V. IS456 2000-Axially Loaded Square Column
Verify the designed results produced by the program with hand calculated design results for an axially loaded square column section as per IS456:2000.
Details
The fixed-base, 2.5 m column is subjected to axial force of 3,300 kN. The section is 500mm x 500mm. The concrete strength is 25 N/mm2 and the yield strength of steel is 415 N/mm2. Use a clear cover of 40 mm. The main reinforcement is 20 mm and the lateral ties are 8 mm.
Validation
Slenderness Ratio
From Table. 28 Clause E-3 of IS 456 : 2000, the effective length of the compression member:
(Leff ) = 2 × L = 2 × 2,500 = 5,000 mm
Least lateral dimension of column = (5,000/500) = 10 < 12
Large lateral dimension of column = (5,000/500) = 10 < 12
So, we can consider and design as a short column.
Check for Minimum Eccentricity of Column
As per Clause 25.4 of IS 456 : 2000, calculate the minimum eccentricity:
For Depth, emin = (2,500/500) + (500/30) = 21.7 mm > 20 mm. (OK)
For Width emin = (2,500/500) + (500/30) = 21.7 mm > 20 mm. (OK)
Hence Minimum Eccentricity is ok.
Check for Maximum Eccentricity of Column
As per Clause 39.3 of IS 456 : 2000 calculate the maximum eccentricity:
For Depth emax = 0.05 × 500 = 25 mm. Hence, emin < emax (OK)
For Width emax = 0.05 × 500 = 25 mm. Hence, emin < emax (OK)
Hence Maximum Eccentricity is ok.
Design for Flexure
Gross Area of Column, Ag = 500 × 500 = 25 × 104 mm2 .
Area of Concrete, Ac = Ag – Asc = 25 × 104 - Asc
Area of Longitudinal Reinforcement, Asc = Pu = 0.4 × fck × Ac + 0.67 × fy × Asc
3,300 × 103 = 0.4 × 25 [ Ag - Asc ] + 0.67 × 415 × Asc
3,300 × 103 = 0.4 × 25 [ 25 × 104 - Asc ] + 0.67 × 415 × Asc
2,985 mm2 .
Let assume 25 mm dia bar. So, Ast = (3.14/4) × 252 = 490.3 mm2 .
Nos. of Bars will be = (2,985/490.3) = 6.1 ≈ 8 Nos
So, the actual reinforcement will be = 8 × (3.14/4) × 252 = 3,925 mm2
As per Clause 26.5.3.2 (c) of IS 456 : 2000 Bar Diameter of Lateral Ties:
¼ × Main Bar dia = ¼ × 25 = 6.3 mm
So, Provide 8 mm dia. bar for lateral ties.
As per Clause 26.5.3.2 (c) of IS 456 : 2000 Pitch of Lateral Ties:
- Least lateral dimension = 500 mm
- 16 × 25 = 400 mm
- 300 mm
Provide 8 mm dia. bar @ 300 mm for lateral ties.
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Reqd. area of steel (mm2) | 2,985 | 2,984.52 | negligible | |
Spacing of rectangular ties reinforcement (mm) | 300 | 300 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\10 Concrete Design\India\IS456 2000-Axially Loaded Square Column.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Aug-20
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 2.5 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC CONCRETE
E 2.17184e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY AMERICAN
1 PRIS YD 0.5 ZD 0.5
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FY -3300
PERFORM ANALYSIS PRINT ALL
START CONCRETE DESIGN
CODE INDIAN
CLEAR 0.04 ALL
ELZ 2 ALL
ELY 2 ALL
FC 25000 ALL
FYMAIN 415000 ALL
MAXMAIN 25 ALL
MAXSEC 8 ALL
MINMAIN 25 ALL
MINSEC 8 ALL
TRACK 2 ALL
DESIGN COLUMN 1
END CONCRETE DESIGN
FINISH
STAAD.Pro Output
========================================================= IS 456 - 2000 C O L U M N D E S I G N R E S U L T S ========================================================= ============================================================================ IS-456 L I M I T S T A T E D E S I G N C O L U M N N O. 1 D E S I G N R E S U L T S M25 Fe415 (Main) Fe415 (Sec.) LENGTH: 2500.0 mm CROSS SECTION: 500.0 mm X 500.0 mm COVER: 40.0 mm ** GUIDING LOAD CASE: 1 END JOINT: 1 SHORT COLUMN DESIGN FORCES (KNS-MET) ----------------------- DESIGN AXIAL FORCE (Pu) : 3300.00 About Z About Y INITIAL MOMENTS : 0.00 0.00 MOMENTS DUE TO MINIMUM ECC. : 0.00 0.00 SLENDERNESS RATIOS : - - MOMENTS DUE TO SLENDERNESS EFFECT : - - MOMENT REDUCTION FACTORS : - - ADDITION MOMENTS (Maz and May) : - - TOTAL DESIGN MOMENTS : 0.00 0.00 REQD. STEEL AREA : 2984.52 Sq.mm. REQD. CONCRETE AREA: 247015.48 Sq.mm. MAIN REINFORCEMENT : Provide 8 - 25 dia. (1.57%, 3926.99 Sq.mm.) (Equally distributed) TIE REINFORCEMENT : Provide 8 mm dia. rectangular ties @ 300 mm c/c SECTION CAPACITY BASED ON REINFORCEMENT REQUIRED (KNS) ------------------------------------------------------ Puz : 3300.00 KNS STAAD SPACE -- PAGE NO. 6 SECTION CAPACITY BASED ON REINFORCEMENT PROVIDED (KNS) ------------------------------------------------------ END JOINT: 1 Puz : 3552.63 KNS IR:0.93 END JOINT: 2 Puz : 3552.63 KNS IR:0.93 ============================================================================ ********************END OF COLUMN DESIGN RESULTS********************