Civil Engineering Reference
In-Depth Information
There are (
m
−
n
+
1) independent cell warping continuity conditions of the type
(see equation 5.27)
(τ/
G
)
d
s
=
0,
wall
cell
and (
n
−
1) junction equilibrium equations of the type
(τ
t
)
=
0.
junction
These equations can be solved simultaneously for the
m
circulating shear
flows
τ
vc
t
.
5.11 Appendix - plastic analysis of beams
5.11.1 Full plastic moment
The fully plastic stress distribution in a section bent about a
y
axis of symmetry
is antisymmetric about that axis, as shown in Figure 5.37a for a channel section
example. The plastic neutral axis, which divides the cross-section into two equal
areassothatthereisnoaxialforceresultantofthestressdistribution,coincideswith
theaxisofsymmetry.Themomentresultantofthefullyplasticstressdistributionis
M
p
,
y
=
f
y
A
n
z
n
−
f
y
A
n
z
n
(5.67)
T
C
in which the summations
T
,
C
are carried out for the tension and com-
pression areas of the cross-section, respectively. Note that
z
n
is negative for
the compression areas of the channel section, so that the two summations in
f
y
f
y
f
y
f
y
f
y
f
y
b
×
t
f
b
×
t
f
C
d
f
×
t
w
M
pz
1
b
1
×
t
C
z
p
C
M
p
y
T
y
T
z
p
z
T
y
1
M
py
1
z
d
f
×
t
w
b
×
t
f
b
2
×
t
z
1
(a) Bending about an
axis of symmetry
(b) Bending of a monosymmetric
section in a plane of symmetry
(c) Bending of an
ymmetric section
Figure 5.37
Full plastic moment.
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