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V.NZS3404 1997-Angle section Non compact

Verify the design capacity of equal leg, non-compact angle section as per NZ3404 1997.

Details

The member is an A150X150X12 section used in a 5 m cantilever member. The cantilever is loaded with a 2 kN point load at the mid-point. Steel grade is 300 MPa.

Validation

Section Classification

Evaluate the slenderness effects of the beam flanges:

λ e f = B t f f y 250 = 138 12 300 250 = 12.60

Section flange classification is non-compact.

Evaluate the slenderness effects of the beam web:

λ e w = d t w f y 250 = 138 12 300 250 = 12.60

Section web classification is non-compact

Section Bending Capacity About Z-Axis

Effective Section Modulus, Zez = 72,560 mm3

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

Msz = 300× 72,560/106 = 21.77 kN·m

ϕMsz = 0.9×21.77 = 19.59 kN·m

Section Bending Capacity About Y-Axis

Effective Section Modulus, Zey = 155,980 mm3

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

Msy = 300× 155,980/106 = 46.794 kN·m

ϕMsy = 0.9×46.794 = 42.11 kN·m

Member Bending Capacity

End restraint arrangement = FU

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 = 1×1×1×5,000 = 5,000 mm

α m = 1.7 M m * ( M 2 * ) 2 + ( M 3 * ) 2 + ( M 4 * ) 2 2.5

αm = 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 = 57.42   k N · m
α s = 0.6 M s x M o a 2 + 3 - M s x M o a = 0.660 [Ref : Clause 5.6.1.1 (c)]

Mbx = αmαsMsx ≤ Msx

Mbz = 2.25 × 0.660 × 42.114 = 62.54 kN·m ≤ (Msz, Msy)Max. [Ref : Clause 5.6.1.1.1(a)]

But as Mbz > Msy, Mbz = Msy = 46.794 kN·m

ϕMbz = 0.9×46.794 = 42.11 kN·m

Check for Shear

Shear Area of the section, Ay = d×tw = 150×12 = 1,800 mm2

Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×300×1,800 = 324 kN

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

ϕVy = 0.9×308.6 = 277.7 kN

Shear Area of the section, AZ = bf× tf = 150×12 = 1,800 mm2

Section Shear Capacity (Along z axis),Vz = 0.6×fy×Az = 0.6×300×1,800 = 324 kN

Vvn = 2×324/(0.9 + 1.2) = 308.6 kN

ϕVz = 0.9×308.6 = 277.7 kN

Check for Axial Compression

Section Compression Capacity:

Gross Area, Ag = 3,480 mm2

Net Area, An = 3,480 mm2

Form factor, Kf = Ae/Ag = 1

The nominal member section capacity for axial compression,

Ns = Kf×An×fy = 1×3,480×300 = 1,044 kN [Ref : Clause 6.2.1]

ϕNs = 0.9×1,044 = 939.6 kN

Member Compression Capacity

Length of the member, L = 5,000 mm

Effective length factor for slenderness & buckling about minor Y- axis, Ky = 2.2

Effective length factor for slenderness & buckling about minor Z- axis, Kz = 2.2

Effective Length of member, Lez = 2.2×5,000 mm = 11,000 mm

Effective Length of member, Ley = 2.2×5,000 mm = 11,000 mm

Geometrical Slenderness Ratio = Lez/rz = 11,000 / 29.6 = 371.62

Geometrical Slenderness Ratio = Lez/rz = 11,000 / 58.609 = 187.7

Member slenderness,

λ n z = L e z r k f f y 250 = 371.62 1 300 250 = 407.1 [Ref : Clause 6.3.3]
λ n y = L e y r k f f y 250 = 187.7 1 300 250 = 205.6 [Ref : Clause 6.3.3]

αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 5.116

αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 9.797

αb = 0.5 [Ref : Table 6.3.3(2)]

λz = λnz + αaz×αz = 409.65

λy = λny + αay×αb = 210.50

η = 1.29

η = 0.64

ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 0.56

ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 0.65

αcz= 0.045

αcy= 0.160

The nominal member capacity,

Ncz= αcz×Ns =0.045×1,044 = 46.98 kN [Ref : Clause 6.3.3]

ϕNcz = 42.28 kN

The nominal member capacity,

Ncy= αcy×Ns =0.160×1,044 = 167.0 kN [Ref : Clause 6.3.3]

ϕNcy = 150.3 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

Kte = 1.00

Nt1 = Ag×fy = 1,044 kN

Nt2 = 0.85×Kte×An×fu = 1,301.5 kN

ϕNt = 0.9×1,044 = 939.6 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) 19.59 19.5911 negligible  
ϕMsy (kN·m) 42.11 42.1144 negligible  
ϕMbz (kN·m) 42.11 42.1144 negligible  
ϕVy (kN) 277.7 277.7143 negligible  
ϕVz (kN) 277.7 277.7143 negligible  
ϕNs (kN) 939.6 939.6 none  
ϕNcz (kN) 42.28 42.57 negligible  
ϕNcy (kN) 150.3 150.7 negligible  
ϕNt (kN) 939.6 939.6 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-Angle section Non compact.std is typically installed with the program.

