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Application Example 13
(Propagation of uncertainty through linear formulas: secondmoment analysis)
DESIGN LOAD FACTORS FOR STRUCTURAL COLUMNS
Load factors are numbers greater than 1 by which nominal loads are multiplied to provide
sufficient safety in structural design. Design codes allow engineers to use different design
load factors on structural columns depending on the number of floors supported by the
column. The factors typically decrease as the number of supported floors increases. This
might sound counterintuitive, since one would expect the code to require a higher level
of safety for taller buildings. The uncertainty analysis that follows explains the rationale
for such code provision.
Second Moment Analysis of Column Load
Suppose that a structural column supports n floors and that the load on the column, F,
comes primarily from dead loads (D) and live occupancy loads (L). Therefore, the total
∑
=
∑
=
1
load on the column is
F
=
D
+
L
(
1
)
where
n
i 1
i
D
=
D
i
(2)
n
L
=
L
i
and D
i
and L
i
are the dead and live loads contributed by floor i. In most cases, dead loads
are much more accurately known that live loads are. Therefore, D may be considered
1
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View Full Documentdeterministically known. A second simplifying assumption we make is that the live loads
L
i
have the same marginal distribution (hence they have the same mean value m, the
same variance
σ
2
, and the same coefficient of variation V =
σ
/m for all floors). Finally,
we assume that the loads L
i
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 Fall '07
 DonHill

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