STAAD.Pro Help

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

Section Bending Capacity About Z-Axis

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

Section Bending Capacity About Y-Axis

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

M o = π 2 E I y L e 2 G J + π 2 E I w L e 2 = 42.25   k N · m
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
Result Type Reference STAAD.Pro Difference Comments
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  

STAAD.Pro Input File

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
*
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -8.4
SELFWEIGHT Y -1 
MEMBER LOAD
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 Output

                       STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0)
                     **************************************************
   AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE:-
   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   PFC250                   (AISC SECTIONS)
   Governing Load Case:     1*
   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
   Nominal Grade            :  300
   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
   -------
   Section Bending Capacity (about Z-axis)
   Critical Load Case :     1*
   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    ]
   Section Bending Capacity (about Y-axis)
   Critical Load Case :     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 Load Case :     1*
   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 Load Case :     1*
   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 Load Case :     1*
   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 Load Case :     1*
   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]
   Member Compression Capacity (about Z-axis)
   Critical Load Case :     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]
   Member Compression Capacity (about Y-axis)
   Critical Load Case :     1*
   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 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    =     4.5200E+03 mm2
   ϕNt   =     1.2204E+03 KN                [NZS3404 7.2]
      STAAD SPACE                                              -- PAGE NO.   13
    *                                           
   COMBINED BENDING AND AXIAL
   ------------------------
   Section Combined Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.213
   Critical Location  :   4.500 m from Start.
   ϕMrz  =   109.4786E+00 KNm               [NZS3404 8.3.2]
   Section Combined Capacity (about Y-axis)
   Critical Load Case :     1*
   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 Load Case :     1*
   Critical Ratio     :   1.689
   Critical Location  :   1.500 m from Start.
   γ     =     1.461                         [NZS3404 8.3.4]
   Member In-plane Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.222
   Critical Location  :   4.500 m from Start.
   ϕMiz  =   105.1701E+00 KNm               [NZS3404 8.4.2]
   Member In-plane Capacity (about Y-axis)
   Critical Load Case :     1*
   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 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     :   3.092
   Critical Location  :   2.250 m from Start.
   ϕMoz,c=     4.1587E+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     :  46.122
   Critical Location  :   2.250 m from Start.
   ********************************************************************************