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V.NZS3404 1997-Tube Section Compact

Verify the design capacity of a PIPX80 section per the NZS3404 1997 code.

Details

Verify the bending capacity of a PIPX80 member. Steel grade = 250 MPa. The simply supported span is 9 m with a 8.4 kN load at 5 m from the left support.

Validation

Section Classification

Evaluate the slenderness effects of the pipe member:

λ e w = OD t f y 250 = 219.1 11.8 250 250 = 18.3

Section classification is compact

Section Bending Capacity About Z-Axis

Effective Section Modulus, Zez = 508×103 mm3

The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez

Msz = 250× 508×103/106 = 127 kN·m

ϕMsz = 0.9×127 = 114.3 kN·m

The pipe is symmetric, thus ϕMsy = ϕMsz

Member Bending Capacity

End restraint arrangement = LL

A twist restraint factor, Kt (SKT) = 1.00

Minor axis rotation restraints = Both

Lateral rotation restraint factor, Kr (SKR) = 1.0

Load Height factor, Kl, (LHT) = 1.00 [Ref : Table 5.6.3(2)]

Effective length = 1×1×1×9,000 = 9,000 mm

αm = 1 [Ref: Cl no -5.6.1.1 (b)]

Reference buckling moment, Mo

M o = π 2 E I y L e 2 G J + π 2 E I w L e 2 = 2,641  kN·m

αs = 1 [Ref : Clause 5.6.1.1 (c)]

Mbx = αmαsMsx ≤ Msx

Mbz = 1 × 1 × 127 = 127 kN·m ≤ (Msz, Msy)Max. [Ref : Clause 5.6.1.1.1(a)]

ϕMbz = 0.9×127 = 114.3 kN·m

Check for Shear

Section Shear Capacity (Along Y axis), Vy = 0.36×fy×Ag = 0.36×250×7,677 = 691 kN

ϕVy = 0.9×691 = 622 kN

The pipe is symmetric, thus ϕVz = ϕVy

Check for Axial Compression

Section Compression Capacity:

Gross Area, Ag = 7,677 mm2

Net Area, An = 7,677 mm2

Form factor, Kf = Ae/Ag = 1.0

The nominal member section capacity for axial compression,

Ns = Kf×An×fy = 1.0×7,677×250 = 1,919 kN [Ref : Clause 6.2.1]

ϕNs = 0.9×1,919 = 1,727 kN

Member Compression Capacity

Length of the member, L = 9,000 mm

Effective length factor for slenderness & buckling about minor Y- axis, Ky = 1.0

Effective length factor for slenderness & buckling about minor Z- axis, Kz = 1.0

Effective Length of member, Lez = 1.0×9,000 mm = 9,000 mm

Effective Length of member, Ley = 1.0×9,000 mm = 9,000 mm

ry = rz = √(41.62×106 / 7,677) = 73.63

Geometrical Slenderness Ratio = Ley/ry = Lez/rz = 9,000 / 73.63 = 122.2

Member slenderness,

λ n = L e r k f f y 250 = 122.2 1 250 250 = 122.2 [Ref : Clause 6.3.3]

αa = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 15.10

αb = -1.0 [Ref : Table 6.3.3(2)]

λ = λn + αa×αb = 107.1

η = 0.3

ξy = ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 1

αcy = αcz = 0.495

The nominal member capacity,

Ncy = Ncz= αcz×Ns =0.495×1,919 = 950 kN [Ref : Clause 6.3.3]

ϕNcy = ϕNcz = 855 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

Kte = 1.00

Nt1 = Ag×fy = 7,677 × 250×10-3 = 1,919 kN

Nt2 = 0.85×Kte×An×fu = 0.85(1.0)(7,677)(250×10-3) = 1,631 kN

ϕNt = 0.9×1,919 = 1,727 kN [Ref : Clause 5.6.1.1.1(a)]

Results

Table 1. Comparison of results
Result Type Reference STAAD.Pro Difference Comments
ϕMsz (kN·m) 114.3 114.2998 negligible  
ϕMbz (kN·m) 114.3 114.2998 negligible  
ϕVy (kN) 622 622.9 negligible  
ϕNs (kN) 1,727 1,727.4 negligible  
ϕNcy (kN) 855 854.7 negligible  
ϕNt (kN) 1,727 1,727.4 negligible  

STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\New Zealand\NZS 3404 1997\NZS3404 1997-Tube Section Compact.std is typically installed with the program.

