CIVIL ENGINEERING FORMULAS

CONCRETE FORMULAS 141

The spacing of closed stirrups, however, should not exceed (x 1 y 1 )/4 or 12 in
(304.8 mm). Torsion reinforcement should be provided over at least a distance
ofdbbeyond the point where it is theoretically required, where bis the
beam width.
At least one longitudinal bar should be placed in each corner of the stirrups.
Size of longitudinal bars should be at least No. 3, and their spacing around the
perimeters of the stirrups should not exceed 12 in (304.8 mm). Longitudinal bars
larger than No. 3 are required if indicated by the larger of the values of Alcom-
puted from the following two equations:

(5.95)

(5.96)

In the second of the preceding two equations, 50bws/fymay be substituted for
2 At.
The maximum allowable torsion is Tu 5 Tc.

WORKING-STRESS DESIGN FOR TORSION

Torsion effects should be considered whenever the torsion Tdue to service
loads exceeds

(5.97)

where x^2 ysum for the component rectangles of the section of the product
of the square of the shorter side and the longer side of each rectangle. The
allowable torsion stress on the concrete is 55 percent of that computed from the
precedingTcequation. Spacing of closed stirrups for torsion should be computed
from

(5.98)

whereAtarea of one leg of closed stirrup

t0.66 , but not more than 1.50

tcallowable torsion stress on concrete

x 1 shorter dimension ctocof legs of closed stirrup

y 1 longer dimension ctocof legs of closed stirrup

0.33y 1

x 1

s

3 Attx 1 y 1 fv

(vtvtc) x^2 y

T0.55(0.5fc x^2 y)

Al

400 xs

fy 

Tu

(TuVu/3Ct)

 2 At

x 1 y 1

s 

Al 2 At

x 1 y 1

s