Verify the combined capacity of a rectangular hollow section per the AS4100:2020
code.
Reference
Standards Australia Committee BD-001. Steel structures AS 4100-2020.
Homebush, NSW. 2020.
American Institute of Steel Construction. Steel Construction
Manual. Thirteenth Edition. AISC. Chicago. 2005.
Problem
A 5 m long, simply-supported beam is subject to 400 kN axial force along with 120
kN/m load along the major axis and 100 kN/m transverse load along the minor axis.
The section is a US HSS20x12x5/8. The steel grade is equivelant to AS/NZS 1163
C250.
Section Properties
From reference #2:
Depth, d = 508 mm (20 in )
Width, b = 304.8 mm (12in)
Thickness, t = 14.8 mm (0.581)
Gross area of section, Ag = 22,580
mm2 (35.0 in2)
Moment of inertia about minor axis, Iy =
354.2×(10)6 mm4 (1,880
in4)
Radius of gyration about z-axis, rz = 186.2 mm
(7.33 in)
Radius of gyration about y-axis, ry = 125.2 mm
(4.930 in)
Member in-plane capacity about major axis,
ϕMiz
(kN·m)
776.8
776.4694
negligible
Member in-plane capacity about minor axis,
ϕMiy
(kN·m)
543.1
542.9421
negligible
Member combined capacity ratio for biaxial bending and
compression
0.826
0.826
negligible
STAAD.Pro Input
File
The file C:\Users\Public\Public Documents\STAAD.Pro
2024\Samples\Verification Models\09 Steel Design\Australia\AS4100 2020 - RHS Combined Capacity.std is typically installed with the program.
The 5 m physical member is modelled
using a single analytical
segment.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 03-Jun-24
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 5 5 0 0;
*
MEMBER INCIDENCES
1 1 5;
DEFINE PMEMBER
1 PMEMBER 1
*
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 FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
*
*
MEMBER PROPERTY 'US (AISC 2023).DB3'
1 TABLE 'HSS RECTANGLE' ST 'HSS20X12X.625'
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 PINNED
5 FIXED BUT FX MY MZ
PRINT ALL
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
JOINT LOAD
5 FX -400
MEMBER LOAD
1 UNI GY -120
1 UNI GZ -100
*
PERFORM ANALYSIS
*
PRINT ANALYSIS RESULTS
*
PARAMETER 1
CODE AS4100 2020
TRACK 2 ALL
CHECK CODE 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.
- Member : 1
|-----------------------------------------------------------------------------|
| Member No: 1 PROFILE: ST HSS20X12X.625 (STANDARD SECTI|NS)
| STATUS: PASS RATIO: 0.826 LOADCASE: 1* |
| LOCATION: 2.50 CRITERIA: AS-8.4.5.1 |
| FX: 400.000 C VY: 0.00000 VZ: 0.00000 |
| MX: 0.00000 MY: 312.500 MZ: -375.000 |
|-----------------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness : 39.921 |
| Allowable Slenderness: 180.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (Unit:mm) |
| Ag : 22.5806E+03 Azz : 9.6774E+03 Ayy : 15.1209E+03 |
| Izz : 782.5151E+06 Iyy : 354.2129E+06 J : 786.6774E+06 |
| Szz : 3.7690E+06 Syy : 2.6547E+06 Iw : 0.0000E+00 |
| Zzz : 3.0808E+06 Zyy : 2.3242E+06 |
| rz : 186.1567E+00 ry : 125.2462E+00 |
|-----------------------------------------------------------------------------|
| Material PROPERTIES (Unit:MPa) |
| Material Standard : AS 1163 |
| Nominal Grade : 250 |
| Residual Stress Category : HW (Heavily welded longitudinally) |
| E (#) : 205.0000E+03 G : 80.00E+03 |
| Fy(Flange): 250.0000E+00 Fy(Web): 250.0000E+00 Fu: 320.0000E+00|
|-----------------------------------------------------------------------------|
| Actual Member Length: 5.000 |
