V.NZS3404 1997-Tube Section Non Compact

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

Details

Verify the capacity of a PIP3239H member. Steel grade = 250 MPa. The simply supported span is 9 m with a 60 kN load at mid-span.

Validation

Section Classification

Evaluate the slenderness effects of the pipe member:

λ_{e f} = \frac{OD}{t} \sqrt{\frac{f_{y}}{250}} = \frac{323.9}{6.3} \sqrt{\frac{250}{250}} = 51.41

Section classification is non-compact ( $λ_{e y} = 120 > λ_{e f} > λ_{e p} = 50$ )

Section Bending Capacity About Z-Axis

Effective Section Modulus for a compact section:

{}_{\min}{| \begin{array}{l} S_{x x} = 636 \times 10^{3} {mm}^{3} ◂ \\ 1.5 \times Z_{x x} = 1.5 (489.6 \times 10^{3}) {mm}^{3} = 734.4 \times 10^{3} {mm}^{3} \end{array}}

Effective section modulus for a non-compact section:

Z_{e} = Z + \frac{λ_{e y} - λ_{e f}}{λ_{e y} - λ_{e p}} (Z_{c} - Z_{x x}) = 489.6 + \frac{120 - 51.41}{120 - 50} (636 - 489.6) = 633.1 \times 10^{3} {mm}^{3}

The nominal section capacity in bending about Z axis, ϕM_s = ϕf_y×Z_e

M_s = 250× 633.1×10³/10⁶ = 158.3 kN·m

ϕM_sz = 0.9×158.3 = 142.4 kN·m

Member Bending Capacity

End restraint arrangement = LL

A twist restraint factor, K_t (SKT) = 1.00

Minor axis rotation restraints = Both

Lateral rotation restraint factor, K_r (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

α_m = 1

[Ref: Cl no -5.6.1.1 (b)]

Reference buckling moment, M_o

M_{o} = \sqrt{\frac{π^{2} E I_{y}}{{L_{e}}^{2}} [G J + (\frac{π^{2} E I_{w}}{{L_{e}}^{2}})]}

= \sqrt{\frac{π^{2} \times 250 \times 10^{3} 79.29 \times 10^{6}}{{9, 000}^{2}} [80, 000 \times 158.58 \times 10^{6} + (\frac{π^{2} \times 250 \times 10^{3} 79.29 \times 10^{6}}{{9, 000}^{2}})]} = 5, 013 kN⋅m

α_s = 1

[Ref : Clause 5.6.1.1 (c)]

Member bending capacity, M_bz

M_bz = α_mα_sM_sz ≤ M_sz

M_bz = 1 × 1 × 158.2 = 158.3 kN·m ≤ (M_sz, M_sy)_Max.

[Ref : Clause 5.6.1.1.1(a)]

ϕM_bz = 0.9×158.3 = 142.4 kN·m

Check for Shear

Nominal shear capacity, V_z, of a circular hollow section: [Ref. Cl no 5.11.4.2]

V_y = 0.36×f_y×A_e = 0.36×250×6,290×10^-3 = 566.1 kN

ϕV_y = 0.9×566.1 = 509.5 kN

Nominal shear capacity, V_y, of a circular hollow section: [Ref. Cl no 5.12.2]

Design bending moment, M = 135 kN·m

0.75×ϕ×M_s ≤ M ≤ ϕ×M_s

0.75×142.4 = 106.8 kN·m

V_{y} = V_{v} [2.2 - (\frac{1.6 \times M}{ϕ M_{S}})] = 566.1 \times [2.2 - (\frac{1.6 \times 135}{142.4})] = 386.9 kN

ϕV_y = 0.9 × 386.9 = 348.3 kN

Check for Axial Capacity

Section Compression Capacity:

Gross Area, A_g = 6,290 mm²

The effective outside diameter is the minimum of d_e1, d_e2, and d_o:

d_{e 1} = d_{o} \sqrt{\frac{λ_{e y}}{λ_{e}}} = 409.1 m m

d_{e 2} = d_{o} {(\frac{3 \times λ_{e y}}{λ_{e}})}^{2} = 7, 415 m m

The effective outside diameter = d_o = 323.9 mm

Net Area, A_n = 6,290 mm²

Form factor, K_f = A_e/A_g = 1.0

The nominal member section capacity for axial compression,

N_s = K_f×A_n×f_y = 1.0×6,290×250 = 1,573 kN

[Ref : Clause 6.2.1]

ϕN_s = 0.9×1,573 = 1,415 kN

Member Compression Capacity

Length of the member, L = 9,000 mm

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

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

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

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

r_{y} = r_{z} = \sqrt{79.29 \times 10^{6} / 6, 290} = 112.3 mm

Geometrical Slenderness Ratio = L_ey/r_y = L_ez/r_z = 9,000 / 112.3 = 80.13

Member slenderness,

λ_{n} = \frac{L_{e}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 80.13 \sqrt{1} \sqrt{\frac{250}{250}} = 80.13

