V. ACI 318-14 Circular Column

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

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 = 6
• Rebar diameter for #8 bar, Ød = 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, $A s t = ( π D 2 4 ) N = 314.159 in 2$

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
Axial Capacity (kip) 694.129 694.079 negligible
Ratio Pu/ϕPn(max) 0.72 0.72 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\US\ACI\318-2014\ACI 318-14 Circular Column.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 29-Aug-17
JOB NAME Circular Column Design
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
2 FY -500
PERFORM ANALYSIS
PRINT SUPPORT REACTION ALL
START CONCRETE DESIGN
CODE ACI 318 14
MAXMAIN 9 ALL
MINMAIN 8 ALL
TRACK 2 ALL
DESIGN COLUMN ALL
END CONCRETE DESIGN
FINISH


                       STAAD.PRO CONCRETE DESIGN - (ACI-318-14)   v2.0
***********************************************
Units: KIP   , FEET   (Unless Noted Otherwise)
Member :      1
DESIGN SUMMARY
-----------------------------------------------------------------------------
| Status         :   Pass         Type    : Column          Length:    5.000 |
| Critical Ratio :   0.720        Criteria: Axial                            |
| Critical Clause:   10.5.2                                                  |
-----------------------------------------------------------------------------
CROSS SECTION
-------------------------------------
| Shape: Circular    | Dia:    1.67 |
-------------------------------------
-------------------------------------------------------------------------
| Concrete | Fc         576.000 |                     | Ec     0.519E+06 |
| Steel    | Fy(main)  8639.999 | Fy(trans)  8639.999 | Es     0.418E+07 |
| Cover    | Top          0.125 | Bottom        0.125 | Sides      0.125 |
-------------------------------------------------------------------------
CRITICAL STRENGTH RESULTS
-----------------------------------------------------------------------
| Category |    Demand     |  Min Capacity  |  Max Capacity  |  Ratio  |
-----------------------------------------------------------------------
| Axial    |       -500.000|       -694.079 |        255.960 |   0.720 |
| Flexure  |          0.000|       -148.011 |        148.011 |   0.000 |
| Shear Y  |          0.000|          0.000 |          0.000 |   0.000 |
| Shear Z  |          0.000|          0.000 |          0.000 |   0.000 |
| Torsion  |          0.000|          0.000 |          0.000 |   0.000 |
-----------------------------------------------------------------------
LONGITUDINAL BAR DETAILS AT CROSS SECTIONS
-----------------------------------------------------------------------
| Distance |  Ast-reqd  |  Ast-prov  | No(s)bars| Size | No of Layers |
-----------------------------------------------------------------------
|    0.000 |      0.022 |      0.033 |     6    |  # 8 |       1      |
|    1.250 |      0.022 |      0.033 |     6    |  # 8 |       1      |
|    2.500 |      0.022 |      0.033 |     6    |  # 8 |       1      |
|    3.750 |      0.022 |      0.033 |     6    |  # 8 |       1      |
|    5.000 |      0.022 |      0.033 |     6    |  # 8 |       1      |
-----------------------------------------------------------------------
LONGITUDINAL BAR LAYOUT
---------------------------------------------------------------------------
|                |    Bars     |      Location     | Distance  |   Anchor  |
|       Position | Nums | Size | Start  |   End    | From Face | Start End |
---------------------------------------------------------------------------
|   Evenly Dist. |    6 | # 8  |    0.00|     5.00 |     0.17  |  Yes  Yes |
---------------------------------------------------------------------------
STAAD SPACE                                              -- PAGE NO.    6
TRANSVERSE BAR LAYOUT
------------------------------------------------------------------------------------
|                                |        Asv        |     Rebar Specification      |
| Zone | Dir.|  From   |    To   |  Reqd.  |  Prov.  | Nums | Size | Spacing | Legs |
------------------------------------------------------------------------------------
|    1 |  Y  |    0.00 |    5.00 |    0.00 |    0.00 |    5 |  # 4 |   1.25  |   2  |
|    1 |  Z  |    0.00 |    5.00 |    0.00 |    0.00 |    5 |  # 4 |   1.25  |   2  |
------------------------------------------------------------------------------------
------------------------ Member:     1 Design Ends ------------------------