V. ACI 318-11 Circular Column

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

References

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), f_c = 4,000 psi
Yield strength of steel, f_y = 60,000 psi
Clear spacing for outermost bottom reinforcement to bottom face, C_c = 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), P_u = 500 kip

Validation

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

Total area of steel reinforcement, $A_{s t} = (π \frac{d^{2}}{4}) N = 4.712 {in}^{2}$

Nominal axial strength at zero eccentricity:

P₀ = 0.85×f_c(A_g - A_st) + f_y×A_st = 1.335×10³ kip

For tied reinforced column:

P_n(max) = 0.8·P₀ = 1.068×10³ kip

Capacity = ϕP_n(max) = 694.129 kip

Ratio = P_u/ϕP_n(max) = 0.72

Results

Table 1. Comparison of results
Parameter	Hand Calculation	STAAD.Pro	Difference
P₀ (kip)	1,335	1,336.43	negligible
P_n (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********************