COMPUTATIONAL MECHANICS New Trends and Applications S.Idelsohn, E. Oñate and E. Dvorkin (Eds.) ©CIMNE, Barcelona, Spain 1998 1 AN APPLICATION OF THE CORE CONGRUENTIAL FORMULATION FOR INSTABILITY ANALYSIS OF PLANE FRAME STRUCTURES Henrique de Paula Faria * , William Taylor Matias Silva * * Departamento de Engenharia Civil - Faculdade de Tecnologia Universidade de Brasília - UnB Campus Darcy Ribeiro, 70910-900 Brasília, Brazil e-mail: faria@guarany.unb.br, taylor@guarany.unb.br, web page: http://www.unb.br /enc/ Key words: Geometrically Nonlinear Analysis, Core Congruential Formulation, Structural Instability Analysis. Abstract. In this paper we adress the formulation and numerical implementation of general purpose and algorithms suitable for the indirect computational of stability points within the context of the Core Congruential Formulation for geometrically nonlinear Total Lagrangian finite elements.The instability is evaluated with an algorithm of arc-length control and test functions, which can provide the value of the critical load. The aim of the work is to apply the Total Lagrangian kinematic description to pratical problems in engineering, such as the instability of plane frames and arches.