Page 252 - Handbook of Civil Engineering Calculations, Second Edition

REINFORCED CONCRETE 2.37

DESIGN OF A SPIRALLY
REINFORCED COLUMN

A short circular column, spirally reinforced, is to support a concentric load of 420 kips
(1868.16 kN). Design the member, using f c
4000 lb/sq.in. (27,580 kPa) and f y
50,000 lb/sq.in. (344,750 kPa).

Calculation Procedure:

1. Assume p g = 0.025 and compute the diameter of the section
Thus, 0.25f c
1000 lb/sq.in. (6895 kPa); f s 20,000 lb/sq.in. (137,900 kPa). By Eq. 40,
2
A g 420/(1 20 0.025) 280 sq.in. (1806.6 cm ). Then D (A g /0.785) 0.5 18.9 in.
2
(130.32 mm). Set D 19 in. (131.01 mm), making A g 283 sq.in. (1825.9 cm ).
2. Select the reinforcing bars
The load carried by the concrete 283 kips (1258.8 kN). The load carried by the steel
420 283 137 kips (609.4 kN). Then the area of the steel is A st , 137/20 6.85 sq.in.
2
2
(44.196 cm ). Use seven no. 9 bars, each having an area of 1 sq.in. (6.452 cm ). Then A st ,
2
7.00 sq.in. (45.164 cm ). The Reinforced Concrete Handbook shows that a 19-in. (482.6-
mm) column can accommodate 11 no. 9 bars in a single row.
3. Design the spiral reinforcement
The portion of the column section bounded by the outer circumference of the spiral is
2
termed the core of the section. Let A c core area, sq.in. (cm ); D c core diameter, in.
2
(mm); a cross-sectional area of spiral wire, sq.in. (cm ); g pitch of spiral, in. (mm);
p s ratio of volume of spiral reinforcement to volume of core.
The ACI Code requires 1.5-in. (38.1-mm) insulation for the spiral, with g restricted to
a maximum of D c /6. Then D c 19 3 16 in. (406.4 mm); A c 201 sq.in. (1296.9
2
cm ); D c /6 2.67 in. (67.818 mm). Use a 2.5-in. (63.5-mm) spiral pitch. Taking a 1-in.
(25.4-mm) length of column,
volume of spiral a s D c /g
p s
2
volume of core D c /4
or
gD c p s
a s (42)
4
The required value of p s , as given by the ACI Code is

0.45(A g /A c 1) f c
p s (43)
f y

or p s 0.45(283/201 1)4/50 0.0147; a s 2.5(16)(0.0147)/4 0.147 sq.in. (0.9484
2
2
1
cm ). Use /2-in. (12.7-mm) diameter wire with a s 0.196 sq.in. (1.2646 cm ).
4. Summarize the design
Thus: column size: 19-in. (482.6-mm) diameter; longitudinal reinforcement: seven no. 9
1
bars; spiral reinforcement: /2-in. (12.7-mm) diameter wire, 2.5-in. (63.5-mm) pitch.