# Column K factor

• To: "SEAINT List Service" <seaint(--nospam--at)seaint.org>
• Subject: Column K factor
• From: "Drew A. Norman, S.E." <DNormanSE(--nospam--at)email.msn.com>
• Date: Tue, 6 Apr 1999 11:24:48 -0500
```Kulwant Brah posted:

... tilt-up building with metal deck for roof  ... VA engineer ... telling
us that the columns should be designed ... with K=2.

Charles Greenlaw responded:

... is your building's lateral force resisting system so flimsy and "free"
that "translation" prevention at the roof and column tops depends on the
stiffness of the columns as downward cantilevers?

My two cents (one from California and one from my new home in Texas):

Kulwant!  Howdy.

Charles is on point (except, I think, for his suggestion that relative
stiffness is at issue, see below).  Your K=1 is probably conservative, but
the "Pope" (your VA engineer), still needs to be convinced.

You may want to give the guy a little bit of slack.  There WERE tilt-up
structure collapses in the '71 and '94 earthquakes in L.A., which some now
ascribe to excessive diaphragm flexibility.  If you give this VA engineer
the benefit of the doubt, what he could be saying is that you need to verify
that the aggregate shear wall/diaphragm flexibility near the middle of the
building is not so large that the stiffness of the columns in that area
becomes significant in proportion, i.e., that they will be forced to provide
their own stability.  In theory, one could imagine a building where he could
have a point.  In practice, it doesn't sound like yours is such a structure.

Your diaphragm is nice and square, and probably relatively stiff.  I assume
you calculated anticipated roof level drift (including diaphragm deflection)
and checked the columns for P-Delta effects in combination with gravity
loads.  For this analysis, you can obviously use the K value that assumes
the top is restrained against translation (as low as 0.8, but your 1.0 would
be conventionally conservative), since you are assuming that lateral forces
are resisted by the diaphragm/shear wall system as opposed to the column.
If your column checks out, the analysis substantiates your assumed K.  If
the column does NOT check for P-Delta, your reviewer may have a point,
however round about his method of getting at it.

For general list discussion, I'd like to offer up for comment my opinion
that Kulwant should NOT try to resolve this issue (which K factor to use) by
consideration of relative stiffness, which will I think lead him into a
morass of unnecessary calculations and the inevitable question of how stiff
is stiff enough to constitute "restraint".  The use of a sidesway restrained
buckling length adjustment factor (K) for "non-seismic" column design should
not depend on the STIFFNESS of an independent lateral force resisting system
but rather on the EXISTENCE of such a system.  The test of the lateral force
resisting system's competency is a deflection calculation and P-Delta stress
check for the "non-seismic" element.  If this calculation shows the column
sufficient, then the lateral force resisting system is sufficiently stiff to
substantiate the assumption.

Just so no one else feels they have to say it, the above argument is
relevant only to the selection of the proper sidesway restraint condition
for assignment of column K factors.  I am not arguing that deflection
compatibility need not be considered, or that potentially serious problems
will not result from the introduction of relatively stiff "non-seismic"
elements into an otherwise satisfactory structural design.  I am simply
saying that this is irrelevant with respect to the question of sidesway
restraint.

Drew Norman, S.E.
Drew A. Norman and Associates
Consulting Structural Engineering

888-787-1667 toll free at Dallas branch office
323-953-1770 at Los Angeles main office

```