V. AS4100 1998 - Cantilever subject to tension and bending
Verify the tension and out-of-plane bending capacities of an I section cantilever beam per the AS 4100 1998 code.
Details
The cantilevered member is 2 m in length. The section is a 250UC89.5 of grade 300 steel. The member is subject to 434 kN in tension.
Section Properties
- Cross-sectional area, Ag = 11,400 mm2
- Plastic section modulus, Sxx = 1.23×106 mm3
Material Properties
- E = 199,947 MPa
- G = 80,000 MPa
- Fy,web = 300 MPa
- Fy,flange = 280 MPa
- Fu = 440 MPa
Calculations
Validation
Axial Tension Capacity
Gross yielding:
Fracture:
Assume net area, An , is equal to the gross area.
Kt = correction factor for distribution of forces = 1.0
Nt is the lesser of Nty and Ntf, Nt = 3,190 kN
Section Bending Capacity
Axial tensile load, N, mitigating flexural-torsional buckling:
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| Axial tension capacity (kN) | 2,870 | 2,872 | negligible | |
| Member combined out-of-plane bending and tension (kN·m) | 310 | 309.96 | negligible |
Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2026\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - Cantilever subject to tension and bending.std is typically installed with the program.
STAAD
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 21-Jul-21
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 PMEMBER
1 PMEMBER 1
DEFINE MATERIAL START
ISOTROPIC STEEL
E 1.99947e+08
POISSON 0.3
DENSITY 76.8191
ALPHA 6.5e-06
DAMP 0.03
G 7.7221e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AUSTRALIAN
1 TABLE ST UC250X89.5
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON X 434 2 0.28
JOINT LOAD
2 FY -88
PERFORM ANALYSIS
PARAMETER 1
CODE AS4100 1998
TRACK 2 PMEMB 1
PBRACE TOP 0 F 1 U PMEMB 1
PBRACE BOTTOM 0 F 1 U PMEMB 1
ALM 1 PMEMB 1
CHECK CODE PMEMB ALL
FINISH
Output
STAAD.Pro CODE CHECKING - ( AS4100-1998 ) V2.3
****************************************************
MEMBER DESIGN OUTPUT FOR PMEMBER 1
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.
DESIGN SUMMARY
=====================================================================================
Designation: ST UC250X89.5 (AUSTRALIAN SECTIONS)
Governing Load Case: 1*
Governing Criteria: AS-5.1
Governing Ratio: 0.581 (PASS)
SECTION PROPERTIES
=====================================================================================
d: 260.0000 mm bf: 256.0000 mm
tf: 17.3000 mm tw: 10.5000 mm
Ag: 11400.0000 mm2 J: 1.0400E+06 mm4 Iw: 712.7298E+09 mm6
Iz: 143.0000E+06 mm4 Sz: 1.2300E+06 mm3 (plastic) Zz: 1.1000E+06 mm3 (elastic)
rz: 111.9994E+00 mm
Iy: 48.4000E+06 mm4 Sy: 575.0000E+03 mm3 (plastic) Zy: 378.1250E+03 mm3 (elastic)
ry: 65.1584E+00 mm
MATERIAL PROPERTIES
=====================================================================================
Material Standard : AS/NZS 3679.1
Nominal Grade : 300
Residual Stress Category : HR (Hot-rolled)
E (#) :199947.000 MPa [AS 4100 1.4]
G : 80000.000 MPa [AS 4100 1.4]
fy, flange : 280.000 MPa [AS 4100 Table 2.1]
fy, web : 320.000 MPa [AS 4100 Table 2.1]
fu : 440.000 MPa [AS 4100 Table 2.1]
SLENDERNESS
=====================================================================================
Actual slenderness: 30.694
Allowable slenderness: 400.000
STAAD SPACE -- PAGE NO. 4
BENDING
=====================================================================================
Section Bending Capacity
Critical Load Case: 1* Critical Ratio: 0.568
Critical Location: 0.000 m from Start.
Mz* = 176.0000E+00 KNm My* = 0.0000E+00 KNm
Z-Axis Section Slenderness: Compact Y-Axis Section Slenderness: Compact
Zez = 1.2300E+06 mm3 Zey = 567.1875E+03 mm3
ϕMsz = 309.9600E+00 KNm ϕMsy = 142.9313E+00 KN[AS 4100 5.2.1]
Member Bending Capacity
Critical Load Case: 1* Critical Ratio: 0.581
Critical Location: 0.000 m from Start.
