Civil Engineering Reference
In-Depth Information
Figure 8.16
Variation of normalized concrete shear with
a/d
8.3.3.3 'Contribution of Concrete' (
V
c
)
As discussed in Section 8.3.2.2, the
V
c
term in Equat
ion
(8.15) must be a function of the
shear-span-to-depth ratio
a/d
, the strength of concrete
f
c
and the web area
b
w
d
. We can now
implement the variable
a/d
into a new shear strength equation using the UH test results of
beams B1-B5, as well as the beams of Hernandez (1958), MacGregor
et al
. (1960), Mattock
and Kaar (1961), Bruce (1962), Hanson and Hulsbos (1965), Lyngberg (1976), Elzanaty
et al
.
(1986), Robertson and Durrani (1987), Kaufman and Ramirez (1988), and Shahawy and
Batchelor (1996).
The concrete shear contribution,
V
c
, of all the specimens were calculated by subtracting the
steel contribution
V
s
as per Equation (
8.1
6), from the total shear capacities of the beams. The
normalized concrete shear stress
V
c
/
f
c
b
w
d
of the specimens was ob
tai
ned thereafter and its
variation versus
a/d
was plotted in Figure 8.16. A conservative
V
c
/
f
c
b
w
d
versus
a/d
curve
can be expressed as:
d
)
0
.
7
f
c
(MPa)
b
w
d
833
f
c
(MPa)
b
w
d
1
.
17
V
c
=
≤
0
.
(8.17)
(
a
/
where
b
w
=
width of the web of the prestressed beam
d
=
effective depth from the centroid of the tendons to the top compression fiber of the
prestressed beam. The value of
d
is not taken to be less than 80% of the total depth of
the beam.
d
)
−
0
.
7
f
c
b
w
d
expression shown in Equation (8.17) was substantiated
by the large-size test specimens of Mattock and Kaar (1961) with beam height of 648 mm
The
V
c
=
1
.
17 (
a
/
