V. IS 801-Column with axial and major axis bending
Verification example for a cold-formed column subject to axial compression and bending moment according to IS:801-1975.
Details
Verifies the calculations for an IS 60CS40x4 (channel with lips) column that is 2 m long and subject to axial compression and major axis bending moment. This example checks for compression, shear, bending, and compression and bending interaction as per IS 801.
- E = 2,074,000 kgf/cm2 = 203,400 MPa
- Fy = 3,569 kgf/cm2 = 353.0 MPa
- Fu = 4,588 kgf/cm2 = 450 MPa
- G = 795,000 kgf/cm2 = 77,963 MPa
- P = 10 kN
- Mz = 4.0 kN·m
- Vy = 2 kN
Verification
Section Dimension Checks
Flanges (ref. cl 5.2.3):
w = 4 - 2× 0.4 - 2× 0.6 = 2
w/t = 2 / 0.4 = 5 < 60, Hence OK
Web (ref. cl 5.2.4):
W/t = (6 - 2×0.4 - 2× 0.6) / 0.4 = 10 < 500 and
h/t = (6 - 2× 0.4) / 0.4 = 13 < 150, Hence OK
Check for limiting slenderness (ref. cl 6.3.3):
K×Ly/ry = 1.0× 200 mm / 1.453 mm = 137.6 < 200
Hence, OK
Allowable Compression Strength
Maximum allowable compressive stress for flexural buckling Y (ref. cl 6.6.1.1 of IS 801)
Design stress, F = 0.6× fy = 2,160 kgf/cm2 = 211.8 MPa
Effective width of flange, Beff
W = 4 - 2×0.4 - 2× 0.6 = 2 cm
Beff = w = 2 cm
Effective width of web, Beff
W/t < 30.87
Beff = w = 10 cm
Aeff = 5.8 cm2
Factor, Q = Aeff / A = 1.0=
Slenderness limit
Maximum allowable compressive stress for flexural torsional buckling (ref. cl 6.6.1.2 of IS 801)
Polar radius of gyration,
σt = 2,036 kgf/cm2
σex = 2,480 kgf/cm2
1,201 kgf/cm2 < 0.5×F = 1,800 kgf/cm2
Fa2 = 0.522×σTF0 = 626.9 kgf/cm2
The allowable compressive stress, Fa is the minimum of Fa1 and Fa1 .
Fa = 546.1 kgf/cm2 = 55.32 MPa
Allowable Bending Strength
C = 1.0 for member under combined axial and bending.
(ref. cl 6.3) |
Maximum allowable compressive stress:
Fb1 = 0.6× Fy = 2,160 kgf/cm2 = 211.8 MPa
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Allowable compressive stress (MPa) | 55.32 | 55.371 | negligible | |
Allowable bending stress (MPa) | 211.8 | 211.854 | negligible | |
Allowable unbraced bending stress (MPa) | 138.5 | 138.583 | negligible | |
Allowable shear stress along Y (MPa) | 141.3 | 141.236 | negligible | |
Axial and Bending interaction | 2.103 | 2.102 | negligible |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\India\IS 801-Column with axial and major axis bending.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 18-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 2 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY COLDFORMED INDIAN
1 TABLE ST 60CS40X4
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
2 FX 2 FY -10
PERFORM ANALYSIS PRINT STATICS CHECK
PARAMETER 1
CODE IS801
TRACK 2 ALL
CHECK CODE ALL
PRINT MEMBER PROPERTIES ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - ( IS:801 ) v3.0 *********************** ALL UNITS ARE IN - METE KN (U.N.O.) |-----------------------------------------------------------------------------| | MEMBER: 1 SECTION: 60CS40X4 LEN: 2.000 LOC: 0.000 | | STATUS: FAIL RATIO: 3.071 REF: 6.3 LTB LC: 1 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Fx:(C) 10.000 Fy: 2.000 Fz: 0.000 | | Mx: 0.000 My: 0.000 Mz: 4.000 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: (Unit: CM) | | Ag: 5.82000 Az: 3.20000 Ay: 3.36000 | | Cz: 1.75000 Cy: 3.00000 Z0: 4.46000 | | Iz: 28.20000 Iy: 12.30000 J: 0.29600 | | Sz: 9.40000 Sy: 5.46000 | | Rz: 2.20122 Ry: 1.45375 Cw: 162.00003 | |-----------------------------------------------------------------------------| | MATERIAL INFO: (Unit: MPa) | | Fy: 353.090 Fu: 449.993 E: 203404.356 G: 77968.401 | | Fya(compression): 353.090 Fya(bending): 353.090 | |-----------------------------------------------------------------------------| | DESIGN PROPERTIES: | | Member Length: 2.000 Lz: 2.000 Ly: 2.000 Lb: 2.000 | | DESIGN PARAMETERS: | | Kz: 1.000 Ky: 1.000 NSF: 1.000 Cb: 0.000 | |-----------------------------------------------------------------------------| | CRITICAL SLENDERNESS: | | Actual: 137.575 Allowable: 200.000 Ratio: 0.688 | |-----------------------------------------------------------------------------| | CHECKS: | Stresses | | | | Loc. | Demand | L/C | Actual | Allow |Ratio | Ref CL | | |(MET) |(KN-MET)| | (MPa) | (MPa) | | | |--------------|------|--------|------|----------|----------|------|----------| | Tension | - | - | - | - | 211.854 | - | 6.1 | | Compression | 0.000| 10.00| 1| 17.183 | 55.371 | 0.310| 6.6.1.1 | | BendZComp | 0.000| 4.00| 1| 425.562 | 211.854 | 2.009| 6.3 | | BendZTens | 0.000| 4.00| 1| 425.562 | 211.854 | 2.009| 6.3 | | BendUnbraced | 0.000| 4.00| 1| 425.562 | 138.583 | 3.071| 6.3 LTB | | BendYComp | - | - | - | - | 211.854 | - | 6.3 | | BendYTens | - | - | - | - | 211.854 | - | 6.3 | | Bend Web | 0.000| 4.00| 1| 368.820 | 211.854 | 1.741| 6.4.2 | | Shear Z | - | - | - | - | 141.236 | - | 6.4.1 | | Shear Y | 0.000| 2.00| 1| 5.953 | 141.236 | 0.042| 6.4.1 | | Axial+Bend | 0.000| - | 1| - | - | 2.102| 6.7.2(a)2| | Bend+Shear | 0.000| - | 1| - | - | 0.020| 6.4.3 | |-----------------------------------------------------------------------------| | Effective Section Properties:(cm) | | Ae: 5.820 SzTop: 9.400 SzBot: 9.400 SyLeft: 7.029 SyRight: 5.467 | | Intermediate Results: Cb = 1.000 | |-----------------------------------------------------------------------------| NOTE: Torsion has not been considered in the design. STAAD SPACE -- PAGE NO. 5