Civil Engineering Reference
In-Depth Information
Elastic buckling is described as in
Chapter 3
about critical. The formulations
to evaluate F
hc
for inelastic buckling are presented by the following equations,
which were modified in the LRFD version issued in 1993.
F
hc
=
0
:
45 F
y
+
0
:
18F
he
for 0
:
55F
y
<
F
he
F
hc
=
1
:
31 F
y
/
ð
1
:
15
+
F
y
/F
he
Þ
for 1
:
6F
y
<
F
he
≤
6
:
2F
y
F
hc
=
F
y
for F
he
>
:
6
2F
y
7.6.6 Combined Axial Tension and Bending
Prior to 1987, RP2A did not contain any provisions for combined axial tension
and bending; however, AISC contained the following equation:
f
by
F
by
≤
f
a
f
bx
F
bx
+
6F
y
+
1
:
0
(7.12)
:
0
In 1987, the seventeenth edition introduced an interaction equation for com-
bined axial tension and bending for the first time. The equation was simply a
modification of the AISC equation to allow for the circular cross-sectional shape:
q
f
bx
+
f
by
f
a
6F
y
+
≤
:
1
0
(7.13)
0
:
F
b
The interaction equation (
Equation 7.13
) has been modified in the LRFD
version.
7.6.7 Combined Axial Compression and Bending
API RP2A did not contain any provisions for combined axial compression and
bending load effects until the sixth edition was introduced in 1975. The eighth
edition of AISC contained the following two interaction equations, one to verify
member stability and the other for plasticity. Where the axial component was
small (
≤
0.15) an alternative equation was suggested. Buckling check:
C
my
f
by
f
a
F
a
+
C
mx
f
bx
f
a
/F
ex
Þ
F
bx
+
f
a
/F
ey
Þ
F
by
≤
1
:
0
(7.14)
ð
1
−
ð
1
−
and Strength check:
f
by
F
by
≤
f
a
f
bx
F
bx
+
6F
y
+
1
:
0
(7.15)
0
:
where
2
E
23
ð
Kl/r
Þ
π
12
F
e
=
2
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