V. AS4100 1998 - Compression Capacity
Verify the capacity of a tubular compression member subjected to axial load only per AS4100-1998.
Given
The member 3.8 m long with pinned ends (no end moments). The section is a 219.1x6.4CHS. The member is subject to an axial load of 1,030 kN.
Section Properties
- Depth of section, d = 219.1 mm
- Thickness, t = 6.4 mm
- Area, Ag = 4,280 mm2
- Moment of inertia about major axis, Izz = 22.2 (10)6 mm4
- Radius of gyration,
Material Properties
- Fy = 350 MPa
Validation
Nominal Section Capacity Check
The effective depth is the minimum of de1 and de2, or 219.1 mm.
di = de - 2 × t = 219.1 - 2(6.4) = 206.3 mm
The effective area,
Net area = 4,280 mm2
Nominal section capacity:
Axial Member Capacity
The effective length for the member pinned at both ends:
Modified slenderness ratio:
The member section has a constant ɑb. The residual stress for cold-formed (non-stress relieved) CHS category. Kf = 1. Therefore, from AS 4100 table 6.3.3(1), ɑb = -0.5.
From interpolating Table 6.6 or AS 4100 Table 6.3.3(3), the slenderness reduction factor, ɑc = 0.863.
Nc = ɑc × Ns = 0.863 × 1,500 = 1,290 kN
Nc < Ns, OK
Comparison
Result Type | Theory | STAAD.Pro | Difference | Comment |
---|---|---|---|---|
Nominal section capacity (kN) | 1,350 | 1,348.2 | negligible | |
Axial member capacity (kN) | 1,160 | 1,163 | negligible |
STAAD Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Australia\AS4100 1998 - Compression Capacity.STD is typically installed with the program.
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 23-Mar-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3.80001 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 COLDFORMED AUSTRALIAN
1 TABLE ST 219.1x6.4CHS
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 PINNED
2 FIXED BUT FX MY MZ
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GX 1030 0
1 CON GX -1030 3.8
PERFORM ANALYSIS
PARAMETER 1
CODE AUSTRALIAN
TRACK 2 PMEMB 1
SGR 5 PMEMB 1
CHECK CODE PMEMB ALL
FINISH
STAAD 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 219.1X6.4CHS (AUSTRALIAN COLDFORMED SECTIONS) Governing Load Case: 1* Governing Criteria: COMPRESSION Governing Ratio: 0.886 (PASS) SECTION PROPERTIES ===================================================================================== d: 219.1000 mm bf: 0.0000 mm tf: 6.4000 mm tw: 6.4000 mm Ag: 4280.0000 mm2 J: 48.4000E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 24.2000E+06 mm4 Sz: 290.0000E+03 mm3 (plastic) Zz: 220.9037E+03 mm3 (elastic) rz: 75.1945E+00 mm Iy: 24.2000E+06 mm4 Sy: 290.0000E+03 mm3 (plastic) Zy: 220.9037E+03 mm3 (elastic) ry: 75.1945E+00 mm MATERIAL PROPERTIES ===================================================================================== Material Standard : AS 1163 Nominal Grade : 350 Residual Stress Category : CF (Cold formed) E (#) :199947.000 MPa [AS 4100 1.4] G : 80000.000 MPa [AS 4100 1.4] fy, flange : 350.000 MPa [AS 4100 Table 2.1] fy, web : 350.000 MPa [AS 4100 Table 2.1] fu : 430.000 MPa [AS 4100 Table 2.1] SLENDERNESS ===================================================================================== Actual