CIVIL ENGINEERING FORMULAS

226 CHAPTER NINE

completely braced laterally, the allowable stress in the flanges is 0.66Fy, where
Fyis the yield strength, ksi (MPa), of the steel. Assuming the steel to carry the
full dead load and the composite section to carry the live load, the maximum unit
stress, ksi (MPa), in the steel is

(9.66)

where MDdead-load moment, inkip (kNmm)
MLlive-load moment, inkip (kNmm)
Sssection modulus of steel beam, in^3 (mm^3 )
Strsection modulus of transformed composite section, in^3 (mm^3 )

An alternative, shortcut method is permitted by the AISC specification. It
assumes that the steel beam carries both live and dead loads and compensates
for this by permitting a higher stress in the steel:

(9.67)

Method 2 The steel beam is connected to the concrete slab by shear connectors.
Design is based on ultimate load and is independent of the use of temporary
shores to support the steel until the concrete hardens. The maximum stress in the
bottom flange is

(9.68)

To obtain the transformed composite section, treat the concrete above the
neutral axis as an equivalent steel area by dividing the concrete area by n, the
ratio of modulus of elasticity of steel to that of the concrete. In determination of
the transformed section, only a portion of the concrete slab over the beam may
be considered effective in resisting compressive flexural stresses (positive-
moment regions). The width of slab on either side of the beam centerline that
may be considered effective should not exceed any of the following:

1.One-eighth of the beam span between centers of supports

2.Half the distance to the centerline of the adjacent beam

3.The distance from beam centerline to edge of slab (Fig. 9.5)

NUMBER OF CONNECTORS REQUIRED
FOR BUILDING CONSTRUCTION

The total number of connectors to resist Vhis computed from Vh/q, where qis
the allowable shear for one connector, kip (kN). Values of qfor connectors in
buildings are given in structural design guides.
The required number of shear connectors may be spaced uniformly between
the sections of maximum and zero moment. Shear connectors should have at

fs

MDML

Str

0.66Fy

fs

MDML

Ss

0.76Fy

fs

MD

Ss



ML

Str

0.66Fy