INTEGRAL CONSTITUTIVE MODEL FOR DEFORMATIONAL ANALYSIS OF FLEXURAL REINFORCED CONCRETE MEMBERS/INTEGRALINIS FIZINIS MODELIS LENKIAMŲJŲ GELŽBETONINIŲ ELEMENTŲ DEFORMACIJOMS SKAIČIUOTI

Abstract

A new integral constitutive model has been developed for short-term deformational analysis of flexural reinforced concrete members. 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. A new method has been developed for determining average stress-strain relations for cracked tensile concrete from flexural tests of reinforced concrete members. For given experimental moment-curvature or moment-average strain curves, the material stress-strain relations (including the descending branch) are computed from the equilibrium equations for incrementally increasing moment assuming portions of the relations obtained from the previous increments. Using the method proposed, a number of average stress-strain relations for concrete in tension has been derived from beam tests reported by different authors. Analysis of the relations has shown that their shape mostly depend on the reinforcement ratio as well as diameter and surface of reinforcement bars. The length of the descending branch of the relations reflecting the tension stiffening effect was far more pronounced for lightly reinforced beams with deformed bars of small diameters. For the first time, a quantitative dependence (1) has been established for flexural members between the length of the descending branch and the reinforcement ratio. On a basis of the derived relations, a new stress-strain relationship, called the integral constitutive relationship (2) for cracked tensile concrete in flexure, has been proposed. Accuracy of the proposed integral constitutive model has been investigated by calculating deflections for a large number of experimental reinforced concrete beams (reported by several investigators) for a wide range of values of parameters such as the specimen dimensions, concrete strength, reinforcement ratio, reinforcement bar diameter and surface characteristics. Comparison has been carried out with the predictions made for well-known constitutive relationships of tensile concrete and design code methods. For beams with average and high reinforcement ratios (p > 0.7%), accurate predictions have been made by all the methods yielding standard deviations for relative deflections from 8.8 to 10.3%. However, predictions for lightly reinforced beams (p ≤ 0.7%) were far less accurate. These inaccuracies are related to the increased influence of the tensile concrete which characterised by is a highly dispersed value. For lightly reinforced beams, the most accurate predictions in terms of standard deviation (14.0%) have been achieved using the proposed integral constitutive model. Relatively accurate predictions were also made by the SNiP (former Soviet code) and the ACI methods yielding standard deviations of 20.1 and 22.0% respectively. The EC2 (Eurocode) method underestimates the cracking moment and often overestimates significantly the corresponding deflection, in some cases yielding an error of over 100%. Surprisingly, predictions made by the design code methods were superior than those based on the use of well-known constitutive relationships for cracked tensile concrete. An efficient combination of accuracy and simplicity has been achieved for the integral constitutive model. This allowed to incorporate the model into a simple engineering technique for deformational analysis of flexural reinforced concrete members based on classical principles of strength of materials extended to layered approach and use of full material diagrams. In the given form, the integral constitutive model can be readily used not only in the simple engineering technique, but also in the finite element analysis. These main directions are envisaged in further development of the integral constitutive model for deformational analysis of reinforced concrete structures: a) based on new experimental data, further quantitative investigation of the influence of such parameters as strength of tensile concrete, reinforcement ratio, diameter and surface of bars, section height, shape of the cross-section, etc on tension stiffening and possible inclusion of these parameters into both functional and neural network constitutive models; b) assessment of long-term deformations due to creep and shrinkage; c) application of the model for cases of a combined action of a bending moment and axial and shear forces.