i-beam torsional stress calculation

huangyhg

i-beam torsional stress calculation
can anyone tell me how to calulate torsional stress on an i-beam section?  i have read texts that state that the shear stress of each individual section is based on the the sum of torsional resistances of each individual section of the beam.  is this the standard way of computing the shear stress (due to torsion) for non-circular members?
what is the torsional constant "j" as listed in the torsion properties table of the aisc manual of steel construction.  is this value used in the stress calculation as described above?
thanks in advance,
torsion is tough.
there are 2 torsional constants which in general are both relevant: pure torsion j which is dominant for closed sections, and warping torsion which governs for i beams.
if you have access to fea, a simple answer is to model the beam with plate elements. this is ideal for warping torsion.
twin beam theory is a hand method for warping torsion of i beams, and it works well for simple models. basically, each flange is considered a beam that is bending about its strong axis but in opposite directions. the resulting stresses are in the longitudinal direction and must be added to the other bending and axial stresses.
you might also see some horrible text book solutions with graphical solutions for torsion - i suggest avoid them unless you are into pain.
the simplest solution however is to avoid torsion if possible. ie change your design to eliminate torsion, or change to hollow sections so that you can analyse it using the j value.
you might look at the tasm program at
the aisc publishes an excellent design guide to do so. it is design guide number 11. you can buy it from their web site
torsion is tough. you have two types of stresses. normal and warping. normal is fairly easy to calculate for open sections as long as you have the torsional stiffness (j). warping is the tough one - you have warping bending and shear stresses. to calcualte the warping constant for a random open section is tough. also, as lufti stated, the boundary conditions and loading patterns also come into the picture. we use staad to calculate some of them. but they dont support angle sections and don't take into consideration all of the boundary conditions. take a look at design guide 11 or aisc t--117.
see the lincoln arc welding foundation book "design of welded structures".  they publish their books at give away prices as a public service.  most college book stores where there is an engineering department have their books especially this one.  it even has photos of torsional tests.  it is a no nonsense how to do it book.
as pointed out above, the torsional effects on an i beam are dominated by warping, so you can ignore the effects of pure torsion in this case.  
one simple, but conservative, way of dealing with torsion on an i beam is to replace the torsion with two lateral forces f on the flange, such that the torsion t = fd, where d is the distance between the flange centres.  you then analyse the flanges alone under the action of this minor axis loading to obtain the stress.  if it is stress that you are interested in, you can use our old friend von mises to check the combined effects of the bending and torsion, or if you are simply checking capacity, you can use the standard interaction checks including the additional term my_flange/mc_flange where my_flange is the minor axis moment due to f and mc_flange is the moment capacity of the flange alone.  you should also check the twist as this is likely to be large for an i section.
martin heywood
tnteng-
if you refer to the text pointed out earlier from lutfi (author: omer blodgett), the section addressing torsion points out (almost in the first paragraph) "design rule no. 1: use closed sections where possible". not only is it tough to calculate the reaction of the section under torsion (since the polar moment is almost impossible to calculate accurately and with justification - leading usually to a very conservative value for this), but you'll probably find that an elastic band will offer you better resistance to torsion!!
-- drej --
just a thought....sometimes you can avoid designing the i-section for torsion by providing some angle or hss bracing from the bottom of the beam diagonally up to the roof or floor structure.  by designing the braces to take the torsional couple, you eliminate the need for complex torsional calculations in the i-beam.
one other thing that is easy to forget...the connections at each end of the beam need to resist the regular shear forces but also the torsional reactions at the end of the beam, which could lead to rather beefy looking connections.