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
STAAD Input
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
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
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
STAAD Output
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********************