A broken branch on a tree isn't usually a big deal unless the branch caused damage coming down or if it was one of the large main branches. The following are some issues to watch for if you have a broken branch on your tree.
When a medium or large branch breaks, it sometimes tears the bark that was on the area of the trunk below the tree. An area with missing bark is more susceptible to disease and pest organisms, so you want the area to heal as quickly as possible.
If the branch is still hanging from a bark strip, cut it off carefully to avoid further damage. Then, use a sharp blade to clean up the rough edges of bark. The tree can more easily and quickly produce wood to cover the damage if the edges are smooth. Avoid sharp angles as you trim, and instead strive for a curved shape as this is easier for the tree to heal over.
The loss of a large branch can affect the entire canopy of the tree. Many tree species produce branches in a balanced manner that more or less equally distributes the weight of the crown around the trunk. When a large branch is lost, this balance is off and a tree can become more prone to falling or blowing over due to the unequal weight distribution.
A professional arborist can remedy this problem by assessing the remaining branches in the canopy. Some trimming and possibly the removal of other branches may be necessary to rebalance the tree.
A falling branch may have come down cleanly, but it could have caused damage to neighboring branches as it fell. You may be able to spot this damage and clean it up on your own, particularly when there are no leaves on the tree.
If the tree is in leaf or you can't reach the damage, an arborist has the tools to get into the canopy. Any collateral damage to neighboring branches must be cleaned up and the broken branches trimmed back to help reduce the chances of disease or pests.
Another concern is a split trunk. This can happen when a particularly large branch comes down and pulls the trunk apart with it. Sometimes the split is severe and the tree cannot be saved.
In some instances, the damage is minor enough that an arborist can splint the trunk back together once the problem branch has been carefully removed. One way this is done is by actually bolting the trunk back together once the wounds are cleaned up. Over time, the tree produces new wood that seals over the wound and splices the trunk back together.
Contact an arborist for more help with tending to damage on your trees.