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
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Australia\AS4100 1998 - Cantilever subject to tension and bending.std is typically installed with the program.
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 AUSTRALIAN
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
STAAD.Pro 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 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 ********************************************************************************