# V. ACI 318-11 Square Column

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

## Details

A square, cantilever column of length 5ft with an ultimate axial load of 998 kip has the following concrete and steel properties.

• Compressive strength of concrete (normal weight concrete), fc = 5,000 psi
• Yield strength of steel, fy = 60,000 psi
• Clear spacing for outermost bottom reinforcement to bottom face, Cc = 1.5 in
• Width of column, B = 20 in
• Depth of column, D = 20 in
• Strength reduction factor, ϕ = 0.65
• Number of #9 bars = 4
• Rebar diameter for #9 bar, Ød = 1.128 in

Factored axial load (axial demand), Pu = 998 kip

## Validation

Gross area of concrete section, Ag = B×D = 400 in2

Total area of steel reinforcement, Ast = 4 in2

Nominal axial strength at zero eccentricity:

P0 = 0.85×fc(Ag - Ast) + fy×Ast = 1.923×103 kip

For tied reinforced column:

Pn(max) = 0.8·P0 = 1.5384×103 kip

Capacity = ϕPn(max) = 999.96 kip

Ratio = Pu/ϕPn(max) = 0.998

## Results

Table 1. Comparison of results
P0 (kip) 1,923 1,923 none
Pn (kip) 1,583 1,583.4 negligible
Bar configuration 4- #9 bars 4- #9 bars none
Column size 20"×20" tied column 20"×20" tied column none

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

``````STAAD SPACE
START JOB INFORMATION
***********************************************************************
* This example is a replica of example no 6.3 of PCA Notes 318-11.
***********************************************************************
ENGINEER DATE 21-June-2020
JOB NAME PCA Example 6.3
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 6 0;
MEMBER INCIDENCES
1 1 2;
UNIT INCHES KIP
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 3150
POISSON 0.17
DENSITY 8.68e-05
ALPHA 5.5e-06
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 4
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 PRIS YD 20 ZD 20
CONSTANTS
MATERIAL CONCRETE ALL
UNIT FEET KIP
SUPPORTS
1 FIXED
UNIT INCHES KIP
2 FY -998
PERFORM ANALYSIS
START CONCRETE DESIGN
CODE ACI 2011
FC 5 ALL
MXMT 9 ALL
MXMB 9 ALL
MXMS 9 ALL
MIMT 9 ALL
MIMB 9 ALL
MIMS 9 ALL
TRACK 2 ALL
DESIGN COLUMN 1
END CONCRETE DESIGN
FINISH
``````

```        ACI 318-11   COLUMN  NO.     1   DESIGN RESULTS
===============================================
FY - 60000  FC - 5000 PSI,  SQRE SIZE - 20.00 X 20.00 INCHES, TIED
ONLY MINIMUM STEEL IS REQUIRED.
AREA OF STEEL REQUIRED =   4.000  SQ. IN.
BAR CONFIGURATION       REINF PCT.   LOAD   LOCATION   PHI-Z  PHI-Y
-------------------------------------------------------------------
4 - NUMBER  9           1.000        1      END     0.000  0.000
(PROVIDE EQUAL NUMBER OF BARS ON EACH FACE)
TIE BAR NUMBER    9 SPACING  18.05 IN
COLUMN INTERACTION: MOMENT ABOUT Z -AXIS (KIP-FT)
--------------------------------------------------------
P0        Pn max    P-bal.    M-bal.   e-bal.(inch)
1923.00   1538.40    716.26    446.51    7.48
M0       P-tens.   Des.Pn    Des.Mn     e/h
156.73   -240.00  Infinity       NaN    0.00000
--------------------------------------------------------
COLUMN INTERACTION: MOMENT ABOUT Y -AXIS (KIP-FT)
--------------------------------------------------------
P0        Pn max    P-bal.    M-bal.   e-bal.(inch)
1923.00   1538.40    716.26    446.51    7.48
M0       P-tens.   Des.Pn    Des.Mn     e/h
156.73   -240.00  Infinity       NaN    0.00000
--------------------------------------------------------
Pn       Mn       Pn       Mn    (@ Z )
|             1420.06   279.88   710.03   446.27
P0 |*            1301.72   332.82   591.69   436.82
| *           1183.38   372.72   473.35   420.15
Pn,max|__*          1065.05   403.75   355.02   373.59
|   *          946.71   425.39   236.68   309.55
Pn    |    *         828.37   438.88   118.34   236.06
NOMINAL|     *         Pn       Mn       Pn       Mn    (@ Y )
AXIAL|      *      1420.06   279.88   710.03   446.27
COMPRESSION|       *     1301.72   332.82   591.69   436.82
Pb|-------*Mb   1183.38   372.72   473.35   420.15
|      *      1065.05   403.75   355.02   373.59
___________|____*_______  946.71   425.39   236.68   309.55
|  * M0   Mn,  828.37   438.88   118.34   236.06
| *   BENDING
P-tens|*     MOMENT
|
********************END OF COLUMN DESIGN RESULTS********************
```