Annotation

One has developed a method for calculating thin composite orthotropic decks based on Winkler elastic foundation. Concerning the proposed method, each part of the deck (macroelement) is considered separately. Expressions on the deflection of the microelement, tangential displacements, moments, transverse forces and generalized transverse forces are obtained. Each expression is called a state function. The collection of state functions describes the stress-deformed state of the deck. Each state function is represented as the sum of the force function and the coordinate function multiplied by unknown coefficients, which are the degrees of freedom of deck deflection. Their total number is always equal to the number of boundary conditions recorded at individual points on the contour of the deck. At each point, two boundary conditions are defined. The force functions also contain unknown parameters of another kind by which the equilibrium conditions on the deck surface are satisfied. Coordinate functions are expressed using basic functions of different orders: deflection – a function of zero order, displacement – the first one, moments – the second one, and transverse forces and generalized transverse forces – a function of the third order.

All state functions are defined in matrix form in order to effectively model the boundary conditions.

As an example, the solution of a two-component deck composed of two rectangular orthotropic decks perfectly connected to each other is obtained. A separate (local) coordinate system is introduced for each deck. Part of the contour of the deck is loosely supported, the other is not fixed. A separate load is applied to each deck. Independent coordinate matrices and force load vectors are constructed for each deck.

One records the conditions of ideal mechanical contact on the common edge of the two decks, and as a result one obtains a composite matrix of boundary conditions and a composite load vector. Zero matrices and zero load vectors are additionally introduced so as to obtain composite matrices and vectors on the outer edges of the deck. Graphs of changes in deflection, displacements and moments in the main sections of the structure are presented, which illustrate the effectiveness of the proposed method.