Civil Engineering Reference
In-Depth Information
Combined stresses
:
σ
flange
= σ
b
L
2
+ σ
w
L
2
=
5.58
+
19.0
=
24.6 ksi,
which is close to the value of 23.5 ksi obtained in Example 8.1.
τ
web
= τ
b
=
1.40 ksi,
τ
flange
= τ
b
+ τ
w
=
0.58
+
0.56
=
1.14 ksi.
The shear stress in the flange and web is correct at
z
=
L/
2, where pure
torsional shear stresses,
0 because
pure torsion is not considered in the flexure analogy. However, for many
typical steel railway bridge elements, torsional shear stresses are of much less
concern than flange normal stresses due to warping torsion. In such cases,
the flexure analogy is appropriate for ordinary torsion design problems.
τ
t
, are zero but are underestimated at
z
=
Example 8.3
The end floorbeam in a ballasted through plate girder bridge is subjected
to a uniformly distributed load,
w
, at an eccentricity of 2.5 in. as shown in
Figure E8.3.
y
2½"
Loading along
z
axis
W 12 x 58
w
= 2.0 kip/ft
t
= 5.0 kip-in./ft
x
Cross section in
xy
plane
9'
9'
Section properties:
I
x
= 475
in.
4
S
x
= 78.0
in.
3
I
y
= 107
in.
3
J
= 2.10
in.
4
C
w
= 3570 in.
6
z
45 kip-in.
T
972 kip-in.
M
EC
w
GJ
a
=
= 66.3 in.
18.0 kips
V
L/a =
216/66.3 = 3.25
FIGURE E8.3
