 # V.NZS3404 1997-Channel Section

Verify the design capacity of a channel section per NZS 3404 1997.

## Details

The member is a PFC250 section used in a 9 m simply supported span. The beam is loaded with a vertical load of 8.4 kN point load at 5m from start end, a 10 kN axial load at the mid-point, and a distributed load that decreases from 0.5 kN/m at the start down to 0.2 kN/m at the end. Steel grade is 300 MPa.

## Validation

Section Classification

Evaluate the slenderness effects of the beam flanges:

$λ e f = B 2 t f f y 250 = 90 15 300 250 = 5.988$

Section flange classification is compact.

Evaluate the slenderness effects of the beam web:

$λ e w = d t w f y 250 = 220 8 300 250 = 30.124 < 89$

Section web classification is compact

Effective Section Modulus, Zez = 421,000 mm3

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

Msz = 300× 421,000/106 = 126.3 kN·m

ϕMsz = 0.9×126.3 = 113.67 kN·m

Effective Section Modulus, Zey = 88,925 mm3

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

Msy = 300× 88,925/106 = 26.68 kN·m

ϕMsy = 0.9×26.68 = 24.01 kN·m

Member Bending Capacity

End restraint arrangement = FF

A twist restraint factor, Kt (SKT) = 1.00

Minor axis rotation restraints = Both

Lateral rotation restraint factor, Kr (SKR) = 0.70

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

Effective length = 1×1×1×9,000 = 9,000 mm
$α m = 1.7 M m * ( M 2 * ) 2 + ( M 3 * ) 2 + ( M 4 * ) 2 = 1.7 × 22.416 ( -12.087 ) 2 + ( -22.416 ) 2 + ( -12.087 ) 2 = 1.352 ≤ 2.25$

Reference buckling moment, Mo

 $α s = 0.6 M s x M o a 2 + 3 - M s x M o a = 0.281$ [Ref : Clause 5.6.1.1 (c)]

Mbx = αmαsMsx ≤ Msx

 Mbz = 1.352 × 0.281 × 126.3 = 48.0 kN·m ≤ (Msz, Msy)Max. [Ref : Clause 5.6.1.1.1(a)]

ϕMbz = 0.9×48.0 = 43.19 kN·m

Check for Shear

Shear Area of the section, Ay = d×tw = 250×8 = 2,000 mm2

Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×300×2,000 = 384 kN

 Vvn = 2×324/(0.9 + 1.2) = 308.6 kN [Ref : Clause 5.11.2]

ϕVy = 0.9×384 = 345.6 kN

Shear Area of the section, AZ = 2×bf× tf = 2×90×15 = 2,700 mm2

Section Shear Capacity (Along z axis),Vz = 0.6×fy×Az = 0.6×300×2,700 = 486 kN

ϕVz = 0.9×486 = 437.4 kN

Check for Axial Compression

Section Compression Capacity:

The flange slenderness, λeb = 5.9884 [Ref : Cl - 6.2.3.1]

Yield slender for flange, λeby = 14 [Ref : Table 6.2.4]

The web slenderness, λew = 30.125

Gross Area, Ag = 4,520 mm2

Net Area, An = 4,520 mm2

Form factor, Kf = Ae/Ag = 1

The nominal member section capacity for axial compression,

 Ns = Kf×An×fy = 1×4,520×300 = 1,356 kN [Ref : Clause 6.2.1]

 ϕNs = 0.9×1,356 = 1,220.4 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 = Lez/rz = 9,000 / 99.89 = 90.10

Geometrical Slenderness Ratio = Ley/ry = 9,000 / 28.37 = 317.2

Member slenderness,

 $λ n z = L e z r k f f y 250 = 90.10 1 300 250 = 98.70$ [Ref : Clause 6.3.3]
 $λny=Leyrkffy250=317.21300250=347.5$ [Ref : Clause 6.3.3]

αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 17.402

αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 5.970

 αb = 0.5 [Ref : Table 6.3.3(2)]

λz = λnz + αaz×αz = 107.4

λy = λny + αay×αb = 350.5

η = 0.31

η = 1.10

ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 0.96

ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 0.57

αcz= 0.493

αcy= 0.061

The nominal member capacity,

 Ncz= αcz×Ns =0.493×1,356 = 668.7 kN [Ref : Clause 6.3.3]

ϕNcz = 601.8 kN

The nominal member capacity,

 Ncy= αcy×Ns =0.061×1,356 = 82.72 kN [Ref : Clause 6.3.3]

ϕNcy = 74.44 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

Kte = 1.00

Nt1 = Ag×fy = 1,356 kN

Nt2 = 0.85×Kte×An×fu = 1,690.5 kN

 ϕNt = 0.9×1,356 = 1,220.4 kN [Ref : Clause 5.6.1.1.1(a)]

## Results

Table 1. Comparison of results
ϕMsz (kN·m) 113.67 113.67 none
ϕMsy (kN·m) 24.01 24.0098 negligible
ϕMbz (kN·m) 43.19 42.9925 negligible
ϕVvy (kN) 345.6 345.600 none
ϕNs (kN) 1,220.4 1,220.4 none
ϕNcz (kN) 601.8 601.8 none
ϕNcy (kN) 74.44 74.74 negligible
ϕNt (kN) 1,220.4 1,220.4 none

