CIVIL ENGINEERING FORMULAS

140 CHAPTER FIVE

ULTIMATE-STRENGTH DESIGN FOR TORSION

When the ultimate torsion Tuis less than the value calculated from the Tuequa-
tion that follows, the area Avof shear reinforcement should be at least

(5.90)

However, when the ultimate torsion exceeds Tucalculated from the Tuequa-
tion that follows, and where web reinforcement is required, either nominally or
by calculation, the minimum area of closed stirrups required is

(5.91)

whereAtis the area of one leg of a closed stirrup resisting torsion within a
distances.
Torsion effects should be considered whenever the ultimate torsion exceeds

(5.92)

where capacity reduction factor0.85
Tuultimate design torsional moment
x^2 ysum for component rectangles of section of product of square of
shorter side and longer side of each rectangle (where T section
applies, overhanging flange width used in design should not exceed
three times flange thickness)

The torsion Tccarried by the concrete alone should not exceed

(5.93)

whereCtbwd/ x^2 y.
Spacing of closed stirrups for torsion should be computed from

(5.94)

whereAtarea of one leg of closed stirrup
t0.660.33y 1 /x 1 but not more than 1.50
fyyield strength of torsion reinforcement
x 1 shorter dimension ctocof legs of closed stirrup
y 1 longer dimension ctocof legs of closed stirrup

s

At fytx 1 y 1

(TuTc)

Tc

0.8 2 fc x^2 y

21 (0.4Vu/CtTu)

2

Tu 0.5fc x^2 y

Av 2 At

50 bws

fy

Av 50

bws

fy