its influence becomes less significant above the limit.