Civil Engineering Reference
In-Depth Information
f
y
12, 000 *
⎡
⎢
0.5
ρ
f
y
⎤
⎥
=
60, 000
12, 000
0.5(0.0125)(60)
0.85
⎡
⎢
⎤
1
−
1
−
⎥
=
4.45
0.85
f
c
ʹ
×
4
*To convert M
u
from ft-kips to in.-lbs
Therefore,
M
u
M
u
M
u
4d
A
s
=
d(constant)
=
d
=
φ
0.9
×
4.45
×
For › = 4000 psi and f
y
= 60,000 psi:
M
u
**
4d
A
s
=
**Note: this equation is in mixed units: M
u
is in ft-kips, d is in in. and A
s
is in sq in.
For all values of
< 0.0125, the simplified A
s
equation is slightly conservative. The maximum deviation in
A
s
is less than + 10% at the minimum and maximum useful tension steel ratios.
3.9
ρ
For members with
reinforcement ratios in the range of approximately 1% to 1.5%, the error is less than 3%.
The range of change in the constant in the denominator in the above equation is very narrow for different
concrete strengths; this allows the use of the above equation for approximate reinforcement area estimination
with other concrete strengths.
The simplified A
s
equation is applicable for rectangular cross sections with tension reinforcement only.
Members proportioned with reinforcement in the range of 1% to 1.5% will be well within the code limits for
singly reinforced members. For positive moment reinforcement in flanged floor beams, A
s
is usually computed
for a rectangular compression zone; rarely will A
s
be computed for a T-shaped compression zone.
The depth of the rectangular compression zone, a, is given by:
A
s
f
y
0.85
a
=
f
c
b
e
ʹ
where b
e
= effective width of slab as a T-beam flange (ACI 8.12).
The flexural member is designed as a rectangular section whenever h
f
≥
a where h
f
is the thickness of the slab
(i.e., flange thickness).
For more accurate calculations, Figure 3-4 shows values for the constant required to calculate the reinforcement
for different concrete strengths and reinforcement ratio. It is important to note that Figures 3-3 and 3-4 can
be used for sizing and reinforcement calculations for rectangular sections for any concrete strength and
reinforcement ratio.
3.5
REINFORCING BAR DETAILS
The minimum and maximum number of reinforcing bars permitted in a given cross section is a function of
cover and spacing requirements given in ACI 7.6.1 and ACI 3.3.2 (minimum spacing for concrete placement),
ACI 7.7.1 (specified cover for protection of reinforcement), and ACI 10.6 (maximum spacing for control of
Search WWH ::
Custom Search