Can you crack a rib by coughing strenuously?

Possible. It is possible but less likely to crack a rib by coughing as most healthy people would actually strain the muscles . Rib fracture by coughing would raise suspicion of brittle bones and most doctors would try to find another cause which would have weakened the bone .
Very unusual. Coughing from pertussis can lead to rib fracture. I previously coughed while holding a heavy object in one hand at a strange angle. My physician was shocked that i snapped a rib clear in half - in this case it was torque or the laws of physics in play (vice pathology). So - it is possible to break a rib while coughing - but not usual.