  Structural, cohesive, and magnetic properties of two symmetric $\Sigma3(111)$
and $\Sigma5(210)$ tilt grain boundaries (GBs) in pure bcc Fe and in dilute
FeCr alloys are studied from first principles. Different concentration and
position of Cr solute atoms are considered. We found that Cr atoms placed in
the GB interstice enhance the cohesion by 0.5-1.2 J/m$^2$. Substitutional Cr in
the layers adjacent to the boundary shows anisotropic effect on the GB
cohesion: it is neutral when placed in the (111) oriented Fe grains, and
enhances cohesion (by 0.5 J/m$^2$) when substituted in the boundary layer of
the (210) grains. The strengthening effect of the Cr solute is dominated by the
chemical component of the adhesive binding energy. Our calculations show that
unlike the free iron surfaces, Cr impurities segregate to the boundaries of the
Fe grains. The magnetic moments on GB atoms are substantially changed and their
variation correlates with the corresponding relaxation pattern of the GB
planes. The moments on Cr additions are 2-4 times enhanced in comparison with
that in a Cr crystal and are antiparallel to the moments on the Fe atoms.