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

STAAD SPACE
*
*  INPUT FILE: NZS3404_Channel_Section_Compact.STD
*
* REFERENCE : Hand Calculation
*
*  OBJECTIVE : TO DETERMINE THE ADEQUACY OF CHANNEL 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;
*
MEMBER INCIDENCES
1 1 4;
DEFINE PMEMBER
1 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 AUSTRALIAN
1 TABLE ST PFC250
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 PINNED
4 FIXED BUT FX MY MZ
PRINT ALL
*
1 CON GY -8.4
SELFWEIGHT Y -1
1 UNI X -10
1 TRAP Z -0.5 -2
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
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   PFC250                   (AISC SECTIONS)
Governing Criteria: Cl.8.4.5.1
Governing Ratio:  46.122 *(FAIL)
Governing Location:   2.250 m from Start.
SECTION PROPERTIES
------------------
d:       250.0000 mm   bf:        90.0000 mm
tf:        15.0000 mm   tw:         8.0000 mm
Ag:      4520.0000 mm2   J:   238.0000E+03 mm4             Iw:    34.8250E+09 mm6
Iz:    45.1000E+06 mm4  Sz:   421.0000E+03 mm3 (plastic)   Zz:   360.8000E+03 mm3 (elastic)
rz:    99.8893E+00 mm
Iy:     3.6400E+06 mm4  Sy:   107.0000E+03 mm3 (plastic)   Zy:    59.2834E+03 mm3 (elastic)
ry:    28.3780E+00 mm
STAAD SPACE                                              -- PAGE NO.   10
*
MATERIAL PROPERTIES
-------------------
Material Standard        :  AS/NZS 3679.1
Residual Stress Category :  HR (Hot-rolled)
E (#)       : 204999.984 MPa         [NZS3404 1.4]
G           :  80000.000 MPa         [NZS3404 1.4]
fy, flange  :    300.000 MPa         [NZS3404 Table 2.1]
fy, web     :    320.000 MPa         [NZS3404 Table 2.1]
fu          :    440.000 MPa         [NZS3404 Table 2.1]
BENDING
-------
Critical Ratio     :   0.205
Critical Location  :   4.500 m from Start.
Mz* =   -23.3483E+00 KNm
Section Slenderness: Compact
Zez =   421.0000E+03 mm3
ϕMsz =   113.6700E+00 KNm                [NZS3404 Cl.5.1    ]
Critical Ratio     :   1.449
Critical Location  :   1.500 m from Start.
My* =    34.7977E+00 KNm
Section Slenderness: Compact
Zey =    88.9251E+03 mm3
ϕMsy =    24.0098E+00 KNm                [NZS3404 Cl.5.1    ]
Member Bending Capacity
Critical Ratio     :   0.544
Critical Location  :   4.500 m from Start.
Crtiical Flange Segment:
Location (Type):   0.00 m(F )-  9.00 m(F )
Mz* =   -23.3483E+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   =     1.352                         [NZS3404 5.6.1.1.1(b)(iii)]
Mo   =    42.2526E+00 KNm                [NZS3404 5.6.1.1.1(d)]
αsz  =     0.279                         [NZS3404 5.6.1.1.1(c)]
ϕMbz =    42.9225E+00 KNm (&lt;= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
STAAD SPACE                                              -- PAGE NO.   11
*
SHEAR
-----
Section Shear Capacity (along Y-axis)
Critical Ratio     :   0.017
Critical Location  :   0.000 m from Start.
Vy*  =     5.7625E+00 KN
ϕVvy =   345.6000E+00 KN                 [NZS3404 5.11.2]
Section Shear Capacity (along Z-axis)
Critical Ratio     :   0.016
Critical Location  :   0.750 m from Start.
Vz*  =     4.0781E+00 KN
ϕVvz =   262.4400E+00 KN                 [NZS3404 5.11.2]
STAAD SPACE                                              -- PAGE NO.   12
*
AXIAL
-----
Section Compression Capacity
Critical Ratio     :   0.074
Critical Location  :   0.000 m from Start.
N*    =    90.0000E+00 KN
Ae    =     4.5200E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
kf    =     1.000                        [AS 4100 6.2.2]
An    =     4.5200E+03 mm2
ϕNs   =     1.2204E+03 KN                [NZS3404 6.2.1]
Critical Ratio     :   0.150
Critical Location  :   0.000 m from Start.
N*    =    90.0000E+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  =    98.699                        [NZS3404 6.3.3]
λ,z   =   107.400                        [NZS3404 6.3.3]
ε,z   =     0.959                        [NZS3404 6.3.3]
αc,z  =     0.493                        [NZS3404 6.3.3]
ϕNcz  = 0.6018E+3 KN                     [NZS3404 6.3.3]
Critical Ratio     :   1.204
Critical Location  :   0.000 m from Start.
N*    =    90.0000E+00 KN
Unbraced Segment:
Location (Type):   0.00 m(U )-  9.00 m(U )
Ley   =      9.00 m
λn,y  =   347.417                        [NZS3404 6.3.3]
λ,y   =   350.403                        [NZS3404 6.3.3]
ε,y   =     0.569                        [NZS3404 6.3.3]
αc,y  =     0.061                        [NZS3404 6.3.3]
ϕNcy  = 0.7474E+2 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    =     4.5200E+03 mm2
ϕNt   =     1.2204E+03 KN                [NZS3404 7.2]
STAAD SPACE                                              -- PAGE NO.   13
*
COMBINED BENDING AND AXIAL
------------------------
Critical Ratio     :   0.213
Critical Location  :   4.500 m from Start.
ϕMrz  =   109.4786E+00 KNm               [NZS3404 8.3.2]
Critical Ratio     :   1.554
Critical Location  :   0.750 m from Start.
ϕMry  =    22.3867E+00 KNm               [NZS3404 8.3.3]
Section Combined Capacity (Biaxial)
Critical Ratio     :   1.689
Critical Location  :   1.500 m from Start.
γ     =     1.461                         [NZS3404 8.3.4]
Critical Ratio     :   0.222
Critical Location  :   4.500 m from Start.
ϕMiz  =   105.1701E+00 KNm               [NZS3404 8.4.2]
Critical Ratio     :  14.256
Critical Location  :   2.250 m from Start.
ϕMiy  =     2.3263E+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)