Structural Concrete - Hassoun

5.11 Examples Using SI Units 221
5. Distance from the face of the support at which 1 φV 2 c = 65 kN is
x ′ 291 − 65
= (3) =2.33 m (from triangles)
291
6. Design of stirrups:
a. Choose stirrups 10 mm in diameter with two branches (A s = 78.5 mm 2 ).
A v = 2 × 78.5 = 157 mm 2
Spacing S 1 = A y f yt d 157 × 280 × 550
= = 168.5mm< 600 mm
V s 143.5 × 10 3
b. Check for maximum spacing of d/4:
S max =
{ (
1 d for V 2 s ≤ 0.33 √ )
f c
′ bd
1
d for If V 4 s > (0.33√ f c ′ )bd
bd(0.33 √ √
f c ′ )=0.33 28 × 350 × 550 = 336.1kN
Actual V s = 143.5 kN < 336.1 kN. Therefore, S max is limited to d/2 = 275 mm.
7. The shear reinforcement, stirrups 10 mm in diameter and spaced at 160 mm, will be needed
only for a distance d = 0.55 m from the face of the support. Beyond that, the shear stress V s
decreases to zero at a distance x = 1.66 m when φV c = 130 kN. It is not practical to provide
stirrups at many different spacings. One simplification is to find out the distance from the face of
the support where maximum spacing can be used and then only two different spacings may be
adopted:
Maximum spacing = 1 d = 275 mm
2
V s (for s max = 275 mm) = A v f yt d
S
=
φV s = 87.9 × 0.75 = 65.94 kN
157 × 0.280 × 550
275
= 87.9kN
The distance from the face of the support where S max = 275 mm can be used (from the triangles):
291 −(130 + 65.94)
x 1 = (3) =0.98 m
291
Then, for 0.98 m from the face of the support, use stirrups 10 mm in diameter at 160 mm, and
for the rest of the beam, minimum stirrups (with maximum spacing) can be used.
8. Distribution of stirrups:
One stirrup at S 2 = 160 = 80 mm
2
Six stirrups at 160 mm = 960 mm
Six stirrups at 270 mm = 1620 mm
Total = 1040 mm = 1.04 m > 0.98 m
Total = 2660 mm = 2.66 m < 3m
The last stirrup is 3 − 2.66 = 0.34 m = 340 mm from the centerline of the beam, which is adequate.
A similar stirrup distribution applies to the other half of the beam, giving a total number of
stirrups of 28.
The other examples in this chapter can be worked out in a similar way using SI equations.