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This study describes two iterative structural analysis procedures under a linear system within a first-order theory that permits the approximate and exact study of flat frames and space frames with independent displacements without having to solve any system of equations. The approximate system provides sufficiently accurate results in few iterations, and the error can be estimated at any time. The exact procedure uses two simple, practical application tables that can be manually implemented in software. The tables provide deformed meshes with fewer operations than those required by matrix algebra. [ABSTRACT FROM AUTHOR]