  This paper is concerned with the diameter of certain word norms on
S-arithmetic split Chevalley groups. Such groups are well known to be boundedly
generated by root elements. We prove that word metrics given by conjugacy
classes on S-arithmetic split Chevalley groups have an upper bound only
depending on the number of conjugacy classes. This property, called strong
boundedness, was introduced by Kedra, Libmann and Martin and proven for ${\rm
SL}_n(R)$, assuming R is a principal ideal domain and $n\geq 3$. We also
provide examples of normal generating sets for S-arithmetic split Chevalley
groups proving our bounds are sharp in an appropriate sense and give a complete
account of obstructions to the existence of small normally generating sets of
${\rm Sp}_4(R)$ and $G_2(R)$. For instance, we prove that ${\rm
Sp}_4(\mathbb{Z}[\frac{1+\sqrt{-7}}{2}])$ cannot be generated by a single
conjugacy class.
