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We show that direct detection and measurement of the vertically thickenedparts of bars (so-called "boxy" or "peanut-shaped" bulges) is possible not onlyfor edge-on galaxies but also for galaxies with moderate inclinations (i < 70deg), 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 thebox/peanut can usually be detected for inclinations as low as i ~ 40 deg -- andin exceptional cases down to i ~ 30 deg. In agreement with the predictions fromN-body simulations, the signature is most easily detectable when the bar'sposition 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 thesignature clearly or at all. For galaxies with i = 40--65 deg and relativeangles < 45 deg, we find evidence for the signature ~ 2/3 of the time; the truefrequency of box/peanut structures in bars may be higher.  Comparison with N-body models also allows us to link observed photometricmorphology with 3D physical structures, and thus estimate the relative sizes ofbox/peanut structures and bars. For our local sample, we find that box/peanutstructures range in radial size (measured along the bar major axis) from0.4--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 whenbars 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 notvertically thickened. We suggest that NGC 3049 and IC 676 may be particularlygood examples, and that the fraction of S0--Sb bars which lack box/peanutstructures is at least ~ 13%.

Peanuts at an Angle: Detecting and Measuring the Three-Dimensional Structure of Bars in Moderately Inclined Galaxies