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Column with torsion

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Thanks to Richard and Chris for their replies to my question on columns
with applied torsion.  For all of you who have waited with bated breath
for further clarification, I got this response from Ted Galambos.  He
turned out to be right; the interaction increased about 0.06; not enough
to break anything.

It probably will not be a serious matter if you ignore the whole torsion
problem. However, if you want to look into it, here is what I suggest:
1. Calculate the maximum warping normal stress due to the torque. ASCE
Design Guide No. 9 will help a lot. "Torsional Analysis of Structural
Members". If you don't have a copy, I have an extra one that I would
gladly give to you. 2. Divide this stress by phi x Fy, to get a ratio
for the interaction equation. 3. Amplify this ratio by dividing it by
1-P/AFez, where Fez is calculated by Eq. A-E3-12 in Appendix E3 (p.
16.1-95 in the 99 LRFD Spec., or in the corresponding section in the 86
or 93 versions).

After you look at the results, decide on what to do.

I hope this helps.
Best regards, Ted"

----- Original Message -----
From: "Michael L. Hemstad" <>
Sent: Tuesday, April 29, 2003 1:18 PM
Subject: Column with torsion

Dr. Galambos,
I have a small problem on a project of mine, recently completed (the new
LRT Maintenance Building).  One of my clients attached a fitting through
the fireproofing to a WF column (W14x61) in his new building.  It
sustains about 7000 pounds of tension horizontally, acting in the strong
axis of the column near the tip of the flange.  In addition to bending,
this induces some torsion in the column.

Can you offer some guidance as to how the torsion component affects my
column interaction?

The bending interaction I know how to analyze, and it makes sense to me;
the bending force is subject to a moment magnifier due to the increased
deflection caused by the axial load.  I have looked through LRFD section
H2, which basically says to add stresses (shear and axial), but that
seems too simple.  I'm concerned about stability, and H2 is only adding
up stresses with no magnification.  If I look at equation H2-3 as the
torsion component goes to zero, and I consider that the bending Mcr
divided by Z is pretty close to the axial Fcr, then I have a simple
elastic interaction equation with no moment magnification.

To re-phrase my question:  won't an applied torsion affect the
calculation of axial Fcr or bending Mcr?  The bending interaction
portion of my calculation addresses the lateral-torsional strength of
the column; I am concerned that an explicit applied torsion, which
doesn't show up in the strength side of the LRFD equations, will reduce
that significantly.

Mike Hemstad, P.E.
St. Paul, Minnesota

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