  We give an upper bound for the maximum number of edges in an $n$-vertex
2-connected $r$-uniform hypergraph with no Berge cycle of length $k$ or
greater, where $n\geq k \geq 4r\geq 12$. For $n$ large with respect to $r$ and
$k$, this bound is sharp and is significantly stronger than the bound without
restrictions on connectivity. It turned out that it is simpler to prove the
bound for the broader class of Sperner families where the size of each set is
at most $r$. For such families, our bound is sharp for all $n\geq k\geq r\geq
3$.
