Principal Stess? 1

[SteelPE]

I have what a question that most of you will probably find simple to answer. This is a hypothetical question as I do not have to solve this problem at the moment.

If I have a tube that has an eccentric load applied. I end up with a bending load and a torsional load applied to the tube itself. The bending load is typically resolved into a tension an compression load at the top and bottom of the tube (pretty simple). The torsional stress can be resolved into a shear stress around the tube (still pretty simple). How do you combine the two stresses? My thought would be to calculate the principal stress as the following:

Sig p = (sig x/2 + sig y/2)) +/- [(sig x /2– sig y/2)^2 + tau x ^2]^.5

Is this the correct approach?

 

[ishvaaag]

I attach the comparison stress (most surely a Von Mises criteria) of (superseded) steel code MV-103.

For a case like yours at the corner you would have as tangential stress tau the sum of the shear stress from the vertical load centered (average, on two webs) plus the shear stress from the torsor induced by the eccentricity of the load. The axial stress sigmax would be M/elastic modulus of section.

Then the comparison stress to compare with Fy would be

sqroot(sigmax^2+3*tau^2)<=Fy

Fy is sigmau in the atachment.

Note in the text you can start to build a comparison stress from principal stresses or stresses at some set of orthogonal faces. It is this comparison stress and not directly the principal stresses what is used to check if the material will meet the limit stress criteria.

The determination of principal stresses must be done in separate way if not inmediately apparent. I once built (and still have it) a Mathcad 2000 worksheet for such task, but I think I have never had to put it to practical use.

 

[onealexis]

I suspect you would want to use an interaction formula where the sum of the ratios of actual stress to allowable stress must be less than or equal to 1.

 

[DHKpeWI]

I don't think you need to worry about principal or Von Mises stresses in this case. For typical beam design the shear limit state and the bending limit state are not combined. See sections F & G 13th Edition AISC Manual. If you had torsion on an open section (i.e. wide flange beam or channel) then you would have warping normal stresses that are additive to the bending stresses.

 

[desertfox]

Hi SteelPE

Follow this link and goto page 19 of the pdf its gives the formula and an example of the stresses your talking about,

http://www.freestudy.co.uk/strength of materials/tutorial 1 1.pdf

desertfox

 

[SteelPE]

Desertfox,

I believe the formula given on page 19 for sigma max is the same equation I gave above just written a little differently.

I am interested in the response from ishvaag but I have not been able to find similar formulas in my mechanics book (partly because I have been busy this morning). Funny how I can understand the equations but not really understand the Spanish text (I can barely understand English).

The others bring up some good responses but I have yet to try and verify them.

 

[SteelPE]

What dumb luck. I was in the middle of trying to figure out how to design a truss made up of tubes (never designed one using tubes, I wanted WF sections turned on their sides) and I find my answer.

Equation 7.2-1 of the AISC Hollow Structural Sections Connection Manual give and equation for "Design for combined torsion, shear, flexure and /or axial force" as as rations of the applied load to the nominal strength (see the equation for the exact formula.

 

[SteelPE]

And it is now equation H3-6 of the AISC 13th edition manual.

 

[DHKpeWI]

SteelPE:

Thanks for your latest post.

DHK

 

[ishvaaag]

DHKpeWI, I agree that normally one wouldn't need to check for the interaction axial stresses with shear stresses (even the paragraph preceding the H3-6 eq. says so for relatively limited torsors, what would be interpretable as ordinary cases), I only was introducing these formulae aiming more than anything to convey the understanding than for a general case we check against a failure criteria (the comparison stress being built either from principal or along some axes' stresses).

 

[civeng80]

Wouldn't it be a lot easier to use Mohr's circle to get the principal stresses ?

 

[desertfox]

Hi civeng80

I agree with you and my link suggests the Mohr circle.

desertfox

 

[DHKpeWI]

ishvaag:

I understand your point.

Actually, I was unaware of the requirements of section H.3.1. I am fairly certain this requirement was not in the old 1989 ASD, and until recently I rarely used LRFD. Thanks to desertfox I am now aware of the requirement for combined stresses in HSS.