V.NZS3404 1997-Unequal Angle Section

Verify the design capacity of an A125x75x8 section as per the NZS3404 1997 code.

Details

Verify the section capacity of an A125x75x8 section used for a 5 m cantilever span. Steel grade = 320 MPa.

Validation

Section Classification

Evaluate the slenderness effects of the beam flanges:

λ_{e f} = \frac{B}{{2 t}_{f}} \sqrt{\frac{f_{y}}{250}} = \frac{117.2}{7.8} \sqrt{\frac{320}{250}} = 17.0

Section flange classification is compact.

Evaluate the slenderness effects of the beam web:

λ_{e w} = \frac{d}{t_{w}} \sqrt{\frac{f_{y}}{250}} = \frac{67.2}{7.8} \sqrt{\frac{320}{250}} = 9.75

Section web classification is compact

Section Bending Capacity About Z-Axis

Effective Section Modulus, Z_ez = 12,720 mm³

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

M_sz = 320× 12,720 ×10^-6 = 4.07 kN·m

ϕM_sz = 0.9×4.07 = 3.66 kN·m

Section Bending Capacity About Y-Axis

Effective Section Modulus, Z_ey = 40,550 mm³

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

M_sy = 320× 40,550×10^-6 = 12.98 kN·m

ϕM_sy = 0.9×12.98 = 11.68 kN·m

Member Bending Capacity

End restraint arrangement = FU

A twist restraint factor, K_t (SKT) = 1.00

Minor axis rotation restraints = Fu

Lateral rotation restraint factor, K_r (SKR) = 0.70

Load Height factor, Kl, = 2.0 [Ref : Table 5.6.3(2)]

Effective length = 1×1×2×5,000 = 10,000 mm

α_m = 1.25

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}})]} = 4.43 kN·m

α_{s} = 0.6 \{\sqrt{[{(\frac{M_{s x}}{M_{o a}})}^{2} + 3]} - (\frac{M_{s x}}{M_{o a}})\} = 0.284

[Ref : Clause 5.6.1.1 (c)]

M_bx = α_mα_sM_sx ≤ M_sx

M_bz = 1.25 × 0.284 × 12.98 = 4.61 kN·m ≤ (M_sz, M_sy)_Max.

[Ref : Clause 5.6.1.1.1(a)]

ϕM_bz = 0.9×4.61 = 4.15 kN·m

Check for Shear

Shear Area of the section, A_y = d×t = 125×7.8 = 975 mm²

Section Shear Capacity (Along Y axis), V_y = 0.6×f_y×A_y = 0.6×320×975 = 187 kN

V_vn = 2×187/(0.9 + 1.2) = 178 kN

[Ref : Clause 5.11.2]

ϕV_y = 0.9×178 = 133.2 kN

Shear Area of the section, A_Z = b× t = 75×7.8 = 585 mm²

Section Shear Capacity (Along z axis),V_z = 0.6×f_y×A_z = 0.6×320×585 = 112.3 kN

V_vn = 2×112.3/(0.9 + 1.2) = 107 kN

ϕV_z = 0.9×107 = 96.3 kN

Check for Axial Compression

Section Compression Capacity:

Gross Area, A_g = 1,500 mm²

Net Area, A_n = 1,500 mm²

Form factor, K_f = A_e/A_g = 1.0

The nominal member section capacity for axial compression,

N_s = K_f×A_n×f_y = 1.0×1,500×320 = 480 kN

[Ref : Clause 6.2.1]

ϕN_s = 0.9×480 = 432 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

r_y = √(2.72×10⁶ / 1,500) = 42.6

r_z = √(398×10³ / 1,500) = 16.3

Geometrical Slenderness Ratio = L_ez/r_z = 11,000 / 16.3 = 674.9

Geometrical Slenderness Ratio = L_ey/r_y = 11,000 / 42.6 = 258.3

Member slenderness,

λ_{n z} = \frac{L_{e z}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 674.9 \sqrt{1} \sqrt{\frac{320}{250}} = 763.5

[Ref : Clause 6.3.3]

λ_{n y} = \frac{L_{e y}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 258.3 \sqrt{1} \sqrt{\frac{320}{250}} = 291.9

[Ref : Clause 6.3.3]

