# V. IS456 2000-Axially Loaded Rectangular Column

Verify the designed results produced by the program with hand calculated design results for an axially loaded rectangular 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 450mm x 600mm. 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 = (5,000/450) = 11.11 < 12

Large lateral dimension of column = (5,000/600) = 8.33 < 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) + (600/30) = 25 mm > 20 mm. (OK)

For Width emin = (2,500/500) + (450/30) = 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 × 600 = 30 mm. Hence, emin < emax (OK)

For Width emax = 0.05 × 450 = 22.5 mm. Hence, emin < emax (OK)

Hence Maximum Eccentricity is ok.

Design for Flexure

Gross Area of Column, Ag = 450 × 600 = 27 × 104 mm2 .

Area of Concrete, Ac = Ag – Asc = 27 × 104 - Asc

Area of Longitudinal Reinforcement, Asc = Pu = 0.4 × fck × Ac + 0.67 × fy × Asc

3300 × 103 = 0.4 × 25 [ Ag - Asc ] + 0.67 × 415 × Asc

3300 × 103 = 0.4 × 25 [ 27 × 104 - Asc ] + 0.67 × 415 × Asc = 2,238 mm2 .

Let assume 20 mm dia bar. So, Ast = (3.14/4) × 202 = 314.15 mm2 .

Nos. of Bars will be = (2238.3/314.15) = 7.12 ≈ 8 Nos

So, the actual reinforcement will be = 8 × (3.14/4) × 202 = 2513.2 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

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 = 450 mm
• 16 × 20 = 320 mm
• 300 mm

Provide 8 mm dia. bar @ 300 mm for lateral ties.

## Results

Reqd. area of steel (mm2) 2,238 2,238.39 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-Axially Loaded Rectangular 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 0.6 ZD 0.45
CONSTANTS
MATERIAL CONCRETE ALL
SUPPORTS
1 FIXED
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 20 ALL
MAXSEC 8 ALL
MINMAIN 20 ALL
MINSEC 8 ALL
TRACK 2 ALL
DESIGN COLUMN 1
END CONCRETE DESIGN
FINISH
``````

```            =========================================================
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:  450.0 mm X  600.0 mm  COVER: 40.0 mm
** GUIDING LOAD CASE:    1 END JOINT:     1  SHORT COLUMN
DESIGN FORCES (KNS-MET)
-----------------------
DESIGN AXIAL FORCE (Pu)             :    3300.00
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   :     2238.39 Sq.mm.
REQD. CONCRETE AREA:   267761.62 Sq.mm.
MAIN REINFORCEMENT : Provide   8 - 20 dia. (0.93%,   2513.27 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 :   3373.68 KNS   IR:0.98
END JOINT:     2 Puz :   3373.68 KNS   IR:0.98
============================================================================
********************END OF COLUMN DESIGN RESULTS********************
```