Steel Beam bending/shear/torsion principle stress calculation help

[Rgold123]

Hi all, I have a situation where i need to analyze stress in a steel beam and was wanting advice on combining the stresses to get principle values.
The job requires isolated analysis of both horizontal and vertical, plus a lesser combined x and y fatigue force, so three sets of calcs in total.
The image represents the position on a simply supported beam where the force is applied and a section view of the beam on the right and shows my understanding of the equations. Both forces are offset from the centroid so also apply some torsion along with bending, and not being in the centre of the beam also gives a shear force i think.
calcs for horizontal force are shown, and i would do calcs for the vertical much the same but with the relevant distances etc changed to suit.
The part hanging me up is what to combine in the principle stress equation, for horizontal (and vertical) only do i include shear force in the principle equation along with shear values? or is that supposed to be just bending/2 +- SQRT (bending/2)^2 + torsion^2
it seems more straight forward when combining x and y forces, do i not combine the shear in this also?
any insight appreciated.

** just note i forgot to half the force in the shear and torsion equations ( Add "2*xxxx" do bottom of equation)

 

[Rgold123]

Bump. Anyone can help?

 

[rb1957]

1) it's principAL (not LE)

2) bending about principal axes (rather than about "x axis" or your complex section)

3) what are your reactions ? you have a "funky" section, where exactly is the support point ? Only once you have reactions can you calculate moments and torsion.

4) Is this homework ?

another day in paradise, or is paradise one day closer ?

 

[Rgold123]

Hi, yep. Poor spelling..
For this analysis it is a beam welded to a plate either side but must be classed as pinned for analysis purposes. Reactions would be 1/2 Force.

 

[Rgold123]

It's more a question on the combined stress equation than anything, as in when I have force only applied horizontally then do I not include shear stress and just use x force and torsion in the principal stress equation

 

[CivilSigma]

There might be equations you can use based on the Vlasaov theory that can help you compute stresses of a thin-walled steel element.
Hope this helps.