When an item says it procs a certain percentage of your weapon damage, is that damage the base weapon damage or the damage multiplied by your Strength?
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Yes, like all other spells and abilities which scale with weapon damage this damage is multiplied by your primary stat (strength for Barbarian).
On a level 60 char you can see this when you show the damage numbers (the numbers for the bleed would be really small in comparison to other numbers if they would not scale with your primary stat).