Civil Engineering Reference
In-Depth Information
8
Design of Steel
Members for
Combined Forces
8.1 INTRODUCTION
Structural steel members in railway superstructures are usually designed to resist
only axial or transverse loads as outlined in Chapters 6 and 7, respectively. These
external loads create internal normal and shear stresses in members of the superstruc-
ture. However, in some situations, it is necessary to consider members subjected to
combinations of forces.
Combined stresses in railway bridges typically arise from biaxial bending of
unsymmetrical cross sections, unsymmetrical bending from transverse force eccen-
tricities and combined axial and bending forces caused by eccentricities, member
out-of-straightness, self-weight,
∗
and applied lateral loads such as wind. For linear
elastic materials and small deformations, superposition of stresses from combined
loads is appropriate.
8.2 BIAXIAL BENDING
If bending moments,
M
x
and
M
y
, are applied at the centroid of an unsymmetrical
section as shown in
Figure 8.1,
bending will occur in both the
yz
and
xz
planes.
However, on unsymmetrical cross sections these planes are not principal planes,
and each moment contributes to a portion of the total bending about each axis. The
flexural stress,
σ
p
, at a location, p, with coordinates
x
and
y
is
σ
p
=
E
ε
x
+
E
ε
y
=−
E(
κ
x
x
+ κ
y
y)
,
(8.1)
where
ε
x
is the strain on the
xz
plane,
ε
y
is the strain on the
yz
plane,
κ
x
is the curvature
on the
xz
plane,
κ
y
is the curvature on the
yz
plane, and
E
is the modulus of elasticity
of steel and is equal to 29,000 ksi.
∗
This is the case for members that are not in a vertical plane.
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