Issue 30

O. Sucharda et alii, Frattura ed Integrità Strutturale, 30 (2014) 375-382; DOI: 10.3221/IGF-ESIS.30.45 381 1.08. In case of the maximum deformation the correlation was not so good. The mean value of w u, Test /w u, Calc for the first and second alternatives is 1.14 and 1.29, respectively. The conclusion, however, is that the results are satisfactory with respect to the input data. It follows from the results that the worst correlation was obtained for the OA1 beam for which the stochastic analysis was performed. Fig. 7 shows the final estimate of the histogram for the total bearing capacity. It follows from the evaluation of the histogram data and comparison with results of the numerical analysis that the bearing capacity ranges in a rather interval from 204.8 kN until 368.4 kN, provided that normal distribution is assumed. The resulting histogram is assumed normal distribution, the mean value is 302.5 kN. It should be also pointed out that the results could be influenced by the modelling of supports and loads, by the size of the loading step or by the size of the finite element. C ONCLUSION he numerical analysis indicate that the calculations performed using the fracture-plastic material [9] for concrete describe the loading process of reinforced concrete beams without shear reinforcement very well, the final bearing capacity correlating well with the experiments. The maximum deformation of the beam also proved good correlation between the calculation and experiment. The calculation was, however, too sensitive to input properties of the concrete. This was the evaluation of results of the stochastic modelling where the final deformation and bearing capacity lied in a rather big interval. Calculations which used the compressive strength of concrete only described well the real behaviour of a beam, with respect to the quantity of estimated input data. The results of the numeric calculation and stochastic modelling can be used in calculation in line with the proposed standards. With this procedure, it is, however, necessary to use a suitable the global safety limits for the design values. The authors will focus now on the stochastic modelling and probabilistic methods which include, for instance, [13], [15] and [16]. The reason is that the stochastic calculations take much time and this makes them inconvenient for wide use and for drawing conclusions. In general, the model of concrete describes well the total bearing capacity of a concrete beam and development of failure during loading. The reason for difference between the experiments and numerical analyses is probably approximation of specific parameters and uncertainty in input data. A CKNOWLEDGEMENT he works were supported from sources for conceptual development of research, development and innovations for 2014 at the VŠB-Technical University of Ostrava which were granted by the Ministry of Education, Youths and Sports of the Czech Republic. R EFERENCES [1] ASCE, Finite element analysis of reinforced concrete, State of-the-Art, (1982) 545. [2] Bresler, B., Scordelis, A. C., Shear strength of reinforced concrete beams, Journal of American Concrete Institute, 60 (1) (1963) 51-72. [3] CEB - FIP Model Code 1990: Design Code. by Comite Euro-International du Beton, Thomas Telford, (1993). [4] CEB – FIP Model Code 2010, First complete draft, Draft Model Code. 1 (2010) [5] Chen, W. F., Plasticity in Reinforced Concrete. Mc. New York, Graw Hill, (1982). [6] Computer program ATENA: Theory Manual. Praha, Červenka Consulting, (2000). [7] Computer Pragram FReET (Computer Program for Statistical, Sensitivity and Probabilistic Analysis): Theory Manual. Brno, (2002). [8] Computer Pragram FReET (Computer Program for Statistical, Sensitivity and Probabilistic Analysis): User Manual. Brno, (2004). [9] Červenka, J., Papanikolaou, V. K., Three dimensional combined fracture-plastic material model for concrete. Int. J. Plasticity, 24(12) (2008) 2192-2220. T T