Civil Engineering Reference
In-Depth Information
The values of various quantities required for shear design are as follows:
h
girder
=
711.2 mm (28 in.)
h
composite
=
914.4 mm (36 in.)
l
=
12.2 m (40 ft)
b
w
=
152.4 mm (6 in.)
f
c
=
68.95 MPa (10 ksi)
f
y
=
413.7 MPa (60 ksi)
A
v
=
142.0 mm
2
(0.22 in.
2
)
A
ps
=
1777 mm
2
(2.75 in.)
w
u
=
131 kN/m (9 kips/ft)
V
p
=
0
φ
for shear
=
0.9
φ
for bending
=
0.95
w
u
l
2
8
2
2
1
φ
1
131
×
12
.
Maximum moment at midspan of girder:
M
u
=
=
0
.
95
8
=
2 565 kN m (1 891 kip ft)
<
2 617 kN m (1 929 kip ft) OK
8.3.7.2 UH Shear Design Solution
Calculate effective depth
d
Distance of the centroid of prestressing strands from bottom of beam
=
107 mm (4.2 in.)
Effective depth of the composite section,
d
=
h
- 107
=
914.4 - 107
=
807 mm (31.8 in.)
d
min
=
0
.
8
h
=
0
.
8
×
914
.
4
=
732 mm (28
.
8in
.
)
<
807 mm (31
.
8in.)
d
=
807 mm (31
.
8 in) governs
Check cross section at distance
d
from support
The size of beam cross-section is checked at the critical section a distance
d
from the support.
Shear force at critical section
w
u
l
2
−
w
u
d
131
×
12
.
2
807
1000
V
u
=
=
−
131
×
=
693 kN (156 kips)
2
Maximum shear capacity at critical section
33
f
c
(MPa)
b
w
d
√
68
φ
V
n
,
max
=
φ
1
.
=
0
.
9
×
1
.
33
×
.
95
×
152
.
4
×
807
=
1222 kN (275 kips)
>
693 kN (156 kips) OK
The size of the chosen cross section is adequate.
Calculate V
c
The amounts of transverse steel at all the chosen sections along one-half of the beam are
calculated using a spreadsheet, and the crucial values are shown in Table 8.2 under the column
UH. The section that requires the smallest stirrup spacing is found to be at a distance 3.05 m
(10 ft) from the support. Physically, failure at the quarter point of a simple span represents a
typical flexural-shear failure mode. Calculations of
V
c
at this critical section are as follows:
Factored shear force at the section
w
u
l
2
−
w
u
x
131
05
×
12
.
2
V
u
=
=
−
131
×
3
.
=
400 kN (90 kips)
2
