Local-average stress field concept in the post-crack analysis of RC members

Common smeared crack approach، which is mainly defined on the basis of average stress field concept، represents average constitutive models for both concrete and steel bars، in the post-cracking phase. These models are highly dependent on the cracking state and the local mechanisms، so the smeared crack approach is not accurate enough in the analysis of the problems including highly localized mechanisms. These mechanisms appear in anisotropically-reinforced or under-reinforced members، members with large crack spacing or the ones include discrete cracking. The «local stress field concept» is proposed herein to introduce the effect of the local characteristics into the average models. To represent a combine local-average stress field concept، the state of local strain and stress in the RC domain must be determined. Based on several parametric studies and validation procedures، a proposed closed form slip-strain relation is introduced to find out the local strain state along the steel rebar embedded in RC domain. This relation includes the effect of rebar diameter، average tensile stress in steel، initial characteristics of concrete and steel and the cover effect. Adopting the local stress-strain model for the steel rebar، along with the known local strains، the local stress distribution is also determined. Afterward، two main stress states are introduced for the definition of the combined local-average stress algorithm، one in the center of the between-crack length and the other، on the crack surface. Introducing the participated local stresses locating on the crack surface in equilibrium with the related local stresses in the centerline of the crack spacing، the cracking growth is detected. The procedure of the cracking is stopped where the concrete’s maximum stress at the centerline is less than the cracking stress and the crack spacing is fixed afterward. Representing another stress equilibrium condition between the local stresses at the crack surface and the average stress of both steel bar and concrete in the centerline، the average tension softening/stiffening parameter of concrete (C) is updated by use of the relation adopted for the average constitutive model of concrete. By use of the yield slip value، corresponding to the crack spacing and average tensile strain، the average yield stress of the steel، as its main average characteristic، is determined by the application of the proposed slip-strain relation. Considering the effects of the local mechanisms by updating average characteristics of concrete and steel، the combined local-average stress field concept is interpreted in the finite element programming procedure. To express the importance of introducing the local effects into the average behavior، the accuracy of the concept is assessed for the analysis of several experimental specimens including RC shear panels and walls. The concept is also evaluated for some specific cases where the localized mechanisms directly affect the total response.