CIVIL ENGINEERING FORMULAS

254 CHAPTER TEN

ALLOWABLE-STRESS DESIGN FOR BRIDGE BEAMS

AASHTO gives the allowable unit (tensile) stress in bending as Fb0.55Fy. The
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):

(10.34)

where Llength, in (mm), of unsupported flange betweenconnections of lat-
eral supports, including knee braces
Sxcsection modulus, in^3 (mm^3 ), with respect to the compression flange
Iycmoment of inertia, in^4 (mm^4 ) of the compression flange about the
vertical axis in the plane of the web
J 1/3(bct
3
cbtt
3
cDt
3
w)
bcwidth, in (mm), of compression flange
btwidth, in (mm), of tension flange
tcthickness, in (mm), of compression flange
ttthickness, in (mm), of tension flange
twthickness, in (mm), of web
Ddepth, in (mm), of web
ddepth, in (mm), of flexural member

In general, the moment-gradient factor Cbmay be computed from the next
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

Cb1.751.05 (10.35)

M 1

M 2 

0.3

M 1

M 2 

2

2.3



B

0.772J

Iyc

9.87

d

L

2

0.55Fy

Fb

5  107 Cb

Sxc 

Iyc

L

TABLE 10.2 Allowable Bending

Stress in Braced Bridge Beams*

Fy Fb

36 (248) 20 (138)

50 (345) 27 (186)

*Units in ksi (MPa).