Q.A third of my crepe myrtle split off at base of trunk should I wrap it
Had beautiful blooms believe it got to heavy on that side and split off
Certified GKH Gardening Expert
The injury looks too old to benefit from a wrap.
This can happen when the shrub isn't properly pruned every year or two. Some cultivars will get so heavy that they fall apart on themselves.
while many won't, absolutely, need pruning some of them will in order to prevent splitting.
This article will help you to prune them properly: https://www.gardeningknowhow.com/ornamental/trees/crepe-myrtle/pruning-crepe-myrtle-trees.htm