  Normal stresses in sheared suspensions of non-Brownian particles are obtained
from numerical simulations. The stresses are determined in homogeneous shear of
non-buoyant particles and by analyzing shear-induced resuspension of buoyant
particles in the framework of the suspension balance model (SBM). The
consistency of both approaches indicates that the SBM describes the steady
state properly. Though in agreement with most available experimental results,
none of previous empirical expressions for the normal stress can describe the
data in the whole range of volume fraction, and in particular in the
semi-dilute regime (25-35\%) where the normal stress is less than expected. New
expressions are proposed. The results also highlight that the normal stress
anisotropy depends on the volume fraction, and that lubrication interactions
significantly contribute to the normal stress in the semi-dilute regime.
