  We study the binding energy, intertube distance and electronic structure of
bundles consisting of single walled carbon nanotubes of the same chirality. We
model various nanotube structures (chiralities) and orientations with van der
Waals density functional theory. The orientation of the tubes in the bundle
strongly influences the properties of the bundles if the chirality of the tubes
shares symmetry with the trigonal bundle structure, meaning chiralities which
have a $60^\circ$-rotational symmetry (C$_6$-axis), e.g. ($12,0$) bundles. The
bundle structure breaks the symmetry depending on the arrangement of the
neighboring tubes. Pseudogaps open in the electronic density of states and
intertube distances ($\pm5$-10%) vary in dependence of the relative orientation
of the tubes in the bundle. Bundles of C$_6$-axis armchair tubes have metallic
configurations. A $15^\circ$ rotation off the high symmetry configuration
(AA-stacked) of a ($6,6$) bundle shows metallic behavior and has higher binding
energy than the high symmetry configuration. We find binding energies between
$19 meV/atom$ and $35 meV/atom$, depending on the chirality of the tubes. The
intertube distances are between $3.2 {\AA}$ and $3.4 {\AA}$ but independent of
orientation for non C$_6$-axis tubes.
