  Stellar bars can lead to gas inflow toward the center of a galaxy and
stimulate nuclear star formation. However, there is no compelling evidence on
whether they also feed a central supermassive black hole: by measuring the
fractions of barred active and inactive galaxies, previous studies have yielded
conflicting results. In this paper, we aim to understand the lack of
observational evidence for bar-driven active galactic nucleus (AGN) activity by
studying a sample of 41 nearby (d < 35 Mpc) barred galaxies from the Spitzer
Survey for Stellar Structure in Galaxies. We use Chandra observations to
measure nuclear 2--10 keV X-ray luminosities and estimate Eddington ratios,
together with Spitzer 3.6um imaging to quantify the strength of the stellar bar
in two independent ways: (1) from its structure, as traced by its ellipticity
and boxiness, and (2) from its gravitational torque Q_b, taken as the maximum
ratio of the tangential force to the mean background radial force. In this way,
rather than discretizing the presence of both stellar bars and nuclear
activity, we are able to account for the continuum of bar strengths and degrees
of AGN activity. We find nuclear X-ray sources in 31 out of 41 galaxies with
median X-ray luminosity and Eddington ratio of L_X=4.3x10^{38} erg/s and
L_bol/L_Edd=6.9x10^{-6} respectively, consistent with low-luminosity AGN
activity. Including upper limits for those galaxies without nuclear detections,
we find no significant correlation between any of the bar strength indicators
and the degree of nuclear activity, irrespective of galaxy luminosity, stellar
mass, Hubble type, or bulge size. Strong bars do not favor brighter or more
efficient nuclear activity, implying that at least for the low-luminosity
regime, supermassive black hole fueling is not closely connected to large scale
features.