| Design Parameters |
| KZ : 1.00 KY : 1.00 NSF 1.00 PHI 0.90 |
| SKL: 1.00 SKT: 1.00 SKR 1.00 |
|-----------------------------------------------------------------------------|
| SECTION CLASSIFICATION |
| Z - Axis : Compact Y - Axis : Compact |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 12
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| Section Tension Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 5.0806E+03 0.000 Cl:7.2 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 22.5806E+03mm^2 Correction Factor (Kt) : 1.00|
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| Section Compression Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 400.0000E+00 5.0806E+03 0.079 Cl:6.2.1 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 22.5806E+03mm^2 |
| Effective Area (Ae) : 22.5806E+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 |
| 400.0000E+00 4.7402E+03 0.084 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Lez): 5.00 m |
| ab : 0.5000 Table 6.3.3(1)/6.3.3(2) |
| ln,z : 26.8591 AS 4100, 6.3.3 |
| aa,z : 11.8850 AS 4100, 6.3.3 |
| l,z : 32.8016 AS 4100, 6.3.3 |
| h,z : 0.0629 AS 4100, 6.3.3 |
| x,z : 4.5010 AS 4100, 6.3.3 |
| ac,z : 0.9330 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
| Member Compression Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 400.0000E+00 4.3947E+03 0.091 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Ley): 5.00 m |
| ab : 0.5000 Table 6.3.3(1)/6.3.3(2) |
| ln,y : 39.9214 AS 4100, 6.3.3 |
| aa,y : 18.2942 AS 4100, 6.3.3 |
| l,y : 49.0685 AS 4100, 6.3.3 |
| h,y : 0.1160 AS 4100, 6.3.3 |
| x,y : 2.3771 AS 4100, 6.3.3 |
| ac,y : 0.8650 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 13
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 208.3333E+00 1.3064E+03 0.159 Cl:5.11.2 1* 0.42 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmz) : 1.3064E+03 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 250.0000E+00 2.0413E+03 0.122 Cl:5.11.2 1* 0.42 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmy) : 2.0413E+03 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -375.0000E+00 848.0305E+00 0.442 Cl:5.2.1 1* 2.50 |
| Intermediate Results : |
| Eff. Section Modulus (Zez): 3.7690E-03 |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 312.4999E+00 597.3085E+00 0.523 Cl:5.2.1 1* 2.50 |
| Intermediate Results : |
| Eff. Section Modulus (Zey): 2.6547E-03 |
|-----------------------------------------------------------------------------|
| Member Bending Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -375.0000E+00 848.0305E+00 0.442 Cl:5.6.1.1(a) 1* 2.50 |
| 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) : 5.00 5.6.3 |
| Moment Modification Factor (am) : 1.17 5.6.1.1(a)(iii) |
| Reference Buckling Moment (Mo) : 42.4749E+03 5.6.1.2(a) |
| Slenderness Reduction Factor(asz) : 1.026 5.6.1.1(a)(iv) |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 14
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR COMBINED INTERACTION |
|-----------------------------------------------------------------------------|
| Section Combined Capacity: |
| RATIO REFERENCE L/C LOC |
| 0.683 Cl 8.3.4 1* 2.50 |
| Intermediate Results : |
| Axial Capacity (fNs/fNt) : 5.0806E+03 8.3.1 |
| Section Moment Capacity (fMsz) : 848.0305E+00 5.2.1 |
| Section Moment Capacity (fMsy) : 597.3085E+00 5.2.1 |
| Reduced Section Moment Capacity (fMrz) : 848.0305E+00 8.3.2 |
