Structural Concrete - Hassoun

8.6 Deep Members 313
Centroid of
strut
12"
w sb
39.7° 39.7°
B
A
w st
w s = 6.4"
w t = 7.2"
Centroid of tie
39.7°
Centroid of
strut
16"
x
(a)
(b)
Figure 8.18 (a) Node zone at B or C. (b) Node zone at A or D.
Spacing for both horizontal and vertical reinforcement shall not exceed d/5 = 7.2 in. or 12 in.,
therefore use s = 7in.
A v = A vh = 0.0025 × 12 × 7 = 0.21 in. 2 (per 7in.)
A v = A vh = 0.21 × 7∕12 = 0.36 in. 2 (per 12in.)
Use No. 4 at 12 in.: A s = 2(0.2) = 0.4 in. 2 (two legs)
a. Vertical Bars: From Fig. 8.18b, the angle between the vertical bars and strut is equal to 50.3 ∘
( )
Asi
sinγ = 0.4 sin 50.3 = 0.0021
bs 12 × 12
b. Horizontal Bars: From Fig. 8.18b, the angle between the vertical bars and strut = 39.7 ∘
( )
Asi
sinγ = 0.4 sin 39.7 = 0.0017
bs 12 × 12
∑ ( )
A si
sinγ = 0.0021 + 0.0017 = 0.0038 > 0.003
b s
9. Design of the horizontal tie AD:
Required tie reinforcement
F u = φA s f y A s = 192.5 = 4.27 in.2
0.75 × 60
Provide six no. 8 bars in three rows, A st = 4.8 in. 2
10. Calculate anchorage length:
Anchorage length is measured from the point beyond the extended nodal zone:
tan 39.7 ∘ = w t
2x = 7.2
2x
x = 4.5in.
Available anchorage length: 4.5 + 16 − 1.5 = 19 in.