V. AS4100 2020 - WF Combined Capacity
Verify the capacity under combined bending and compression load of a compact wide flange section as per the AS4100:2020 code.
Reference
-
Standards Australia Committee BD-001. Steel structures AS 4100-2020. Homebush, NSW. 2020.
- Liberty Steel. Hot Rolled and Structural Steel Products. Ninth Edition. October, 2019. Liberty OneSteel Pty. Sydney, NSW, Australia. https://www.infrabuild.com/resources/product-guides-resources/hot-rolled-structural-steel-products-catalogue/
Problem
The member is a 2 m long, simply-supported beam with a tensile load of 1,500 kN and transverse loads of 4 kN/m along both major and minor axes. The section is a 250 UB 37.3. The material is grade AS/NZS 3679.1 350 steel. Use a net section factor of 0.905.
Section Properties
From reference #2:
- Depth, d = 256.2 mm
- Flange width, bf = 146 mm
- Flange thickness, tf = 10.9 mm
- Web thickness, tw = 6.4 mm
- Depth between flanges, d1 = 234.4 mm
- Gross area of section, Ag = 4,750 mm2
- Elastic section modulus about x-axs, Zx = 435×(10)3 mm3
- Plastic section modulus about x-axs, Sx = 486×(10)3 mm3
- Elastic section modulus about y-axs, Zy = 77.5×(10)3 mm3
- Plastic section modulus about y-axs, Sy = 119×(10)3 mm3
- Torsional moment of inertia, J = 158×(10)3 mm4
- Warping constant, Iw = 85.2×(10)9 mm6
Material Properties
From references # 1 and #2:
- Yield strength of flanges, fyf = 360 MPa
- Yield strength of web, fyw = 360 MPa
- Ultimate strenght, fu = 480 MPa
- Modulus of elasticity, E = 200,000 MPa
- Shear modulus, G = 80,000 MPa
Calculations
Design Forces
Section Slenderness
From reference #2, a 250 UB 37.3 is compact
about the Z and Y axes
(noted as x and y axes in the reference) for grade AS/NZS 3679.1-350 steel.
The elastic section moduli for design, Zez =
486×(10)3 mm3 and
Zey = 116×(10)3
mm3.
The nominal moment capacity:
Capacity ratio for bending about the z axis:
The nominal moment capacity:
Capacity ratio for bending about the y axis:
The net area: An = 0.905 Ag = 0.905 × 4,750 = 4,299 mm3.
Capacity ratio for tension:
Combined Bending and Tension Interaction
Uniaxial bending capacity about the major axis (per Cl. 8.3.2):
The section is compact, so
Capacity ratio for bending about the z axis:
Uniaxial bending capacity about the minor axis (per Cl. 8.3.2):
The section is compact, so
Capacity ratio for bending about the z axis:
Biaxial Bending
The section is compact, so
Member Out-of-Plane Capcity
Assume that the length coefficients, kt, kl, and kr are all equal 1.0. Therefore, le = L = 2,000 mm
The moment modification factor, αm = 2.5, per Cl. 5.6.1.1 (a) iii.
The slenderness reduction factor:
Capacity ratio for bending about the z axis:
Biaxial Bending per Cl. 8.4.5.2
Comparison
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Reduced moment section capacty about Z axis (kN·m) | 4.71 | 4.7086 | negligible | |
| Reduced moment section capacty about Y axis (kN·m) | 2.24 | 2.2438 | negligible | |
| Biaxial bending ratio | 0.975 | 0.975 | none | |
| Out-of-plane Combined Capacity in Tension (kN·m) | 4.71 | 4.7086 | negligible | |
| Biaxial bending ratio for tension | 1.153 | 1.153 | none |
STAAD.Pro Input File
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples\Verification Models\09 Steel Design\Australia\AS4100 2020 - WF Combined Capacity.STD is typically installed with the program.
