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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

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  

STAAD Input

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
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 (&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
   ********************************************************************************
Parent topic: V. Australia