THE RITZ METHOD IN NONLINEAR CALCULATIONS OF SINGLE-SPAN REINFORCED CONCRETE BEAMS.

Abstract

The paper considers the calculations of single-span reinforced concrete bent beams, taking into account the nonlinear relationship between stresses and strains. Deflections of beams according to the Ritz method are given as a series of trigonometric functions with undetermined coefficients. Nonlinearity is taken into account by the "moment-curvature" dependence in the form of a cubic parabola. The functional of the total energy of the beam and the load acting on it has a non-linear form with respect to indefinite coefficients, which are found with the help of a computer mathematics package from the condition of the minimum of this functional. Two examples are given for a statically determinate reinforced concrete articulated beam under the action of a uniformly distributed load and a statically indefinite reinforced concrete beam under the action of a concentrated force. A comparison with an elastic solution is made. The coordinate functions of the Ritz method are given for single-span beams with other boundary conditions.