Im looking for a mathematical equation for determining the torque
required to bend a piece of round steel tubing of x outside diameter &
y wall thickness around a die of z radius (typical numbers would be
1.5" diameter, 0.95" wall thickness, and a bending die radius of 8" on
the centerline of the tubing).

Assume the die is rotated around its axial centerline by some
torque-producing device, and that the matieral is mild steel. Also
assume that there is no wiper die, internal mandrel, and that any
friction created my parts sliding past each other is zero.

I assume that bending other materials requires knowing only the
tensile strength of that particular material. If baseing the formula
strictly on these inputs is an over-simlification, please explain as
best you can or explain how further variables play a role.

Id like some type of answer that will allow me to plug in different
tubing sizes,  wall thicknbesses, die radius, and materials to arrive
and an torque number. Formulas need not arrive at an exact number, but
need to factor in appropriate inputs to get a good approximation.

dear inquiring mind

  Trick is to imagine your tube to be a beam with particular crosssection

then search for 'beam bending equation' e.g. by

SEARCH TERM: cantilever beam bending

Here is one of many pages which describe beam bending:

http://www.engineersedge.com/beam_bending/beam_bending8.htm

The bending of the beam happens to depend on moment of inertia I
and E =Modulus of Elasticity. Modulus E is NOT same things as 
tensile strength, which is


"The resistance of a material to a force tending to tear it apart,
measured as the maximum tension the material can withstand without
tearing"
http://www.answers.com/topic/tensile-strength

E is the Young?s (tensile) modulus, which measures elastic elongation 
http://homepages.which.net/~paul.hills/Materials/MaterialsBody.html

 It remains is to find moment of inertia of your particular tube crosssection.
It depends on radiuses d and D:
Moment of inertia, round tube = (PI/64)*(D^4 - d^4)
http://mnhpva.org/tech/frame_tubes.html

Here is a calculated example:
http://astro.umsystem.edu/atm/ARCHIVES/FEB95/0146.html

Here is a spreadsheet - but please test it before using it.
http://www.eaa.org/benefits/sportaviation/ 0305_stucture_wksht_v5.xls

and finally a technical overview with derivations and definitions.
www.aa.washington.edu/courses/aa332/handout2.pdf

Hedgie

Everything you need seems to be right here:

http://www.bendtooling.com/bending_formulas.htm

Sorry...scratch that....does NOT answer tourque! Doh!

I don't know what got hedgie off to the wrong track, but what is
posted as the answer has nothing to do with your question (as you
probably already know). If you want to ask the question again, maybe
someone who is familiar with tube bending/engineering will take a shot
at it. I don't think that you got your $35 worth yet.