 # 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

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

 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
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

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\New Zealand\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
*
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 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   PIPX80                   (AISC SECTIONS)
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
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:     122.231  LOAD:     1   LOC.(MET):   0.000
ALLOWABLE SLENDERNESS RATIO:  400.000
BENDING
-------
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    ]
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 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 (&lt;= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
STAAD SPACE                                              -- PAGE NO.   14
*
SHEAR
-----
Section Shear Capacity (along Y-axis)
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
Vy*   =     4.2000E+00 KN
ϕVvmy =   622.9389E+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 =   622.9389E+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    =     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]
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]
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 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
------------------------
Critical Ratio     :   0.165
Critical Location  :   4.500 m from Start.
ϕMrz  =   114.2998E+00 KNm               [NZS3404 8.3.2]
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 Ratio     :   0.165
Critical Location  :   4.500 m from Start.
γ     =     1.400                         [NZS3404 8.3.4]
Critical Ratio     :   0.165
Critical Location  :   4.500 m from Start.
ϕMiz  =   114.2998E+00 KNm               [NZS3404 8.4.2]
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 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)