 # V.NZS3404 1997-RHS Section

Verify the design capacity of a rectangular hollow section as per NZS3404 1997.

## Details

Verify the section bending capacity of an HSST20X12X75 spanning 6 m. Steel grade is 250 MPa.

Note: This is the left column in the STAAD.Pro model (i.e., physical member no. 2).

## Validation

Section Classification

Evaluate the slenderness effects of the Y axis:

$λ e f = B 2 t f f y 250 = 269.3 2(17.73) 250 250 = 15.19$

Section classification is compact.

Evaluate the slenderness effects of the Z axis:

$λ e w = d t w f y 250 = 472.5 17.73 250 250 = 26.65$

Section classification is compact

Effective Section Modulus, Zez = 4.425×106 mm3

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

Msz = 250× 4.425×106/106 = 1,106 kN·m

ϕMsz = 0.9×1,106 = 995.6 kN·m

Effective Section Modulus, Zey = 3.114×106 mm3

The nominal section capacity in bending about Z axis, Msy = ϕfy×Zey

Msy = 250× 3.114×106/106 = 778.5 kN·m

ϕMsy = 0.9×778.5 = 700.7 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 = 1×1×1×6,000 = 6,000 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 × 1,106 = 1,106 kN·m ≤ (Msz, Msy)Max. [Ref : Clause 5.6.1.1.1(a)]

ϕMbz = 0.9×1,106 = 995.6 kN·m

Check for Axial Compression

Section Compression Capacity:

Gross Area, Ag = 26,774 mm2

Net Area, An = 26,774 mm2

Form factor, Kf = Ae/Ag = 1.0

The nominal member section capacity for axial compression,

 Ns = Kf×An×fy = 1.0×26,774×250 = 6,694 kN [Ref : Clause 6.2.1]

 ϕNs = 0.9×6,694 = 6,024 kN

Member Compression Capacity

Length of the member, L = 6,000 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 = 1.0×6,000 mm = 6,000 mm

Effective Length of member, Ley = 1.0×6,000 mm = 6,000 mm

rz = √(911.5×106 / 26,774) = 184.5

ry = √411.2×106 / 26,774) = 123.9

Geometrical Slenderness Ratio = Lez/rz = 6,000 / 184.5 = 32.5

Geometrical Slenderness Ratio = Ley/ry = 6,000 / 123.9 = 48.4

Member slenderness,

 $λ n z = L e z r k f f y 250 = 32.5 1 250 250 = 32.5$ [Ref : Clause 6.3.3]
 $λ n y = L e y r k f f y 250 = 48.4 1 250 250 = 48.4$ [Ref : Clause 6.3.3]

αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 15.30

αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 20.07

 αb = -1.0 [Ref : Table 6.3.3(2)]

λz = λnz + αaz×αz = 17.22

λy = λny + αay×αb = 28.34

η = 0.012

η = 0.048

ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 14.33

ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 5.785

αcz= 0.988

αcy= 0.949

The nominal member capacity,

 Ncz= αcz×Ns =0.988×6,694 = 6,611 kN [Ref : Clause 6.3.3]

ϕNcz = 5,950 kN

The nominal member capacity,

 Ncy= αcy×Ns =0.949×6,694 = 6,353 kN [Ref : Clause 6.3.3]

ϕNcy = 5,717 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

Kte = 1.00

Nt1 = Ag×fy = 6,024 kN

Nt2 = 0.85×Kte×An×fu = 6,694 kN

 ϕNt = 0.9×6,694 = 6,024 kN [Ref : Clause 5.6.1.1.1(a)]

## Results

Table 1. Comparison of results
ϕMsz ( kN·m ) 995.6 995.5142 negligible
ϕMsy ( kN·m ) 700.7 700.547 negligible
ϕMbz ( kN·m ) 995.6 995.5142 negligible
ϕNcz (kN) 5,950 5,949 negligible

