[Frame3dd] frame3dd, need help finding stress

[mark a. <andersom@q.com>]

Hey all--

I'm helping a friend build a single helix spiral stairway and I've used
Frame3dd to help with the structural analysis.  By way of introduction,
I'm an electrical engineer by day and it's been a great many years (beers)
since I had statics in college.  Never had any strength of materials.

Frame3dd is an excellent bit of software.  I had no problems getting
my design into Frame3dd and the results I've gotten out are promising.
One load case is for three, 300# people standing in the middle of the
run with a 3x safety factor.  The stringer at this point of load sees
a displacement of (all units are in inches and pounds):

  X-dsp     Y-dsp     Z-dsp     X-rot     Y-rot     Z-rot
 -0.153096 -0.055226 -0.152578 -0.000050 -0.001968  0.005960

Combining X,Y,Z displacement into a single displacement yields a total
of 0.225" which is nothing for 2700# of blubber.

The member connected to the above joint sees the following end loads.

    Nx        Vy       Vz       Txx        Myy        Mzz
 510.072c -426.820 -120.534 -15590.949  25120.657  -8492.681
-510.072c  426.820  142.663  15590.949 -24247.803   5624.725

At this point, I need to make sure these numbers stay below the allowable
stress for the beam.  The beam associated with the above example is a
8x3 rectangular steel tube with 3/16" wall and 6.7" long.  I've got all
sorts of good info about that piece of steel.

weight/foot  13.25 lbs
b/f  14.2
h/f  43.0
Xc   3.63 in^2 cross sectional area
Ix   27.8 in^4
Sx   6.94 in^3
rx   2.77 in
Zx   8.87 in^3
Iy   5.94 in^4
Sy   3.96 in^3
ry   1.28 in
Zy   4.43 in^3
J    16.2 in^4  torsional stiffness constant
C    7.68 in^3 torsional shear constant

Changing XYZ to get the load system to match the materials system:

    Nz        Vx       Vy       Tzz        Mxx       Myy
 510.072c -426.820 -120.534 -15590.949  25120.657 -8492.681
-510.072c  426.820  142.663  15590.949 -24247.803  5624.725

So, given all the above info, how do I calculate the actual stress in
this stinking 7" long chunk of steel?

I have a feeling that this is an easy question for a trained professional.
Speaking of which, we will be running the design past a *real*
PE/structural engineer, but I'd like to know how to solve this problem
myself.  Besides, it's always good to get independent confirmation.

For fun, I've attached an image from gnuplot showing the design (presuming
the list server will pass the attachment).

Thanks in advance.

--mark