weapons damage type

[Balint]

I still don't really know which kind of damage type the main attr gives.
For example:
I have a staff with lighting damage, then it's ok, my inteligence will turn into lighting damage.
But what's happen when I have a staff with fire and piercing damage? (sambro's staff)
Warriors have often 3 damage type on their weapon. Do you know how calculating the damage from strenght? Daen bow have piercing and fire too. etc.