The stiffness of a reinforced concrete beam with random parameters the cracks formation

The work of a reinforced concrete beam lying on an elastic foundation is considered, the deformation characteristics which are described by model with two Vlasov-Pasternak bed coefficients. coefficients considered as stationary random normally distributed functions x coordinate. Strength concrete: cube strength and tensile assumed to be variables Gaussian probability density distributions. concentrated forces approximating columns building applied at regular intervals values. After formation cracks in sections under beam, areas reduced bending stiffness formed, therefore becomes variable along length beam. solution differential equation proposed sought variational method minimizing functional additional energy principle. deflections will approximated function that satisfies boundary conditions equilibrium condition. From equality constant equivalent due cracking, its statistical parameters determined. Knowing using known solutions properties, it possible find probabilistic moments shear determine onset limit states normal inclined sections.