Non-linear time-dependent analysis of cracked reinforced concrete bar

Abstract

A numerical model for analysis of crack appearance and propagation along reinforced concrete bar due to external load with the influence of aggregate bridging is presented. The governing equations are solved by a novel strain-based finite element method. The concrete cover and the reinforcing bar are each modelled separately. The tangential slip between the concrete and the reinforcing bar is fully accounted for, whereas the delamination is neglected. The discrete crack concept is employed, in which the aggregate bridging between two uncracked parts of concrete, separated by a crack, is accounted for by a non-linear spring. The adequacy, accuracy and the efficiency of the present model are verified in studies of reinforced concrete bar subjected to short-term tensile tests. It is found out that by the present numerical model, the spreading of cracks and varying of the length of reinforced concrete bar may be described relatively well. The model also enables the time-dependent analysis of the appearance and propagation of cracks due to restrained shrinkage and creep of concrete.

A novel strain-based finite element family for mesh-independent analysis of the tensile failure of reinforced concrete bars

“…Governing equations of the uncracked RC bar, depicted in Figure 2(a), are taken as in Bajc et al (2018) and include kinematic, equilibrium and constitutive equation, separately for concrete cover and for reinforcing bar, as well as three constraining equations:…”

“…However, a system of discrete generalized equilibrium equations of finite element without crack is briefly presented first. This system of equations is applicable in the model of RC bar with discrete crack at 'excluded' point previous to cracking, and has already been presented in detail by Bajc et al (2013Bajc et al ( , 2018.…”

“…The system of discrete generalized equilibrium equation of uncracked RC bar with tensile load can be found in Bajc et al (2018). Therefore, the equations themselves are not written down in the present paper, only their most important characteristics are presented.…”

“…Principle of virtual work states that virtual work of internal forces equals virtual work of external forces. Here, we begin with modified principle as it is given in Bajc et al (2013Bajc et al ( , 2018 for RC bar with discrete cracks at nodes of finite element, however, applicable adaptations for RC bar with discrete crack at 'excluded' point (at material coordinates À x r c and þ x r c somewhere along the length of finite element) are introduced…”

“…In the finite element, where the crack appears during the numerical analysis, the equations for cracked finite element (as presented in previous sections of this paper) are applied. In the remaining finite elements, the equations for uncracked finite element (as in Bajc et al (2013;2018)) are used. All equations are then combined into the equation of system through well established procedures of numerical theory of structures Gðx,λÞ ¼ RðxÞ À λP ¼ 0 (45)…”