orsion in wide flange beams

huangyhg

torsion in wide flange beams
i seamed to have hit my head on a wall and can't think straight.
i'm having difficulty calculating the torsional stresses in a wide flange cantilever beam.  there's simply a torque at the free end of the beam.
using the polar moment of inertia, j (ix+iy), not the torsional constant (j), which is very confusing, is the stress for an open section simply tc/j, with c the perpendicual dimension to the centre of the flange...
---*---    -
    |        c
    |     ----
    |
-------
or does this calculation for torsional stress not apply unless the section is circular.
thanks for your input.
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cottageguy,
in the case of a wide flange beam, you cannot use the polar moment of inertia as ix+iy.  this method only works in closed sections, such as pipes and tubes.  in fact you will need to use the torsional constant (j).  for a wide flange this is (you will find that the torsional constant found in the steel code is in fact ix+iy for tubes and pipes.)
t^3*(2b+d)  
t= thickness
b= mean width
d= mean depth
this should give the same values that you will find in the steel code.  from here you do just use
(torque)*(c)/(j)
c is the distance from the centroid of the wideflange, to the furthest point of the section (assume top right corner).
an excellent reference for torsion is design of welded structured by omar blodgett.
another good reference is aisc's design guide 9: torsional analysis of structural steel members / seaburg and carter (1996.
while the free end of the cantilever can warp, the fixed end of the cantilever beam is prevented from warping.  such nonuniform warping results in additional shearing stress that should be accounted for.  therefore, additional warping stress shall be added to (torque)*c/j suggested by drgeers.
regards
you can refer to the steel construction institute's (uk) publication for the design of steel   
cottageguy,
i apologise in advance, but this may well introduce some confusion to your thread.
1.  the polar moment of inertia of a section ip is always = ix + iy, for all types of section.  (since ip = sum da.r^2 = sum da.(x^2+y^2) = sum da.x^2 + sum da.y^2 = ix + iy).
  but ip is only relevant to the calculation of torsional stresses in the case of circular sections.  (ie not even for square hollow sections).
2. if you care to look up timoshenko and goodier "theory of elasticity" (section 98 in the international student ediition, 1951) you will find that they do not share drgeers' view as to the value of c in the formula tc/j.
the value of c that t&g use is not the maximum polar radius (as drgeers suggests), but the thickness of the flange or the web (whichever is the greater).  the difference could be a factor of 20 or more.
roark "formulas for stress and strain" (tables 21 and 22 in my copy - 6th. edition, international edition) ends up saying the same thing, but in a more convoluted way than timoshenko and goodier.  but roark does give guidance on warping stresses (which i will readily confess have been buried deep in a black hole for the past 40 years as far as i am concerned).
thanks for all your help.
i will look up those references and read them myself.
to you last comment austim.  i also have buried the thought of torsion on wide flange beams (although not for so long).  as soon as a hear "torsion" i avoid wide flanges.  though it's a must in this situation.
thanks again,
cottage guy
the number 1 rule of torsion:  use closed sections.  a round, square, or rectangular section can carry the torsion with a much lower weight of material.
butelja is right, and you can simply weld on additional angles or brackets to a square or rect. tube to carry whatever you wanted to carry with your wide flange.
another thought: when i see the words cantilever & torsion & wide flange, i get queezy (images of lateral torsional buckling failures appear as i close my eyes...). are you sure that you only have a torque at the free end, or is there a transverse load associated with that torque which will cause bending moment?
cottageguy.
there's a booklet from bethlehem steel called torsional analysis of rolled steel sections that not only outline the theory an design phylosophy of torsional loading of steel   
thanks to all.
your comments are useful and interesting.
i agree with you all and have "convinced" the others to go with a tube section.  i normally go with closed sections when torsion is involved, as butelja stated.
our new beam is similar to an existing condition, and we were trying to make them look the same as to not raise any questions or concerns. "why are they different".
i didn't like the wide flange, and have altered the design to a hollow section.
thanks all, for your input.
cottage guy.