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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, r x = I zz A = 75.2  mm

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
d e1 = d 0 λ ey λ e = 219.1 82 47.9 = 287 ≤ d o = 219.1  mm
d e1 = d 0 ( 3 × λ ey λ e ) 2 = 219.1 ( 3 × 82 47.9 ) 2 = 5,780  mm

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,

A e = π d e 2 4 - π d i 2 4 = π ( 219.1 ) 2 4 - π ( 206.3 ) 2 4 = 4,280  mm 2
K f = A e A g = 4,280 4,280 = 1

Net area = 4,280 mm2

Nominal section capacity:

N s = K f × A n × F y = 1 × 4,280 × 350 ( 10 ) -3 = 1,500  kN
ϕ N s = 0.9 × 1,500 = 1,350  kN

Axial Member Capacity

The effective length for the member pinned at both ends:

l e = K e × L = 1 × 3,800 = 3,800  mm
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

ϕ N c = 0.9 × 1,290 = 1,160  kN

Comparison

表 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  

STAAD Input

ヒント: 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 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 
   ********************************************************************************
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