V. AS4100 1998 - Welded section subject to bending
Verify the bending capacity of a welded girder per the AS 4100 1998 code.
Details
The member is 21 m in length, with pinned supports at both ends. The section has top & bottom flanges of 450 mm × 60 mm and a web of 1,390 mm × 32 mm. The plates are all grade 280 steel. The member is subject to major axis bending. The section is partially restrained at the supports and at the third points along the span. The point loads are applied at the top flange.
Material Properties
- E = 199,947 MPa
- G = 80,000 MPa
- Fy = 280 MPa
- Fu = 440 MPa
Section Properties
- Depth of section, D = 1,390 + 2 × 60 = 1,510 mm
- Cross-sectional area, Ag = 1,390 × 32 + 2 × 450 × 60 = 98,480 mm2
- Moment of inertia about major axis:
- Moment of inertia about minor axis:
- Elastic section modulus,
- Plastic section modulus,
- Warping constant:
(AS 4100-1998, Section H4) - Torsional constant:
(AS 4100-1998, Section H4)
Section Slenderness Ratio
Flange section slenderness parameter:
Hence, the flange is compact.
Web section slenderness parameter:
Hence, the web is compact.
Section Bending Capacity
Zcx is the lesser of Sxx and 1.5×Zxx = 1.5(47.1×106) = 70.7(106).
Member Bending Capacity
The length between braced points, l = 7,000 mm
Top flange load height position: kl = 1.4. No lateral rotational restraint: kr = 1.0.
The effective length, le = ktklkrl = 1.33 × 1.4 ×1.0 ×7,000 = 13,000 mm.
The reference buckling moment:
The moment modification factor:
意味= | ||
= |
The slenderness reduction factor per AS 4100 Eq. 5.6.1.1(2):
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - Welded section subject to 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 7.00001 0 0; 3 14 0 0; 4 21 0 0;
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
DEFINE PMEMBER
1 TO 3 PMEMBER 1
START USER TABLE
TABLE 2
UNIT METER KN
WIDE FLANGE
1510X450X60X32
0.09848 1.51 0.032 0.45 0.06 0.0355616 0.000915046 7.99825e-05 0.04832 -
0.036 0.45 0.06
END
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
1 TO 3 UPTABLE 2 1510X450X60X32
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
4 FIXED BUT FX MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 TO 3 UNI GY -40
JOINT LOAD
2 3 FY -250
MEMBER LOAD
1 TO 3 CON GY -250
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN
TRACK 2 PMEMB 1
LHT 1 PMEMB 1
IST 4 PMEMB 1
PBRACE TOP 0 P 0.333 P 0.666 P 1 P PMEMB 1
PBRACE BOTTOM 0 P 0.333 P 0.666 P 1 P 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 1510X450X60X32 (UPT) Governing Load Case: 1* Governing Criteria: AS-8.4.4.2 Governing Ratio: 0.869 (PASS) SECTION PROPERTIES ===================================================================================== d: 1510.0000 mm bf: 450.0000 mm tf: 60.0000 mm tw: 32.0000 mm Ag: 98480.0000 mm2 J: 79.9825E+06 mm4 Iw: 480.9710E+12 mm6 Iz: 35.5616E+09 mm4 Sz: 54.6068E+06 mm3 (plastic) Zz: 47.1015E+06 mm3 (elastic) rz: 600.9199E+00 mm Iy: 915.0460E+06 mm4 Sy: 6.4308E+06 mm3 (plastic) Zy: 4.0669E+06 mm3 (elastic) ry: 96.3934E+00 mm MATERIAL PROPERTIES ===================================================================================== Material Standard : AS/NZS 3679.1 Nominal Grade : 300 Residual Stress Category : LW (Lightly welded longitudinally) 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 : 280.000 MPa [AS 4100 Table 2.1] fu : 440.000 MPa [AS 4100 Table 2.1] SLENDERNESS ===================================================================================== Actual slenderness: 217.857 Allowable slenderness: 400.000 STAAD SPACE -- PAGE NO. 4 BENDING ===================================================================================== Section Bending Capacity Critical Load Case: 1* Critical Ratio: 0.446 Critical Location: 10.500 m from Start. Mz* = -6.1425E+03 KNm My* = 0.0000E+00 KNm Z-Axis Section Slenderness: Compact Y-Axis Section Slenderness: Compact Zez = 54.6068E+06 mm3 Zey = 6.1003E+06 mm3 ϕMsz = 13.7609E+03 KNm ϕMsy = 1.5373E+03 KN[AS 4100 5.2.1] Member Bending Capacity Critical Load Case: 1* Critical Ratio: 0.869 Critical Location: 10.500 m from Start. Crtiical Segment/Sub-segment: Location (Type): 6.99 m(P )- 13.99 m(P ) Length: 6.99 m Mz* = -6.1425E+03 KNm My* = 0.0000E+00 KNm kt = 1.33 [AS4100 Table 5.6.3(1)] kl = 1.40 [AS4100 Table 5.6.3(2)] kr = 1.00 [AS4100 Table 5.6.3(3)] le = 13.00 m [AS4100 5.6.3] αm = 1.012 [AS4100 5.6.1.1(a)(iii)] Mo = 11.3341E+03 KNm [AS4100 5.6.1.1(a)(iv)] αsz = 0.508 [AS4100 5.6.1.1(a)(iv)] ϕMbz = 7.0722E+03 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)] SHEAR ===================================================================================== Section Shear Capacity Critical Load Case: 1* Critical Ratio: 0.140 Critical Location: 0.583 m from Start. Vy* = 1.0217E+03 KN ϕVvy = 7.3060E+03 KN [AS 4100 5.11.2] ϕVvmy = 7.3060E+03 KN [AS 4100 5.12.3] Vz* = 0.0000E+00 KN ϕVvz = 5.4432E+03 KN [AS 4100 5.11.2] ϕVvmz = 5.4432E+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 = 92.7036E+03 mm2 [AS 4100 6.2.3 / 6.2.4] kf = 0.941 [AS 4100 6.2.2] An = 98.4800E+03 mm2 ϕNs = 23.3613E+03 KN [AS 4100 6.2.1] Member Compression Capacity Lz = 21.00 m Ly = 21.00 m Lez = 21.00 m Ley = 21.00 m αb = 1.00 [AS 4100 Table 6.3.3(1)/6.3.3(2)] λn,z = 35.883 [AS 4100 6.3.3] αa,z = 16.856 [AS 4100 6.3.3] λ,z = 52.739 [AS 4100 6.3.3] h ,z = 0.128 [AS 4100 6.3.3] x ,z = 2.142 [AS 4100 6.3.3] αc,z = 0.847 [AS 4100 6.3.3] ϕNcz = 0.1979E+5 KN [AS 4100 6.3.3] λn,y = 223.694 [AS 4100 6.3.3] αa,y = 9.070 [AS 4100 6.3.3] λ,y = 232.764 [AS 4100 6.3.3] h ,y = 0.715 [AS 4100 6.3.3] x ,y = 0.628 [AS 4100 6.3.3] αc,y = 0.133 [AS 4100 6.3.3] ϕNcy = 0.3109E+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: 0.000 Critical Location: 0.000 m from Start. N* = 0.0000E+00 KN kt = 1.00 [User defined] An = 98.4800E+03 mm2 ϕNt = 24.8170E+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: 0.446 Critical Location: 10.500 m from Start. N* = 0.0000E+00 KN Mz* = -6.1425E+03 KNm My* = 0.0000E+00 KNm ϕNs = 23.3613E+03 KN [AS 4100 8.3.1] ϕMsz = 13.7609E+03 KNm ϕMsy = 1.5373E+03 KNm ϕMrz = 13.7609E+03 KNm [AS 4100 8.3.2] ϕMry = 1.5373E+03 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: 0.869 Critical Location: 10.500 m from Start. N* = 0.0000E+00 KN Mz* = -6.1425E+03 KNm My* = 0.0000E+00 KNm ϕMbz = 7.0722E+03 KNm ϕNt = 24.8170E+03 KN [AS 4100 8.4.4.2] ϕMozt = 7.0722E+03 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: 0.821 Critical Location: 10.500 m from Start. N* = 0.0000E+00 KN Mz* = -6.1425E+03 KNm My* = 0.0000E+00 KNm ϕMtz = 7.0722E+03 KNm [AS 4100 8.4.5.2] ϕMry = 1.5373E+03 KNm [AS 4100 8.4.5.2] STAAD SPACE -- PAGE NO. 7 ******************************************************************************** ************** END OF TABULATED RESULT OF DESIGN **************