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} = \frac{B}{t_{f}} \sqrt{\frac{f_{y}}{250}} = \frac{138}{12} \sqrt{\frac{300}{250}} = 12.60

Section flange classification is non-compact.

Evaluate the slenderness effects of the beam web:

λ_{e w} = \frac{d}{t_{w}} \sqrt{\frac{f_{y}}{250}} = \frac{138}{12} \sqrt{\frac{300}{250}} = 12.60

Section web classification is non-compact

Section Bending Capacity About Z-Axis

Effective Section Modulus, Z_ez = 72,560 mm³

The nominal section capacity in bending about Z axis, M_sz = ϕf_y×Z_ez

M_sz = 300× 72,560/10⁶ = 21.77 kN·m

ϕM_sz = 0.9×21.77 = 19.59 kN·m

Section Bending Capacity About Y-Axis

Effective Section Modulus, Z_ey = 155,980 mm³

The nominal section capacity in bending about Z axis, M_sy = ϕf_y×Z_ey

M_sy = 300× 155,980/10⁶ = 46.79 kN·m

ϕM_sy = 0.9×46.79 = 42.11 kN·m

Member Bending Capacity

End restraint arrangement = FU

A twist restraint factor, K_t = 1.00

Lateral rotation restraint factor, K_r = 1.0

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

Effective length = 1×1×1×5,000 = 5,000 mm

α_{m} = \frac{1.7 M_{m}^{*}}{\sqrt{{(M_{2}^{*})}^{2} + {(M_{3}^{*})}^{2} + {(M_{4}^{*})}^{2}}} \leq 2.5

α_m = 1.25 [Table 5.6.2]

Reference buckling moment, M_o

M_{o} = \sqrt{\frac{π^{2} E I_{y}}{{L_{e}}^{2}} [G J + (\frac{π^{2} E I_{w}}{{L_{e}}^{2}})]} = 57.42 k N \cdot m

α_{s} = 0.6 \{\sqrt{[{(\frac{M_{s y}}{M_{o a}})}^{2} + 3]} - (\frac{M_{s y}}{M_{o a}})\} = 0.660

[Ref : Clause 5.6.1.1 (c)]

M_bx = α_mα_sM_sy ≤ M_sy

M_bz = 1.25 × 0.660 × 46.79 = 38.61 kN·m ≤ (M_sz, M_sy)_Max.

[Ref : Clause 5.6.1.1.1(a)]

ϕM_bz = 0.9×38.61 = 34.74 kN·m

Check for Shear

Shear Area of the section, A_y = d×t_w = 150×12 = 1,800 mm²

Section Shear Capacity (Along Y axis), V_y = 0.6×f_y×A_y = 0.6×300×1,800 = 324 kN

V_vn = 2×324/(0.9 + 1.2) = 308.6 kN

[Ref : Clause 5.11.2]

ϕV_y = 0.9×308.6 = 277.7 kN

Shear Area of the section, A_Z = b_f× t_f = 150×12 = 1,800 mm²

Section Shear Capacity (Along z axis),V_z = 0.6×f_y×A_z = 0.6×300×1,800 = 324 kN

V_vn = 2×324/(0.9 + 1.2) = 308.6 kN

ϕV_z = 0.9×308.6 = 277.7 kN

Check for Axial Compression

Section Compression Capacity:

Gross Area, A_g = 3,480 mm²

Net Area, A_n = 3,480 mm²

Form factor, K_f = A_e/A_g = 1

The nominal member section capacity for axial compression,

N_s = K_f×A_n×f_y = 1×3,480×300 = 1,044 kN

[Ref : Clause 6.2.1]

ϕN_s = 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, K_y = 2.2

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

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

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

Geometrical Slenderness Ratio = L_ez/r_z = 11,000 / 29.6 = 371.62

Geometrical Slenderness Ratio = L_ez/r_z = 11,000 / 58.609 = 187.7

Member slenderness,

λ_{n z} = \frac{L_{e z}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 371.62 \sqrt{1} \sqrt{\frac{300}{250}} = 407.1

[Ref : Clause 6.3.3]

λ_{n y} = \frac{L_{e y}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 187.7 \sqrt{1} \sqrt{\frac{300}{250}} = 205.6

[Ref : Clause 6.3.3]

α_az = 2,100×(λ_nz - 13.5)/(λ_nz² - 15.3λ_nz + 2,050) = 5.116

α_ay = 2,100×(λ_ny - 13.5)/(λ_ny² - 15.3λ_ny + 2,050) = 9.797

α_b = 0.5

[Ref : Table 6.3.3(2)]

λ_z = λ_nz + α_az×α_z = 409.65

λ_y = λ_ny + α_ay×α_b = 210.50

η = 1.29

η = 0.64

ξ_z = ((λ_z/90)²+ 1 + η)/(2×(λ_z/90)²) = 0.56

ξ_y = ((λ_y/90)²+ 1 + η)/(2×(λ_y/90)²) = 0.65

α_cz= 0.045

α_cy= 0.160

The nominal member capacity,

N_cz= α_cz×N_s =0.045×1,044 = 46.98 kN

[Ref : Clause 6.3.3]

ϕN_cz= 42.28 kN

The nominal member capacity,

N_cy= α_cy×N_s =0.160×1,044 = 167.0 kN [Ref : Clause 6.3.3]

ϕN_cy = 150.3 kN

Nominal Section tension Capacity [Ref : Clause 7.1]

K_te = 1.00

N_t1 = A_g×f_y = 1,044 kN

N_t2 = 0.85×K_te×A_n×f_u = 1,301.5 kN

ϕN_t = 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
ϕM_sz (kN·m)	19.59	19.5911	negligible
ϕM_sy (kN·m)	42.11	42.1144	negligible
ϕM_bz (kN·m)	34.74	34.6143	negligible
ϕV_y (kN)	277.7	277.7143	negligible
ϕV_z (kN)	277.7	277.7143	negligible
ϕN_s (kN)	939.6	939.6	none
ϕN_cz (kN)	42.28	42.57	negligible
ϕN_cy (kN)	150.3	150.7	negligible
ϕN_t (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\NZS3404 1997-Angle section Non compact.std is typically installed with the program.

The following design parameters are used:

The twist restraint factor, K_t = 1 is specified by SKT 1.0 (default value; K_t is calculated)
The lateral rotation restraint factor, K_r = 1.0 is specified by SKR 1.0 (default value; K_r is calculated)

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 FOR Y UP :-
   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:   112.4115E+03 mm3 (elastic)
   rz:    29.6000E+00 mm
   Iy:    11.9540E+06 mm4  Sy:   176.0526E+03 mm3 (plastic)   Zy:    52.2925E+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]
  SLENDERNESS:   ACTUAL SLENDERNESS RATIO:     168.919  LOAD:     1   LOC.(MET):   0.000
                 ALLOWABLE SLENDERNESS RATIO:  400.000
   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     :   0.289
   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   =     1.250                         [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 =    34.6143E+00 KNm (&lt;= 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
   ϕVvmy =   277.7143E+00 KN                [NZS3404 5.12.2]
   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
   ϕVvmz =   277.7143E+00 KN                [NZS3404 5.12.2]
      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]
   ********************************************************************************