Investigating the effect of probabilistic distribution of crack at the limit state on the seismic reliability of concrete buildings

Description of the real behavior of the structures depends on the sources of uncertainty or effective random parameters of the inputs and structural characteristics. These uncertainties may appear as changes and dispersal in external forces and environmental conditions, boundary conditions, geometric parameters or specification of the materials. One of the effective factors in the analysis of concrete structures is consideration of the effect of cracking on the structural elements, which directly affects the calculation of the natural periods, the story displacement and other response parameters. In different codes for design of concrete structures, cracking effect is considered as a mean and constant coefficient for each element, while clearly the condition of various components will be different based on loading situation and specifications. In this paper, reliability of stiffness reduction coefficients of the beams and columns due to cracking of concrete in the ACI code is investigated under random distribution of floor live loads using Monte Carlo simulation method. By considering 1000 modelling loops, calculating accurate crack coefficients of beams and columns and applying them in each model, the reliability of cracking coefficients has been obtained. The results show that the reliability index of these coefficients is very low. Also, other results of this modeling and applying accurate cracking coefficients, show that the story displacements and time period of first and second modes decrease about 40-55% and 20-30%, respectively and the reaction forces of the elements, especially the axial forces and torsional moments increase about 20-30%.