Seismology Opinion - Cantilever Columns

• To: <seaint(--nospam--at)seaint.org>
• Subject: Seismology Opinion - Cantilever Columns
• Date: Sat, 5 Feb 2000 13:27:39 -0800
I just read the Seismology Opinion for the use of Cantilever Columns. The
provisions are not too bad until you get to issue number 5 which state:
"The total shear in all columns combined shall be less than 15% of the story
shear based on tributary area."

I interpreted the document to read:

You may design by factoring up the loads to the embedded columns only IF and
only if these provisions are met - otherwise, you must factor up the entire
structure in the direction of force to match the lower R.

Let's look at a couple of conditions to see how restrictive this actually
is:

1. It eliminates most conditions where embedded columns are used between
lines of adjacent shear (assumed 50% of the tributary force) or at either
end of a series of diaphragms (assumed to be one) resisted by three lines of
shear (approximately 25% of the load at the ends) or any condition that does
not result in a very small tributary width totaling no more than 15% of the
story shear.

This is a very restrictive clause which will require most structures to be
penalized by forming them into compliance with a total lowered R in the

In my opinion, limiting the rule by a percentage of the base shear is too
generic a method of determining appropriate application because it tends to
eliminate most conditions other than the edge of a patio structure. If this
was the intention, why not just restrict it this way rather than trying to
do it mathematically?

What appear rational, is the restriction of story drift to 0.005H or "the
approximate deflection of the adjacent shear walls in the same orthogonal
directing". I agree with this - it is rational and insures a uniform
stiffness - it makes sense. 15% of total base shear makes no sense.

The opinion also limits the column axial stress ratio based on a K=2.1
(which is typical of a column allowed to rotate and translate at the top
while fixed at the bottom) to be less than 10% of the allowable axial stress
(fa/Fa). This does not makes sense, simply because the steel section
required to resist the story drift restriction will make this a moot point.
In most cases, in lightweight wood construction, the axial capacity of the
column will be many time greater than the actual load.

Let's look at a simple 10' Pipe column which is designed for a one kip
moment). The minimum size of a pipe column to resist the load will be P8xs
(8" diameter extra strong schedule 40 pipe column).  This is required to
keep the story drift below 0.6" at 0.005H (a P8std will deflect about 0.685"
exceeding 0.005H). The allowable Axial Stress Fa is around 22.7ksi for
DL+Short Term loading. This is where the axial ratio gets kind of ridiculous
because the columns would be allowed up to approximately 24.3 kips just to
meet 10% of their capacity.

I'm trying to understand how these restrictions were arrived at - maybe the
Seismology committee can provide notes as to what rationale led to these
restrictions so, as designers, we can understand what the group is
attempting to protect. This example uses a relatively small lateral load of
only 1000 pounds. The load to a front of a 22' deep garage caused by wind
loads is closer to 2000 pounds of shear or 5 kips applied to two columns
(factored 2.5 times).

Now here is the next part that confuses me:

In my mind the stiffness of the resisting element has less to do with it's
material than the ability to calculate the actual deflection under a given
load. Therefore, why does it matter whether we are dealing with an embedded
steel column, a plywood shearwall or a masonry wall. As long as we can
calculate the deflection on each element we can compare performance under
load. The stiffness or rigidity becomes a comparison between calculated
deflections in each line of shear.

If the goal is to balance deflection - essentially equalizing stiffness
between lines of shear - why would we want to factor uniformly through the
structure. I would think that we would want only to factor up the loads to
elements that are normally more flexible in order to make them converge on
the same stiffness as the more rigid elements.

I would like to read the rationale on how this Opinion was formulated. Any
suggestions on how this can be accomplished?

Regards,
Dennis S. Wish, PE
Structural Engineering Consultant
(208) 361-5447 E-Fax