Civil Engineering Reference
In-Depth Information
3.6.1 Example: Design for Shear Reinforcement
The example shown in Fig. 3-13 illustrates the simple procedure for selecting stirrups using design values for
V
c
and V
s
.
(1) Design data: › = 4000 psi, f
y
= 60,000 psi, w
u
= 7 kips/ft.
(2) Calculations: V
u
@ column centerline:
w
u
˜/2 = 7
24/2 = 84.0 kips
V
u
@ face of support:
84 - 1.17(7) = 75.8 kips
V
u
@ d from support face (critical section):
75.8 - 2(7) = 61.8 kips
(
φ
V
c
+
φ
V
s
)
max
:
0.48 b
w
d = 0.48(12)(24) = 138.2 kips
φ
V
c
:
0.095 b
w
d= 0.095(12)(24) = 27.4 kips
φ
V
c
/2:
0.048 b
w
d = 0.048(12)(24) = 13.80 kips
(3) Beam size is adequate for shear strength, since 138.2 kips > 61.8 kips (also see Fig. 3-12).
V
s
(required)
= 61.8 - 27.4 = 34.4 kips. From Table 3-9, No.4 @ d/2 = 12 in. is adequate for full length where stirrups
are required since
φ
V
s
= 36 kips > 34.4 kips. Length over which stirrups are required is (75.8 - 13.8)/7
= 8.86 ft from support face.
φ
Check maximum stirrup spacing:
φ
4
f
c
b
w
d
ʹ
=
0.19b
w
d
=
54.6 kips
Since
φ
V
s
= 36 kips < 54.6 kips, the maximum spacing is the least of the following:
⎧
d/2
=
12in.(governs)
⎪
s
max
=
24in.
A
v
f
y
/50b
w
=
⎨
⎪
⎪
40in.
⎩
Use 10-No.4 U-stirrups at 12 in. at each end of beam.
The problem may also be solved graphically as shown in Fig. 3-13.
φ
V
s
for No.3 stirrups at d/2, d/3, and d/4
are scaled vertically from
V
s
values (20 kips, 30 kips, and 40 kips) with
the shear diagram automatically sets the distances where the No.3 stirrups should be spaced at d/2, d/3, and d/4.
The exact numerical values for these horizontal distances are calculated as follows (although scaling from the
sketch is close enough for practical design):
φ
V
c
. The horizontal intersection of the
φ
No.3
@ d/4 = 6 in.: (75.8 - 57.4)/7 = 2.63 ft (31.5 in.)
use 6 @ 6 in.
@ d/3 = 8 in.: (57.4 - 47.4)/7 = 1.43 ft (17.0 in.)
use 2 @ 8 in.
@ d/2 = 12 in.: (47.4 - 13.8)/7 = 4.8 ft (57.6 in.)
use 5 @ 12 in.
A more practical solution may be to eliminate the 2 @ 8 in. and use 9 @ 6 in. and 5 @ 12 in.
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