= Unilateral beam contact
{title2=$w\geq f,\ R\geq0,\ (w-f)R=0$}
An <elastic beam> above a smooth obstacle cannot penetrate it, and a nonadhesive obstacle can only push. The displayed constraints express this when $R$ is an upward distributed <normal contact force>; concentrated <point forces> must also be nonnegative. In the small-<slope> <Euler-Bernoulli beam equation>,
$$
Bw''''-Tw''+p=R.
$$
Integrating across a contact point with no applied couple gives <jump conditions> $[w]=[w']=[Bw'']=0$ and $[Bw''']=R_i$, provided the <tension> is continuous. For a flat obstacle, no distributed load and zero <tension>, an open contact interval has $R=0$; its entire <normal contact force> can therefore be concentrated at its endpoints.
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