V. IS 800 2007 LSD - Pipe - Tension and Bending
Verify the design of a pipe section subject to axial tension and biaxial bending per the IS 800:2007 limit state method.
Details
The member is a 3 m long cantilever subject to a 10 kN tensile force and uniform bending moments of 1 kN/m along both major and minor axes. The section used is a 90 mm nominal bore with a wall thickness of 3.6 mm (STAAD.Pro section designation PIP10106L) and is braced to prevent lateral-torsional buckling. The steel has a yield strength of 250 MPa, an ultimate tensile strength of 420 MPa, and a modulus of elasticity of 205×(10)3 MPa.
Validation
Section Properties
Outer diameter, OD = 101.6 mm
Wall thickness, t = 3.6 mm
Inner diameter, ID = 101.6 - 2 × 3.6 = 94.4 mm
Cross-section area,
Moment of inertia about both axes,
Radius of gyration about both axes,
Elastic section modulus about both axes,
Plastic section modulus about both axes,
Constants
- γm0 = 1.1
- γm1 = 1.25
Section Classification
For circular, hollow tubes subjected to moment, OD/t = 28.22 < 42ε2 = 42
Therefore, the classification of the section is "plastic".
Hence, from Table 10 of IS 800:2007, the buckling class about both axes is "a".
Check Slenderness Ratio
ky = kz = 1
The maximum allowable slenderness ratio is 180.
Slenderness ratio about both axes, kzL / rz = 86.67 < 180
So the slenderness is within the limit.
Axial Tension Capacity
Check for yielding of gross section per Cl. 6.2:
Tdg = Ag × fy / γm0 = 11.08 × 250 / 1.1 = 251.8 kN
Check for rupture of critical section per Cl. 6.3:
α = 0.8
Tdn = α × Anet × fu / γm1 = 0.8 × 11.08 × 420 / 1.25 = 297.8 kN
Block shear areas are not specified and therefore not checked.
The critical tension ratio 10 / 251.8 = 0.040
Check Axial Compression
The non-dimensional slenderness ratio,
For buckling class "a", the imperfection factor, α = 0.21
So, as per Cl. 7.1.2.1 of IS 800:2007,
Therefore, axial compression capacity for both axes: Pdz = Axfcdz = 147.3 kN
The critical ratio for axial compression is 0 (i.e., no compression).
Check Shear Capacity
As per Cl. 8.4.1.1 of IS 800:2007, the shear area, Avz = 2×Ax / π = 7.054 cm2
So, as per Cl. 8.4.1,
Hence, shear capacity along major axis:
Shear force along both axes = 3 kN.
Critical shear ratio along both axes: 3 / 92.56 = 0.032
Check Bending Capacity
Since the section has been classified as "plastic", βb = 1.
Actual shear force in both axes, V = 3 kN < 0.6Vd = 55.53 kN. Hence, the section is subjected to low shear.
So, the governing bending strength with respect to the minor axis is Mdy = 7.861 kN·m
Actual bending moment about the minor axis is Mz = 4.5 kN·m.
The critical bending ratio in the minor axis is 4.5 / 7.861 = 0.572
Check Combined Interaction of Axial Compression and Bending
Section strength calculation as per Cl. 9.3.1:
n = N / Nd = 0.004
Hence, from Table 17:
α1 = 2
α2 = 2
Mndy = Mdy = 9.341 kN·m | (Cl. 9.3.1.2(c) ) |
1.04·Mdz·(1 - n1.7) = 8.175 kN·m > Mdz
Mndz = Mdz = 7.861 kN·m
Overall member strength in bending and axial compression
Meff / Mdz = 4.263 / 7.861 = 0.542
The loading and section is the same in both axes.
