Page 327 - Civil Engineering Formulas

260 CHAPTER TEN

Bending Stresses
In composite beams in bridges, stresses depend on whether or not the members are
shored; they are determined as for beams in buildings (see “Composite Construc-
tion” in Chap. 9,“Building and Structures Formulas”), except that the stresses in the
steel may not exceed 0.55F . (See the following equations.)
y
For unshored members,
M D M L
f s 0.55F y (10.43)
S s S tr
where f yield strength, ksi (MPa).
y
For shored members,

M D M L
f s 0.55F y (10.44)
S tr

where f stress in steel, ksi (MPa)
s
M dead-load moment, in . kip (kN . mm)
D
M live-load moment, in . kip (kN mm)
L
3
3
S section modulus of steel beam, in (mm )
s
3
3
S section modulus of transformed composite section, in (mm )
tr
V shear range (difference between minimum and maximum shears at
r
the point) due to live load and impact, kip (kN)
Q static moment of transformed compressive concrete area about neu-
3
3
tral axis of transformed section, in (mm )
4
4
I moment of inertia of transformed section, in (mm )
Shear Range
Shear connectors in bridges are designed for fatigue and then are checked for
ultimate strength. The horizontal-shear range for fatigue is computed from
V r Q
S r (10.45)
I
where S horizontal-shear range at the juncture of slab and beam at point under
r
consideration, kip/linear in (kN/linear mm).
The transformed area is the actual concrete area divided by n (Table 10.5).
The allowable range of horizontal shear Z , kip (kN), for an individual con-
r
nector is given by the next two equations, depending on the connector used.
3
For channels, with a minimum of 16 in (4.76 mm) fillet welds along heel
and toe,
Z r Bw (10.46)