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In this paper, the procedure for deriving the geometric stiffness matrix of a three-dimensional rigid beam element is summarized.Such a matrix can be used along with the elastic stiffness matrix in the predictor phase of the geometric nonlinear analysis of structures, concerning the solution of structural displacements for given applied loads.As for the corrector phase, the elastic stiffness matrix alone is used in computing the elastic force increments, while the rigid body rule is exclusively used for updating the initial nodal forces.All the above concepts will be demonstrated in the solution of the load-deflection responses of space frames involving complicated postbuclding responses.The proposed procedure is featured by the fact that the element can be easily derived and that the entire procedure can be robustly applied to the solution of nonlinear problems involving large rotations in the the postbuckling response.