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Slenderness ratio | 86.46 | 86.67 | negligible | |
Tension capacity, gross yielding (kN) | 251.8 | 252.273 | negligible | |
Tension capacity, rupture of critical section (kN) | 297.8 | 298.368 | negligible | |
Axial compression capacity about both axes (kN) | 174.3 | 174.338 | negligible | |
Shear capacity in both axes (kN) | 92.56 | 92.723 | negligible | |
Ratio for shear | 0.032 | 0.032 | none | |
Bending capacity about both axes (kN·m) | 7.861 | 7.864 | negligible | |
Ratio for bending about both axes | 0.572 | 0.572 | none | |
Ratio per Cl. 9.3.1.1 | 0.655 | 0.655 | none | |
Ratio for both axes per Cl. 9.3.2.1 | 0.542 | 0.542 | 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 - Pipe - Tension and Bending.STD is typically installed with the program.
The following design parameters are used:
- The default value of ALPHA is used.
- The default values of KY and KZ are used.
- The default value of the maximum allowable slenderness ratio, MAIN, of 180 is used.
- The default value of Ψ.
- The beam type is a cantilever, specified by CAN 1
- The beam is laterally supported, specified by LAT 1
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 29-Jul-20
END JOB INFORMATION
*****************************************************************************
*This problem has been created to validate the program calculated design
*results of laterally supported pipe 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 PIP1016L
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 PIP1016L (INDIAN SECTIONS) | | Status: PASS Ratio: 0.655 Critical Load Case: 1 Location: 0.00 | | Critical Condition: Sec. 9.3.1.1 | | 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: 11.100E+00 IZZ: 133.000E+00 RZZ: 3.462E+00| | AYY: 7.066E+00 IYY: 133.000E+00 RYY: 3.462E+00| | AZZ: 7.066E+00 IXX: 266.000E+00 CW: 0.000E+00| | ZEZ: 26.181E+00 ZPZ: 34.600E+00 | | ZEY: 26.181E+00 ZPY: 34.600E+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: 86.67 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 PIP1016L (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: 252.273E+00 As per: Sec. 6.2 | | Rupture : Design Force: 10.000E+00 LC: 1 | | Capacity: 298.368E+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: 174.338E+00 As per: Sec. 7.1.2 | | Minor Axis: Design Force: 0.000E+00 LC: 0 Loc: 0.000 | | Capacity: 174.338E+00 As per: Sec. 7.1.2 | |----------------------------------------------------------------------------------| | Shear: (Unit: KN ) | | Major Axis: Design Force: 3.000E+00 LC: 1 Loc: 0.000 | | Capacity: 92.723E+00 As per: Sec. 8.4 | | Minor Axis: Design Force: 3.000E+00 LC: 1 Loc: 0.000 | | Capacity: 92.723E+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: 7.864E+00 As per: Sec. 8.2.1.2 | | Minor Axis: Design Force: -4.500E+00 LC: 1 Loc: 0.000 | | Capacity: 7.864E+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: 0.655 As per: Sec. 9.3.1.1 | | LC: 1 Loc: 0.000 | | Overall Member Strength (Bending+Tension): | | Equation 1(Z): Ratio: 0.542 As per: Sec. 9.3.2.1 | | LC: 1 Loc: 0.000 | | Equation 2(Y): Ratio: 0.542 As per: Sec. 9.3.2.1 | | LC: 1 Loc: 0.000 | |----------------------------------------------------------------------------------| | Checks Ratio Load Case No. Location from Start( METE) | | | | Tension 0.040 1 0.000E+00 | | Compression 0.000 0 0.000E+00 | | Shear Major 0.032 1 0.000E+00 | | Shear Minor 0.032 1 0.000E+00 | | Bend Major 0.572 1 0.000E+00 | | Bend Minor 0.572 1 0.000E+00 | | Sec. 9.3.1.1 0.655 1 0.000E+00 | | Sec. 9.3.2.1 (Z) 0.542 1 0.000E+00 | | Sec. 9.3.2.1 (Y) 0.542 1 0.000E+00 | |----------------------------------------------------------------------------------|