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d.
Dynamic Analysis.
(1) Columns are not subjected to the blast loading directly.
Rather, the load that a column must resist is transmitted through the roof
slab, beams, and girders. These members "filter" the dynamic effects of the
blast load. Thus, the dynamic load reaching the columns is typically a fast
"static" load, that is, a flat top pressure time load with a relatively long
rise time.
(2) The roof members and columns act together to resist the applied
blast load. However, a reasonable design can be achieved by considering the
column separately from the roof members. The response (resistancetime
function) of the roof members to the blast load is taken as the applied
dynamic load acting on the columns.
(3) Columns are subjected to an actual axial load (with associated
eccentricity) equal to the ultimate resistance of the appropriate roof
members acting over the tributary area supported by the column. It is
recommended for design of columns the ultimate axial load be equal to 1.2
times the actual axial load. This increase insures that the maximum
response of the column will be limited to a ductility ratio, Xm/XE, of
3.0 or less. If the rise time of the load (time to reach yield for the
appropriate roof members) divided by the natural period of the column is
small (approximately 0.1), the maximum ductility is limited to 3.0.
Whereas, if the time ratio is equal to or greater than 1.0, the column will
remain elastic. For the usual design cases, the ratio of the rise time to
the natural period will be in the vicinity of 1.0. Therefore, the columns
will remain elastic or, at best, sustain slight plastic action.
e.
Design of Tied Columns.
(1) Interior columns are not usually subjected to excessive bending
moments since sidesway is eliminated by the shear walls. However,
significant moments about both axes can result from unsymmetrical loading
conditions. These moments may be due to unequal spacing between columns or
to time phasing of the applied loads. As a result of the complex load
conditions, the columns must be proportioned considering bending about both
the x and yaxes simultaneously.
(2)
One method of analysis is to use the basic principles of
with the acceptable ultimate strength assumptions. This method
essentially
involves a trial and error process for obtaining the position of
an inclined
neutral axis. This method is sufficiently complex so that no
formula may
be developed for practical use.
(3) An approximate design method has been developed which gives
satisfactory results for biaxial bending. The equation is in the form of
an interaction formula which for design purposes can be written in the
form:
1
1
1
1
EQUATION:
=
+ 
(78)
Pu
Px
Py
Po
2.08101


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