V. AS4100 1998 - Combined Section and Member In-Plane Capacity
Verify the bending capacity in major and minor axis bending, biaxial bending, and in-plane bending for a UC member subject an axial load per AS4100-1998.
Given
The member is 7 m long and part of a steel frame structure. The section is a 200UC52.2. The member is subject to an axial load of 143.9 kN.
Section Properties
- Depth of section, D = 206 mm
- Width of section, B = 204 mm
- Thickness of web, tw = 8 mm
- Thickness of flange, tf = 12.5 mm
- Area, Ag = 6,660 mm2
- Moment of inertia about major axis, Izz = 52.8 (10)6 mm4
- Moment of inertia about minor axis, Iyy = 17.7 (10)6 mm4
- Elastic section modulus about major axis, Zxx = 513 (10)3 mm3
- Elastic section modulus about minor axis, Zyy = 174 (10)3 mm3
- Plastic section modulus about major axis, Sxx = 570 (10)3 mm3
- Plastic section modulus about minor axis, Syy = 264 (10)3 mm3
- Radius of gyration,
- Radius of gyration,
Material Properties
- fy = 300 MPa (flange); fy = 320 MPa (web)
Validation
Combined Major Axis Section Moment Capacity
Nominal axial capacity:
Nominal section capacity:
The section is compact, so the alternate method is applicable.
Combined Minor Axis Section Moment Capacity
Nominal section capacity:
The section is compact, so the alternate method is applicable.
Member In-plane Capacity Check
The section is compact, so the alternate method is applicable. Per Cl. 4.4.2.2:
Comparison
Result Type | Theory | STAAD.Pro | Difference | Comment |
---|---|---|---|---|
Combined major axis section moment capacity (kN·m) | 153.9 | 153.9 | none | |
Combined minor axis section moment capacity (kN·m) | 153.9 | 153.9 | none | |
Menber in-plane capacity check (kN·m) | 134.6 | 134.5893 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - Combined Section and Member In-Plane Capacity.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 16-Apr-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 7 0; 3 12 7 0; 4 12 0 0; 5 0 12 0; 6 12 12 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 2 5; 5 3 6; 6 5 6;
DEFINE PMEMBER
1 PMEMBER 4
4 PMEMBER 5
6 PMEMBER 6
2 PMEMBER 7
5 PMEMBER 8
3 PMEMBER 9
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
G 7.88462e+07
TYPE STEEL
STRENGTH RY 1.5 RT 1.2
END DEFINE MATERIAL
MEMBER PROPERTY AUSTRALIAN
4 5 TABLE ST UC150X30.0
1 3 TABLE ST UC200X52.2
6 TABLE ST UB250X25.7
2 TABLE ST UB310X40.4
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 4 FIXED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
6 CON GY -40
2 CON GY -80
JOINT LOAD
5 6 FY -20
2 3 FY -50
5 FX 10
2 FX 30
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN 1998
TRACK 2 PMEMB 9
CHECK CODE PMEMB 9
FINISH
STAAD Output
STAAD.Pro CODE CHECKING - ( AS4100-1998 ) V2.3
****************************************************
MEMBER DESIGN OUTPUT FOR PMEMBER 9
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 UC200X52.2 (AUSTRALIAN SECTIONS)
Governing Load Case: 1*
Governing Criteria: AS-8.4.4.1
Governing Ratio: 0.987 (PASS)
SECTION PROPERTIES
=====================================================================================
d: 206.0000 mm bf: 204.0000 mm
tf: 12.5000 mm tw: 8.0000 mm
Ag: 6660.0000 mm2 J: 325.0000E+03 mm4 Iw: 165.6820E+09 mm6
Iz: 52.8000E+06 mm4 Sz: 570.0000E+03 mm3 (plastic) Zz: 512.6214E+03 mm3 (elastic)
rz: 89.0389E+00 mm
Iy: 17.7000E+06 mm4 Sy: 264.0000E+03 mm3 (plastic) Zy: 173.5294E+03 mm3 (elastic)
ry: 51.5525E+00 mm
MATERIAL PROPERTIES
=====================================================================================
Material Standard : AS/NZS 3679.1
Nominal Grade : 300
Residual Stress Category : HR (Hot-rolled)
E (#) :204999.984 MPa [AS 4100 1.4]
G : 80000.000 MPa [AS 4100 1.4]
fy, flange : 300.000 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: 135.784
Allowable slenderness: 180.000
STAAD SPACE -- PAGE NO. 4
BENDING
=====================================================================================
Section Bending Capacity
Critical Load Case: 1* Critical Ratio: 0.722
Critical Location: 0.000 m from Start.
Mz* = 111.0612E+00 KNm My* = 0.0000E+00 KNm
Z-Axis Section Slenderness: Compact Y-Axis Section Slenderness: Compact
Zez = 570.0000E+03 mm3 Zey = 260.2941E+03 mm3
ϕMsz = 153.9000E+00 KNm ϕMsy = 70.2794E+00 KN[AS 4100 5.2.1]
Member Bending Capacity
Critical Load Case: 1* Critical Ratio: 0.722
Critical Location: 0.000 m from Start.
