  We derive an effective one-dimensional limit from a three-dimensional
Kelvin-Voigt model for viscoelastic thin-walled beams, in which the elastic and
the viscous stress tensor comply with a frame-indifference principle. The
limiting system of equations comprises stretching, bending, and twisting both
in the elastic and the viscous stress. It coincides with the model already
identified via [Friedrich-Kru\v{z}\'ik '20] and [Friedrich-Machill '22] by a
successive dimension reduction, first from 3D to a 2D theory for von
K\'{a}rm\'{a}n plates and then from 2D to a 1D theory for ribbons. In the
present paper, we complement the previous analysis by showing that the limit
can also be obtained by sending the height and width of the beam to zero
simultaneously. Our arguments rely on the static $\Gamma$-convergence in
[Freddi-Mora-Paroni '13], on the abstract theory of metric gradient flows, and
on evolutionary $\Gamma$-convergence by Sandier and Serfaty.
