Journal of Theoretical
and Applied Mechanics

14, 1, pp. 163-173, Warsaw 1976

Stateczność płaskiej postaci zginania belki o osi załamanej

Arnold Wilczyński
In the paper the problem of stability of plane form of bending of a beam with the vertically deflected axid is considered. Authors's considerations deal with the symmetrical system of the arms of the beam loaded by uniformly distributed vertical loads and by a vertical force applied to the rigid node connecting the two arms. The both beam ends are supported in such a way that their rotation is possible only around the axis perpendicular to the plane in which the axis of the beam is placed. The problem is limited to beams of neglegible rigidity for constrained torsion. After reducing the differential equations of neutral equilibrium to the Volterra-type integral equations, approximate solutions are obtained. Then, by using the boundary conditions, the critical load values as functions of the following parameters are calculated: inclination angle of the beam arm, the ratio of the resultant of the uniform load to the concentrated force, and the parameter describing the manner the uniform load is applied.