Page 320 - Civil Engineering Formulas

254 CHAPTER TEN

TABLE 10.2 Allowable Bending
Stress in Braced Bridge Beams*

F y F b
36 (248) 20 (138)
50 (345) 27 (186)
*Units in ksi (MPa).

ALLOWABLE-STRESS DESIGN FOR BRIDGE BEAMS

AASHTO gives the allowable unit (tensile) stress in bending as F 0.55F . The
y
b
same stress is permitted for compression when the compression flange is support-
ed laterally for its full length by embedment in concrete or by other means.
When the compression flange is partly supported or unsupported in a bridge,
the allowable bending stress, ksi (MPa), is (Table 10.2):
5 10 C b
7
I yc
F b
S xc L
0.772J d 2
9.87 0.55F y (10.34)
B I yc L
where L length, in (mm), of unsupported flange between connections of lat-
eral supports, including knee braces
3
3
S section modulus, in (mm ), with respect to the compression flange
xc
4
4
I moment of inertia, in (mm ) of the compression flange about the
yc
vertical axis in the plane of the web
3
3
3
J 1/3(b t b t Dt )
w
t c
c c
b width, in (mm), of compression flange
c
b width, in (mm), of tension flange
t
t thickness, in (mm), of compression flange
c
t thickness, in (mm), of tension flange
t
t thickness, in (mm), of web
w
D depth, in (mm), of web
d depth, in (mm), of flexural member
In general, the moment-gradient factor C may be computed from the next
b
equation. It should be taken as unity, however, for unbraced cantilevers and
members in which the moment within a significant portion of the unbraced
length is equal to, or greater than, the larger of the segment end moments. If
cover plates are used, the allowable static stress at the point of cutoff should be
computed from the preceding equation.
The moment-gradient factor may be computed from
2
M 1
M 1
C b 1.75 1.05 0.3 2.3 (10.35)
M 2 M 2