...
Simply
...
supported
...
beam
...
P-δ
...
P-δ
...
is
...
a
...
local
...
effect
...
associated
...
with
...
axial
...
load
...
on
...
displacement
...
relative
...
to
...
element
...
chord
...
extending
...
between
...
end
...
nodes.
...
Figure
...
1
...
illustrates
...
the
...
influence
...
of
...
P-δ
...
on
...
a
...
simply
...
supported
...
beam.
...
Here,
...
a
...
transverse
...
distributed
...
load
...
ω
...
correlates
...
with
...
elastic
...
bending-stiffness
...
properties
...
K
...
E
...
to
...
induce
...
vertical
...
displacement
...
δ
...
.
...
An
...
additional
...
flexural
...
contribution
...
comes
...
from
...
the
...
relationship
...
between
...
this
...
deformed
...
configuration
...
and
...
axial
...
load
...
P
...
.
...
The
...
geometric
...
stiffness
...
properties
...
K
...
G
...
which
...
dictate
...
this
...
relationship
...
are
...
discussed
...
further
...
in
...
Dr.
...
Edward
...
L.
...
Wilson's
...
text
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Cantilevered column P-δ
Now, when observing P-δ effect on a cantilevered column, response is shown in Figure 2:
However, columns seldom displace with single curvature. More commonly, especially with multi-story-building analysis and design, columns deform according to a third-order (cubic) displacement pattern under double curvature. As shown in Figure 3, P-δ effect is much less pronounced because an inflection point intersects the element chord near midspan, previously where displacement from chord was greatest.
Cantilevered column P-∆
However, what is often of significance, given this loading condition and double-curvature displacement pattern, is P-∆ effect. Although displacement deviates from element chord much less, the lateral displacement associated with story drift is significant. With increasing levels of drift, gravity load has a greater effect on mechanical behavior, as shown in Figure 4. P-∆ effect should be implemented during design, whether static or dynamic, linear or nonlinear.
References
- Wilson, E. L. (2004). Static and Dynamic Analysis of Structures (4th ed.). Berkeley, CA: Computers and Structures, Inc.
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