Civil Engineering Reference
In-Depth Information
(25.5 in.). The shear strengths of their beams agreed very well with the proposed expression
in Figure 8.16 for
a/d
ratios
of 4.5, 3.2
5, 2.0, 1.5, and all the way down to 1.0.
The upper limit of 0
833
f
c
(MPa)
b
w
d
in Equation (8.17) is imposed for simply supported
beams to ensure that the end anchorage will be sufficient to produce yielding of the stirrups,
as observed in the web-shear failure of beams B1-B3. Mattock and Kaar tested continuous
beams, which did not have the anchorage problems at beam ends associated with simply
supported beams.
.
8.3.3.4 Shear/bond Failure at Beam Ends
Shahawy and Batchelor (1996) showed that the prestressed strands at the ends of AASHTO
Type II pretensioned concrete beams would slip before the web crushing of shear failures.
They referred to this type of failure as 'shear/bond failure'. When
a/d
ratio is greater than about
1.6, the bond slip did not appear to have a noticeable effect on the shear strengths. However, in
their B1 series of 10 beams, where
a/d
ratios varied from 1.37 to 1.52, the bond slip appeared
to have reduced the shear strengths. It was not clear, however, whether the transverse stirrups
in the shear span had yielded.
Ma
et al.
(2000) tested two NU1100 pretensioned beams with
a/d
ratios varying from 1.16
to 1.28. At both ends of their beam A, the strands were extended beyond the end face, bent
upward, and securely anchored into a large concrete diaphragm attached to the end face. Since
bond slip was not allowed to occur, beam A failed in web crushing, a typical shear failure, at
both ends. One failed end of beam A was then sawed off, leaving the ends of strands flush
with the end face. Application of shear loads then produced a 'shear/bond' failure, rather than
a web crushing failure. The 'shear/bond' failure load of the saw-cut end was 25% less than
the web-crushing failure load of the ends with perfectly anchored strands.
Since shear failures at beam ends (
a/d
ratios less than 1.6) are significantly affected by the
bond slip of prestressing strands, the limitation in Equation (8-17) at low
a/d
ratios must be
a function of the anchorage length of the strands. A satisfactory anchorage length for shear
should be one that ensures the yielding of the transverse stirrups at shear failure in the web.
The upper limit in Equation (8.17) for
a/d
less than 1.6 appears to be valid for the TxDOT
Type A beams tested at UH. The UH beams have twelve 7-wire strands of 12.7 mm (0.5 in.
diameter, with an extension of 152 mm (6 in.) beyond the support resultant and a supporting
plate of 152 mm (6 in.) wide. More research is required to determine a satisfactory anchorage
length of prestressed strands to prevent shear/bond failure.
8.3.3.5 Total Shear Strengths
Assuming that the transverse steel yields at failure, the final equation for the shear strength
of prestressed I-beams is obtained by substituting Equations (8.16) and (8.17) into Equation
(8.15) and by generalizing the ratio
a/d
to become
M
u
/
V
u
d
:
17
V
u
d
M
u
0
.
7
A
v
f
y
d
1
f
c
(MPa)
b
w
d
V
u
=
.
+
s
−
+
1
V
p
(8.18)
M
u
)
0
.
7
where 1
.
17 (
V
u
d
/
≤
0
.
833.
