The paper reviews both analytical and finite element methods for deformational analysis of flexural reinforced concrete members subjected to short-term loading. In a state-of-the-art summary of various proposed stress-strain relationships for concrete and reinforcement, a special emphasis is made on critical survey of modelling post-cracking behaviour of tensile concrete in smeared crack approach.
Empirical code methods of different countries (American Code (ACI Committee 318 [7]), the Eurocode EC2 [8], and the Russian (old Soviet) Code (SNiP 2.03.01-84 [5]) for deflection calculation of flexural reinforced concrete members are briefly described in section 2. Although these methods are based on different analytical approaches, all of them proved to be accurate tools for deflection assessment of members with high and average reinforcement ratios. It should be noted that these methods have quite a different level of complexity since the Russian Code method employs a great number of parameters and expressions whereas the ACI and EC2 methods are simple and include only basic parameters.
Approaches of numerical simulation and constitutive relationships are discussed in Chapter 3. All numerical simulation research can be classified into two large groups according to two different approaches for crack modelling (subsection 3.1): 1) Discrete cracking model. In this approach, cracks are traced individually as they progressively alter the topology of the structure. 2) Smeared cracking model. The cracked concrete is assumed to remain a continuum, ie the cracks are smeared out in the continuous fashion. After cracking, the concrete becomes orthotropic with one of the material axes being oriented along the direction of cracking. Constitutive relationships for steel and plain concrete are presented in subsection 3.2. A special emphasis is made on critical survey of modelling post-cracking behaviour of tensile concrete in smeared crack approach.
It has been concluded that although empirical design codes of different countries ensure safe design, they do not reveal the actual stress-strain state of cracked structures and often lack physical interpretation. Numerical methods which were rapidly progressing within last three decades are based on universal principles and can include all possible effects such as material nonlinearities, concrete cracking, creep and shrinkage, reinforcement slip, etc. However, the progress is mostly related to the development of mathematical apparatus, but not material models or, in other words, the development was rather qualitative than quantitative. Constitutive relationships often are too simplified and do not reflect complex multi-factor nature of the material. Existing constitutive relationships for concrete in tension do not assure higher statistical accuracy of deflection estimates for flexural reinforced concrete members in comparison to those obtained by empirical code methods.
The author has developed integral constitutive model for deformational analysis of flexural reinforced concrete members [36]. The integral constitutive model consists of traditional constitutive relationships for reinforcement and compressive concrete and the integral constitutive relationship for cracked tensile concrete which accumulates cracking, tension stiffening, reinforcement slippage and shrinkage effects. This constitutive model can be applied not only in a finite element analysis, but also in a simple iterative technique based on classical principles of strength of materials extended to layered approach.
The effect of concrete creep on the long-term tension-stiffening law and prediction of a time-dependent inertia moment of the cracked RC flexural cross-sections
