Civil Engineering Reference
In-Depth Information
w
T
T
Δ
FIGURE 8.4
Member subjected to combined tensile axial force and bending.
may be applied to ensure that failure by yielding does not occur. AREMA (2008)
recommends that, if bending (even with superimposed axial tensile stresses) causes
compression in some parts of the cross section, the flexural compressive stress and
stability criteria should be considered. Therefore, the allowable flexural stress may
differ from the allowable axial tensile stress, which provides the interaction equation
±
σ
b
F
b
+
σ
t
F
t
≤
1,
(8.25)
where
σ
t
is the maximum
tensile axial stress,
F
b
is the allowable tensile or compressive bending stress,
F
t
is the
allowable axial tensile stress on the gross section and is equal to 0.55
F
y
.
When flexural compression with axial tension results in tensile stresses, Equa-
tion 8.25 is
σ
b
is the maximum tensile or compressive bending stress,
σ
b
+ σ
t
≤
0.55
F
y
,
(8.26)
which is theAREMA (2008) recommendation.When flexural compression with axial
tension results in compressive stresses, AREMA (2008) recommends
−σ
b
+ σ
t
≤
F
call
,
(8.27)
where
F
call
is the allowable compressive bending stress.
8.4.2 A
XIAL
C
OMPRESSION AND
U
NIAXIAL
B
ENDING
The compressive load increases the bending effects on the member when compressive
axial loads act simultaneously with bending (Figure 8.5). For the beam shown in
Figure 8.5
wL
2
8
+
M
=
P
Δ
.
(8.28)
Again, the deflection,
, is dependent on the bending moment,
M
, which is itself
dependent on the deflection
Δ
. The deflection is
Δ
5
wL
4
384
EI
+
L
2
8
EI
P
Δ
Δ =
(8.29)
