Combined Stresses: Torsion plus bending 1

[whyun]

AISC Steel Manual (ASD) 9th Edition Chapter H talks about checking combined stresses due to bi-axial bending and axial loads.

Given that a member is subject to bi-axial bending and torsion, and pure torsional stress is obtained, what should be the combined stress check equation?

What about bi-axial + axial + torsion?

I appreciate your input in advance.

 

[Lutfi]

Use the following formula which will take you back to the days of strength of material. I created a spreadsheet to perform these computations:

sigma-x (major axis bending stress)
sigma-y (minor axis bending stress)
tau (shearing stress, torsional and vertical shear)

sigma max, sigma min = (sigma-x +sigma-y/2) +/- ((sigma-x-sigma-y/2)^2 + (tau)^2)^0.5

I hope this helps

 

[whyun]

Why does sigma-y get divided by 2?

Should the term be [(sigma-x + sigma-y)/2]?

Assuming sigma, max and sigma,min gives the maximum and minimum actual combined stress, what allowable stress shall be used to compare this to?

Thanks for elaborating.

LRFD 3rd Edition talks of combined forces and torsion in Appendix H but no parallel info in the ASD...

 

[haynewp]

That is from Mohr's circle

http://www.efunda.com/formulae/solid_mechanics/mat_mechanics/mohr_circle.cfm

What shape are you checking?

 

[whyun]

Thanks haynewp.

Situation I have is a tube steel (HSS8x4x1/4) laid horizontally. Assume pinned ends.

Loading consists of gravity loads (self weight plus a black box attached near midspan) and lateral load of 4 kips at the black box. This lateral load is applied with eccentricity imposing torque in the member.

There is no axial tension or compression.

Thanks for the link. Nice refresher course in mechanics...

 

[haynewp]

Specification for the design of steel hss sections is what you need. The LRFD version can be downloaded from here,

http://www.aisc.org/ContentManagement/ContentDisplay.cfm?ContentID=4203

See section 7.2

 

[trainguy]

Your ends must be fixed (against twist) for any torsional resistance to occur.

tg

 

[whyun]

Thanks trainguy. when i stated pinned, it was for the moments for the flexural load reaction (i.e. Mx and My = 0). Mz shall be fixed to take the torsional reaction. My bad for not being clear.

 

[Lutfi]

whyun,

You are correct. The term be [(sigma-x + sigma-y)/2]

Thanks for carefully reviewing the formaula.

Lutfi

 

[whyun]

Thanks Lutfi. It's so much easier with Greek notation!

Thanks y'all for your input.

Cheers