In the Steelmaking industry and in many others that involve the processing of molten metal, the metallurgical vessels can be lined with refractory bricks, with and without mortar. The design of these linings poses a complex problem, since the material itself is nonlinear regarding the mechanical behavior and the bricks/joints subsystem imposes considerable computational problems due to the large amount of interfaces between them. The Periodic Linear Homogenization (PLH) is a technique that allows the consideration of the expansion joints effect in the reduction of the stresses, providing a better estimation of the applicability of a given lining to the thermo-mechanical loads imposed by operational conditions. In this work, the PLH is coupled to a commercial Finite Element Analysis software and a complete steel ladle is simulated, considering the working, safety and insulating linings.