CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 135

The excess shear vvcshould not exceed 4.4 in sections with web rein-
forcement. Stirrups and bent bars should be capable of resisting the excess
shearVVvcbd.
The area required in the legs of a vertical stirrup, in^2 (mm^2 ), is

(5.63)

wheresspacing of stirrups, in (mm); and fvallowable stress in stirrup
steel, (lb/in^2 ) (MPa).
For a single bent bar or a single group of parallel bars all bent at an angle 
with the longitudinal axis at the same distance from the support, the required
area is

(5.64)

For inclined stirrups and groups of bars bent up at different distances from the
support, the required area is

(5.65)

Stirrups in excess of those normally required are provided each way from the
cutoff for a distance equal to 75 percent of the effective depth of the member.
Area and spacing of the excess stirrups should be such that

(5.66)

where Avstirrup cross-sectional area, in^2 (mm^2 )
bwweb width, in (mm)
sstirrup spacing, in (mm)
fyyield strength of stirrup steel, (lb/in^2 ) (MPa)

Stirrup spacing sshould not exceed d/8b, where bis the ratio of the area of
bars cut off to the total area of tension bars at the section and dis the effec-
tive depth of the member.

ULTIMATE-STRENGTH DESIGN OF RECTANGULAR
BEAMS WITH COMPRESSION BARS

The bending-moment capacity of a rectangular beam with both tension and
compression steel is

Mu0.90(AsAs)fyd (5.67)

a

2 

Asfy(dd)

Av 60

bws

fy

Av

Vs

fvd(sincos)

Av

V

fv sin 

Av

Vs

fvd

fc