V. IS 801-Zee with lips having axial compression and bending
Verification example for a cold-formed beam subject to axial compression and bending moment according to IS:801-1975.
Details
The section used is a IS 125ZS45x2.55 section. The beam is a 2 m span subject to axial compression and major axis bending moments. The span is a propped cantilever (one end fixed, the other pinned).
- E = 203,400 MPa = 2,074,000 kgf/cm2
- Fyi = 350 MPa = 3,569 kgf/cm2
- G = 77,968 MPa = 795,000 kgf/cm2
- P = 25 kN
- Mz = 2.71 kN·m
- Vy = 6.85 kN
- Depth of section, d = 125 mm
- Width of section, b = 45 mm
- Thickness, t = 2.55 mm
- Length of lips, c = 20 mm
- Fillet radius, r = 3.825 mm
- Area, A = 5.94 cm2
- Moment of inertia about the major axis, Izz = 135 cm3
- Moment of inertia about the minor axis, Iyy = 27.5 cm3
- Section modulus about the major axis, Zxx = 21.6 cm3
- Section modulus about the minor axis, Zyy = 6.3 cm3
- Torsion constant, J = 0.125 cm4
- Warping constant, Cw = 834 cm6
- Number of corners, Nc = 4
- Area of corner, Ac = 74 mm2
Section Dimension Checks
Check flat width ratio per Cl. 5.2.3:
w = b - 2 × (r + t) = 4.5 - 2 × (0.3825 + 0.255) = 3.225 cm
Hence, OK.
Check web height to thickness ratio per Cl. 5.2.4:
h = D - 2(t + r) = 125 - 2×(2.55 + 3.825) = 112.3 mm
Hence, OK.
Check slenderness ratio limits per Cl. 6.3.3:
Radius of gyration, about major axis
Radius of gyration, about minor axis
Hence, OK.
Compressive Stress
Actual stress in compressionCalculate the factor, Q, per Cl. 6.6.1.1(a):
Therefore, beff = w = 3.225 cm and Alost,f = (w - beff) × t = 0 cm2
Compression stress:
Calculate the effective depth of the section by re-arranging the flange ratio:
(5.2.1.1) |
and Alost,d = (h - heff) × t = (11.23 - 9.015) × 0.255 = 0.565 cm2
Therefore the effective area, Aeff = A - Alost,f - Alost,d = 5.94 - 0 - 0.565 = 5.38 cm2
Allowable compression stress:
Allowable compression stress for members braced against twisting (Ref Cl. 6.6.1.1):
Maximum allowable compressive stress for flexural torsional buckling (Ref Cl.6.6.1.2). The section is symmetric, so the distance between the geometric and shear center, x0 = 0.
Therefore, the allowable compressive stress:
Stress ratio in compression: 42.1 / 108.9 = 0.387
Bending Stress
Actual bending stress:
Per Cl. 6.8, the maximum allowable stress on the extreme fiber:
Per Cl. 6.3(b) , the allowable bending stress for laterally unbraced beams:
Since ,
Stress ratio in bending: 125.5 / 130.1 = 0.963Shear Stress
Shear area:
Clear distance between flanges, h = d - 2t = 12.5 - 2× 0.255 = 11.99 cm
Actual shear stress:
Stress ratio in shear: 17.36 / 140 = 0.124
Bending in Web Stress
The actual bending stress in the web is calculated by interpolating from the bending stress diagram:
(6.4.2) |
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Allowable compression stress (MPa) | 108.9 | 109.052 | negligible | |
Actual compression stress (MPa) | 42.1 | 42.090 | negligible | |
Compression stress ratio | 0.387 | 0.386 | negligible | |
Allowable bending stress (MPa) | 130.1 | 130.131 | negligible | |
Actual bending stress (MPa) | 125.5 | 125.339 | negligible | |
Bending stress ratio | 0.963 | 0.963 | none | |
Allowable shear stress (MPa) | 140 | 140.01 | negligible | |
