Keywords: FEA, RC column, simulation, reliability, Latin Hypercube Sampling, random behaviour, uncertainties.

At this time many industrial companies change the manufacturing range of their products. The production process increases operation requirements and therefore leads to the installation of bigger bridge cranes with higher bearing capacity into the manufacturing halls (often times more than double or triple values of the initial bridge crane bearing capacity). Most industrial manufacturing halls, where the bridge cranes are installed, are reinforced (RC) structures, which are constructed from monolitic or prefabricated reinforced basement, crosswise roof girders and columns with short direct embedded cantilevers. These cantilevers are supporting members of reinforced concrete or steel longitudinal girders, which support railways of bridge cranes. In the most cases the bearing capacity of the columns especially of short cantilevers does not satisfy the changes of bridge crane bearing capacity. Usually, the short cantilevers are the limiting members of the crane railway supporting structure. The necessary strengthening can be done (i) by building a new bearing system for a new crane railway with a higher bearing capacity into the current manufacturing hall, (ii) by strengthening of the short cantilevers and RC columns using bandages with a steel band or full-area steel clamping plate, or (iii) by strengthening of the short cantilevers using internal or external prestressing cables or prestressing bars.

The paper presents the reliability analysis of RC columns with short cantilevers in the manufacturing hall in Kovolit Modrice Co., Czech Republic [1,2], whose bearing capacity is increased by internal prestressing cables. The reliability analysis enables to take into account the uncertainties in input variables and thus to obtain improved results not obtainable by standard deterministic analysis.

The FEM model of the RC column with short cantilevers strengthened by 3 internal prestressing cables is made by the ANSYS system. The model is defined parametrically using plane element PLANE42. According in-situ crack control is used linear model for concrete. Prestressing is modelled using equivalent load method as external load.

To take uncertainties into account, the basic input variables describing geometry of the structure, material characteristics as well as prestressing are supposed to be random variables. Totally 32 basic random variables described by generally three-parametric non-normal CDF's are used in the study and are supposed to be mutually statistically independent. Their statistical parameters are carefully evaluated. They are based on in-situ measurements, on experimental tests, on the professional judgment and the information obtained from literature. They incorporate not only the influence of uncertainties due to random nature of input variables, but also the uncertainties due to our incomplete knowledge of the structure, modelling errors etc. Reliability analysis of the problem analysed consists of two types of analyses - statistical and sensitivity analysis. Modern simulation technique Updated Latin Hypercube Sampling technique is used for statistical analysis [4]. It provides estimates of some statistical parameters - mean value, statistical moments, cumulative distribution function (CDF) - which are unbiased and whose variance is reduced compared with other sampling techniques. Thus the number of simulations needed for reliable estimates of commonly used statistical parameters is generally very low The number of simulation equals 50 in the presented study. In the sensitivity analysis, the measure based on the Spearman rank correlation coefficient is used [5].

The results of deterministic and reliability analysis of RC columns in different construction stages are presented ((i) before strengthening with old bridge crane and testing weight, (ii) after strengthening, (iii) after strengthening with old bridge crane and testing weight) are presented.

1

L. Klusacek, J. Pencik "Increase of the bearing capacity of short cantilevers by post-tensioning in Kovolit Modrice Co., Czech Republic", final project report, 2001. (in Czech)

2

J. Chalabala, L. Klusacek, J. Pencik, M. Solarik, "Increase of the bearing capacity of crane tracks of assembled reinforced concrete hall structures", Beton, technologie, konstrukce, sanace, Vol. 2, No. 5, ISSN 1213-3116, pp. 13-15, 2002. (in Czech)

3

L. Klusacek, J. Pencik, "Project of in-situ measurement of short cantilevers in Kovolit Modrice Co., Czech Republic", final project report, 2001. (in Czech)

4

A. Florian, "An Efficient Sampling Scheme: Updated Latin Hypercube Sampling", Journal of Probabilistic Engineering Mechanics, 7(2), pp. 123-130, 1992. doi:10.1016/0266-8920(92)90015-A

5

A. Florian, J. Navratil, "Reliability Analysis of the Cable Stayed Bridge in Construction and Service Stages", 6th International Conference on Structural Safety and Reliability ICOSSAR'93, Innsbruck, Austria, pp. 869-877, 1993.

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