The following design parameters are used:
- Hot-rolled steel is specified using
IST 2 - Grade AS/NZS 3679.1 350 steel:
SGR 2 - The 2 m physical member is modelled using a single analytical segment
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 10-June-2024
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 0 2;
MEMBER INCIDENCES
1 2 1;
DEFINE PMEMBER
1 PMEMBER 1
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2e+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 'AUSTRALIA (AS 2024).DB3'
1 TABLE 'UNIVERSAL BEAM' ST '250 UB 37.3'
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED BUT FZ MX MY
2 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -4
1 UNI GX 4
JOINT LOAD
1 FZ -1500
PERFORM ANALYSIS
PARAMETER 1
CODE AS4100 2020
SGR 2 PMEMB 1
IST 2 PMEMB 1
NSF 0.905 PMEMB 1
TRACK 2 PMEMB 1
CHECK CODE PMEMB ALL
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
ALL UNITS ARE IN - KN MET UNLESS OTHERWISE Noted
**DESIGN Notes**
------------
1. (*) next to a Load Case number signifies that a P-Delta analysis has not been performed for
that particular Load Case; i.e. analysis does not include second-order effects.
2. ϕ = 0.9 for all the calculations [AS4100 Table 3.4]
3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per AS4100 1.4.
- PMember : 1
|-----------------------------------------------------------------------------|
|* PMember No: 1 PROFILE: ST 250 UB 37.3 (STANDARD SECTI|NS)
| STATUS: FAIL RATIO: 1.153 LOADCASE: 1* |
| LOCATION: 0.03 CRITERIA: AS-8.4.5.2 |
| FX: 1500.00 T VY: 0.00000 VZ: 0.00000 |
| MX: 0.00000 MY: -2.00000 MZ: -2.00000 |
|-----------------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness : 57.939 |
| Allowable Slenderness: 400.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (Unit:mm) |
| Ag : 4.7500E+03 Azz : 3.1828E+03 Ayy : 1.6384E+03 |
| Izz : 55.7000E+06 Iyy : 5.6600E+06 J : 158.0000E+03 |
| Szz : 485.9999E+03 Syy : 119.0000E+03 Iw : 85.0047E+09 |
| Zzz : 435.1562E+03 Zyy : 77.5342E+03 |
| rz : 108.2881E+00 ry : 34.5193E+00 |
|-----------------------------------------------------------------------------|
| Material PROPERTIES (Unit:MPa) |
| Material Standard : AS/NZS 3679.1 |
| Nominal Grade : 350 |
| Residual Stress Category : HR (Hot-rolled) |
| E (#) : 200.0000E+03 G : 80.00E+03 |
| Fy(Flange): 360.0000E+00 Fy(Web): 360.0000E+00 Fu: 480.0000E+00|
|-----------------------------------------------------------------------------|
| Actual Member Length: 2.000 |
| Design Parameters |
| KZ : 1.00 KY : 1.00 NSF 0.90 PHI 0.90 |
| SKL: 1.00 SKT: 1.00 SKR 1.00 |
|-----------------------------------------------------------------------------|
| SECTION CLASSIFICATION |
| Z - Axis : Compact Y - Axis : Compact |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 4
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| Section Tension Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -1.5000E+03 1.5390E+03 0.975 Cl:7.2 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 4.2987E+03mm^2 Correction Factor (Kt) : 1.00|
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| Section Compression Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 1.5390E+03 0.000 Cl:6.2.1 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 4.7500E+03mm^2 |
| Effective Area (Ae) : 4.7500E+03mm^2 Ref : Cl. 6.2.3 / 6.2.4 |
| Form Factor (Kf) : 1.000 Ref : Cl. 6.2.2 |
|-----------------------------------------------------------------------------|