Actual shear stress (MPa) | 17.36 | 17.353 | negligible | |
Shear stress ratio | 0.124 | 0.124 | none | |
Web bending stress ratio | 0.568 | 0.572 | negligible | |
Combined Bending and Shear Stress Ratio | 0.132 | 0.132 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\India\IS 801-Zee with lips having axial compression and bending.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 27-Mar-19
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 2 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 COLDFORMED INDIAN
1 TABLE ST 125ZS45X2.55
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
2 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -5.5
LOAD 2 LOADTYPE None TITLE LOAD CASE 3
MEMBER LOAD
1 CON GX -25 0
LOAD COMB 4 COMBINATION LOAD CASE 4
1 1.0 2 1.0
PERFORM ANALYSIS
PRINT MEMBER PROPERTIES ALL
LOAD LIST 4
PARAMETER 1
CODE IS801
FU 450000 ALL
FYLD 350000 ALL
RATIO 1 ALL
TRACK 2 ALL
CWY 0 ALL
CHECK CODE 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: 125ZS45X2.55 LEN: 2.000 LOC: 0.000 | | STATUS: PASS RATIO: 0.963 REF: 6.3 LTB LC: 4 | |-----------------------------------------------------------------------------| | DESIGN FORCES: | | Fx:(C) 25.000 Fy: 6.854 Fz: 0.000 | | Mx: 0.000 My: 0.000 Mz: 2.707 | |-----------------------------------------------------------------------------| | SECTION PROPERTIES: (Unit: CM) | | Ag: 5.94000 Az: 2.29500 Ay: 3.94740 | | Cz: 4.37250 Cy: 6.25000 Z0: 0.00000 | | Iz: 135.00002 Iy: 27.50000 J: 0.12600 | | Sz: 21.60000 Sy: 6.30000 | | Rz: 4.76731 Ry: 2.15166 Cw: 834.00017 | |-----------------------------------------------------------------------------| | MATERIAL INFO: (Unit: MPa) | | Fy: 350.025 Fu: 450.032 E: 203404.356 G: 77968.401 | | Fya(compression): 350.025 Fya(bending): 350.025 | |-----------------------------------------------------------------------------| | 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: 92.952 Allowable: 200.000 Ratio: 0.465 | |-----------------------------------------------------------------------------| | CHECKS: | Stresses | | | | Loc. | Demand | L/C | Actual | Allow |Ratio | Ref CL | | |(MET) |(KN-MET)| | (MPa) | (MPa) | | | |--------------|------|--------|------|----------|----------|------|----------| | Tension | 2.000| -0.00| 4| 0.000 | 210.015 | 0.000| 6.1 | | Compression | 0.000| 25.00| 4| 42.090 | 109.052 | 0.386| 6.6.1.1 | | BendZComp | 0.000| 2.71| 4| 125.339 | 210.015 | 0.597| 6.3 | | BendZTens | 0.000| 2.71| 4| 125.339 | 210.015 | 0.597| 6.3 | | BendUnbraced | 0.000| 2.71| 4| 125.339 | 130.131 | 0.963| 6.3 LTB | | BendYComp | - | - | - | - | 210.015 | - | 6.3 | | BendYTens | - | - | - | - | 210.015 | - | 6.3 | | Bend Web | 0.000| 2.71| 4| 120.225 | 210.015 | 0.572| 6.4.2 | | Shear Z | - | - | - | - | 140.010 | - | 6.4.1 | | Shear Y | 0.000| 6.85| 4| 17.363 | 140.010 | 0.124| 6.4.1 | | Axial+Bend | 0.000| - | 4| - | - | 0.851| 6.7.2(a)2| | Bend+Shear | 0.000| - | 4| - | - | 0.132| 6.4.3 | |-----------------------------------------------------------------------------| | Effective Section Properties:(cm) | | Ae: 5.377 SzTop: 21.600 SzBot: 21.600 SyLeft: 6.275 SyRight: 6.275 | | Intermediate Results: Cb = 1.000 | |-----------------------------------------------------------------------------| NOTE: Torsion has not been considered in the design.