  Recent numerical simulations of magnetized accretion discs show that the
radial-azimuthal component of the stress tensor due to the magnetorotational
instability (MRI) is well represented by a power-law function of the gas
pressure rather than a linear relation which has been used in most of the
accretion disc studies. The exponent of this power-law function which depends
on the net flux of the imposed magnetic field is reported in the range between
zero and unity. However, the physical consequences of this power-law
stress-pressure relation within the framework of the standard disc model have
not been explored so far. In this study, the structure of an accretion disc
with a power-law stress-pressure relation is studied using analytical solutions
in the steady-state and time-dependent cases. The derived solutions are
applicable to different accreting systems, and as an illustrative example, we
explore structure of protoplanetary discs using these solutions. We show that
the slopes of the radial surface density and temperature distributions become
steeper with decreasing the stress exponent. However, if the disc opacity is
dominated by icy grains and value of the stress exponent is less than about
$0.5$, the surface density and temperature profiles become so steep that make
them unreliable. We also obtain analytical solutions for the protoplanetary
discs which are irradiated by the host star. Using these solutions, we find
that the effect of the irradiation becomes more significant with decreasing the
stress exponent.
