Civil Engineering Reference
In-Depth Information
0.65 or 0.70 to 0.9 for columns supporting very small axial loads
0.65 for bearing on concrete
The sizes of these factors are rather good indications of our knowledge of the subject in
question. For instance, calculated nominal moment capacities in reinforced concrete mem-
bers seem to be quite accurate, whereas computed bearing capacities are more questionable.
For ductile or tension-controlled beams and slabs where
t
0.005, the value of
for bending is 0.90. Should
t
is not less than certain values. This situation is shown in Figure 3.5, which is a copy of
Figure R.9.3.2 in the ACI Commentary to the 2002 Code.
Members subject to axial loads equal to or less than
t
be less than 0.005 it is still possible to use the sections if
c
A
g
t
is
as low as 0.004 (ACI Section 10.3.5). Should the members be subject to axial loads
0.10
f
may be used when
c
A
g
0.10
f
t
values fall between 0.002
and 0.005, they are said to be in the transition range between tension-controlled and com-
pression-controlled sections. In this range
they may be used when
t
is as small as 0.002. When
values will fall between 0.65 or 0.70 and 0.90
as shown in the figure.
The procedure for determining
values in the transition range is described later in
this section.
You must clearly understand that the use of flexural members in this range is
usually uneconomical, and it is probably better, if the situation permits, to increase mem-
ber depths and/or decrease steel percentages until
t
is equal to or larger than 0.005.
If
this is done, not only will
values equal 0.9 but also steel percentages will not be so large
as to cause crowding of reinforcing bars. The net result will be slightly larger concrete
sections, with consequent smaller deflections. Furthermore, as we will learn in subsequent
chapters, the bond of the reinforcing to the concrete will be increased as compared to
cases where higher percentages of steel are used.
We have computed values of steel percentages for different grades of concrete and
steel for which
t
will exactly equal 0.005 and present them in Appendix Tables A.7 and
B.7 of this textbook. It is therefore desirable, under ordinary conditions, to design beams
with steel percentages that are no larger than these values, and we have shown them as
suggested maximum percentages to be used.
φ
= 0.57 + 67
t
ε
0.90
Spiral
φ
= 0.48 + 83
t
ε
0.70
φ
0.65
Other
Compression
controlled
Transition
Tension
controlled
ε
t
= 0.002
ε
t
= 0.005
Figure 3.5
Variation of
with net
tensile
t
and
c
/
d
for Grade 60
reinforcement and for prestressing
steel. (Printed with permission of
American Concrete Institute.)
d
d
= 0.375
= 0.600
Interpolation on c/d: Spiral
φ
φ
= 0.37 + 0.20/(c/d)
Other
= 0.23 + 0.25/(c/d)
