Civil Engineering Reference
In-Depth Information
where the critical hoop buckling coefficient C
h
includes the effect of initial geo-
metric imperfections within API Spec 2B tolerance limits.
C
h
=
0
:
44t/D for M
≥
1
:
6D/t
3
/M
4
0
C
h
=
0
:
44t/D
+
0
:
21
ð
D/t
Þ
:
825D/t
≤
M
<
1
:
6D/t
C
h
=
0
:
736/
ð
M
−
0
:
636
Þ
3
:
5
≤
M
<
0
:
825D/t
C
h
=
:
736/
ð
M
−
:
559
Þ
1
:
≤
<
:
0
0
5
M
3
5
C
h
=
:
<
:
5
The geometric parameter M is defined as:
0
8M
1
r
2D
t
L
D
M
=
(3.82)
where L = length of cylinder between stiffening rings, diaphragms, or end con-
nections, in inches (m).
Note: For M
1.6D/t, the elastic buckling stress is approximately equal to
that of a long unstiffened cylinder. Thus, stiffening rings, if required, should
be spaced such that M
>
<
1.6D/t in order to be beneficial.
Critical Hoop Buckling Stress
The material yield strength relative to the elastic hoop buckling stress deter-
mines whether elastic or inelastic hoop buckling occurs and the critical hoop
buckling stress, F
hc
, in ksi (MPa), is defined by the appropriate formula.
Elastic buckling:
F
hc
=
F
he
for F
he
≤
0
:
55F
y
Inelastic buckling:
F
hc
=
0
:
45F
y
+
0
:
18
+
F
he
for 0
:
55F
y
<
F
he
≤
1
:
6F
y
1
:
31F
y
F
hc
=
for 1
:
6F
y
<
F
he
<
6
:
2F
y
(3.83)
1
:
15
+ ð
F
y
/F
he
Þ
F
hc
=
F
y
for F
he
>
6
:
2F
y
Combined Stresses for Cylindrical Members
The method of calculating the applied combined stress between bending with
compression and tensile stress in addition to the hydrostatic stress is discussed
in the following section based on AISC.
Combined Axial Compression and Bending
Cylindrical members subjected to combined compression and flexure should be
proportioned to satisfy both the following requirements at all points along their
length.
q
f
bx
+
f
by
C
m
f
a
F
a
+
F
b
≤
1
:
0
(3.84)
f
a
F
e
1
−
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