Civil Engineering Reference
In-Depth Information
Equations (8.4)-(8.8) show that the ACI shear provisions are quite complicated. The com-
plexity stems from two sources. First, the
V
c
term is taken as the lesser of
V
ci
or
V
c
w
.Thisis
because the ACI provisions recognize two types of shear failure forces,
V
ci
for flexural shear
failure and
V
c
w
for web shear failure. Second,
V
c
w
is assumed to be the cracking strength and
V
ci
is assumed to be the sum of a cracking strength plus an empirical post-cracking strength.
Since the cracking strengths for
V
ci
or
V
c
w
are strongly affected by the prestress force, the
ACI shear strength becomes a complicated function of the prestress force as shown above.
8.3.1.2 AASHTO (2007) Shear Design Provisions
V
n
=
V
c
+
V
s
(8.9)
β
f
c
(
MPa
)
b
v
d
v
V
c
=
0
.
083
(8.10)
β
v
u
/
f
c
and
ε
x
where
is a function of
A
v
f
y
d
v
cot
θ
V
s
=
(8.11)
s
f
c
where
ε
x
An engineer must calculate a factor
θ
is a function of
v
u
/
and
β
for the
V
c
term and a crack angle
θ
for the
V
s
term.
f
c
Both
β
and
θ
are functions of the shear stress ratio
v
u
/
and the longitudinal strain
ε
x
in
the web. The strain
ε
x
is calculated at the mid-depth under the combined action of bending
moment, shear force and axial force acting on the member:
5
V
u
−
V
p
cot
|
M
u
|
d
v
+
0
.
5
N
u
+
0
.
θ
−
A
ps
f
po
ε
x
=
2
E
s
A
s
+
E
ps
A
ps
(8.12)
v
u
is calculated by
and the shear stress
V
u
−
φ
V
p
v
u
=
(8.13)
φ
b
w
d
v
are obtained from Table 8.1 using an iterative procedure.
Two points should be noted: First, the AASHTO shear provisions do not distinguish between
web-shear and flexural-shear failure modes. As a result, beams in shear are always critical in
web-shear failure mode near the supports, where the largest shear stresses are located. Second,
even without recognizing the two modes of failure, Equations (8.9)-(8.13) and Table 8.1 show
that the AASHTO shear provisions are more complicated than the ACI shear provisions. To
make matters worse, the tables (or graphs) provided by the AASHTO specifications give no
physical meaning.
Then,
β
and
θ
8.3.2 Prestressed Concrete I-Beam Tests at University of Houston
8.3.2.1 Test Set-up and Test Variables
Five full-scale prestressed concrete I-beams, B1-B5, were tested at the University of Houston
(UH), as shown in Figure 8.9. The cross-sections of these beams, known as TxDOT Type
A, are shown in Figure 8.10. Each beam has twelve 7-wire, low-lax prestressing strands of
