Civil Engineering Reference
In-Depth Information
0.5
f
y
compression
0.3
f
y
tension
y
z
0.3
f
y
compression
Figure 3.9
Idealised residual stress pattern.
(a)
Load
N
N= 0
0.25
N
y
0.5
N
y
N
y
d
e
Residual stress pattern
f
y
(b)
Stress
distribution
0.5
f
y
c
c
0
t
0.5
f
y
Shaded areas due
to axial load
First yield
Elastic
core
Fully
yielded
d
e
d
(c)
Cross-
section
z
b
Elastic
Elastic
y
(
EI
)
t
=
EI
(d)
Effective flexural
rigidity
Yielded
areas
EI
EI
(
EI
)
t
(
EI
)
t
= 0
Figure 3.10
Effective section of a member with residual stresses.
the strain-hardened regions. This use is based on the slip theory of dislocation,
in which yielding is represented by a series of dynamic jumps instead of by a
smooth quasi-static flow. Thus the material in the yielded region is either elastic
orstrain-hardened,anditssubsequentbehaviourmaybeestimatedconservatively
by using the strain-hardening modulus. However, the even more conservative
assumption that the tangent modulus
E
t
is zero in both the yielded and strain-
hardened regions is frequently used because of its simplicity. According to this
assumption, these regions of the member are ineffective during buckling, and the
moment of resistance is entirely due to the elastic core of the section.
Search WWH ::
Custom Search