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9.15 Using the column interaction diagrams in Appendix A (
c
f′=
4000 psi and
y
f=
60,000 psi) with ρt
approximately equal to 2%, design square columns with equal reinforcement on all sides to carry
each of the following loads and select the longitudinal and transverse reinforcement:
(a) Pu = 2000 kips and Mu = 160 ft-kips
(b) Pu = 1000 kips and Mu = 220 ft-kips
(c) Pu = 500 kips and Mu = 160 ft-kips
(a) Pu = 2000 kips and Mu = 160 ft-kips
29 in.bh
= =
(b) Pu = 1000 kips and Mu = 220 ft-kips
Assume h = 20 in.
220 12 15
0.132; using 2.5 in. cover to the center of the outer longitudinal bars, = 0.75
1000 20 20
e
h
g
×
= = =
×
On Graph A.7 (
0.8
g
=
),
0.83 for 0.13
u
n
cg
Pe
KfA h
f
= = =
′
1000 23 in.
0.65 4 0.83 20
u
cn
P
bfKh
f
= = =
′×× ×
9.15 continued
16 0.76
21 in.bh
= =
(c) Pu = 500 kips and Mu = 160 ft-kips
160 12 0.15
0.65 4 289 17
uu
n
cg cg
Pe M
RfAh fAh
ff
×
= = = =
′′ ×× ×
From Graph A.6 (
0.7
g
=
),
ρ
g ≅ 0.024, giving Ast = 0.024 × 289 = 6.94 in2. Use 4 No. 9 bars at the
corners and 4 No. 8 bars at the midsides, which provides Ast = 7.16 in2
Column ties:
17 in.bh
= =