slenderness: 50.536 Allowable slenderness: 180.000 STAAD SPACE -- PAGE NO. 4 BENDING ===================================================================================== Section Bending Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Mz* = 0.0000E+00 KNm My* = 0.0000E+00 KNm Z-Axis Section Slenderness: N/A Y-Axis Section Slenderness: N/A Zez = 0.0000E+00 mm3 Zey = 0.0000E+00 mm3 ϕMsz = 0.0000E+00 KNm ϕMsy = 0.0000E+00 KN[AS 4100 5.2.1] Member Bending Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Crtiical Segment/Sub-segment: Location (Type): 0.00 m(U )- 0.00 m(U ) Length: 0.00 m Mz* = 0.0000E+00 KNm My* = 0.0000E+00 KNm kt = 0.00 [AS4100 Table 5.6.3(1)] kl = 0.00 [AS4100 Table 5.6.3(2)] kr = 0.00 [AS4100 Table 5.6.3(3)] le = 0.00 m [AS4100 5.6.3] αm = 0.000 [AS4100 5.6.1.1(a)(iii)] Mo = 0.0000E+00 KNm [AS4100 5.6.1.1(a)(iv)] αsz = 0.000 [AS4100 5.6.1.1(a)(iv)] ϕMbz = 0.0000E+00 KNm (<= ϕMsz) [AS4100 5.6.1.1(a)] SHEAR ===================================================================================== Section Shear Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A Vy* = 0.0000E+00 KN ϕVvy = 0.0000E+00 KN [AS 4100 5.11.2] ϕVvmy = 0.0000E+00 KN [AS 4100 5.12.3] Vz* = 0.0000E+00 KN ϕVvz = 0.0000E+00 KN [AS 4100 5.11.2] ϕVvmz = 0.0000E+00 KN [AS 4100 5.12.3] STAAD SPACE -- PAGE NO. 5 AXIAL ===================================================================================== Section Compression Capacity Critical Load Case: 1* Critical Ratio: 0.886 Critical Location: 0.317 m from Start. N* = 1.0300E+03 KN Ae = 4.2766E+03 mm2 [AS 4100 6.2.3 / 6.2.4] kf = 0.999 [AS 4100 6.2.2] An = 4.2800E+03 mm2 ϕNs = 1.3471E+03 KN [AS 4100 6.2.1] Member Compression Capacity Lz = 3.80 m Ly = 3.80 m Lez = 3.80 m Ley = 3.80 m αb = -0.50 [AS 4100 Table 6.3.3(1)/6.3.3(2)] λn,z = 59.771 [AS 4100 6.3.3] αa,z = 20.639 [AS 4100 6.3.3] λ,z = 49.451 [AS 4100 6.3.3] h ,z = 0.117 [AS 4100 6.3.3] x ,z = 2.350 [AS 4100 6.3.3] αc,z = 0.863 [AS 4100 6.3.3] ϕNcz = 0.1163E+4 KN [AS 4100 6.3.3] λn,y = 59.771 [AS 4100 6.3.3] αa,y = 20.639 [AS 4100 6.3.3] λ,y = 49.451 [AS 4100 6.3.3] h ,y = 0.117 [AS 4100 6.3.3] x ,y = 2.350 [AS 4100 6.3.3] αc,y = 0.863 [AS 4100 6.3.3] ϕNcy = 0.1163E+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 = 4.2800E+03 mm2 ϕNt = 1.3482E+03 KN [AS 4100 7.2] STAAD SPACE -- PAGE NO. 6 COMBINED BENDING AND AXIAL ===================================================================================== Section Combined Capacity Critical Load Case: N/A Critical Ratio: N/A Critical Location: N/A N* = 0.0000E+00 KN Mz* = 0.0000E+00 KNm My* = 0.0000E+00 KNm ϕNs = 0.0000E+00 KN [AS 4100 8.3.1] ϕMsz = 0.0000E+00 KNm ϕMsy = 0.0000E+00 KNm ϕMrz = 0.0000E+00 KNm [AS 4100 8.3.2] ϕMry = 0.0000E+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: N/A Critical Ratio: N/A Critical Location: N/A 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: N/A Critical Ratio: N/A Critical Location: N/A STAAD SPACE -- PAGE NO. 7 ********************************************************************************