ϕNcy (kN)

5,717 5,719 negligible
ϕNs (kN) 6,024 6,024.2 negligible
ϕNt (kN) 6,024 6,024.2 negligible

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

STAAD PLANE
*
*  INPUT FILE: NZS3404_Frame 2.STD
*
* REFERENCE : Hand Calculation
*
*  OBJECTIVE : TO DETERMINE THE ADEQUACY OF  TUBE,HSST SHAPE  PER
*              THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 21-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 6 0; 3 8 6 0; 4 8 0 0;
*
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
DEFINE PMEMBER
2 PMEMBER 1
1 PMEMBER 2
3 PMEMBER 3
*
*
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 INDIAN
2 TABLE ST TUB1251256
*
MEMBER PROPERTY AMERICAN
1 3 TABLE ST HSST20X12X.75
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 FIXED
4 PINNED
*
1 UNI Y -10
2 UMOM GZ 25
3 TRAP GZ 4 6
3 CON Y 10 0.1 0
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
IST 2 PMEMB 1 TO 3
TRACK 2 PMEMB 1 TO 3
SGR 0 PMEMB 1 TO 3
CHECK CODE PMEMB 2 3
*
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     2
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   HSST20X12X.75            (AISC SECTIONS)
Governing Criteria: Cl.8.4.4.1
Governing Ratio:   0.090  (PASS)
Governing Location:   0.000 m from Start.
SECTION PROPERTIES
------------------
d:       508.0000 mm    b:       304.8000 mm
t:        17.7292 mm
Ag:     26774.1387 mm2   J:   924.0338E+06 mm4             Iw:     0.0000E+00 mm6
Iz:   911.5469E+06 mm4  Sz:     4.4245E+06 mm3 (plastic)   Zz:     3.5888E+06 mm3 (elastic)
rz:   184.5150E+00 mm
Iy:   411.2367E+06 mm4  Sy:     3.1135E+06 mm3 (plastic)   Zy:     2.6984E+06 mm3 (elastic)
ry:   123.9333E+00 mm
STAAD PLANE                                              -- PAGE NO.    4
*
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:      48.413  LOAD:     1   LOC.(MET):   0.000
ALLOWABLE SLENDERNESS RATIO:  180.000
BENDING
-------
Critical Ratio     :   0.090
Critical Location  :   0.000 m from Start.
Mz* =   -89.2106E+00 KNm
Section Slenderness: Compact
Zez =     4.4245E+06 mm3
ϕMsz =   995.5142E+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 =     3.1135E+06 mm3
ϕMsy =   700.5470E+00 KNm                [NZS3404 Cl.5.1    ]
Member Bending Capacity
Critical Ratio     :   0.090
Critical Location  :   0.000 m from Start.
Crtiical Flange Segment:
Location (Type):   0.00 m(F )-  6.00 m(F )
Mz* =   -89.2106E+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   =      6.00 m                       [NZS3404 5.6.3]
αm   =     1.000                         [NZS3404 5.6.1.1.1(b)(iii)]
Mo   =    41.0351E+03 KNm                [NZS3404 5.6.1.1.1(d)]
αsz  =     1.000                         [NZS3404 5.6.1.1.1(c)]
ϕMbz =   995.5142E+00 KNm (&lt;= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
STAAD PLANE                                              -- PAGE NO.    5
*
SHEAR
-----
Section Shear Capacity (along Y-axis)
Critical Ratio     :   0.001
Critical Location  :   0.000 m from Start.
Vy*   =     1.1125E+00 KN
ϕVvmy =     2.1765E+03 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 =     1.2893E+03 KN                [NZS3404 5.12.2]
STAAD PLANE                                              -- PAGE NO.    6
*
AXIAL
-----
Section Compression Capacity
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
N*    =    40.2237E+00 KN
Ae    =    26.7741E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
kf    =     1.000                        [AS 4100 6.2.2]
