Civil Engineering Reference
In-Depth Information
In SI units
f
c
120
w
V
u
M
u
b
w
d
7
c
b
w
d
V
c
0.3
f
A
s
/
b
w
d
and
M
u
is the factored moment occurring simultane-
ously, with
V
u
the factored shear at the section considered. The quantity
V
u
d
/
M
u
may not
be taken to be greater than unity in computing
V
c
by means of the above expressions.
From these expressions it can be seen that
V
c
increases as the amount of reinforcing
(represented by
In these expressions
w
w
) is increased. As the amount of steel is increased, the length and width
of cracks will be reduced. If the cracks are kept narrower, more concrete is left to resist
shear and there will be closer contact between the concrete on opposite sides of the
cracks. Hence there will be more resistance to shear by friction (called
aggregate inter-
lock
) on the two sides of cracks.
Although this more complicated expression for
V
c
can easily be used for computer
designs, it is quite tedious to apply when hand-held calculators are used. The reason is
that the values of
w
,
V
u
, and
M
u
are constantly changing as we move along the span, re-
quir
in
g the computation of
V
c
at numerous positions. As a result, the alternate value
is normally used. If the same member is to be constructed many times, the use
of the more complex expression may be justified.
c
b
w
d
2
f
8.4
LIGHTWEIGHT CONCRETE
If the shear strength of a lightweight concr
ete
section is being determined, the term is
to be replaced with
f
ct
/6.7 not to exceed ,
wh
ere
f
ct
is the split-cylinder strength of the
concrete. If
f
ct
is not available, all values of affecting
V
c
and
M
cr
are to be multiplied
by 0.75 for “all-lightweight concrete” and by 0.85 for “sand-lightweight concrete.” When
partial sand replacement is used, linear interpolation between the values is permitted.
These provisions are made in ACI Section 11.2.
c
f
c
f
c
f
8.5
SHEAR CRACKING OF REINFORCED CONCRETE BEAMS
Inclined cracks can develop in the webs of reinforced concrete beams either as extensions
of flexural cracks or occasionally as independent cracks. The first of these two types is the
flexure-shear crack
, an example of which is shown in Figure 8.1. These are the ordinary
types of shear cracks found in both prestressed and nonprestressed beams. For them to
occur, the moment must be larger than the cracking moment and the shear must be rather
large. The cracks run at angles of about 45
with the beam axis and probably start at the
top of a flexure crack. The approximately vertical flexure cracks shown are not dangerous
unless a critical combination of shear stress and flexure stress occurs at the top of one of
the flexure cracks.
Occasionally, an inclined crack will develop independently in a beam, even though
no flexure cracks are in that locality. Such cracks, which are called
web-shear cracks
,
will sometimes occur in the webs of prestressed sections, particularly those with large
flanges and thin webs. They also sometimes occur near the points of inflection of con-
