  We show that direct detection and measurement of the vertically thickened
parts of bars (so-called "boxy" or "peanut-shaped" bulges) is possible not only
for edge-on galaxies but also for galaxies with moderate inclinations (i < 70
deg), and that examples are relatively common in the nearby universe.
  Analysis of a sample of 78 nearby, moderately inclined (i < 65 deg)
early-type (S0--Sb) barred galaxies shows that the isophotal signature of the
box/peanut can usually be detected for inclinations as low as i ~ 40 deg -- and
in exceptional cases down to i ~ 30 deg. In agreement with the predictions from
N-body simulations, the signature is most easily detectable when the bar's
position angle is within ~ 50 deg of the galaxy major axis; in particular,
galaxies where the bar lies very close to the minor axis do not show the
signature clearly or at all. For galaxies with i = 40--65 deg and relative
angles < 45 deg, we find evidence for the signature ~ 2/3 of the time; the true
frequency of box/peanut structures in bars may be higher.
  Comparison with N-body models also allows us to link observed photometric
morphology with 3D physical structures, and thus estimate the relative sizes of
box/peanut structures and bars. For our local sample, we find that box/peanut
structures range in radial size (measured along the bar major axis) from
0.4--3.8 kpc (mean = 1.5 +/- 0.9 kpc) and span 0.26--0.58 of the bar length
(mean of 0.38 +/- 0.08). This is a clear observational confirmation that when
bars thicken, it is not the entire bar which does so, but only the inner part.
  This technique can also be used to identify galaxies with bars which have not
vertically thickened. We suggest that NGC 3049 and IC 676 may be particularly
good examples, and that the fraction of S0--Sb bars which lack box/peanut
structures is at least ~ 13%.
