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The current work examines the buckling behaviour of an axially loaded framed spliced steel column. The general behaviour is characterized using a polynomial Rayleigh–Ritz approximation substituted into the potential energy function, in combination with the method of Lagrange multipliers, and the critical load is found. Analysis is run within an algebraic manipulator and checked against results from the classical equilibrium methodology. A set of parametric studies is implemented. Results are evaluated with respect to the following variables: (i) splice location and rotational stiffness, (ii) change in the column section serial size and (iii) column end-restraints stiffness coefficients. Simple relationships are developed for use as a basic stiffness design criterion for column splices.