[Ref : Clause 6.3.3]

α_{a} = 2, 100 \frac{λ_{n z} - 13.5}{λ_{n z}^{2} - 15.3 λ_{n z} + 2, 050} = 19.31

α_b = -0.5

[Ref : Table 6.3.3(2)]

λ = λ_n + α_a×α_b = 70.48

η = 0.19

ξ_{y} = ξ_{z} = \frac{{(λ_{z} / 90)}^{2} + 1 + η}{2 {\times (λ_{z} / 90)}^{2}} = \frac{{(70.48 / 90)}^{2} + 1 + 0.19}{2 {\times (70.48 / 90)}^{2}} = 1.47

α_{c z} = ξ_{z} [1 + \sqrt{1 - {(\frac{90}{ξ_{z} \times λ_{z}})}^{2}}] = 0.74

The nominal member capacity,

N_cy = N_cz= α_cz×N_s =0.74×1,573 = 1,171 kN

[Ref : Clause 6.3.3]

ϕN_cy = ϕN_cz= 1,054 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

K_te = 1.00

N_t1 = A_g×f_y = 6,290 × 250×10^-3 = 1,573 kN

N_t2 = 0.85×K_te×A_n×f_u = 0.85(1.0)(6,290)(250×10^-3) = 1,711 kN

ϕN_t = 0.9×1,573 = 1,415 kN

[Ref : Clause 5.6.1.1.1(a)]

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
ϕM_sz (kN·m)	142.4	142.4352	negligible
ϕM_sy (kN·m)	142.4	142.4352	negligible
ϕM_bz (kN·m)	142.4	142.4352	negligible
ϕV_y (kN)	348.3	348.022	negligible
ϕV_z (kN)	509.5	509.16	negligible
ϕN_s (kN)	1,415	1,414.3	negligible
ϕN_cz (kN)	1,054	1,054	none
ϕN_cy (kN)	1,054	1,054	none
ϕN_t (kN)	1,415	1,415.3	negligible

