On Flexibility of a Sliding Vertical Support of a Flat Structure

A flat body on hinged supports is considered. One of the supports is connected to the body by means of a slipping attachment. A flexibility of the support rods is modeled by a hinge with a helical spring of sufficient stiffness to prevent relative rotation. It is shown that the linearization of the equilibrium equations makes it impossible to estimate the equilibrium position. The equilibrium position is sought in the form of a series in terms of the reciprocal of the stiffness coefficient of the helical spring. It is shown that as the coefficient of stiffness of the helical spring tends to infinity, the moment of the helical spring, which models the internal bending forces in the rods, tends to infinity. For the case of vertical equilibrium, an estimate is given for a tangential reaction in the support hinge, which occurs when additional loads are introduced and in the case of small oscillations.
In all the cases considered, the reaction that occurs in the supports is much greater than the weight of the body.