STAAD SPACE
*
*  INPUT FILE: NZS3404_Angle_Section_Non_Compact.STD
*
* REFERENCE : Hand Calculation
*
*  OBJECTIVE : TO DETERMINE THE ADEQUACY OF  EQUAL ANGLE SHAPE  PER
*              THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 13-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0;
*
MEMBER INCIDENCES
1 1 2;
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 A150X150X12
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 FIXED
*
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
JOINT LOAD
2 FZ 2
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
TRACK 2 PMEMB 1
PBRACE TOP 0 U 1 F PMEMB 1
PBRACE BOTTOM 0 U 1 F PMEMB 1
PBCRES ZZ 0 T 1 U PMEMB 1
PBCRES YY 0 T 1 U PMEMB 1
DUCT 1 PMEMB 1
GLD 1 PMEMB 1
CHECK CODE PMEMB 1
*
FINISH

STAAD.Pro Output

                       STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0)
                     **************************************************
   AXIS NOTATION FOR ST ANGLE SECTION:-
   STAAD.Pro     NZS3404 Spec.     Description
   ---------     -------------     ---------------
      X/x             Z/z          Longitudinal axis of section
      Y/y             X/x          Major principal axis of section
      Z/z             Y/y          Minor 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   A150X150X12              (AISC SECTIONS)
   Governing Load Case:     1*
   Governing Criteria:                                                             
   Governing Ratio:   1.400 *(FAIL)
   Governing Location:   0.000 m from Start.
   SECTION PROPERTIES
   ------------------
    d:       150.0000 mm    b:       150.0000 mm
    t:        12.0000 mm
   Ag:      3480.0000 mm2   J:   167.0400E+03 mm4             Iw:   286.6545E+06 mm6
   Iz:     3.0490E+06 mm4  Sz:    88.4845E+03 mm3 (plastic)   Zz:    65.3007E+03 mm3 (elastic)
   rz:    29.6000E+00 mm
   Iy:    11.9540E+06 mm4  Sy:   176.0526E+03 mm3 (plastic)   Zy:   112.4115E+03 mm3 (elastic)
   ry:    58.6094E+00 mm
      STAAD SPACE                                              -- PAGE NO.    4
    *                                           
   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     :    300.000 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     :   0.000
   Critical Location  :   0.000 m from Start.
   Mz* =     0.0000E+00 KNm
   Section Slenderness: Noncompact
   Zez =    72.5597E+03 mm3
   ϕMsz =    19.5911E+00 KNm                [NZS3404 Cl.5.1    ]
   Section Bending Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.237
   Critical Location  :   0.000 m from Start.
   My* =   -10.0000E+00 KNm
   Section Slenderness: Noncompact
   Zey =   155.9794E+03 mm3
   ϕMsy =    42.1144E+00 KNm                [NZS3404 Cl.5.1    ]
   Member Bending Capacity
   Critical Load Case :     1*
   Critical Ratio     :   0.237
   Critical Location  :   0.000 m from Start.
   Crtiical Flange Segment: 
   Location (Type):   0.00 m(U )-  5.00 m(F )
   Mz* =    10.0000E+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   =      5.00 m                       [NZS3404 5.6.3]
   αm   =     2.250                         [NZS3404 5.6.1.1.1(b)(iii)]
   Mo   =    57.0084E+00 KNm                [NZS3404 5.6.1.1.1(d)]
   αsy  =     0.658                         [NZS3404 5.6.1.1.1(c)]
   ϕMby =    42.1144E+00 KNm (<= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
      STAAD SPACE                                              -- PAGE NO.    5
    *                                           
   SHEAR
   -----
   Section Shear Capacity (along Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   Vy*  =     0.0000E+00 KN
   ϕVvy =   277.7143E+00 KN                 [NZS3404 5.11.2]
   Section Shear Capacity (along Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.007
   Critical Location  :   0.000 m from Start.
   Vz*  =     2.0000E+00 KN
   ϕVvz =   277.7143E+00 KN                 [NZS3404 5.11.2]
      STAAD SPACE                                              -- PAGE NO.    6
    *                                           
   AXIAL
   -----
   Section Compression Capacity
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*    =     0.0000E+00 KN
   Ae    =     3.4800E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
   kf    =     1.000                        [AS 4100 6.2.2]
   An    =     3.4800E+03 mm2
   ϕNs   =   939.6000E+00 KN                [NZS3404 6.2.1]
   Member Compression Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*    =     0.0000E+00 KN
   Unbraced Segment: 
   Location (Type):   0.00 m(T )-  5.00 m(U )
   Lez   =     11.00 m
   αb    =      0.50                        [NZS3404 Table 6.3.3(1)/6.3.3(2)]
   λn,z  =   407.091                        [NZS3404 6.3.3]
   λ,z   =   409.649                        [NZS3404 6.3.3]
   ε,z   =     0.555                        [NZS3404 6.3.3]
   αc,z  =     0.045                        [NZS3404 6.3.3]
   ϕNcz  = 0.4257E+2 KN                     [NZS3404 6.3.3]
