  We present an analytical study of bent twisted ribbons. We first describe the
elastic response of a ribbon within a purely mechanical framework. We then
study the role of thermal fluctuations in modifying its elastic response. We
predict the moment angle relation of bent and twisted ribbons. Such a study is
expected to shed light on the role of twist in the "J factor" for DNA looping
and on bending elasticity of twisted graphene ribbons.
