canned green beans safe to eat!
As it stands this question is unanswerable as we don't know the specifics of your method - how long, what sort of pressure, acidity etc.

However, I would take crisp beans to mean that you probably didn't cook them for long, which means there is potential for the process to have not been heated to a high enough temperature for long enough to sterilize during the canning process. This means that you are at risk for Clostridium botulinum growth. 

Is Clostridium common? - No, not very, but those cases of it are generally serious.

Now, the question remains: Is this a risk for you and your family? The answer to that is possibly! The National Center for Home Food Preservation page on green beans indicates that botulism is a risk for beans that have been incorrectly canned. They state that if you are worried and it is within 24 hours or the canning process, then you can eat immediately, store in the fridge up to 7 days (while eating), or repeat the canning process.