Page 199 - Civil Engineering Formulas

CONCRETE FORMULAS 135

The excess shear v v should not exceed 4.4 f c in sections with web rein-
c
forcement. Stirrups and bent bars should be capable of resisting the excess
shear V V v bd.
c
2
2
The area required in the legs of a vertical stirrup, in (mm ), is
V s
A v (5.63)
f v d
where s spacing of stirrups, in (mm); and f allowable stress in stirrup
v
2
steel, (lb/in ) (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
V
A v (5.64)
f v sin
For inclined stirrups and groups of bars bent up at different distances from the
support, the required area is
V s
A v (5.65)
f v d(sin cos )
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
b w s
A v 60 (5.66)
f y
2
2
where A stirrup cross-sectional area, in (mm )
v
b web width, in (mm)
w
s stirrup spacing, in (mm)
2
f yield strength of stirrup steel, (lb/in ) (MPa)
y
Stirrup spacing s should not exceed d/8 , where is the ratio of the area of
b
b
bars cut off to the total area of tension bars at the section and d is 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

M u 0.90 (A s A s ) f y d a 2 A s f y (d d ) (5.67)