# 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:

$λef=ODtfy250=323.96.3250250=51.41$

Section classification is non-compact ($λey=120>λef>λep=50$)

Effective Section Modulus for a compact section:

$|Sxx=636×103mm3◂1.5×Zxx=1.5(489.6×103)mm3=734.4×103mm3min⁡$

Effective section modulus for a non-compact section:

The nominal section capacity in bending about Z axis, ϕMs = ϕfy×Ze

Ms = 250× 633.1×103/106 = 158.3 kN·m

ϕMsz = 0.9×158.3 = 142.4 kN·m

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

$M o = π 2 E I y L e 2 [ G J + ( π 2 E I w L e 2 ) ]$

 αs = 1 [Ref : Clause 5.6.1.1 (c)]

Member bending capacity, Mbz

Mbz = αmαsMsz ≤ Msz

 Mbz = 1 × 1 × 158.2 = 158.3 kN·m ≤ (Msz, Msy)Max. [Ref : Clause 5.6.1.1.1(a)]

ϕMbz = 0.9×158.3 = 142.4 kN·m

Check for Shear

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

Vy = 0.36×fy×Ae = 0.36×250×6,290×10-3 = 566.1 kN

ϕVy = 0.9×566.1 = 509.5 kN

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

Design bending moment, M = 135 kN·m

0.75×ϕ×Ms ≤ M ≤ ϕ×Ms

0.75×142.4 = 106.8 kN·m

ϕVy = 0.9 × 386.9 = 348.3 kN

Check for Axial Capacity

Section Compression Capacity:

Gross Area, Ag = 6,290 mm2

The effective outside diameter is the minimum of de1, de2, and do:

The effective outside diameter = do = 323.9 mm

Net Area, An = 6,290 mm2

Form factor, Kf = Ae/Ag = 1.0

The nominal member section capacity for axial compression,

 Ns = Kf×An×fy = 1.0×6,290×250 = 1,573 kN [Ref : Clause 6.2.1]

 ϕNs = 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, 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

Geometrical Slenderness Ratio = Ley/ry = Lez/rz = 9,000 / 112.3 = 80.13

Member slenderness,

 $λ n = L e r k f f y 250 = 80.13 1 250 250 = 80.13$ [Ref : Clause 6.3.3]
$αa=2,100λnz−13.5λnz2−15.3λnz+2,050=19.31$

 αb = -0.5 [Ref : Table 6.3.3(2)]

λ = λn + αa×αb = 70.48

η = 0.19

$ξy=ξz=(λz/90)2+1+η2×(λz/90)2=(70.48/90)2+1+0.192×(70.48/90)2=1.47$
$αcz=ξz[1+1−(90ξz×λz)2]=0.74$

The nominal member capacity,

 Ncy = Ncz= αcz×Ns =0.74×1,573 = 1,171 kN [Ref : Clause 6.3.3]

ϕNcy = ϕNcz = 1,054 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

Kte = 1.00

Nt1 = Ag×fy = 6,290 × 250×10-3 = 1,573 kN

Nt2 = 0.85×Kte×An×fu = 0.85(1.0)(6,290)(250×10-3) = 1,711 kN

 ϕNt = 0.9×1,573 = 1,415 kN [Ref : Clause 5.6.1.1.1(a)]

## Results

Table 1. Comparison of results
ϕMsz (kN·m) 142.4 142.4352 negligible
ϕMsy (kN·m) 142.4 142.4352 negligible
ϕMbz (kN·m) 142.4 142.4352 negligible
ϕVy (kN) 348.3 348.022 negligible
ϕVz (kN) 509.5 509.16 negligible
ϕNs (kN) 1,415 1,414.3 negligible
ϕNcz (kN) 1,054 1,054 none
ϕNcy (kN) 1,054 1,054 none
ϕNt (kN) 1,415 1,415.3 negligible

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
*
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 CODE CHECKING - NZS-3404-1997 (v1.0)
**************************************************
AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE:-
---------     -------------     ---------------
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 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
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
-------
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    ]
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 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 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 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 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]
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]
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 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
------------------------
Critical Ratio     :   0.948
Critical Location  :   4.500 m from Start.
ϕMrz  =   142.4352E+00 KNm               [NZS3404 8.3.2]
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 Ratio     :   0.948
Critical Location  :   4.500 m from Start.
γ     =     1.400                         [NZS3404 8.3.4]
Critical Ratio     :   0.948
Critical Location  :   4.500 m from Start.
ϕMiz  =   142.4352E+00 KNm               [NZS3404 8.4.2]
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 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 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 Ratio     :   0.000
Critical Location  :   0.000 m from Start.
Member Biaxial Capacity (Compression)
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
STAAD SPACE                                              -- PAGE NO.   17
*
SEISMIC PROVISIONS
------------------
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]
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 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 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 Ratio     : N/A
Critical Location  : N/A
Status           =   Passed              [NZS3404 12.4.1.2]
Section Symmetry Requirement
Critical Ratio     : N/A
Critical Location  : N/A
Status           =   Passed              [NZS3404 12.5.2]
Min Web Thickness Requirement for Beam
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 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 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 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