# Snap-through of a shallow arch by arc length

A shallow sinusoidal arch y₀ = a sin(πx/L), L = 100, depth 1, unit width (40 × 2 × 1 hex20,
E = 10⁴, ν = 0), pinned at mid-depth at both ends, under a sinusoidal dead load q₀ sin(πx/L)
applied per element on its top face, in a nonlinear static step with arc-length control. With
a/r = 3.5 the symmetric path has two limit points and the antisymmetric mode does not bifurcate
before them. The load is scaled to the closed form's upper limit load, so the path peaks at load
factor 1; the step snaps through, passes the lower limit point and stops at a midspan deflection
of 2.2 a. Measured: both limit points' load factors (from the change of the tangent's inertia)
and the one negative eigenvalue between them.