According to the Wikipedia article:
Doomsday possesses extreme superhuman strength that, variable as it is, at one point enabled him to effortlessly stand his ground against the entire Justice League, including Superman and Orion. He was able to break Superman's left arm with limited effort, as well as outmatch and beat Darkseid unconscious in combat. However, his strength has limits: the immensely strong Calatonian alloy cables, in which he was entombed, continued to partially restrain during his initial rampage on Earth. It was never stated how long he had struggled to free his left hand before his escape.
I also agree with Keith H Weston, in that having your arm pinned in an awkward position will make it a lot harder to utilize the muscles to their full potentional. A person in a straight-jacket is at a huge disadvantage because their muscles usually work the opposite way.