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The paper deals with strength of a grillage loaded by lateral load and in-plane compression load (in one direction). It consists of a system of prismatic girders crossing under 90°. The compression load is taken by the longitudinal girders that are elastically fixed on rigid supports. The system of aggregated differential equations is derived for solution of the problem using the Lagrange method. It allows for replacement of the system of aggregated differential equations by a system of independent differential equations. These equations for the case of simultaneous action of lateral and longitudinal compression load have the form of differential equations for bending of prismatic girders laying on elastic foundation and loaded with lateral and longitudinal compression forces. When only lateral load exists, the form of these equations coincides with the form of differential equations for bending of girders laying on elastic foundation and loaded with lateral load alone. When only longitudinal compression load exists, the form of these equations coincides with the form of differential equations for buckling of girders laying on elastic foundation.
Solutions are given for bending of a grillage (the first two problems). Formulas are derived for calculation of the parameters of longitudinal girders’ bending when girders’ end sections are elastically fixed. Also, formulas are derived for calculation of the reaction forces at cross-points of transverse and longitudinal girders. When only longitudinal compression load exists (third problem), a solution is given for the connection between the coefficient of elastic foundation’s rigidity and the Euler force. Results obtained by using the proposed method are compared with FEA simulations.