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.
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.
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 2024\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 1998
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
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