Page 204 - Civil Engineering Formulas

140 CHAPTER FIVE

ULTIMATE-STRENGTH DESIGN FOR TORSION

When the ultimate torsion T is less than the value calculated from the T equa-
u
u
tion that follows, the area A of shear reinforcement should be at least
v
b w s
A v 50 (5.90)
f y
However, when the ultimate torsion exceeds T calculated from the T equa-
u
u
tion that follows, and where web reinforcement is required, either nominally or
by calculation, the minimum area of closed stirrups required is
50b w s
A v 2A t (5.91)
f y
where A is the area of one leg of a closed stirrup resisting torsion within a
t
distance s.
Torsion effects should be considered whenever the ultimate torsion exceeds
T u 0.5 f c
x y (5.92)
2
where capacity reduction factor 0.85
T ultimate design torsional moment
u
2

x y sum 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 T carried by the concrete alone should not exceed
c
2
f
0.8 2 c
x y
T c (5.93)
2 1 (0.4V u /C t T u ) 2
2
where C b d/
x y.
t
w
Spacing of closed stirrups for torsion should be computed from
A t f y t x 1 y 1
s (5.94)
(T u T c )
where A area of one leg of closed stirrup
t
0.66 0.33y /x but not more than 1.50
1
t
1
f yield strength of torsion reinforcement
y
x shorter dimension c to c of legs of closed stirrup
1
y longer dimension c to c of legs of closed stirrup
1