In the present work, we propose a novel implementation of arc-length method for the computation of equilibrium paths for frame-like structures. We exploit the advantages of velocity-based beam formulations and adapt it to quasi-static analysis with path following control. We show that such formulation allows the arc-length control constraint equation to be directly employed in its originally defined differential form, while the arc-length parameter is replaced by time in our adaptation. This simplifies the treatment of the extended system of equations and its solution procedure. Our approach also enables the rotational degrees of freedom to be members of control parameters. The ability of the proposed method to successfully and efficiently compute complex equilibrium paths in post-buckling regime is demonstrated by several numerical examples.