| Member Compression Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 1.4942E+03 0.000 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Lez): 2.00 m |
| ab : 0.0000 Table 6.3.3(1)/6.3.3(2) |
| ln,z : 22.1631 AS 4100, 6.3.3 |
| aa,z : 8.2614 AS 4100, 6.3.3 |
| l,z : 22.1631 AS 4100, 6.3.3 |
| h,z : 0.0282 AS 4100, 6.3.3 |
| x,z : 8.9779 AS 4100, 6.3.3 |
| ac,z : 0.9709 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
| Member Compression Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 1.1562E+03 0.000 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Ley): 2.00 m |
| ab : 0.0000 Table 6.3.3(1)/6.3.3(2) |
| ln,y : 69.5264 AS 4100, 6.3.3 |
| aa,y : 20.2151 AS 4100, 6.3.3 |
| l,y : 69.5264 AS 4100, 6.3.3 |
| h,y : 0.1826 AS 4100, 6.3.3 |
| x,y : 1.4909 AS 4100, 6.3.3 |
| ac,y : 0.7513 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 5
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -3.3333E+00 618.7363E+00 0.005 Cl:5.11.2 1* 0.17 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmz) : 618.7363E+00 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 3.3333E+00 318.5049E+00 0.010 Cl:5.11.2 1* 0.17 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmy) : 318.5049E+00 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -2.0000E+00 157.4640E+00 0.013 Cl:5.2.1 1* 1.00 |
| Intermediate Results : |
| Eff. Section Modulus (Zez): 485.9999E-06 |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -2.0000E+00 37.6816E+00 0.053 Cl:5.2.1 1* 1.00 |
| Intermediate Results : |
| Eff. Section Modulus (Zey): 116.3014E-06 |
|-----------------------------------------------------------------------------|
| Member Bending Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -2.0000E+00 147.7509E+00 0.014 Cl:5.6.1.1(a) 1* 1.00 |
| Intermediate Results : |
| Twist Restraint Factor (kt) : 1.00 Table 5.6.3(1) |
| Load Height Factor (kl) : 1.00 Table 5.6.3(2) |
| Lat. Rot. Restraint Factor (kr) : 1.00 Table 5.6.3(3) |
| Effective Length (le) : 2.00 5.6.3 |
| Moment Modification Factor (am) : 1.17 5.6.1.1(a)(iii) |
| Reference Buckling Moment (Mo) : 390.4741E+00 5.6.1.2(a) |
| Slenderness Reduction Factor(asz) : 0.805 5.6.1.1(a)(iv) |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 6
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR COMBINED INTERACTION |
|-----------------------------------------------------------------------------|
| Section Combined Capacity: |
| RATIO REFERENCE L/C LOC |
| 0.975 Cl 8.3.4 1* 1.00 |
| Intermediate Results : |
| Axial Capacity (fNs/fNt) : 1.5390E+03 8.3.1 |
| Section Moment Capacity (fMsz) : 157.4640E+00 5.2.1 |
| Section Moment Capacity (fMsy) : 37.6816E+00 5.2.1 |
| Reduced Section Moment Capacity (fMrz) : 4.7086E+00 8.3.2 |
| Reduced Section Moment Capacity (fMry) : 2.2438E+00 8.3.3 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Out-of-plane(Tens) |
| RATIO REFERENCE L/C LOC |
| 0.425 Cl:8.4.4.2 1* 1.00 |
| Intermediate Results : |
| Axial Capacity (fNt) : 1.5390E+03 8.4.4.2 |
| Moment Capacity (fMbz) : 147.7509E+00 8.4.4.2 |
| Moment Capacity (fMozt) : 4.7086E+00 8.4.4.2 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Biaxial(Tens) |
| RATIO REFERENCE L/C LOC |
| 1.153 Cl:8.4.5.2 1* 1.00 |
| Intermediate Results : |
| Moment Capacity (fMtz) : 4.7086E+00 8.4.5.2 |
| Moment Capacity (fMry) : 2.2438E+00 8.4.5.2 |
|-----------------------------------------------------------------------------|