| Reduced Section Moment Capacity (fMry) : 597.3085E+00 8.3.3 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: In-plane |
| RATIO REFERENCE L/C LOC |
| 0.576 Cl:8.4.2.2 1* 2.50 |
| Intermediate Results : |
| Axial Capacity (fNcz) : 4.7402E+03 8.4.2.2 |
| Axial Capacity (fNcy) : 4.3947E+03 8.4.2.2 |
| Moment Capacity (fMiz) : 776.4694E+00 8.4.2.2 |
| Moment Capacity (fMiy) : 542.9421E+00 8.4.2.2 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Out-of-plane(Comp) |
| RATIO REFERENCE L/C LOC |
| 0.486 Cl:8.4.4.1 1* 2.50 |
| Intermediate Results : |
| Axial Capacity (fNcy) : 4.3947E+03 8.4.4.1 |
| Moment Capacity (fMbz) : 848.0305E+00 8.4.4.1 |
| Moment Capacity (fMozc) : 770.8436E+00 8.4.4.1 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Biaxial(Comp) |
| RATIO REFERENCE L/C LOC |
| 0.826 Cl:8.4.5.1 1* 2.50 |
| Intermediate Results : |
| Moment Capacity (fMcz) : 770.8436E+00 8.4.5.1 |
| Moment Capacity (fMiy) : 542.9421E+00 8.4.5.1 |
|-----------------------------------------------------------------------------|
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.
- Member : 1
|-----------------------------------------------------------------------------|
| Member No: 1 PROFILE: ST HSS20X12X.625 (STANDARD SECTI|NS)
| STATUS: PASS RATIO: 0.826 LOADCASE: 1* |
| LOCATION: 2.50 CRITERIA: AS-8.4.5.1 |
| FX: 400.0 C VY: 0.000 VZ: 0.000 |
| MX: 0.000 MY: 312.5 MZ: -375.0 |
|-----------------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness : 39.921 |
| Allowable Slenderness: 180.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (Unit:mm) |
| Ag : 22.5806E+03 Azz : 9.6774E+03 Ayy : 15.1209E+03 |
| Izz : 782.5151E+06 Iyy : 354.2129E+06 J : 786.6774E+06 |
| Szz : 3.7690E+06 Syy : 2.6547E+06 Iw : 0.0000E+00 |
| Zzz : 3.0808E+06 Zyy : 2.3242E+06 |
| rz : 186.1567E+00 ry : 125.2462E+00 |
|-----------------------------------------------------------------------------|
| Material PROPERTIES (Unit:MPa) |
| Material Standard : AS 1163 |
| Nominal Grade : 250 |
| Residual Stress Category : HW (Heavily welded longitudinally) |
| E (#) : 205.0000E+03 G : 80.00E+03 |
| Fy(Flange): 250.0000E+00 Fy(Web): 250.0000E+00 Fu: 320.0000E+00|
|-----------------------------------------------------------------------------|
| Actual Member Length: 5.000 |
| Design Parameters |
| KZ : 1.00 KY : 1.00 NSF 1.00 PHI 0.90 |
| SKL: 1.00 SKT: 1.00 SKR 1.00 |
|-----------------------------------------------------------------------------|
| SECTION CLASSIFICATION |
| Z - Axis : Compact Y - Axis : Compact |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 12
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| Section Tension Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+0 5.0806E+03 0.000 Cl:7.2 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 22.5806E+03mm^2 Correction Factor (Kt) : 1.00|
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| Section Compression Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 400.0000E+0 5.0806E+03 0.079 Cl:6.2.1 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 22.5806E+03mm^2 |
| Effective Area (Ae) : 22.5806E+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 |
| 400.0000E+0 4.7402E+03 0.084 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Lez): 5.00 m |
| ab : 0.5000 Table 6.3.3(1)/6.3.3(2) |
| ln,z : 26.8591 AS 4100, 6.3.3 |
