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 2023\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
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 ********************************************************************************