Civil Engineering Reference
In-Depth Information
where
F
a
is the allowable stress f
or axial
compression alone and
K
is the effective
length factor and is equal to
/L
√
EI/P
cr
(see Chapter 6).
The yield criterion (Equation 8.71) and the stability criteria (Equation 8.75)
should be investigated for all members subjected to simultaneous bending and axial
compression.
π
8.4.3 A
XIAL
C
OMPRESSION AND
B
IAXIAL
B
ENDING
The strength of members subjected to axial compression and biaxial bending is
complex. Theoretical procedures have been developed for short members and longer
members to produce interaction curves (Chen and Astuta, 1977; Culver, 1966) and
confirmed as reasonable by experiment and in computer studies for typical members
by Birnstiel (1968), Pillai (1980), and others (see Galambos, 1988).
Since a design methodology for axial compression and biaxial bending must
include the case of axial compression and uniaxial bending, it would appear reason-
able to extend the interaction Equations 8.71 and 8.75 to the case of biaxial bending
with axial compression. Therefore, the interaction formula relating to the stability
criterion is
σ
a
F
a
+
σ
b
x
F
b
x
1
2
E (K
x
L
x
/r
x
)
2
− σ
a
/
0.514
π
σ
b
y
F
b
y
1
2
E
K
y
L
y
/r
y
2
=
+
1.0.
(8.76)
− σ
a
/
0.514
π
Formemberswithlowslenderness(whereyieldingcontrols)oratlocationsofsupports
or where braced in the plane of bending,
σ
a
F
a
+
σ
b
x
F
b
x
+
σ
b
y
F
b
y
=
1.0,
(8.77)
where
F
a
=
=
σ
b
x
is the normal
0.55
F
y
when
L/r
0 (points of bracing or supports),
bending stress about the
x
axis,
σ
b
y
is the normal bending stress about the
y
axis,
F
bx
is the allowable bending stress about the
x
axis,
F
b
y
is the allowable bending stress
about the
y
axis, and
K
x
L
x
/r
x
and
K
y
L
y
/r
y
are the effective slenderness ratios of the
member about the axes
x
and
y
, respectively (see Chapter 6).
8.4.4 AREMA R
ECOMMENDATIONS FOR
C
OMBINED
A
XIAL
C
OMPRESSION AND
B
IAXIAL
B
ENDING
AREMA (2008) recommends that members subjected to axial compression and biax-
ial bending be designed in accordance with Equations 8.76, 8.77, and 8.70 extended
for biaxial bending.
However,AREMA (2008) recognizes that, for members with relatively small axial
compressive forces, the secondary effects are negligible. Therefore, when
σ
a
/F
a
≤
0.15, Equation 8.76 may be expressed as
σ
a
F
a
+
σ
b
x
F
b
x
+
σ
b
y
F
b
y
≤
1.0.
(8.78)
