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V. ACI 318-14 Rectangular Column

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

Details

A rectangular, cantilever column of length 5ft with an ultimate axial load of 1,538 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 = 30 in
  • Strength reduction factor, ϕ = 0.65
  • Number of #9 bars = 10
  • Rebar diameter for #9 bar, Ød = 1.128 in

Factored axial load (axial demand), Pu = 1,538 kip

Validation

Gross area of concrete section, Ag = B×D = 600 in2

Total area of steel reinforcement, Ast = 10 in2

Nominal axial strength at zero eccentricity:

P0 = 0.85×fc(Ag - Ast) + fy×Ast = 3.108×103 kip

For tied reinforced column:

Pn(max) = 0.8·P0 = 2.486×103 kip

Capacity = ϕPn(max) = 1,615.9 kip

Ratio = Pu/ϕPn(max) = 0.952

Results

Table 1. Comparison of results
Parameter Hand Calculation STAAD.Pro Difference Comments
Axial Capacity (kip) 1,615.9 1,615.9 none  
Ratio Pu/ϕPn(max) 0.952 0.952 none  

STAAD Input

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

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 01-Jan-18
JOB CLIENT Bentley Systems Inc.
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 30 ZD 20
CONSTANTS
MATERIAL CONCRETE ALL
UNIT FEET KIP
SUPPORTS
1 FIXED
UNIT INCHES KIP
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FY -1538
PERFORM ANALYSIS
START CONCRETE DESIGN
CODE ACI 2014
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

STAAD Output

                       STAAD.PRO CONCRETE DESIGN - (ACI-318-14)   v2.0                
                       ***********************************************
Units: KIP   , INCHES (Unless Noted Otherwise)
 Member :      1 
DESIGN SUMMARY
-----------------------------------------------------------------------------
| Status         :   Pass         Type    : Column          Length:   72.000 |
| Critical Ratio :   0.952        Criteria: Axial                            |
| Critical Clause:   10.5.2                                                  |
-----------------------------------------------------------------------------
CROSS SECTION
-------------------------------------------------------
| Shape: Rectangular | Width:   20.00 | Depth:   30.00 |
-------------------------------------------------------
DESIGN INPUTS
-------------------------------------------------------------------------
| Concrete | Fc           5.000 |                     | Ec     0.403E+04 |
| Steel    | Fy(main)    60.000 | Fy(trans)    60.000 | Es     0.290E+05 |
| Cover    | Top          1.500 | Bottom        1.500 | Sides      1.500 |
-------------------------------------------------------------------------
CRITICAL STRENGTH RESULTS
-----------------------------------------------------------------------
| Category |    Demand     |  Min Capacity  |  Max Capacity  |  Ratio  |
-----------------------------------------------------------------------
| Axial    |      -1538.000|      -1615.900 |        540.000 |   0.952 |
| Flexure  |          0.000|      -4780.603 |       4780.603 |   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 |      8.660 |     10.000 |    10    |  # 9 |       1      |
|   18.000 |      8.660 |     10.000 |    10    |  # 9 |       1      |
|   36.000 |      8.660 |     10.000 |    10    |  # 9 |       1      |
|   54.000 |      8.660 |     10.000 |    10    |  # 9 |       1      |
|   72.000 |      8.660 |     10.000 |    10    |  # 9 |       1      |
-----------------------------------------------------------------------
LONGITUDINAL BAR LAYOUT
---------------------------------------------------------------------------
|                |    Bars     |      Location     | Distance  |   Anchor  |
|       Position | Nums | Size | Start  |   End    | From Face | Start End |
---------------------------------------------------------------------------
|            Top |    3 | # 9  |    0.00|    72.00 |     2.06  |  Yes  Yes |
|         Bottom |    3 | # 9  |    0.00|    72.00 |     2.06  |  Yes  Yes |
|           Left |    2 | # 9  |    0.00|    72.00 |     2.06  |  Yes  Yes |
|          Right |    2 | # 9  |    0.00|    72.00 |     2.06  |  Yes  Yes |
      STAAD SPACE                                              -- PAGE NO.    5
---------------------------------------------------------------------------
TRANSVERSE BAR LAYOUT
------------------------------------------------------------------------------------
|                                |        Asv        |     Rebar Specification      |
| Zone | Dir.|  From   |    To   |  Reqd.  |  Prov.  | Nums | Size | Spacing | Legs |
------------------------------------------------------------------------------------
|    1 |  Y  |    0.00 |   72.00 |    0.02 |    0.02 |    5 |  # 4 |  18.00  |   2  |
|    1 |  Z  |    0.00 |   72.00 |    0.02 |    0.02 |    5 |  # 4 |  18.00  |   2  |
------------------------------------------------------------------------------------
------------------------ Member:     1 Design Ends ------------------------