Civil Engineering Reference
In-Depth Information
Combined stresses
:
σ
flange
= σ
b
L
2
+ σ
w
L
2
=
12.46
+
9.65
=
22.1 ksi,
which is very close to the value of 22.3 ksi obtained in Example 8.3.
τ
web
= τ
b
=
4.37 ksi,
τ
flange
= τ
b
+ τ
w
=
1.11
+
0.93
=
2.04 ksi.
The shear stress in the flange and web are underestimated at
z
=
0 because
pure torsion is not considered in the flexural analogy.
8.4 COMBINED AXIAL FORCES AND BENDING OF MEMBERS
Members are subjected to axial forces and bending moments due to axial force
eccentricities (often unintentional and related to connection eccentricities, member
out-of-straightness and/or secondary deflection effects) and when axial members are
laterally loaded (typically self-weight and/or wind). These normal axial and flexu-
ral stresses must be combined. Axial tension combined with bending is generally of
lesser concern than axial compression combined with bending due to the potential
for instability of slender compression members.
8.4.1 A
XIAL
T
ENSION AND
U
NIAXIAL
B
ENDING
The tensile load reduces the bending effects on the member when tensile axial loads
act simultaneously with bending. For the beam shown in
Figure 8.4
wL
2
8
−
M
=
T
Δ
.
(8.22)
However, the deflection,
, is dependent on the bending moment,
M
, which is itself
dependent on the deflection
Δ
Δ
. The deflection
5
wL
4
384
EI
−
L
2
8
EI
T
Δ
Δ =
(8.23)
may be solved iteratively.
∗
The bending moment,
M
,is
5
wL
4
384
−
.
wL
2
8
−
L
2
T
EI
T
Δ
M
=
(8.24)
8
However, since the effect of the tensile force on the deflection,
, can conservatively
be neglected in the analysis
†
of linear elastic members, the principle of superposition
Δ
∗
A digital computer algorithm is generally required.
†
In usual structures the effect is small (Bresler, Lin and Scalzi, 1968).
