V. ACI 318-14 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
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\US\ACI 318-14 Square Column.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 29-Aug-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 20 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 -998
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 : 0.998 Criteria: Axial | | Critical Clause: 10.5.2 | ----------------------------------------------------------------------------- CROSS SECTION ------------------------------------------------------- | Shape: Rectangular | Width: 20.00 | Depth: 20.00 | ------------------------------------------------------- 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 | -998.000| -999.960 | 216.000 | 0.998 | | Flexure | 0.000| -1740.458 | 1740.458 | 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 | 4.000 | 4.000 | 4 | # 9 | 1 | | 18.000 | 4.000 | 4.000 | 4 | # 9 | 1 | | 36.000 | 4.000 | 4.000 | 4 | # 9 | 1 | | 54.000 | 4.000 | 4.000 | 4 | # 9 | 1 | | 72.000 | 4.000 | 4.000 | 4 | # 9 | 1 | ----------------------------------------------------------------------- LONGITUDINAL BAR LAYOUT --------------------------------------------------------------------------- | | Bars | Location | Distance | Anchor | | Position | Nums | Size | Start | End | From Face | Start End | --------------------------------------------------------------------------- | Top | 2 | # 9 | 0.00| 72.00 | 2.06 | Yes Yes | | Bottom | 2 | # 9 | 0.00| 72.00 | 2.06 | Yes Yes | --------------------------------------------------------------------------- STAAD SPACE -- PAGE NO. 5 TRANSVERSE BAR LAYOUT (Using Standard Ties) ------------------------------------------------------------------------------------ | | Asv | Rebar Specification | | Zone | Dir.| From | To | Reqd. | Prov. | Nums | Size | Spacing | Legs | ------------------------------------------------------------------------------------ | 1 | Y | 0.00 | 72.00 | 0.0222 | 0.0222 | 5 | # 4 | 18.00 | 2 | | 1 | Z | 0.00 | 72.00 | 0.0222 | 0.0222 | 5 | # 4 | 18.00 | 2 | ------------------------------------------------------------------------------------ ------------------------ Member: 1 Design Ends ------------------------