  We derive the membrane elastic stress and torque tensors using the standard
Helfrich model and a direct variational method in which the edges of a membrane
are infinitesimally translated and rotated. We give simple expressions of the
stress and torque tensors both in the local tangent frame and in projection
onto a fixed frame. We recover and extend the results of Capovilla and Guven
[J. Phys. A, 2002, \textbf{35}, 6233], which were obtained using covariant
geometry and Noether's theorem: we show that the Gaussian rigidity contributes
to the torque tensor and we include the effect of a surface potential in the
stress tensor. Many interesting situations may be investigated directly using
force and torque balances instead of full energy minimization. As examples, we
consider the force exerted at the end of a membrane tubule, membrane adhesion
and domain contact conditions.
