In this paper we present PMAS optical (3800-7200A) IFS of the northern hemisphere portion of a volume-limited sample of 11 LIRGs. The PMAS observations typically cover the central ~5kpc and are complemented with HST/NICMOS images. For most LIRGs in our sample, the peaks of the continuum and gas (e.g., Halpha, [NII]) emissions coincide, unlike what is observed in local, strongly interacting ULIRGs. The only exceptions are galaxies with circumnuclear rings of star formation where the most luminous Halpha emitting regions are found in the rings rather than in the nuclei, and the displacements are well understood in terms of differences in the stellar populations. A large fraction of the nuclei of these LIRGs are classified as LINER and intermediate LINER/HII, or composite objects. The excitation conditions of the integrated emission depend on the relative contributions of HII regions and the diffuse emission to the line emission over the PMAS FoV. Galaxies dominated by high surface-brightness HII regions show integrated HII-like excitation. A few galaxies show slightly larger integrated [NII]/Halpha and [SII]/Halpha line ratios than the nuclear ones, probably because of more contribution from the diffuse emission. The Halpha velocity fields over the central few kpc are generally consistent, at least to first order, with rotational motions. The velocity fields of most LIRGs are similar to those of disk galaxies, in contrast to the highly perturbed fields of most local, strongly interacting ULIRGs. The peak of the Halpha velocity dispersion coincides with the position of the nucleus and is likely to be tracing mass. All these results are similar to the properties of z~1 LIRGs, and they highlight the importance of detailed studies of flux-limited samples of local LIRGs. (Abridged)
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