Civil Engineering Reference
In-Depth Information
The curve for
L/r
=
0 may be approximated as
P
P
y
+
M
1.18
M
u
=
1.0
(8.68)
or
σ
a
0.55
F
y
+
σ
b
1.18
F
u
=
1.0.
(8.69)
For service load design, Equation 8.69 may be conservatively expressed as
σ
a
0.55
F
y
+
σ
b
F
b
=
1.0,
(8.70)
where
σ
b
is the normal
stress due to applied bending moment,
F
u
is the ultimate bending stress,
F
b
is the
allowablecompressivestressforbendingalone.Thisinteractionequationisapplicable
to members with low slenderness, such as locations that are braced in the plane of
bending, where yielding will be the failure criterion. However, for members with
larger slenderness, stability must also be investigated in the yielding criterion.
The yield criterion for members of larger slenderness is established as Equa-
tion 8.70 but by considering
F
a
instead of
F
y
due to the potential for allow
able
axial
compressive stresses to be controlled by instability when
KL/r
σ
a
is the normal stress due to applied axial compression,
0.629
E/F
y
(see
≥
Chapter 6). Equation 8.70 is then
F
a
+
σ
b
σ
a
F
b
=
1.0.
(8.71)
The interaction curves may be approximated for various values of slenderness,
L/r
, by interaction equations as
P
P
cr
+
M
P/P
e
)
=
1.0
(8.72)
M
u
(
1
−
or
σ
a
F
cr
+
σ
b
σ
e
)
=
1.0,
(8.73)
F
u
(
1
− σ
a
/
where
P
cr
is the critical axial buckling load,
P
e
is the Euler buckling load and is equal
to
2
EI/L
2
,
F
cr
is the critical axial buckling stress,
π
σ
e
is the Euler buckling stress
2
E/(KL/r)
2
.
Equation 8.73, using an
FS
π
and is equal to
=
1.95 for service load design for axial buckling, may
be conservatively expressed as
σ
a
F
a
+
σ
b
]
=
1.0
(8.74)
F
b
[
1
− σ
a
/(
σ
e
/
1.95
)
or
σ
a
F
a
+
σ
b
F
b
1
2
E) (KL/r)
2
=
1.0,
(8.75)
−
(
σ
a
/
0.514
π
