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# Re: Displaced Center of Mass Question

• To: seaint(--nospam--at)seaint.org
• Subject: Re: Displaced Center of Mass Question
• From: "Mark T. Swingle" <mswingle(--nospam--at)earthlink.net>
• Date: Sat, 31 Jul 1999 01:31:33 -0700

```Dennis:

1997 UBC Section 1630.6 says in part "the
mass....shall be assumed to be displaced....in
each direction....perpendicular to the direction
of force under consideration."

My understanding and interpretation is as
follows:  If one is considering accidental
eccentricity, one must move the CM <both>
directions for each direction of force, yielding
two (2) separate analyses for each direction, or
four (4) total analyses for a (typical) building
with two (2) orthogonal lines of shear walls.  The
four analyses can be accomplished by assuming the
CM to be in two different locations.

I would agree that "displacing....can produce
added torsional shears in all walls" as you
quoted.  The other method you mentioned appears to
be wrong the way you described it, IMHO.  However,
displacing the mass does NOT ALWAYS increase all
wall shears, as I will describe two paragraphs
down.

Assuming north = up = y positive axis and east =
right = x positive axis etc, and that the shear
walls line up with these major axes, let me
describe an example.  Assume also that the lower
left hand corner of the building is at (0,0).
Suppose the building is 40' wide (EW) and 100'
long (NS), the CM is at the geometric center
(20,50), and the CR is at (19,49).  To add the 5%
eccentricity, ONE WAY would be to assume the CM to
be at either of the following two points: point 1
= (18,45) or point 2 = (22,55).  The analysis
assuming point 1 as the CM would yield the highest
shear for all NS walls to the left of the CR and
all EW walls below the CR.  The analysis assuming
point 2 as the CM would yield the highest shear
for all NS walls to the right of the CR and all EW
walls above the CR.

In the particular case I described, the 5%
eccentricity "goes past" the CR on both sides, so
that the x- and y-values for the CR are bracketed
by the two CM values.  However, this is not always
the case.  Suppose in my example the CR was at
(16,43) and all other items remain the same.  Now
the CR is not "between" the two displaced CM
points.  In this case, using point 2 is still
valid and appropriate, since it is 5% from the CM
for both x and y.  However, using point 1 results
in a LOWER shear for the walls to the left and
below the CR than would be obtained by using
DIRECT SHEAR ONLY.  This is a no-no since 1994 UBC
Section 1603.3.3 says that "Forces shall not be
decreased due to torsional effects."  [I THINK
it's in 1997 UBC Section 1605.2.1 also, but my 2nd
printing is missing that sentence.  I'm pretty
sure it was put back in a later printing.]
Anyway, 97 UBC 1605.2.1 also says "Provision shall
be made for increased forces....resulting from
torsion....", implying that forces shall not be
reduced.

Applying this to a building with wood shear walls
is another whole can of worms, however.  And the
question of whether this results in a significant
difference depends upon the distribution of the
shear walls in plan.  All buildings are
different.  The more the walls are located at the
perimeter, the lower the effect of torsion will
be, as a percentage of the direct shear.

I hope I have explained clearly.

Mark Swingle, SE
Oakland, CA

Dennis Wish wrote on 7/29/99:

Displaced Center of Mass Question

The design examples from the Feb 1998 SEAOC Wood
Seminar for the 97 UBC (and the draft of the
ICBO Design Manual Volume II) note "by displacing
the center of mass by 5% can result in the C.M.
being on either side of the C.R. and can produce
added torsional shears in all walls."

However, the Reinforced Masonry Engineering
Handbook
by James Amrhein (5th edition 1994 UBC compliant)
simply adds the 5% of the diaphragm depth
it to the difference between the C.M. and C.R.
- leaving the displaced C.M. in only one location.

Which is considered the standard of practice in
rigid diaprhagm analysis?  If the more involved
method is applied in wood construction, has anyone
been able to calculate a significant difference
in added shear from torsion?  If so, how many of
these buildings were residential (single and
mulitple residential) etc.

Dennis Wish PE

```