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:

(L_eff ) = 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, e_min = (2,500/500) + (500/30) = 21.7 mm > 20 mm. (OK)

For Width e_min = (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 e_max = 0.05 × 500 = 25 mm. Hence, e_min < e_max (OK)

For Width e_max = 0.05 × 500 = 25 mm. Hence, e_min < e_max(OK)

Hence Maximum Eccentricity is ok.

Design for Flexure

Gross Area of Column, A_g = 500 × 500 = 25 × 10⁴ mm² .

Area of Concrete, A_c = A_g – A_sc = 25 × 10⁴ - A_sc

Area of Longitudinal Reinforcement, A_sc = P_u = 0.4 × f_ck × Ac + 0.67 × f_y × A_sc

3,300 × 10³ = 0.4 × 25 [ A_g - A_sc ] + 0.67 × 415 × A_sc

3,300 × 10³ = 0.4 × 25 [ 25 × 10⁴ - A_sc ] + 0.67 × 415 × A_sc

2,985 mm² .

Let assume 25 mm dia bar. So, A_st = (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 CONNECT Edition\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********************