| aa,z : 11.8850 AS 4100, 6.3.3 |
| l,z : 32.8016 AS 4100, 6.3.3 |
| h,z : 0.0629 AS 4100, 6.3.3 |
| x,z : 4.5010 AS 4100, 6.3.3 |
| ac,z : 0.9330 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
| Member Compression Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 400.0000E+0 4.3947E+03 0.091 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Ley): 5.00 m |
| ab : 0.5000 Table 6.3.3(1)/6.3.3(2) |
| ln,y : 39.9214 AS 4100, 6.3.3 |
| aa,y : 18.2942 AS 4100, 6.3.3 |
| l,y : 49.0685 AS 4100, 6.3.3 |
| h,y : 0.1160 AS 4100, 6.3.3 |
| x,y : 2.3771 AS 4100, 6.3.3 |
| ac,y : 0.8650 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 13
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 208.3333E+0 1.3064E+03 0.159 Cl:5.11.2 1* 0.42 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmz) : 1.3064E+03 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 250.0000E+0 2.0413E+03 0.122 Cl:5.11.2 1* 0.42 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmy) : 2.0413E+03 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -375.0000E+0 848.0305E+00 0.442 Cl:5.2.1 1* 2.50 |
| Intermediate Results : |
| Eff. Section Modulus (Zez): 3.7690E+06 mm3 |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 312.4999E+0 597.3085E+00 0.523 Cl:5.2.1 1* 2.50 |
| Intermediate Results : |
| Eff. Section Modulus (Zey): 2.6547E+06 mm3 |
|-----------------------------------------------------------------------------|
| Member Bending Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| -375.0000E+0 848.0305E+00 0.442 Cl:5.6.1.1(a) 1* 2.50 |
| 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) : 5.00 5.6.3 |
| Moment Modification Factor (am) : 1.17 5.6.1.1(a)(iii) |
| Reference Buckling Moment (Mo) : 42.4749E+03 5.6.1.2(a) |
| Slenderness Reduction Factor(asz) : 1.026 5.6.1.1(a)(iv) |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 14
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR COMBINED INTERACTION |
|-----------------------------------------------------------------------------|
| Section Combined Capacity: |
| RATIO REFERENCE L/C LOC |
| 0.683 Cl 8.3.4 1* 2.50 |
| Intermediate Results : |
| Axial Capacity (fNs/fNt) : 5.0806E+03 8.3.1 |
| Section Moment Capacity (fMsz) : 848.0305E+00 5.2.1 |
| Section Moment Capacity (fMsy) : 597.3085E+00 5.2.1 |
| Reduced Section Moment Capacity (fMrz) : 848.0305E+00 8.3.2 |
| Reduced Section Moment Capacity (fMry) : 597.3085E+00 8.3.3 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: In-plane |
| RATIO REFERENCE L/C LOC |
| 0.576 Cl:8.4.2.2 1* 2.50 |
| Intermediate Results : |
| Axial Capacity (fNcz) : 4.7402E+03 8.4.2.2 |
| Axial Capacity (fNcy) : 4.3947E+03 8.4.2.2 |
| Moment Capacity (fMiz) : 776.4694E+00 8.4.2.2 |
| Moment Capacity (fMiy) : 542.9421E+00 8.4.2.2 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Out-of-plane(Comp) |
| RATIO REFERENCE L/C LOC |
| 0.486 Cl:8.4.4.1 1* 2.50 |
| Intermediate Results : |
| Axial Capacity (fNcy) : 4.3947E+03 8.4.4.1 |
| Moment Capacity (fMbz) : 848.0305E+00 8.4.4.1 |
| Moment Capacity (fMozc) : 770.8436E+00 8.4.4.1 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Biaxial(Comp) |
| RATIO REFERENCE L/C LOC |
| 0.826 Cl:8.4.5.1 1* 2.50 |
| Intermediate Results : |
| Moment Capacity (fMcz) : 770.8436E+00 8.4.5.1 |
| Moment Capacity (fMiy) : 542.9421E+00 8.4.5.1 |
|-----------------------------------------------------------------------------|