Civil Engineering Reference
In-Depth Information
Minimum stirrup requirement gives
s
max
as:
A
v
f
y
142
(413
.
7)
s
max
=
0625
f
c
(MPa)
b
w
=
0625
√
68
4)
743 mm (29
.
3in
.
)
>
406 mm
0
.
0
.
.
95(152
.
(16 in
.
)
>
305 mm (12 in
.
) does not govern
Arrangement of stirrups along the beam
Table 8.2 shows the shear design calculations over one half-span of the beam under the column
UH. Since this girder is critical in flexural-shear at a section 3.05 m (10 ft) from the support,
we adopt the concept that 'transverse steel should be the same from the flexural-shear critical
section to the support'. Then we should provide #3 rebars with a spacing of 305 mm (12 in.)
in the whole region from the support to a distance of 4.27 m (14 ft) from the support. Beyond
4.27 m (14 ft), the spacing is increased to 406 mm (16 in.).
8.3.7.3 ACI and AASHTO Shear Design Solutions
The shear design calculations of the above example using the UH method are compared in
Table 8.2 with those designed by the ACI method (see Section 8.3.1.1) and the AASHTO
method (see Section 8.3.1.2). Table 8.2 records the crucial steps of shear design calculations
of these two methods under the column ACI and the column AASHTO. Detailed calculations
of shear design using ACI and AASHTO methods can be found in a report by Hsu
et al.
(2008).
In Table 8.2 under the column ACI, the required stirrups spacing is most critical at a distance
h
/2 from the support. The provided stirrup spacing of the #3 rebars is 102 mm (4 in. c/c) up to
a distance 1.22 m (4 ft) from the support. The spacing is thereafter increased to 203 mm (8 in.)
between 1.22 m (4 ft) and 2.44 m (8 ft). Beyond 2.44 m (8 ft) the spacing is further increased
to 610 mm (24 in.) up to midspan.
In Table 8.2 under the column ASHTO, the required stirrup spacing is most critical at a
distant
d
v
from the support. The provided stirrup spacings of the #3 rebars is 203 mm (8 in.
c/c) up to a distance 1.22 m (4 ft) from the support. The spacing is thereafter increased to
305 mm (12 in. c/c) up to a distance 3.66 m (12 ft) from the support. Beyond 3.66 m, the
spacing is 559 mm (22 in. c/c).
In summary, the ACI and AASHTO methods would predict the beam to fail in web-shear
failure near the support. The provided stirrup spacing will be small near the support and will
increase rapidly from the support to the one-quarter point of the beam. In other words, these
two shear design methods will result in excessive stirrups near the support and insufficient
stirrups near the quarter point of the beam. In contrast, the UH shear design method requires
a constant and moderate stirrup spacing from the support to about the one-third point of
the beam.
8.3.8 Three Shear Design Examples
The report by Hsu
et al.
(2008) also includes two more bridge design examples solved in detail
by the three shear design methods (UH, ACI, AASHTO). The bridge example given in Section
8.3.7 is called Example 1, and the other two examples are called Examples 2 and 3.
