Civil Engineering Reference
In-Depth Information
In this expression,
V
d
is the shear at the section in question due to service dead load,
M
max
is the factored maximum bending moment at the section due to externally applied design
loads,
V
i
is the shear that occurs simultaneously with
M
max
, and
M
cr
is the cracking mo-
ment, which is to be determined as follows:
I
y
t
c
f
pe
f
d
)
M
cr
(6
f
(ACI Equation 11-11)
where
I
the moment of inertia of the section that resists the externally applied loads
y
t
the distance from the centroidal axis of the gross section (neglecting the rein-
forcing) to the extreme fiber in tension
f
pe
the compressive stress in the concrete due to prestress after all losses at the ex-
treme fiber of the section where the applied loads cause tension
f
d
the stress due to unfactored dead load at the extreme fiber where the applied
loads cause tension
From a somewhat simplified principal tension theory, the shear capacity of a beam
is eq
ua
l to the value given by the following expression but need not be less than
c
b
w
d
.
1.7
f
c
0.3
f
pc
)
b
w
d
V
p
V
cw
(3.5
f
(ACI Equation 11-12)
In this expression,
f
pc
is the calculated compressive stress (in pounds per square inch) in
the concrete at the centroid of the section resisting the applied loads due to the effective
prestress after all losses have occurred. (Should the centroid be in the flange,
f
pc
is to be
computed at the junction of the web and flange.)
V
p
is the vertical component of the ef-
fective prestress at the section under consideration. Alternately, the Code (11.4.2.2)
states that
V
cw
may be taken as the shear force that corresponds to a multiple of d
ea
d load
plus live load, which results in a calculated principal tensile stress equal to at the
centroid of the member or at the intersection of the flange and web if the centroid falls in
the web.
A further comment should be made here about the computation of
f
pc
for pretensioned
members, since it is affected by the transfer length. The Code (11.4.4) states that the
transfer length can be taken as 50 diameters for strand tendons and 100 diameters for wire
tendons. The prestress force may be assumed to vary linearly from zero at the end of the
tendon to a maximum at the aforesaid transfer distance. If the value of
h
/2 is less than the
transfer length, it is necessary to consider the reduced prestress when
V
cw
is calculated
(ACI 11.4.3).
c
4
f
19.11
DESIGN OF SHEAR REINFORCEMENT
Should the computed value of
V
u
exceed
V
c
, the area of vertical stirrups (the Code not
permitting inclined stirrups or bent-up bars in prestressed members) must not be less than
A
v
as determined by the following expression from the Code (11.5.6.2):
A
v
f
y
d
V
s
(ACI Equation 11-15)
s
