Total stability of two constant section beams. Development of payment provisions

Abstract

The paper presents the derivation of formulas for the method of calculating bent elements for general stability, given in SP 16.13330, which is based on the theory of thin-walled elastic rods and the system of differential equations of V. Z. Vlasov. Formulas are given for a single-span beam with a hinged mounting of supports. A general equation has been compiled for calculating the bending stability coefficient φ_1, which allows adapting the requirements of SP16.13330 standards to various types of load action in the beam span. The results are presented for twenty-five different types of external load action. The formulas take into account the arbitrary location of the load along the height of the beam section, from the lower edge of the lower belt to the upper edge of the upper belt. The values of the critical moment M_cr, at which a new form of equilibrium state arises in the beam, are determined, according to the conclusions of the work [6]. The critical moment M_cr is calculated in the form of a stability problem of the first kind – the loss of a stable position of an element of a rectilinear shape (the load acts along the line of the bending center, the neutral axis of the beam is rectilinear, the material is elastic). The formulas of the presented table can be used to perform verification calculations.