STAAD SPACE
*
*  INPUT FILE: NZS3404_Tube_Section_Compact.STD
*
* REFERENCE : Hand Calculation
*
*  OBJECTIVE : TO DETERMINE THE ADEQUACY OF  TUBE SHAPE  PER
*              THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 03-Jan-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 4 9 0 0; 5 3 0 0; 6 6 0 0;
*
MEMBER INCIDENCES
1 1 5; 2 5 6; 3 6 4;
DEFINE PMEMBER
1 TO 3 PMEMBER 1
*
*
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
TYPE STEEL
STRENGTH FY 253200 FU 407800 RY 1.5 RT 1.2
END DEFINE MATERIAL
*
MEMBER PROPERTY AMERICAN
1 TO 3 TABLE ST PIPX80
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 PINNED
4 FIXED BUT FX MY MZ
PRINT ALL
*
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
2 CON GY -8.4
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
*
PARAMETER 1
CODE NZS3404 1997
BEAM 1 PMEMB 1
IST 2  PMEMB 1
SGR 6  PMEMB 1
SKL 1  PMEMB 1
SKR 1  PMEMB 1
SKT 1  PMEMB 1
TRACK 2  PMEMB 1
CHECK CODE  PMEMB 1
*
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0)
                     **************************************************
   AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE:-
   STAAD.Pro     NZS3404 Spec.     Description
   ---------     -------------     ---------------
      X/x             Z/z          Longitudinal axis of section
      Y/y             Y/y          Minor principal axis of section
      Z/z             X/x          Major Principal axis of section
   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 [NZS3404 Table 3.4]
   3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per NZS3404 1.4.
   DESIGN SUMMARY
   --------------
   Designation: ST   PIPX80                   (AISC SECTIONS)
   Governing Load Case:     1*
   Governing Criteria: Cl.5.1                                                      
   Governing Ratio:   0.165  (PASS)
   Governing Location:   4.500 m from Start.
   SECTION PROPERTIES
   ------------------
   OD:       219.0750 mm    t:        11.8110 mm
   Ag:      7677.4033 mm2   J:    83.2463E+06 mm4             Iw:     0.0000E+00 mm6
   Iz:    41.6231E+06 mm4  Sz:   507.9990E+03 mm3 (plastic)   Zz:   379.9899E+03 mm3 (elastic)
   rz:    73.6309E+00 mm
   Iy:    41.6231E+06 mm4  Sy:   507.9990E+03 mm3 (plastic)   Zy:   379.9899E+03 mm3 (elastic)
   ry:    73.6309E+00 mm
      STAAD SPACE                                              -- PAGE NO.   13
    *                                           
   MATERIAL PROPERTIES
   -------------------
   Material Standard        :  AS 1163
   Nominal Grade            :  250
   Residual Stress Category :  HR (Hot-rolled)
   E (#)       : 204999.984 MPa         [NZS3404 1.4]
   G           :  80000.000 MPa         [NZS3404 1.4]
   fy, flange  :    250.000 MPa         [NZS3404 Table 2.1]
   fy, web     :    250.000 MPa         [NZS3404 Table 2.1]
   fu          :    320.000 MPa         [NZS3404 Table 2.1]
   BENDING
   -------
   Section Bending Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.165
   Critical Location  :   4.500 m from Start.
   Mz* =   -18.9000E+00 KNm
   Section Slenderness: Compact
   Zez =   507.9990E+03 mm3
   ϕMsz =   114.2998E+00 KNm                [NZS3404 Cl.5.1    ]
   Section Bending Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   My* =     0.0000E+00 KNm
   Section Slenderness: Compact
   Zey =   507.9990E+03 mm3
   ϕMsy =   114.2998E+00 KNm                [NZS3404 Cl.5.1    ]
   Member Bending Capacity
   Critical Load Case :     1*
   Critical Ratio     :   0.165
   Critical Location  :   4.500 m from Start.
   Crtiical Flange Segment: 
   Location (Type):   0.00 m(F )-  9.00 m(F )
   Mz* =   -18.9000E+00 KNm
   kt   =      1.00                         [NZS3404 Table 5.6.3(1)]
   kl   =      1.00                         [NZS3404 Table 5.6.3(2)]
   kr   =      1.00                         [NZS3404 Table 5.6.3(3)]
   le   =      9.00 m                       [NZS3404 5.6.3]
   αm   =     1.000                         [NZS3404 5.6.1.1.1(b)(iii)]
   Mo   =     2.6123E+03 KNm                [NZS3404 5.6.1.1.1(d)]