Crtiical Segment/Sub-segment:
Location (Type): 0.00 m(F )- 7.00 m(F )
Length: 7.00 m
Mz* = 111.0612E+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 = 7.00 m [AS4100 5.6.3]
αm = 2.435 [AS4100 5.6.1.1(a)(iii)]
Mo = 154.9263E+00 KNm [AS4100 5.6.1.1(a)(iv)]
αsz = 0.570 [AS4100 5.6.1.1(a)(iv)]
ϕMbz = 153.9000E+00 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)]
SHEAR
=====================================================================================
Section Shear Capacity
Critical Load Case: 1* Critical Ratio: 0.110
Critical Location: 0.000 m from Start.
Vy* = 31.3075E+00 KN
ϕVvy = 284.7744E+00 KN [AS 4100 5.11.2]
ϕVvmy = 284.7744E+00 KN [AS 4100 5.12.3]
Vz* = 0.0000E+00 KN
ϕVvz = 826.2000E+00 KN [AS 4100 5.11.2]
ϕVvmz = 826.2000E+00 KN [AS 4100 5.12.3]
STAAD SPACE -- PAGE NO. 5
AXIAL
=====================================================================================
Section Compression Capacity
Critical Load Case: 1* Critical Ratio: 0.269
Critical Location: 0.000 m from Start.
N* = 143.8336E+00 KN
Ae = 6.6600E+03 mm2 [AS 4100 6.2.3 / 6.2.4]
kf = 1.000 [AS 4100 6.2.2]
An = 6.6600E+03 mm2
ϕNs = 1.7982E+03 KN [AS 4100 6.2.1]
Member Compression Capacity
Lz = 7.00 m
Ly = 7.00 m
Lez = 7.00 m
Ley = 7.00 m
αb = 0.00 [AS 4100 Table 6.3.3(1)/6.3.3(2)]
λn,z = 86.121 [AS 4100 6.3.3]
αa,z = 18.714 [AS 4100 6.3.3]
λ,z = 86.121 [AS 4100 6.3.3]
h ,z = 0.237 [AS 4100 6.3.3]
x ,z = 1.175 [AS 4100 6.3.3]
αc,z = 0.637 [AS 4100 6.3.3]
ϕNcz = 0.1146E+4 KN [AS 4100 6.3.3]
λn,y = 148.744 [AS 4100 6.3.3]
αa,y = 12.969 [AS 4100 6.3.3]
λ,y = 148.744 [AS 4100 6.3.3]
h ,y = 0.441 [AS 4100 6.3.3]
x ,y = 0.764 [AS 4100 6.3.3]
αc,y = 0.298 [AS 4100 6.3.3]
ϕNcy = 0.5353E+3 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: 0.000
Critical Location: 0.000 m from Start.
N* = 0.0000E+00 KN
kt = 1.00 [User defined]
An = 6.6600E+03 mm2
ϕNt = 1.7982E+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: 0.722
Critical Location: 0.000 m from Start.
N* = 143.8336E+00 KN Mz* = 111.0612E+00 KNm My* = 0.0000E+00 KNm
ϕNs = 1.7982E+03 KN [AS 4100 8.3.1]
ϕMsz = 153.9000E+00 KNm
ϕMsy = 70.2794E+00 KNm
ϕMrz = 153.9000E+00 KNm [AS 4100 8.3.2]
ϕMry = 70.2794E+00 KNm [AS 4100 8.3.3]
Member Combined Capacity - In-plane
Critical Load Case: 1* Critical Ratio: 0.825
Critical Location: 0.000 m from Start.
N* = 143.8336E+00 KN Mz* = 111.0612E+00 KNm My* = 0.0000E+00 KNm
ϕNcz = 1.1463E+03 KN [AS 4100 8.4.2.2]
ϕMiz = 134.5893E+00 KNm [AS 4100 8.4.2.2]
ϕNcy = 535.3019E+00 KN [AS 4100 8.4.2.2]
ϕMiy = 51.3956E+00 KNm [AS 4100 8.4.2.2]
Member Combined Capacity - Out-of-plane(compression)
Critical Load Case: 1* Critical Ratio: 0.987
Critical Location: 0.000 m from Start.
N* = 143.8336E+00 KN Mz* = 111.0612E+00 KNm My* = 0.0000E+00 KNm
ϕMbz = 153.9000E+00 KNm
ϕNcy = 535.3019E+00 KN
ϕMozc = 112.5477E+00 KNm [AS 4100 8.4.4.1]
Member Combined Capacity - Out-of-plane(tension)
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
Member Combined Capacity - Biaxial(compression)
Critical Load Case: 1* Critical Ratio: 0.982
Critical Location: 0.000 m from Start.
N* = 143.8336E+00 KN Mz* = 111.0612E+00 KNm My* = 0.0000E+00 KNm
ϕMcz = 112.5477E+00 KNm [AS 4100 8.4.5.1]
ϕMiy = 51.3956E+00 KNm [AS 4100 8.4.5.1]
Member Combined Capacity - Biaxial(tension)
Critical Load Case: N/A Critical Ratio: N/A
Critical Location: N/A
STAAD SPACE -- PAGE NO. 7
********************************************************************************