  Many barred galaxies exhibit upturns (shoulders) in their bar major-axis
density profile. Simulation studies have suggested that shoulders are supported
by looped $x_1$ orbits, occur in growing bars, and can appear after
bar-buckling. We investigate the orbital support and evolution of shoulders via
frequency analyses of orbits in simulations. We confirm that looped orbits are
shoulder-supporting, and can remain so, to a lesser extent, after being
vertically thickened. We show that looped orbits appear at the resonance
$(\Omega_\varphi - \Omega_\mathrm{P})/\Omega_R=1/2$ (analogous to the classical
Inner Lindblad Resonance, and here called ILR) with vertical-to-radial
frequency ratios $1 \lesssim\Omega_z/\Omega_R \lesssim 3/2$ (vertically warm
orbits). Cool orbits at the ILR (those with $\Omega_z/\Omega_R > 3/2$) are
vertically thin and have no loops, contributing negligibly to shoulders. As
bars slow and thicken, either secularly or by buckling, they populate warm
orbits at the ILR. Further thickening carries these orbits towards crossing the
vertical ILR [vILR, $(\Omega_\varphi - \Omega_\mathrm{P})/\Omega_z=1/2$], where
they convert in-plane to vertical motion, become chaotic, kinematically hotter
and less shoulder-supporting. Hence, persistent shoulders require bars to trap
new stars, consistent with the need for a growing bar. Since buckling speeds up
trapping on warm orbits at the ILR, it can be followed by shoulder formation,
as seen in simulations. This sequence supports the recent observational finding
that shoulders likely precede the emergence of BP-bulges. The python module for
the frequency analysis, naif, is made available.