STAAD.Pro Input File

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

STAAD SPACE
*
*  INPUT FILE: NZS3404_Tube_Section_Non_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
*
UNIT MMS NEWTON
MEMBER PROPERTY INDIAN
1 TO 3 TABLE ST PIP3239H
*
UNIT METER KN
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 -60
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
DUCT 3 PMEMB 1
GLD 1 PMEMB 1
CHECK CODE PMEMB ALL
*
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0)
                     **************************************************
   AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE FOR Y UP :-
   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   PIP3239H                 (AISC SECTIONS)
   Governing Load Case:     1*
   Governing Criteria: T.12.4                                                      
   Governing Ratio:   0.977  (PASS)
   Governing Location:   0.000 m from Start.
   SECTION PROPERTIES
   ------------------
   OD:       323.9000 mm    t:         6.3000 mm
   Ag:      6290.0005 mm2   J:   158.5800E+06 mm4             Iw:     0.0000E+00 mm6
   Iz:    79.2900E+06 mm4  Sz:   636.0001E+03 mm3 (plastic)   Zz:   489.5957E+03 mm3 (elastic)
   rz:   112.2752E+00 mm
   Iy:    79.2900E+06 mm4  Sy:   636.0001E+03 mm3 (plastic)   Zy:   489.5957E+03 mm3 (elastic)
   ry:   112.2752E+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]
  SLENDERNESS:   ACTUAL SLENDERNESS RATIO:      80.160  LOAD:     1   LOC.(MET):   0.000
                 ALLOWABLE SLENDERNESS RATIO:  400.000
   BENDING
   -------
   Section Bending Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.948
   Critical Location  :   4.500 m from Start.
   Mz* =  -135.0000E+00 KNm
   Section Slenderness: Noncompact
   Zez =   633.0454E+03 mm3
   ϕMsz =   142.4352E+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: Noncompact
   Zey =   633.0454E+03 mm3
   ϕMsy =   142.4352E+00 KNm                [NZS3404 Cl.5.1    ]
   Member Bending Capacity
   Critical Load Case :     1*
   Critical Ratio     :   0.948
   Critical Location  :   4.500 m from Start.
   Crtiical Flange Segment: 
   Location (Type):   0.00 m(F )-  9.00 m(F )
   Mz* =  -135.0000E+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   =     4.9763E+03 KNm                [NZS3404 5.6.1.1.1(d)]
   αsz  =     1.000                         [NZS3404 5.6.1.1.1(c)]
   ϕMbz =   142.4352E+00 KNm (&lt;= 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     :   0.086
   Critical Location  :   4.500 m from Start.
   Vy*   =    30.0000E+00 KN
   ϕVvmy =   348.0229E+00 KN                [NZS3404 5.12.2]
   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
   ϕVvmz =   509.1619E+00 KN                [NZS3404 5.12.2]
      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    =     6.2859E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
   kf    =     0.999                        [AS 4100 6.2.2]
   An    =     6.2900E+03 mm2
   ϕNs   =     1.4143E+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    =     -0.50                        [NZS3404 Table 6.3.3(1)/6.3.3(2)]
   λn,z  =    80.134                        [NZS3404 6.3.3]
   λ,z   =    70.478                        [NZS3404 6.3.3]
   ε,z   =     1.467                        [NZS3404 6.3.3]
   αc,z  =     0.745                        [NZS3404 6.3.3]
   ϕNcz  = 0.1054E+4 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  =    80.134                        [NZS3404 6.3.3]
   λ,y   =    70.478                        [NZS3404 6.3.3]
   ε,y   =     1.467                        [NZS3404 6.3.3]
   αc,y  =     0.745                        [NZS3404 6.3.3]
   ϕNcy  = 0.1054E+4 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    =     6.2900E+03 mm2
   ϕNt   =     1.4153E+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     :   0.948
   Critical Location  :   4.500 m from Start.
   ϕMrz  =   142.4352E+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  =   142.4352E+00 KNm               [NZS3404 8.3.3]
   Section Combined Capacity (Biaxial)
   Critical Load Case :     1*
   Critical Ratio     :   0.948
   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     :   0.948
   Critical Location  :   4.500 m from Start.
   ϕMiz  =   142.4352E+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  =   142.4352E+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.
      STAAD SPACE                                              -- PAGE NO.   17
    *                                           
   SEISMIC PROVISIONS
   ------------------
   Section Slenderness (Bending about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.791
   Critical Location  :   0.000 m from Start.
   λsz              =     51.41             [NZS3404 12.5.1.1]
   λez              =     65.00             [NZS3404 Table 12.5]
   Section Slenderness (Bending about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.791
   Critical Location  :   0.000 m from Start.
   λsy              =     51.41             [NZS3404 12.5.1.1]
   λey              =     65.00             [NZS3404 Table 12.5]
   Max Specific Yield Stress
   Critical Load Case :     1*
   Critical Ratio     :   0.694
   Critical Location  :   0.000 m from Start.
   Fy,actual        =    250.00
   Fy,limit         =    360.00             [NZS3404 Table 12.4(1)]
   Max Actual Yield Ratio (Fy/Fu)
   Critical Load Case :     1*
   Critical Ratio     :   0.977
   Critical Location  :   0.000 m from Start.
   Fy/Fu,actual     =      0.78
   Fy/Fu,limit      =      0.80             [NZS3404 Table 12.4(3)]
   Fabrication Requirement
   Critical Load Case : N/A
   Critical Ratio     : N/A
   Critical Location  : N/A
   Status           =   Passed              [NZS3404 12.4.1.2]
   Section Symmetry Requirement
   Critical Load Case : N/A
   Critical Ratio     : N/A
   Critical Location  : N/A
   Status           =   Passed              [NZS3404 12.5.2]
   Min Web Thickness Requirement for Beam
   Critical Load Case :     1*
   Critical Ratio     :   0.489
   Critical Location  :   0.000 m from Start.
   tw,actual        =      6.30
   tw,min           =      3.08             [NZS3404 12.7.2]
   Max Axial Force Limit for Column (a)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*/ϕNs - actual  =      0.00
   N*/ϕNs - limit   =      0.80             [NZS3404 Table 12.8.1]
   Max Axial Force Limit for Column (b)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
    b m               =      0.00
   NoL              =     1.9806E+03 KN
   λEYC             =      0.89
   N*/ϕNs - actual  =      0.00
   N*/ϕNs - limit   =      0.26             [NZS3404 12.8.3.1(b)]
   Max Axial Force Limit for Column (c)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   Ng*/ϕNs - actual =      0.00
   Ng*/ϕNs - limit  =      0.78             [NZS3404 12.8.3.1(c)]
   Shear-Y + Bend-Z Interaction
   Critical Load Case :     1*
   Critical Ratio     :   0.948
   Critical Location  :   4.500 m from Start.
   Mz*  =   135.0000E+00 KN
   ϕMsvz=   142.4352E+00 KN                 [NZS3404 12.10.3.1]
   Shear-Z + Bend-Y Interaction
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   My*  =     0.0000E+00 KN
   ϕMsvy=   142.4352E+00 KN                 [NZS3404 12.10.3.1]
   ********************************************************************************