   Member Compression Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*    =     0.0000E+00 KN
   Unbraced Segment: 
   Location (Type):   0.00 m(T )-  5.00 m(U )
   Ley   =     11.00 m
   λn,y  =   205.597                        [NZS3404 6.3.3]
   λ,y   =   210.495                        [NZS3404 6.3.3]
   ε,y   =     0.650                        [NZS3404 6.3.3]
   αc,y  =     0.160                        [NZS3404 6.3.3]
   ϕNcy  = 0.1507E+3 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    =     3.4800E+03 mm2
   ϕNt   =   939.6000E+00 KN                [NZS3404 7.2]
      STAAD SPACE                                              -- PAGE NO.    7
    *                                           
   COMBINED BENDING AND AXIAL
   ------------------------
   Section Combined Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ϕMrz  =    19.5911E+00 KNm               [NZS3404 8.3.2]
   Section Combined Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.237
   Critical Location  :   0.000 m from Start.
   ϕMry  =    42.1144E+00 KNm               [NZS3404 8.3.3]
   Section Combined Capacity (Biaxial)
   Critical Load Case :     1*
   Critical Ratio     :   0.237
   Critical Location  :   0.000 m from Start.
   γ     =     1.400                         [NZS3404 8.3.4]
   Member In-plane Capacity (about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ϕMiz  =    19.5911E+00 KNm               [NZS3404 8.4.2]
   Member In-plane Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.237
   Critical Location  :   0.000 m from Start.
   ϕMiy  =    42.1144E+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
   ϕNoy  =     0.0000E+00 KN                [NZS3404 8.4.4.1.2]
   ϕMoy,t=     0.0000E+00 KNm               [NZS3404 8.4.4.1]
   Member Out-of-plane Capacity (Compression)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   ϕMoy,c=     0.0000E+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     :   0.000
   Critical Location  :   0.000 m from Start.
      STAAD SPACE                                              -- PAGE NO.    8
    *                                           
   SEISMIC PROVISIONS
   ------------------
   Section Slenderness (Bending about Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   1.400
   Critical Location  :   0.000 m from Start.
   λsz              =     12.60             [NZS3404 12.5.1.1]
   λez              =      9.00             [NZS3404 Table 12.5]
   Section Slenderness (Bending about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   1.400
   Critical Location  :   0.000 m from Start.
   λsy              =     12.60             [NZS3404 12.5.1.1]
   λey              =      9.00             [NZS3404 Table 12.5]
   Max Specific Yield Stress
   Critical Load Case :     1*
   Critical Ratio     :   0.833
   Critical Location  :   0.000 m from Start.
   Fy,actual        =    300.00
   Fy,limit         =    360.00             [NZS3404 Table 12.4(1)]
   Max Actual Yield Ratio (Fy/Fu)
   Critical Load Case :     1*
   Critical Ratio     :   0.852
   Critical Location  :   0.000 m from Start.
   Fy/Fu,actual     =      0.68
   Fy/Fu,limit      =      0.80             [NZS3404 Table 12.4(3)]
   Fabrication Requirement
   Critical Load Case : N/A
   Critical Ratio     : N/A
   Critical Location  : N/A
   Status           =   Passed              [NZS3404 12.4.1.2]
   Section Symmetry Requirement
   Critical Load Case : N/A
   Critical Ratio     : N/A
   Critical Location  : N/A
   Status           =   Passed              [NZS3404 12.5.2]
   Min Web Thickness Requirement for Beam
   Critical Load Case :     1*
   Critical Ratio     :   0.154
   Critical Location  :   0.000 m from Start.
   tw,actual        =     12.00
   tw,min           =      1.84             [NZS3404 12.7.2]
   Max Axial Force Limit for Column (a)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   N*/ϕNs - actual  =      0.00
   N*/ϕNs - limit   =      0.50             [NZS3404 Table 12.8.1]
   Max Axial Force Limit for Column (b)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
    b m               =      0.50
   NoL              =   967.4472E+00 KN
   λEYC             =      1.04
   N*/ϕNs - actual  =      0.00
   N*/ϕNs - limit   =      0.32             [NZS3404 12.8.3.1(b)]
   Max Axial Force Limit for Column (c)
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   Ng*/ϕNs - actual =      0.00
   Ng*/ϕNs - limit  =      1.00             [NZS3404 12.8.3.1(c)]
   Shear-Y + Bend-Z Interaction
   Critical Load Case :     1*
   Critical Ratio     :   0.000
   Critical Location  :   0.000 m from Start.
   Mz*  =     0.0000E+00 KN
   ϕMsvz=    19.5911E+00 KN                 [NZS3404 12.10.3.1]
   Shear-Z + Bend-Y Interaction
   Critical Load Case :     1*
   Critical Ratio     :   0.237
   Critical Location  :   0.000 m from Start.
   My*  =    10.0000E+00 KN
   ϕMsvy=    42.1144E+00 KN                 [NZS3404 12.10.3.1]
   ********************************************************************************