# V. AS4100 1998 - SHS section subject to compression

Verify the axial compression capacities of an SHS section beam per the AS 4100 1998 code.

## Details

The member is 3.8 m in length, with pinned supports at both ends. The section is a 200 x 200 x 5.0 SHS of grade 250 steel. The member is subject to 1,030 kN in compression.

Section Properties

• Depth of section, b = d = 200 mm
• Thickness, t = 5 mm
• Cross-sectional area, Ag = 3,810 mm2
• Radius of gyration, rx = 79.2 mm

Material Properties

• E = 199,947 MPa
• G = 80,000 MPa
• Fy = 250 MPa
• Fu = 320 MPa

## Validation

Nominal Section Capacity

Clear width: bcw = b - 2t = 200 - 2×5 = 190 mm

$λ e = b cw t f y 250 = 190 5 250 250 = 38$
$λ ey = 40$

Effective width, be, for each compression element:

$b e = b cw λ ey λ e ≤ b cw = 190 40 38 = 195 > 190$

Use be = 190 mm

Effective area, Ae = 4×be×t = 4 × 190 × 5 = 3,800 mm2

$K f = A e A g = 3,800 3,810 = 1.0$

Assume the net area, An, is equal to the gross area (i.e., no holes).

The nominal section capacity:

Axial Member Capacity

The effective length, le = Ke × L = 1 × 3,800 mm = 3,800 mm

The modified slenderness ratio:

$λ n = l e r K f f y 250 = 3,800 79.2 1 × 250 250 = 47.97$

Member section constant, ɑb, for shape of section, residual stress cold-formed (non-stress relieved) CHS category, and Kf = 1.0 from AS 4100 Table 6.3.3.(2): ɑb = -0.5.

From linear interpolation of Table 6.3.3(3), the slenderness reduction factor, ɑc = 0.913.

## Results

Nominal section capacity (kN) 855 857.2499 negligible
Axial member capacity (kN) 780.6 782.7 negligible

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\Australia\AS4100 1998 - SHS section subject to compression.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 200X200X5.0SHS
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 0 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   200X200X5.0SHS           (AUSTRALIAN COLDFORMED SECTIONS)
Governing Criteria: COMPRESSION
Governing Ratio:   1.316 *(FAIL)
SECTION PROPERTIES
=====================================================================================
d:       200.0000 mm   bf:       200.0000 mm
tf:         5.0000 mm   tw:         5.0000 mm
Ag:      3809.9998 mm2   J:    37.8000E+06 mm4             Iw:     0.0000E+00 mm6
Iz:    23.9000E+06 mm4  Sz:   277.0000E+03 mm3 (plastic)   Zz:   239.0000E+03 mm3 (elastic)
rz:    79.2021E+00 mm
Iy:    23.9000E+06 mm4  Sy:   277.0000E+03 mm3 (plastic)   Zy:   239.0000E+03 mm3 (elastic)
ry:    79.2021E+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 :   250.000 MPa    [AS 4100 Table 2.1]
fy, web    :   250.000 MPa    [AS 4100 Table 2.1]
fu         :   320.000 MPa    [AS 4100 Table 2.1]
SLENDERNESS
=====================================================================================
Actual slenderness   :  47.979
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:   1.316
Critical Location:        0.317 m from Start.
N*    =     1.0300E+03 KN
Ae    =     3.8100E+03 mm2               [AS 4100 6.2.3 / 6.2.4]
kf    =     1.000                        [AS 4100 6.2.2]
An    =     3.8100E+03 mm2
ϕNs   =   857.2499E+00 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  =    47.979                        [AS 4100 6.3.3]
αa,z  =    20.013                        [AS 4100 6.3.3]
λ,z   =    37.972                        [AS 4100 6.3.3]
h ,z   =     0.080                        [AS 4100 6.3.3]
x ,z   =     3.533                        [AS 4100 6.3.3]
αc,z  =     0.913                        [AS 4100 6.3.3]
ϕNcz  = 0.7827E+3 KN                     [AS 4100 6.3.3]
λn,y  =    47.979                        [AS 4100 6.3.3]
αa,y  =    20.013                        [AS 4100 6.3.3]
λ,y   =    37.972                        [AS 4100 6.3.3]
h ,y   =     0.080                        [AS 4100 6.3.3]
x ,y   =     3.533                        [AS 4100 6.3.3]
αc,y  =     0.913                        [AS 4100 6.3.3]
ϕNcy  = 0.7827E+3 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    =     3.8100E+03 mm2
ϕNt   =   857.2499E+00 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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************** END OF TABULATED RESULT OF DESIGN **************