V. IS 800 2007 LSD - Tube - Tension and Bending
Verify the capacity of a tube section subject to axial tension and combined bending per the IS 800:2007 code.
Reference
- Bureau of Indian Standards. General Construction in Steel - Code of Practice. IS 800:2007. New Delhi. 2007.
- Bureau of Indian Standards. Hollow steel sections for structural use - Specification. IS 4923:1997. New Delhi. 1997. p.5
Details
A 3m cantilever member is subject to a 10 kN tensile force applied at the free end. The member is also subject to 1 kN/m uniformly distributed loads along the length in both the local y and z directions. The section used is a 125.0x125.0x6.0 square hollow section. The material is steel with a yield strength of 250 MPa and a rupture strength of 420 MPa. Consider the member as laterally supported along the length.
Validation
Section Properties
From Ref. 2:
- Depth or width, D = 125.5 mm
- Thickness, t = 6.0 mm
- Area of section, A = 27.63 cm2
- Moment of inertia, I = 640.89 cm4
- Radius of gyration, r = 4.82 cm
- Elastic modulus, Ze = 102.54 cm3
- Plastic modulus, Zp = 121.87 cm3
Design Forces
The design tensile force (uniform along length):
T = 10 kN
The design shear force (occurs at support):
T = w×l = 1 (3) = 3 kN
The design bending moment (occurs at support):
Section Classification
Per Figure 2 of IS 800:2007:
d = D - 2×t = 125.5 - 2×6 = 113.5 mm
Per Table 2 of Ref. 1:
Therefore, the section is classified as "plastic".
From Table 10 of Ref. 1, the buckling class of a hot-rolled hollow section is "a".
Slenderness Ratio
Assume values of ky = 1 and kz = 1. Further assume similar bracing in both lateral directions (i.e., Ly = Lz = L = 3.0 m.
The slenderness ratio of the section is:
Tension Capacity
(Cl. 6.2) |
Assume a welded connection as the net section has not been specified: ɑ = 0.8.
(Cl. 6.3) |
Critical stress ratio: T / Tdg = 10 / 628 = 0.016
Compression Capacity
(Checked for completeness even though the member is loaded in tension)
Non-dimensional slenderness ratio for section:
For buckling class "a", the imperfection factor, ɑ = 0.21 (Table 7 of Ref. 1).
The stress reduction factor is:
(Cl. 7.1.2.1) |
Shear Capacity
The shear area, Av, for a rectangular hollow section is .
Since , shear buckling check per Cl. 8.4.2.1 does not apply.
Critical stress ratio: V / Vd = 3 / 181 = 0.017
Bending Capacity
For a "plastic" section, βb = 1.
The section is subject to low shear (V = 3 kN < 0.6Vd = 0.6(181) = 109 kN).
(Cl. 8.2.1.2) |
Check against excessive deformation under service loads for a cantilever member:
Does not govern.
Critical stress ratio: M / Md = 4.5 / 27.7 = 0.162
Combined Tension and Bending Capacity
(Cl. 9.3.1.1) |
= | |T| / Tdg = 10 / 628 = 0.016 | |
= | ||
= |
= |
Check the reduced effective moment under tension:
(Cl. 9.3.2.1) |
= |
Critical stress ratio: Meff / Md = 4.13 / 27.7 = 0.149
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Slenderness ratio | 62.2 | 62.25 | negligible | |
Tension capacity, yielding of gross section (kN) | 628 | 627.273 | negligible | |
Tension capacity, rupture of net section (kN) | 743 | 741.888 | negligible | |
Critical stress ratio for tension capacity | 0.016 | 0.016 | none | |
Axial compression capacity (kN) | 535 | 534.107 | negligible | |
Shear capacity (kN) | 181 | 181.078 | negligible | |
Critical stress ratio for shear | 0.017 | 0.017 | none | |
Bending capacity (kN·m) | 27.7 | 27.727 | negligible | |
Critical stress ratio for bending | 0.162 | 0.162 | none | |
Ratio as per clause 9.3.1.1 | 0.098 | 0.098 | none | |
Ratio as per clause 9.3.2.1 | 0.149 | 0.149 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\India\IS 800 2007 LSD - Tube - Tension and Bending.STD is typically installed with the program.
The following design parameters are used:
- The value of CAN 1 is used to indicate a cantilever member.
