# 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

Material Properties

• Fy = 350 MPa

## Validation

Nominal Section Capacity Check

$λ e = ( d o t ) ( F y 250 ) = 219.1 6.5 × 350 250 = 47.9$
$λ ey = 82$

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,

$K f = A e A g = 4,280 4,280 = 1$

Net area = 4,280 mm2

Nominal section capacity:

Axial Member Capacity

The effective length for the member pinned at both ends:

$l e r x = 3,800 75.2 = 50.5$

Modified slenderness ratio:

$λ n = l e r x K f F y 250 = 50.5 1 × 350 250 = 59.8$

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

Table 1. Comparison of results
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

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\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
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.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 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
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 (&lt;= 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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