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Most sternum pain in ring dips and push ups is people lacking internal rotation in the shoulder and they default into an internally rotated position when they start the dip. This puts the pec in a shortened position and pulls on the sternum. You also have to make sure you address any stiffness in the thoracic spine as well. Check the site for videos on how to clear these things up. It may also be a technique issue where you aren’t setting up correctly before you descend into the dip or push up. In the ring dip, the palms should be facing almost forward when you are at the top of the move. A lot of people have their palms facing backwards at the top, which would be a set up error and it will be impossible to not put all the load on the sternum during the decent.