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 0.55Fy.(See the following equations.)
For unshored members,

(10.43)

wherefyyield strength, ksi (MPa).

For shored members,

(10.44)

where fsstress in steel, ksi (MPa)
MDdead-load moment, in.kip (kN.mm)
MLlive-load moment, in.kip (kNmm)
Sssection modulus of steel beam, in^3 (mm^3 )
Str section modulus of transformed composite section, in^3 (mm^3 )
Vrshear range (difference between minimum and maximum shears at
the point) due to live load and impact, kip (kN)
Qstatic moment of transformed compressive concrete area about neu-
tral axis of transformedsection, in^3 (mm^3 )
Imoment of inertia of transformed section, in^4 (mm^4 )

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

(10.45)

whereSrhorizontal-shear range at the juncture of slab and beam at point under
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 Zr, kip (kN), for an individual con-
nector is given by the next two equations, depending on the connector used.
For channels, with a minimum of in (4.76 mm) fillet welds along heel
and toe,

ZrBw (10.46)

(^3) 
16
Sr
VrQ
I
fs

MDML

Str

0.55Fy

fs

MD

Ss



ML

Str

0.55Fy