α_az = 2,100×(λ_nz - 13.5)/(λ_nz² - 15.3λ_nz + 2,050) = 2.747

α_ay = 2,100×(λ_ny - 13.5)/(λ_ny² - 15.3λ_ny + 2,050) = 7.061

α_b = 0.5

[Ref : Table 6.3.3(2)]

λ_z = λ_nz + α_az×α_z = 764.9

λ_y = λ_ny + α_ay×α_b = 295.5

η = 2.45

η = 0.92

ξ_z = ((λ_z/90)²+ 1 + η)/(2×(λ_z/90)²) = 0.52

ξ_y = ((λ_y/90)²+ 1 + η)/(2×(λ_y/90)²) = 0.59

α_cz= 0.013

α_cy= 0.085

The nominal member capacity,

N_cz= α_cz×N_s =0.013×480 = 6.42 kN

[Ref : Clause 6.3.3]

ϕN_cz= 5.78 kN

The nominal member capacity,

N_cy= α_cy×N_s =0.085×480 = 40.7 kN

[Ref : Clause 6.3.3]

ϕN_cy = 36.66 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

K_te = 1.00

N_t1 = A_g×f_y = 480 kN

N_t2 = 0.85×K_te×A_n×f_u = 516 kN

ϕN_t = 0.9×480 = 432 kN

[Ref : Clause 5.6.1.1.1(a)]

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
ϕMsz(KN·m)	3.66	3.6625	negligible
ϕMsy(KN·m)	11.68	11.6789	negligible
ϕMbz (KN-m)	4.15	4.1237	negligible
ϕVz (KN)	133.2	133.18	negligible
ϕVy(KN)	96.3	96.2743	negligible
ϕNs( KN)	432	432	none
ϕNcz (KN)	5.78	5.78	none
ϕNcy (KN)	36.66	36.66	none
ϕNt (KN)	432	432	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-Unequal Angle Section.std is typically installed with the program.

The following design parameters are used in this example:

The load height position is at the top flange: LHT 1.

