  We present some novel equilibrium shapes of a clamped Euler beam (Elastica
from now on) under uniformly distributed dead load orthogonal to the straight
reference configuration. We characterize the properties of the minimizers of
total energy, determine the corresponding Euler-Lagrange conditions and prove,
by means of direct methods of calculus of variations, the existence of curled
local minimizers. Moreover, we prove some sufficient conditions for stability
and instability of particular solutions of the Euler-Lagrange conditions that
can be applied to numerically found curled shapes.
