Małe Ugięcia Sprężysto-Plastyczne Belek o Dowolnym Przekroju

An approximate method is proposed for computing small elastic-plastic deflections of a beam. This method consists in replacing the beam under consideration by a beam with a substitutive cross-section with concentrated masses, called also a enables us, with «multipoint» cross-section. Such an approach an appropriate device of this multi-point section (of which the principles are explained in [26] and [28], for instance) to derive differential equations of deflection the form of which is independent of the form of the given cross-section. These equations express the simplest relation possible - a linear one - between the curvature of the beam, the bending moment and the longitudinal force (cf. (3.8)). Main attention is paid to substitutive four-point sections which seem to be most advantageous from the practical viewpoint. For such sections detailed differential equations of deflection (4.2) are derived, their solutions being found for various types of external loading. It is seen from the solutions quoted that in spite of the drawback of the necessity of «joining», expressions valid for each particular segment the method proposed enables us either to obtain results in cases that cannot be solved in an accurate manner or a much simpler solution than the accurate one. In particular, in the case of forces normal to the undeformed beam axis we obtain very simple expressions for deflections and slopes in the form of polynomials. In conclusion a few numerical examples are given. The accuracy of the results is discussed.