- The value of LAT 1 is used to indicate that member is laterally supported.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 6-Sep-22
ENGINEER NAME TK
END JOB INFORMATION
*****************************************************************************
*This problem has been created to validate the program calculated design
*results of laterally supported tube section subjected to axial tension and
*biaxial bending, designed using IS 800 2007 (LSD)
*****************************************************************************
INPUT WIDTH 79
SET SHEAR
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 0 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 INDIAN
1 TABLE ST TUB1251256
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
JOINT LOAD
2 FX 10
MEMBER LOAD
1 UNI GY -1
1 UNI GZ -1
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
PARAMETER 1
CODE IS800 LSD
CAN 1 ALL
LAT 1 ALL
TRACK 2 ALL
CHECK CODE ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - IS-800-2007-LSD (V2.2) **************************************************** |----------------------------------------------------------------------------------| | Member Number: 1 | | Member Section: ST TUB1251256 (INDIAN SECTIONS) | | Status: PASS Ratio: 0.162 Critical Load Case: 1 Location: 0.00 | | Critical Condition: Sec. 8.2.1.2 | | Critical Design Forces: (Unit: KN METE) | | FX: -10.000E+00 T FY: 3.000E+00 FZ: 3.000E+00 | | MX: 0.000E+00 MY: -4.500E+00 MZ: 4.500E+00 | |----------------------------------------------------------------------------------| | Section Properties: (Unit: CM ) | | AXX: 27.600E+00 IZZ: 641.000E+00 RZZ: 4.819E+00| | AYY: 13.800E+00 IYY: 641.000E+00 RYY: 4.819E+00| | AZZ: 13.800E+00 IXX: 1.038E+03 CW: 0.000E+00| | ZEZ: 102.560E+00 ZPZ: 122.000E+00 | | ZEY: 102.560E+00 ZPY: 122.000E+00 | |----------------------------------------------------------------------------------| | Slenderness Check: (Unit: KN METE) | | Actual Length: 3.000E+00 | | Parameters: LZ: 3.000E+00 LY: 3.000E+00 | | KZ: 1.000 KY: 1.000 | | Actual Ratio: 62.25 Allowable Ratio: 400.00 LOAD: 1 | |----------------------------------------------------------------------------------| | Section Class: Plastic; Flange Class: Plastic; Web Class: Plastic| |----------------------------------------------------------------------------------| STAAD SPACE -- PAGE NO. 7 STAAD.PRO CODE CHECKING - IS-800-2007-LSD (V2.2) **************************************************** |----------------------------------------------------------------------------------| | Member Number: 1 | | Member Section: ST TUB1251256 (INDIAN SECTIONS) | |----------------------------------------------------------------------------------| | Tension: (Unit: KN METE) | | Parameters: FYLD: 250.000E+03 FU: 420.000E+03 | | NSF: 1.000 ALPHA: 0.800 | | Yielding : Design Force: 10.000E+00 LC: 1 | | Capacity: 627.273E+00 As per: Sec. 6.2 | | Rupture : Design Force: 10.000E+00 LC: 1 | | Capacity: 741.888E+00 As per: Sec. 6.3 | |----------------------------------------------------------------------------------| | Compression: (Unit: KN METE) | | Buckling Class: Major: a Minor: a As per:Cl. 7.1.2.2 | | Major Axis: Design Force: 0.000E+00 LC: 0 Loc: 0.000 | | Capacity: 534.107E+00 As per: Sec. 7.1.2 | | Minor Axis: Design Force: 0.000E+00 LC: 0 Loc: 0.000 | | Capacity: 534.107E+00 As per: Sec. 7.1.2 | |----------------------------------------------------------------------------------| | Shear: (Unit: KN ) | | Major Axis: Design Force: 3.000E+00 LC: 1 Loc: 0.000 | | Capacity: 181.078E+00 As per: Sec. 8.4 | | Minor Axis: Design Force: 3.000E+00 LC: 1 Loc: 0.000 | | Capacity: 181.078E+00 As per: Sec. 8.4 | |----------------------------------------------------------------------------------| | Bending: (Unit: KN METE) | | Parameters: Laterally Supported KX: 1.00 LX: 3.000E+00 Cantilever | | Major Axis: Design Force: 4.500E+00 LC: 1 Loc: 0.000 | | Capacity: 27.727E+00 As per: Sec. 8.2.1.2 | | Minor Axis: Design Force: -4.500E+00 LC: 1 Loc: 0.000 | | Capacity: 27.727E+00 As per: Sec. 8.2.1.2 | |----------------------------------------------------------------------------------| | Combined Interaction: | | Parameters: PSI: 1.00 CMX: 0.900 CMY: 0.900 CMZ: 0.900 | | Section Strength: Ratio: 0.098 As per: Sec. 9.3.1.1 | | LC: 1 Loc: 0.000 | | Overall Member Strength (Bending+Tension): | | Equation 1(Z): Ratio: 0.149 As per: Sec. 9.3.2.1 | | LC: 1 Loc: 0.000 | | Equation 2(Y): Ratio: 0.149 As per: Sec. 9.3.2.1 | | LC: 1 Loc: 0.000 | |----------------------------------------------------------------------------------| | Checks Ratio Load Case No. Location from Start( METE) | | | | Tension 0.016 1 0.000E+00 | | Compression 0.000 0 0.000E+00 | | Shear Major 0.017 1 0.000E+00 | | Shear Minor 0.017 1 0.000E+00 | | Bend Major 0.162 1 0.000E+00 | | Bend Minor 0.162 1 0.000E+00 | | Sec. 9.3.1.1 0.098 1 0.000E+00 | | Sec. 9.3.2.1 (Z) 0.149 1 0.000E+00 | | Sec. 9.3.2.1 (Y) 0.149 1 0.000E+00 | |----------------------------------------------------------------------------------|