Civil Engineering Reference
In-Depth Information
Using the US customary system, Equation (8.18) becomes:
14
V
u
d
M
u
0
.
7
A
v
f
y
d
1
f
c
(psi)
b
w
d
V
u
=
+
s
−
+
V
p
(8.18a)
M
u
)
0
.
7
where 14 (
V
u
d
10.
The additional shear strength contributed by the vertical component of prestressing force
V
p
of draped strands is also taken into account in Equation (8.18) (see last paragraph of
Section 8.3.2.2). Following the ACI Code (2008) and the AASHTO Specifications (2007),
V
p
is calculated from the effective prestressing force after loss, because this force appears to give
a conservative estimate of the observed additional shear strength.
It should be noted that the
V
p
term in Equation (8.18) is applicable to prestressed beams
failing in web-shear as well as in flexural-shear. This is not the same as the provisions of the
ACI Code, which utilizes the vertical component of the prestressing force in draped strands in
the case of web-shear failure only, and not in the case of flexural-shear failure.
/
≤
8.3.4 Maximum Shear Strength
8.3.4.1 Maximum Shear Strengths in Code Provisions
Since Equation (8.18) is based on the yielding of transverse steel reinforcement, a maximum
shear strength
V
n
,
max
must be defined to ensure that transverse steel will yield before the web
crushing of concrete. However,
V
n
,
max
in the ACI Code and the AASHTO Specifications are
quite different.
ACI Code
ACI-ASCE Committee 326, Shear (1962) first proposed the following equation, which was
later incorporated into the ACI Code (1963) for nonprestressed beams:
83
f
c
(MPa)
b
w
d
or 10
f
c
(psi)
b
w
d
V
n
,
max
=
0
.
(8.19)
Equation (8.19) was slightly liberalized in 1971 for application to both nonprestressed and
prestressed concrete beams (ACI, 1971), in the form of limiting the
V
s
term to a 'maximum
contribution of steel':
66
f
c
(MPa)
b
w
d
or 8
f
c
(psi)
b
w
d
V
s
,
max
=
0
.
(8.20)
17
f
c
(MPa)
b
w
d
(or 2
f
c
(psi)
b
w
d
), then the
V
n
,
max
in 197
1 Code is
identical t
o that i
n the 1963 Code. Since the
V
c
term could be greater than
0
If
V
c
is taken conservatively as 0
.
17
f
c
(MPa)
b
w
d
(or 2
f
c
(psi)
b
w
d
), the
V
n
,
max
for p
restressed be
ams in
1971 ACI Code
is allowed to be somewhat greater than 0
.
83
f
c
(MPa)
b
w
d
(or 10
f
c
(psi)
b
w
d
). The ACI
formula for
V
s
,
max
has continued to be used up to the present time (ACI, 2008).
.
AASHTO Specifications
The current AASHTO Specifications (2007) require:
25
f
c
b
w
d
v
225
f
c
b
w
d
V
n
,
max
=
0
.
or 0
.
,
(8.21)
if
d
v
isassumedtobe0.9
d
.
