Civil Engineering Reference
In-Depth Information
2. Points 2-4
⎡
⎤
⎛
⎜
C
2
d
i
d
1
⎞
⎟
φ
P
n
=φ
C
1
d
1
b
+
87
∑
n
i = 1
A
si
1
−
(kips)
⎢
⎥
⎣
⎦
⎡
⎤
⎛
⎜
−
β
1
d
1
C
2
⎞
⎟
+
⎛
⎜
C
2
d
i
⎞
⎟
h
2
−
⎛
⎜
⎞
⎟
(ft-kips)
φ
M
n
=φ
0.5C
1
d
1
bh
87
∑
n
i = 1
A
si
1
−
d
i
/12
⎢
⎥
d
1
⎣
⎦
⎛
⎜
⎞
⎟
0.003
0.003
C
1
=
0.85
f
c
β
1
ʹ
where
−ε
S1
0.003
−ε
S1
0.003
C
2
=
To ensure that the stress in the reinforcement at each layer
≤
f
y
= 60 ksi:
⎛
⎜
⎞
⎟ ≤
C
2
d
i
d
1
60
87
=
1
−
0.69
0.85
≥β
1
=
1.05
−
0.05
f
c
ʹ
≥
0.65
Where :
h = column dimension in the direction of bending, in.
b = column dimension perpendicular to the direction of bending
d
1
= distance from compression face to centroid of reinforcing steel in layer 1 (layer closest to tension side) in.
d
i
= distance from compression face to centroid of reinforcing steel in layer i in.
A
si
= total steel area in layer i, in.
2
n = total number of layers of reinforcement
ε
s1
= steel strain in layer 1
ε
i
= steel strain in layer i
Values for C
1
and C
2
are presented in Table 5-1
Point 5 Pure bending
In lieu of Iterative procedure to determine
φ
Mn, the simplified approach introduced in Chapter 3
may be used.
Table 5-1 Constants for strain compatibility analysis - Rectangular section
C
2
for
f
c
ʹ
(ksi)
4
5
6
7
8
9
10
11
12
f
s1
/f
y
ε
s1
f
c
ʹ
all
Point 2 2.89
3.40
3.83
4.17
4.42
4.97
5.53
6.08
6.63
1.00
0
0
C1 Point 3 2.15
2.53
2.84
3.10
3.29
3.70
4.11
4.52
4.93
1.34
-0.5
-0.001
Point 4
1.71
2.01
2.26
2.47
2.62
2.94
3.27
3.60
3.92
1.69
-1
-0.002
β
1
0.85
0.8
0.75
0.7
0.65
0.65
0.65
0.65
0.65
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