  When a thin elastic sheet crumples, the elastic energy condenses into a
network of folding lines and point vertices. These folds and vertices have
elastic energy densities much greater than the surrounding areas, and most of
the work required to crumple the sheet is consumed in breaking the folding
lines or ``ridges''. To understand crumpling it is then necessary to understand
the strength of ridges. In this work, we consider the buckling of a single
ridge under the action of inward forcing applied at its ends. We demonstrate a
simple scaling relation for the response of the ridge to the force prior to
buckling. We also show that the buckling instability depends only on the ratio
of strain along the ridge to curvature across it. Numerically, we find for a
wide range of boundary conditions that ridges buckle when our forcing has
increased their elastic energy by 20% over their resting state value. We also
observe a correlation between neighbor interactions and the location of initial
buckling. Analytic arguments and numerical simulations are employed to prove
these results. Implications for the strength of ridges as structural elements
are discussed.