An    =    26.7741E+03 mm2
ϕNs   =     6.0242E+03 KN                [NZS3404 6.2.1]
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
N*    =    40.2237E+00 KN
Unbraced Segment:
Location (Type):   0.00 m(U )-  6.00 m(U )
Lez   =      6.00 m
αb    =     -1.00                        [NZS3404 Table 6.3.3(1)/6.3.3(2)]
λn,z  =    32.518                        [NZS3404 6.3.3]
λ,z   =    17.215                        [NZS3404 6.3.3]
ε,z   =    14.331                        [NZS3404 6.3.3]
αc,z  =     0.988                        [NZS3404 6.3.3]
ϕNcz  = 0.5949E+4 KN                     [NZS3404 6.3.3]
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
N*    =    40.2237E+00 KN
Unbraced Segment:
Location (Type):   0.00 m(U )-  6.00 m(U )
Ley   =      6.00 m
λn,y  =    48.413                        [NZS3404 6.3.3]
λ,y   =    28.343                        [NZS3404 6.3.3]
ε,y   =     5.785                        [NZS3404 6.3.3]
αc,y  =     0.949                        [NZS3404 6.3.3]
ϕNcy  = 0.5719E+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    =    26.7741E+03 mm2
ϕNt   =     6.0242E+03 KN                [NZS3404 7.2]
STAAD PLANE                                              -- PAGE NO.    7
*
COMBINED BENDING AND AXIAL
------------------------
Critical Ratio     :   0.090
Critical Location  :   0.000 m from Start.
ϕMrz  =   995.5142E+00 KNm               [NZS3404 8.3.2]
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
ϕMry  =   700.5470E+00 KNm               [NZS3404 8.3.3]
Section Combined Capacity (Biaxial)
Critical Ratio     :   0.034
Critical Location  :   0.000 m from Start.
γ     =     1.407                         [NZS3404 8.3.4]
Critical Ratio     :   0.090
Critical Location  :   0.000 m from Start.
ϕMiz  =   995.5142E+00 KNm               [NZS3404 8.4.2]
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
ϕMiy  =   695.6196E+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     :   0.090
Critical Location  :   0.000 m from Start.
ϕMoz,c=   988.5120E+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.
********************************************************************************
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
STAAD PLANE                                              -- PAGE NO.    8
*
MEMBER DESIGN OUTPUT FOR PMEMBER     3
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   HSST20X12X.75            (AISC SECTIONS)
Governing Criteria: Cl.8.4.4.1
Governing Ratio:   0.053  (PASS)
Governing Location:   0.000 m from Start.
SECTION PROPERTIES
------------------
d:       508.0000 mm    b:       304.8000 mm
t:        17.7292 mm
Ag:     26774.1387 mm2   J:   924.0338E+06 mm4             Iw:     0.0000E+00 mm6
Iz:   911.5469E+06 mm4  Sz:     4.4245E+06 mm3 (plastic)   Zz:     3.5888E+06 mm3 (elastic)
rz:   184.5150E+00 mm
Iy:   411.2367E+06 mm4  Sy:     3.1135E+06 mm3 (plastic)   Zy:     2.6984E+06 mm3 (elastic)
ry:   123.9333E+00 mm
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:      48.413  LOAD:     1   LOC.(MET):   0.000
ALLOWABLE SLENDERNESS RATIO:  180.000
BENDING
-------
STAAD PLANE                                              -- PAGE NO.    9
*
Critical Ratio     :   0.053
Critical Location  :   0.000 m from Start.
Mz* =    52.3655E+00 KNm
Section Slenderness: Compact
Zez =     4.4245E+06 mm3
ϕMsz =   995.5142E+00 KNm                [NZS3404 Cl.5.1    ]
Critical Ratio     :   0.022
Critical Location  :   6.000 m from Start.