Crtiical Segment/Sub-segment:
Location (Type): 0.00 m(F )- 2.00 m(U )
Length: 2.00 m
Mz* = 176.0000E+00 KNm My* = 0.0000E+00 KNm
kt = 1.00 [AS4100 Table 5.6.3(1)]
kl = 1.00 [AS4100 Table 5.6.3(2)]
kr = 1.00 [AS4100 Table 5.6.3(3)]
le = 2.00 m [AS4100 5.6.3]
αm = 1.000 [AS4100 5.6.1.1(a)(iii)]
Mo = 3.2222E+03 KNm [AS4100 5.6.1.1(a)(iv)]
αsz = 0.977 [AS4100 5.6.1.1(a)(iv)]
ϕMbz = 302.8551E+00 KNm (<= ϕMsz) [AS4100 AS4100 5.6.1.1(a)]
SHEAR
=====================================================================================
Section Shear Capacity
Critical Load Case: 1* Critical Ratio: 0.187
Critical Location: 0.000 m from Start.
Vy* = 88.0000E+00 KN
ϕVvy = 471.7441E+00 KN [AS 4100 5.11.2]
ϕVvmy = 471.7441E+00 KN [AS 4100 5.12.3]
Vz* = 0.0000E+00 KN
ϕVvz = 1.3393E+03 KN [AS 4100 5.11.2]
ϕVvmz = 1.3393E+03 KN [AS 4100 5.12.3]
STAAD SPACE -- PAGE NO. 5
AXIAL
=====================================================================================
Section Compression Capacity
Critical Load Case: 1* Critical Ratio: 0.000
Critical Location: 0.000 m from Start.
N* = 0.0000E+00 KN
Ae = 11.4000E+03 mm2 [AS 4100 6.2.3 / 6.2.4]
kf = 1.000 [AS 4100 6.2.2]
An = 11.4000E+03 mm2
ϕNs = 2.8728E+03 KN [AS 4100 6.2.1]
Member Compression Capacity
Lz = 2.00 m
Ly = 2.00 m
Lez = 2.00 m
Ley = 2.00 m
αb = 0.00 [AS 4100 Table 6.3.3(1)/6.3.3(2)]
λn,z = 18.898 [AS 4100 6.3.3]
αa,z = 5.352 [AS 4100 6.3.3]
λ,z = 18.898 [AS 4100 6.3.3]
h ,z = 0.018 [AS 4100 6.3.3]
x ,z = 12.039 [AS 4100 6.3.3]
αc,z = 0.982 [AS 4100 6.3.3]
ϕNcz = 0.2821E+4 KN [AS 4100 6.3.3]
λn,y = 32.484 [AS 4100 6.3.3]
αa,y = 15.285 [AS 4100 6.3.3]
λ,y = 32.484 [AS 4100 6.3.3]
h ,y = 0.062 [AS 4100 6.3.3]
x ,y = 4.576 [AS 4100 6.3.3]
αc,y = 0.934 [AS 4100 6.3.3]
ϕNcy = 0.2684E+4 KN [AS 4100 6.3.3]
ϕNc = N/A [AS 4100 6.3.3 / AS 4600 3.4.1(b)]
Section Tension Capacity
Critical Load Case: 1* Critical Ratio: 0.151
Critical Location: 0.000 m from Start.
N* = -434.0000E+00 KN
kt = 1.00 [User defined]
An = 11.4000E+03 mm2
ϕNt = 2.8728E+03 KN [AS 4100 7.2]
STAAD SPACE -- PAGE NO. 6
COMBINED BENDING AND AXIAL
=====================================================================================
Section Combined Capacity
Critical Condition: Cl 8.3.2
Critical Load Case: 1* Critical Ratio: 0.568
Critical Location: 0.000 m from Start.
N* = -434.0000E+00 KN Mz* = 176.0000E+00 KNm My* = 0.0000E+00 KNm
ϕNs = 2.8728E+03 KN [AS 4100 8.3.1]
ϕMsz = 309.9600E+00 KNm
ϕMsy = 142.9313E+00 KNm
ϕMrz = 309.9600E+00 KNm [AS 4100 8.3.2]
ϕMry = 142.9313E+00 KNm [AS 4100 8.3.3]
Member Combined Capacity - In-plane
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Out-of-plane(compression)
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Out-of-plane(tension)
Critical Load Case: 1* Critical Ratio: 0.568
Critical Location: 0.000 m from Start.
N* = -434.0000E+00 KN Mz* = 176.0000E+00 KNm My* = 0.0000E+00 KNm
ϕMbz = 302.8551E+00 KNm
ϕNt = 2.8728E+03 KN [AS 4100 8.4.4.2]
ϕMozt = 309.9600E+00 KNm [AS 4100 8.4.4.2]
Member Combined Capacity - Biaxial(compression)
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Biaxial(tension)
Critical Load Case: 1* Critical Ratio: 0.453
Critical Location: 0.000 m from Start.
N* = -434.0000E+00 KN Mz* = 176.0000E+00 KNm My* = 0.0000E+00 KNm
ϕMtz = 309.9600E+00 KNm [AS 4100 8.4.5.2]
ϕMry = 142.9313E+00 KNm [AS 4100 8.4.5.2]
STAAD SPACE -- PAGE NO. 7
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