Civil Engineering Reference
In-Depth Information
b
f
f
y
t
f
t
w
N
y,r
=
2
f
y
z
n
t
w
h
y
z
n
M
f
b
t
h
t
(
-
)
=
pl
,
r
f
y
f
f
2
f
t
{(
h
2
t
)
2
}
-
/
4-
z
+
y
w
f
n
f
y
z
(a) Section
(b) Stress distribution
(c) Stress resultants
Figure 7.8
Fully plastic cross-section.
1.0
M
pl,r
/
M
pl
= 1.18[1 - (
N
y,r
/
N
y
)]
Analytical solution
0.5
y
y
L
=
0
i
y
0
0
0.5
1.0
M
pl,r
/
M
pl
Figure 7.9
Interaction curves for 'zero length' members.
and members with axial force only (
M
=
0), which become fully plastic at
N
y
=
f
y
[
2
b
f
t
f
+
(
h
−
2
t
f
)
t
w
]
.
(7.16)
The variations of
M
pl
,
r
and
N
y
,
r
are shown by the dashed interaction curve in
Figure7.9.Thesecombinationscanbeuseddirectlyforveryshortbeam-columns
for which the bending moment at the fully plastic cross-section is approximately
equal to the applied end moment
M
.
Also shown in Figure 7.9 is the approximation
M
pl
,
r
,
y
M
pl
,
y
=
1.18
1
−
N
y
,
r
N
y
≤
1.0,
(7.17)
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