# V. IS456 2000-Circular Column

Verify the designed results produced by the program with hand calculated design results for an axially loaded circular column section as per IS456:2000.

## References

Bureau of Indian Standards. SP 16 - Design aids for reinforced concrete to IS: 456-1978. 1980. New Dehli: Indian Standards Institution. p. 141.

## Details

The fixed-base, 2.5 m cantilever column is subjected to axial force of 800 kN and a moment at the top of 162.5 kN·m. The section is 500 mm in diameter. The concrete strength is 20 N/mm2 and the yield strength of steel is 415 N/mm2. Use a clear cover of 50 mm. The main reinforcement is 20 mm and the lateral ties are 10 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 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 Width emax = 0.05 × 500 = 25 mm. Hence, emin < emax (OK)

Hence Maximum Eccentricity is ok.

Design for Flexure

Determine the non-dimenstional parameters to use with interaction chart 56 of SP 16:

$P u / f ck D 2 = 800 ( 10 3 ) / ( 20 × 500 2 ) = 0.16$
$M u / f ck D 3 = 162.5 ( 10 6 ) / ( 20 × 500 3 ) = 0.065$

From the chart, $P / f ck = 0.06$, and thus $P = 20 × 0.06 = 1.2$

The area of longitudinal reinforcement required then is given by:

Let assume 20 mm dia bar. So, Ast = (3.14/4) × 252 = 314 mm2 .

Number of bars = (2,355/314) = 7.5 ≈ 8 bars

So, the actual reinforcement will be = 8 × 314 mm2 = 2,513 mm2

As per Clause 26.5.3.2 (c) of IS 456 : 2000 Bar Diameter of Lateral Ties:

¼ × Main Bar dia = ¼ × 20 = 5 mm

or, 6 mm

So, Provide 10 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 × 20 = 320 mm
• 300 mm

Provide 10 mm dia. bar @ 300 mm for lateral ties.

## Results

Reqd. area of steel (mm2) 2,355 2,367.71 negligible
Spacing of rectangular ties reinforcement (mm) 300 300 none

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\10 Concrete Design\India\IS456 2000-Circular Column.STD is typically installed with the program.

STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 09-Dec-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 2.17185e+07
POISSON 0.17
DENSITY 23.5616
ALPHA 1e-05
DAMP 0.05
TYPE CONCRETE
STRENGTH FCU 27579
END DEFINE MATERIAL
MEMBER PROPERTY
1 PRIS YD 0.5
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
2 FY -800
2 MZ 162.5
1 1.0 2 1.0
PERFORM ANALYSIS PRINT ALL
START CONCRETE DESIGN
CODE INDIAN
FC 20000 ALL
FYMAIN 415000 ALL
FYSEC 415000 ALL
CLEAR 0.050 ALL
MAXMAIN 20 ALL
MAXSEC 10 ALL
MINMAIN 20 ALL
MINSEC 10 ALL
TRACK 2 ALL
DESIGN COLUMN 1
END CONCRETE DESIGN
FINISH


 COLUMN
=========================================================
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
M20                    Fe415 (Main)               Fe415 (Sec.)
LENGTH:  2500.0 mm   CROSS SECTION:  500.0 mm dia.  COVER: 50.0 mm
** GUIDING LOAD CASE:    3 END JOINT:     1  SHORT COLUMN
DESIGN FORCES (KNS-MET)
-----------------------
DESIGN AXIAL FORCE (Pu)             :     800.00
INITIAL MOMENTS                     :     162.50               0.00
MOMENTS DUE TO MINIMUM ECC.         :      17.33              17.33
SLENDERNESS RATIOS                  :     -                  -
MOMENTS DUE TO SLENDERNESS EFFECT   :     -                  -
MOMENT REDUCTION FACTORS            :     -                  -
ADDITION MOMENTS (Maz and May)      :     -                  -
TOTAL DESIGN MOMENTS                :     162.50              17.33
REQD. STEEL AREA   :     2367.71 Sq.mm.
REQD. CONCRETE AREA:   193981.83 Sq.mm.
MAIN REINFORCEMENT : Provide   8 - 20 dia. (1.28%,   2513.27 Sq.mm.)
(Equally distributed)
TIE REINFORCEMENT  : Provide 10 mm dia. circular ties @ 300 mm c/c
SECTION CAPACITY BASED ON REINFORCEMENT REQUIRED (KNS-MET)
----------------------------------------------------------
Puz :   2482.79   Muz1 :    173.76   Muy1 :    173.76
INTERACTION RATIO: 0.98 (as per Cl. 39.6, IS456:2000)
STAAD SPACE                                              -- PAGE NO.    7
SECTION CAPACITY BASED ON REINFORCEMENT PROVIDED (KNS-MET)
----------------------------------------------------------