Civil Engineering Reference
In-Depth Information
P
P
y
M
M
y
0
1.5
0.25
0.50
1.0
0.75
5.0
j
j
y
1.0
3.0
FIGURE 8.7
Typical plot of moment-curvature relationship for a member subjected to
bending and axial compression.
Once the moment-curvature-axial compression relationship is established, each
value of
P/P
y
with a slenderness ratio,
KL
/
r
(where
r
is the radius of gyration in the
plane of bending), is combined with various values of
M/M
y
until instability occurs
(at
M
u
)
. Since
M/M
y
creates deflection,
Δ
, which creates an additional bending
moment (
P/P
y
)
, an iterative analysis, such as numerical integration by Newmark's
method or other step-by-step numerical integration techniques, is often used. Once the
appropriate values of
P/P
y
and
M/M
u
are determined (when deflections calculated
in two successive iterations are in sufficient agreement) for various values of
KL
/
r
,
interactiondiagrams,suchasthatshowninFigure8.8,maybemade.Theseinteraction
curves may be approximated by interaction equations for various values of
L/r
.
Δ
1.0
0
L
r
P
P
y
40
80
60
0.5
120
M
M
u
0.5
1.0
FIGURE 8.8
Typical interaction curves for a member subjected to bending and axial
compression.
