# V. ACI 318-11 Circular Column

Calculate the axial capacity of a circular column subjected to axial compressive force, given Ast

ACI 318-11

## Details

A circular, cantilever column of length 5ft with an ultimate axial load of 500 kip has the following concrete and steel properties.

• Compressive strength of concrete (normal weight concrete), fc = 4,000 psi
• Yield strength of steel, fy = 60,000 psi
• Clear spacing for outermost bottom reinforcement to bottom face, Cc = 1.5 in
• Diameter of column, D = 20 in
• Strength reduction factor, ϕ = 0.65
• Number of #8 bars, N = 6
• Rebar diameter for #8 bar, d = 1 in

Factored axial load (axial demand), Pu = 500 kip

## Validation

Gross area of concrete section, Ag = πD2/4 = 314.159 in2

Total area of steel reinforcement,

Nominal axial strength at zero eccentricity:

P0 = 0.85×fc(Ag - Ast) + fy×Ast = 1.335×103 kip

For tied reinforced column:

Pn(max) = 0.8·P0 = 1.068×103 kip

Capacity = ϕPn(max) = 694.129 kip

Ratio = Pu/ϕPn(max) = 0.72

## Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
P0 (kip) 1,335 1,336.43 negligible
Pn (kip) 1,068 1,069.14 negligible
Bar configuration 6- #8 bars 6- #8 bars none
Column size 20" dia. tied column 20" dia. tied column none

## STAAD Input

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\US\ACI 318-11 Circular Column.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 15-May-2020
ENGINEER NAME Design of Circular Column
JOB CLIENT Bentley Systems Inc.
ENGINEER NAME TK
END JOB INFORMATION
INPUT WIDTH 79
UNIT FEET KIP
JOINT COORDINATES
1 0 0 0; 2 0 5 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 453600
POISSON 0.17
DENSITY 0.14999
ALPHA 5.5e-06
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 576
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 PRIS YD 1.66667
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead  TITLE LOAD CASE 1
JOINT LOAD
2 FY -500
PERFORM ANALYSIS
SECTION 0 0.25 0.5 0.75 1 ALL
PRINT SUPPORT REACTION ALL
START CONCRETE DESIGN
CODE ACI 2011
MAXMAIN 8 ALL
MINMAIN 8 ALL
TRACK 2 ALL
DESIGN COLUMN ALL
END CONCRETE DESIGN
FINISH


## STAAD Output

        ACI 318-11   COLUMN  NO.     1   DESIGN RESULTS
===============================================
FY - 60000  FC - 4000 PSI,  CIRC SIZE  20.00 INCHES DIAMETER  TIED
ONLY MINIMUM STEEL IS REQUIRED.
AREA OF STEEL REQUIRED =   3.142  SQ. IN.
BAR CONFIGURATION       REINF PCT.   LOAD   LOCATION   PHI
----------------------------------------------------------
6 - NUMBER  8           1.509        1      END     0.650
(EQUALLY SPACED)
TIE BAR NUMBER    4 SPACING  16.00 IN
COLUMN INTERACTION: MOMENT ABOUT Z/Y -AXIS (KIP-FT)
--------------------------------------------------------
P0        Pn max    P-bal.    M-bal.   e-bal.(inch)
1336.43   1069.14    475.51    247.89    6.26
M0       P-tens.   Des.Pn    Des.Mn     e/h
153.92   -284.40    769.23      0.00    0.00000
--------------------------------------------------------
Pn       Mn       Pn       Mn
|              986.90   144.54   493.45   246.76
P0 |*             904.66   176.00   411.21   248.11
| *            822.42   201.19   328.97   246.46
Pn,max|__*           740.18   220.34   246.73   239.25
|   *          657.93   233.38   164.48   222.95
Pn    |    *         575.69   242.15    82.24   190.02
NOMINAL|     *
AXIAL|      *
COMPRESSION|       *
Pb|-------*Mb
|      *
___________|____*_______
|  * M0   Mn,
| *   BENDING
P-tens|*     MOMENT
|
********************END OF COLUMN DESIGN RESULTS********************