Analysis of cracked slender-beams on Winkler's foundation using a simplified computational model - Skrinar, Matjaž (Acta geotechnica Slovenica, 2011)
This paper discusses the coupling of Winkler's soil model with a simplified computational model that is widely used for the calculation of transverse displacements in transversely cracked slender beams. The bending problem of a cracked beam embedded in Winkler's soil is addressed by means of an analytical approach. The solving of the corresponding differential equation solutions is studied in order to obtain exact analytical expressions for the transverse displacements of the simplified computational model. After the solutions for the displacements of the beam are obtained, the inner bending moment and the shear force distributions within the beam can be calculated, either by using known, established relationships from the Euler-Bernoulli beam theory or by implementing two mechanical equilibrium conditions. Numerical examples covering several load situations are briefly presented in order to support the discussed approach. The results obtained with the presented approach are then further compared with the values from huge 2D finite-element models, where a detailed description of the crack was achieved using the discrete approach. It is evident that any drastic difference in the computational effort is not reflected in the significant differences in the results between the models.
Keywords: beams with transverse cracks; bending moment; elastic foundation; elastična podlaga; nosilci s prečnimi razpokami; poenostavljeni računski model; prečne sile; prečni pomiki; shear forces; simplified computational model; transverse displacements; upogibni momenti; Winklerjeva zemljina; Winkler's soil