STAAD SPACE
*
*  INPUT FILE: NZS3404_Unequal_Angle_section.STD
*
* REFERENCE : Hand Calculation
*
*  OBJECTIVE : TO DETERMINE THE ADEQUACY OF  UNEQUAL 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 A125X75X8
*
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
LHT 1 PMEMB 1
TRACK 2 PMEMB 1
PBCRES ZZ 0 T 1 U PMEMB 1
PBCRES YY 0 T 1 U PMEMB 1
PBRACE TOP 0 FR 1 U PMEMB 1
PBRACE BOTTOM 0 FR 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   A125X75X8                (AISC SECTIONS)
   Governing Load Case:     1*
   Governing Criteria: Cl.5.1                                                      
   Governing Ratio:   2.425 *(FAIL)
   Governing Location:   0.000 m from Start.
   SECTION PROPERTIES
   ------------------
    d:       125.0000 mm    b:        75.0000 mm
    t:         7.8000 mm
   Ag:      1500.0000 mm2   J:    30.4200E+03 mm4             Iw:    28.1486E+06 mm6
   Iz:   398.5350E+03 mm4  Sz:    20.2467E+03 mm3 (plastic)   Zz:    32.4411E+03 mm3 (elastic)
   rz:    16.3000E+00 mm
   Iy:     2.7259E+06 mm4  Sy:    55.9491E+03 mm3 (plastic)   Zy:    13.3505E+03 mm3 (elastic)
   ry:    42.6290E+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  :    320.000 MPa         [NZS3404 Table 2.1]
   fy, web     :    320.000 MPa         [NZS3404 Table 2.1]
   fu          :    440.000 MPa         [NZS3404 Table 2.1]
  SLENDERNESS:   ACTUAL SLENDERNESS RATIO:     306.748  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 =    12.7170E+03 mm3
   ϕMsz =     3.6625E+00 KNm                [NZS3404 Cl.5.1    ]
   Section Bending Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.856
   Critical Location  :   0.000 m from Start.
   My* =   -10.0000E+00 KNm
   Section Slenderness: Noncompact
   Zey =    40.5518E+03 mm3
   ϕMsy =    11.6789E+00 KNm                [NZS3404 Cl.5.1    ]
   Member Bending Capacity
   Critical Load Case :     1*
   Critical Ratio     :   2.425
   Critical Location  :   0.000 m from Start.
   Crtiical Flange Segment: 
   Location (Type):   0.00 m(FR)-  5.00 m(U )
   Mz* =    10.0000E+00 KNm
   kt   =      1.00                         [NZS3404 Table 5.6.3(1)]
   kl   =      2.00                         [NZS3404 Table 5.6.3(2)]
   kr   =      1.00                         [NZS3404 Table 5.6.3(3)]
   le   =     10.00 m                       [NZS3404 5.6.3]
   αm   =     1.250                         [NZS3404 5.6.1.1.1(b)(iii)]
   Mo   =     4.3977E+00 KNm                [NZS3404 5.6.1.1.1(d)]
   αsy  =     0.282                         [NZS3404 5.6.1.1.1(c)]
   ϕMby =     4.1237E+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 =    96.2743E+00 KN                [NZS3404 5.12.2]
   Section Shear Capacity (along Z-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.015
   Critical Location  :   0.000 m from Start.
   Vz*   =     2.0000E+00 KN
   ϕVvmz =   133.1808E+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    =     1.5000E+03 mm2               [NZS3404 6.2.3 / 6.2.4]
   kf    =     1.000                        [AS 4100 6.2.2]
   An    =     1.5000E+03 mm2
   ϕNs   =   432.0000E+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  =   763.502                        [NZS3404 6.3.3]
   λ,z   =   764.875                        [NZS3404 6.3.3]
   ε,z   =     0.524                        [NZS3404 6.3.3]
   αc,z  =     0.013                        [NZS3404 6.3.3]
   ϕNcz  = 0.5782E+1 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  =   291.939                        [NZS3404 6.3.3]
   λ,y   =   295.469                        [NZS3404 6.3.3]
   ε,y   =     0.589                        [NZS3404 6.3.3]
   αc,y  =     0.085                        [NZS3404 6.3.3]
   ϕNcy  = 0.3666E+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    =     1.5000E+03 mm2
   ϕNt   =   432.0000E+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  =     3.6625E+00 KNm               [NZS3404 8.3.2]
   Section Combined Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.856
   Critical Location  :   0.000 m from Start.
   ϕMry  =    11.6789E+00 KNm               [NZS3404 8.3.3]
   Section Combined Capacity (Biaxial)
   Critical Load Case :     1*
   Critical Ratio     :   0.856
   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  =     3.6625E+00 KNm               [NZS3404 8.4.2]
   Member In-plane Capacity (about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   0.856
   Critical Location  :   0.000 m from Start.
   ϕMiy  =    11.6789E+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     :   1.889
   Critical Location  :   0.000 m from Start.
   λsz              =     17.00             [NZS3404 12.5.1.1]
   λez              =      9.00             [NZS3404 Table 12.5]
   Section Slenderness (Bending about Y-axis)
   Critical Load Case :     1*
   Critical Ratio     :   1.083
   Critical Location  :   0.000 m from Start.
   λsy              =     17.00             [NZS3404 12.5.1.1]
   λey              =      9.00             [NZS3404 Table 12.5]
   Max Specific Yield Stress
   Critical Load Case :     1*
   Critical Ratio     :   0.889
   Critical Location  :   0.000 m from Start.
   Fy,actual        =    320.00
   Fy,limit         =    360.00             [NZS3404 Table 12.4(1)]
   Max Actual Yield Ratio (Fy/Fu)
   Critical Load Case :     1*
   Critical Ratio     :   0.909
   Critical Location  :   0.000 m from Start.
   Fy/Fu,actual     =      0.73
   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     :   0.207
   Critical Location  :   0.000 m from Start.
   tw,actual        =      7.80
   tw,min           =      1.62             [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              =   220.6053E+00 KN
   λEYC             =      1.48
   N*/ϕNs - actual  =      0.00
   N*/ϕNs - limit   =      0.20             [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=     3.6625E+00 KN                 [NZS3404 12.10.3.1]
   Shear-Z + Bend-Y Interaction
   Critical Load Case :     1*
   Critical Ratio     :   0.856
   Critical Location  :   0.000 m from Start.
   My*  =    10.0000E+00 KN
   ϕMsvy=    11.6789E+00 KN                 [NZS3404 12.10.3.1]
   ********************************************************************************