Civil Engineering Reference
In-Depth Information
the I beam or girder is then
V
0.55
F
y
/
√
3
≈
V
0.35
F
y
A
w
≥
.
(7.32)
7.2.4 B
IAXIAL
B
ENDING OF
B
EAMS AND
G
IRDERS
Biaxial bending is not generally a concern for ordinary steel railway longitudi-
nal beams and girders. However, biaxial bending of stringers and floorbeams or
unsymmetrical bending of floorbeams
∗
may warrant consideration (see Chapter 8).
Stresses in perpendicular principal directions may be superimposed at critical
symmetric sections. This is shown in Equations 7.33 and 7.34.
M
x
F
b
x
S
x
±
M
y
F
b
y
S
y
1.0
≤±
,
(7.33)
V
x
Q
x
I
x
t
x
±
V
y
Q
y
I
y
t
y
F
v
≤±
,
(7.34)
where
F
b
x
,
F
b
y
are the allowable bending stresses in the
x
and
y
directions,
respectively;
F
v
is the allowable shear stress.
7.2.5 P
RELIMINARY
D
ESIGN OF
B
EAMS AND
G
IRDERS
For planning purposes, preliminary proportioning of plate girders may be necessary
before detailed design. Preliminary dimensions may be needed for estimating the
weight and cost and for assessing the site geometry constraints. Preliminary propor-
tions may also be required in order to estimate splice requirements and for fabrication,
shipping, and erection methodologies.
There are many techniques used by experienced bridge engineers to assess the
preliminary dimensions of beams and girders. One method is by simplification of
the bending resistance into that resisted by equal flanges and webs separately as
t
w
(h)
2
6
( f
bw
)
,
M
=
M
f
+
M
w
=
bt
f
(d
−
t
f
)(f
bf
)
+
(7.35)
where
M
f
is the moment carried by flanges,
M
w
is the moment carried by the web,
f
bf
is the allowable flange bending stress, and
f
bw
is the allowable web bending stress.
Assuming that
f
bf
∼
f
bw
∼
f
b
and, for usual railway beams and girders,
h
∼
(d
−
t
f
)
,
Equation 7.35 yields
M
f
b
h
−
A
w
6
.
bt
f
=
A
f
=
(7.36a)
∗
May occur at transverse floorbeams with horizontal longitudinal live load forces applied due to
traction and/or braking (see Chapter 4).