My* =    15.6295E+00 KNm
Section Slenderness: Compact
Zey =     3.1135E+06 mm3
ϕMsy =   700.5470E+00 KNm                [NZS3404 Cl.5.1    ]
Member Bending Capacity
Critical Ratio     :   0.053
Critical Location  :   0.000 m from Start.
Crtiical Flange Segment:
Location (Type):   0.00 m(F )-  6.00 m(F )
Mz* =    52.3655E+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   =      6.00 m                       [NZS3404 5.6.3]
αm   =     1.000                         [NZS3404 5.6.1.1.1(b)(iii)]
Mo   =    41.0351E+03 KNm                [NZS3404 5.6.1.1.1(d)]
αsz  =     1.000                         [NZS3404 5.6.1.1.1(c)]
ϕMbz =   995.5142E+00 KNm (&lt;= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
SHEAR
-----
Section Shear Capacity (along Y-axis)
Critical Ratio     :   0.004
Critical Location  :   0.500 m from Start.
Vy*   =     8.8875E+00 KN
ϕVvmy =     2.1765E+03 KN                [NZS3404 5.12.2]
Section Shear Capacity (along Z-axis)
Critical Ratio     :   0.013
Critical Location  :   6.000 m from Start.
Vz*   =    16.2009E+00 KN
ϕVvmz =     1.2893E+03 KN                [NZS3404 5.12.2]
STAAD PLANE                                              -- PAGE NO.   10
*
AXIAL
-----
Section Compression Capacity
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
N*    =    39.7763E+00 KN
Ae    =    26.7741E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
kf    =     1.000                        [AS 4100 6.2.2]
An    =    26.7741E+03 mm2
ϕNs   =     6.0242E+03 KN                [NZS3404 6.2.1]
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
N*    =    39.7763E+00 KN
Unbraced Segment:
Location (Type):   0.00 m(U )-  6.00 m(U )
Lez   =      6.00 m
αb    =     -1.00                        [NZS3404 Table 6.3.3(1)/6.3.3(2)]
λn,z  =    32.518                        [NZS3404 6.3.3]
λ,z   =    17.215                        [NZS3404 6.3.3]
ε,z   =    14.331                        [NZS3404 6.3.3]
αc,z  =     0.988                        [NZS3404 6.3.3]
ϕNcz  = 0.5949E+4 KN                     [NZS3404 6.3.3]
Critical Ratio     :   0.007
Critical Location  :   0.000 m from Start.
N*    =    39.7763E+00 KN
Unbraced Segment:
Location (Type):   0.00 m(U )-  6.00 m(U )
Ley   =      6.00 m
λn,y  =    48.413                        [NZS3404 6.3.3]
λ,y   =    28.343                        [NZS3404 6.3.3]
ε,y   =     5.785                        [NZS3404 6.3.3]
αc,y  =     0.949                        [NZS3404 6.3.3]
ϕNcy  = 0.5719E+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    =    26.7741E+03 mm2
ϕNt   =     6.0242E+03 KN                [NZS3404 7.2]
STAAD PLANE                                              -- PAGE NO.   11
*
COMBINED BENDING AND AXIAL
------------------------
Critical Ratio     :   0.053
Critical Location  :   0.000 m from Start.
ϕMrz  =   995.5142E+00 KNm               [NZS3404 8.3.2]
Critical Ratio     :   0.022
Critical Location  :   6.000 m from Start.
ϕMry  =   700.5470E+00 KNm               [NZS3404 8.3.3]
Section Combined Capacity (Biaxial)
Critical Ratio     :   0.020
Critical Location  :   0.000 m from Start.
γ     =     1.407                         [NZS3404 8.3.4]
Critical Ratio     :   0.053
Critical Location  :   0.000 m from Start.
ϕMiz  =   989.0403E+00 KNm               [NZS3404 8.4.2]
Critical Ratio     :   0.022
Critical Location  :   6.000 m from Start.
ϕMiy  =   695.8025E+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)