   αsz  =     1.000                         [NZS3404 5.6.1.1.1(c)]
   ϕMbz =   114.2998E+00 KNm (<= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
      STAAD SPACE                                              -- PAGE NO.   14
    *                                           
   SHEAR
   -----
   Section Shear Capacity (along Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.007
   Critical Location  :   0.000 m from Start.
   Vy*  =     4.2000E+00 KN
   ϕVvy =   622.9389E+00 KN                 [NZS3404 5.11.2]
   Section Shear Capacity (along Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   Vz*  =     0.0000E+00 KN
   ϕVvz =   622.9389E+00 KN                 [NZS3404 5.11.2]
      STAAD SPACE                                              -- PAGE NO.   15
    *                                           
   AXIAL
   -----
   Section Compression Capacity
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*    =     0.0000E+00 KN
   Ae    =     7.6774E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
   kf    =     1.000                        [AS 4100 6.2.2]
   An    =     7.6774E+03 mm2
   ϕNs   =     1.7274E+03 KN                [NZS3404 6.2.1]
   Member Compression Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*    =     0.0000E+00 KN
   Unbraced Segment: 
   Location (Type):   0.00 m(U )-  9.00 m(U )
   Lez   =      9.00 m
   αb    =     -1.00                        [NZS3404 Table 6.3.3(1)/6.3.3(2)]
   λn,z  =   122.231                        [NZS3404 6.3.3]
   λ,z   =   107.130                        [NZS3404 6.3.3]
   ε,z   =     0.961                        [NZS3404 6.3.3]
   αc,z  =     0.495                        [NZS3404 6.3.3]
   ϕNcz  = 0.8547E+3 KN                     [NZS3404 6.3.3]
   Member Compression Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*    =     0.0000E+00 KN
   Unbraced Segment: 
   Location (Type):   0.00 m(U )-  9.00 m(U )
   Ley   =      9.00 m
   λn,y  =   122.231                        [NZS3404 6.3.3]
   λ,y   =   107.130                        [NZS3404 6.3.3]
   ε,y   =     0.961                        [NZS3404 6.3.3]
   αc,y  =     0.495                        [NZS3404 6.3.3]
   ϕNcy  = 0.8547E+3 KN                     [NZS3404 6.3.3]
   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    =     7.6774E+03 mm2
   ϕNt   =     1.7274E+03 KN                [NZS3404 7.2]
      STAAD SPACE                                              -- PAGE NO.   16
    *                                           
   COMBINED BENDING AND AXIAL
   ------------------------
   Section Combined Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.165
   Critical Location  :   4.500 m from Start.
   ϕMrz  =   114.2998E+00 KNm               [NZS3404 8.3.2]
   Section Combined Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ϕMry  =   114.2998E+00 KNm               [NZS3404 8.3.3]
   Section Combined Capacity (Biaxial)
   Critical Load Case :     1*
   Critical Ratio     :   0.165
   Critical Location  :   4.500 m from Start.
   γ     =     1.400                         [NZS3404 8.3.4]
   Member In-plane Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.165
   Critical Location  :   4.500 m from Start.
   ϕMiz  =   114.2998E+00 KNm               [NZS3404 8.4.2]
   Member In-plane Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ϕMiy  =   114.2998E+00 KNm               [NZS3404 8.4.2]
   Member Out-of-plane Capacity (Tension)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   αbc   =      0.00
   ϕNoz  =     0.0000E+00 KN                [NZS3404 8.4.4.1.2]
   ϕMoz,t=     0.0000E+00 KNm               [NZS3404 8.4.4.1]
   Member Out-of-plane Capacity (Compression)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ϕMoz,c=     0.0000E+00 KNm               [NZS3404 8.4.4.2]
   Member Biaxial Capacity (Tension)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   Member Biaxial Capacity (Compression)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ********************************************************************************