# 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:

$λ e f = B 2 t f f y 250 = 117.2 7.8 320 250 = 17.0$

Section flange classification is compact.

Evaluate the slenderness effects of the beam web:

$λ e w = d t w f y 250 = 67.2 7.8 320 250 = 9.75$

Section web classification is compact

Effective Section Modulus, Zez = 12,720 mm3

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

Msz = 320× 12,720 ×10-6 = 4.07 kN·m

ϕMsz = 0.9×4.07 = 3.66 kN·m

Effective Section Modulus, Zey = 40,550 mm3

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

Msy = 320× 40,550×10-6 = 12.98 kN·m

ϕMsy = 0.9×12.98 = 11.68 kN·m

Member Bending Capacity

End restraint arrangement = FU

A twist restraint factor, Kt (SKT) = 1.00

Minor axis rotation restraints = Fu

Lateral rotation restraint factor, Kr (SKR) = 0.70

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

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

αm = 2.25

Reference buckling moment, Mo

 $α s = 0.6 M s x M o a 2 + 3 - M s x M o a = 0.284$ [Ref : Clause 5.6.1.1 (c)]

Mbx = αmαsMsx ≤ Msx

 Mbz = 2.25 × 0.284 × 12.98 = 8.29 kN·m ≤ (Msz, Msy)Max. [Ref : Clause 5.6.1.1.1(a)]

ϕMbz = 0.9×8.29 = 7.46 kN·m

Check for Shear

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

Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×320×975 = 187 kN

 Vvn = 2×187/(0.9 + 1.2) = 178 kN [Ref : Clause 5.11.2]

ϕVy = 0.9×178 = 133.2 kN

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

Section Shear Capacity (Along z axis),Vz = 0.6×fy×Az = 0.6×320×585 = 112.3 kN

Vvn = 2×112.3/(0.9 + 1.2) = 107 kN

ϕVz = 0.9×107 = 96.3 kN

Check for Axial Compression

Section Compression Capacity:

Gross Area, Ag = 1,500 mm2

Net Area, An = 1,500 mm2

Form factor, Kf = Ae/Ag = 1.0

The nominal member section capacity for axial compression,

 Ns = Kf×An×fy = 1.0×1,500×320 = 480 kN [Ref : Clause 6.2.1]

 ϕNs = 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, 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

ry = √(2.72×106 / 1,500) = 42.6

rz = √(398×103 / 1,500) = 16.3

Geometrical Slenderness Ratio = Lez/rz = 11,000 / 16.3 = 674.9

Geometrical Slenderness Ratio = Ley/ry = 11,000 / 42.6 = 258.3

Member slenderness,

 $λ n z = L e z r k f f y 250 = 674.9 1 320 250 = 763.5$ [Ref : Clause 6.3.3]
 $λ n y = L e y r k f f y 250 = 258.3 1 320 250 = 291.9$ [Ref : Clause 6.3.3]

αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 2.747

αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 7.061

 αb = 0.5 [Ref : Table 6.3.3(2)]

λz = λnz + αaz×αz = 764.9

λy = λny + αay×αb = 295.5

η = 2.45

η = 0.92

ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 0.52

ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 0.59

αcz= 0.013

αcy= 0.085

The nominal member capacity,

 Ncz= αcz×Ns =0.013×480 = 6.42 kN [Ref : Clause 6.3.3]

ϕNcz = 5.78 kN

The nominal member capacity,

 Ncy= αcy×Ns =0.085×480 = 40.7 kN [Ref : Clause 6.3.3]

ϕNcy = 36.66 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

Kte = 1.00

Nt1 = Ag×fy = 480 kN

Nt2 = 0.85×Kte×An×fu = 516 kN

 ϕNt = 0.9×480 = 432 kN [Ref : Clause 5.6.1.1.1(a)]

## Results

Table 1. Comparison of results
ϕMsz(KN·m) 3.66 3.6625 negligible
ϕMsy(KN·m) 11.68 11.6789 negligible
ϕMbz (KN-m) 7.46 7.47 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

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

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
*
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 CODE CHECKING - NZS-3404-1997 (v1.0)
**************************************************
AXIS NOTATION FOR ST ANGLE SECTION:-
---------     -------------     ---------------
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 Criteria:
Governing Ratio:   1.889 *(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:    10.1735E+03 mm3 (elastic)
rz:    16.3000E+00 mm
Iy:     2.7259E+06 mm4  Sy:    55.9491E+03 mm3 (plastic)   Zy:    32.4411E+03 mm3 (elastic)
ry:    42.6290E+00 mm
STAAD SPACE                                              -- PAGE NO.    4
*
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  :    320.000 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     :   0.000
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    ]
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 Ratio     :   1.347
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   =     2.250                         [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 =     7.4227E+00 KNm (&lt;= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
STAAD SPACE                                              -- PAGE NO.    5
*
SHEAR
-----
Section Shear Capacity (along Y-axis)
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
Vy*  =     0.0000E+00 KN
ϕVvy =    96.2743E+00 KN                 [NZS3404 5.11.2]
Section Shear Capacity (along Z-axis)
Critical Ratio     :   0.015
Critical Location  :   0.000 m from Start.
Vz*  =     2.0000E+00 KN
ϕVvz =   133.1808E+00 KN                 [NZS3404 5.11.2]
STAAD SPACE                                              -- PAGE NO.    6
*
AXIAL
-----
Section Compression Capacity
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]
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]
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 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
------------------------
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
ϕMrz  =     3.6625E+00 KNm               [NZS3404 8.3.2]
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 Ratio     :   0.856
Critical Location  :   0.000 m from Start.
γ     =     1.400                         [NZS3404 8.3.4]
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
ϕMiz  =     3.6625E+00 KNm               [NZS3404 8.4.2]
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 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 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 Ratio     :   0.000
Critical Location  :   0.000 m from Start.
Member Biaxial Capacity (Compression)
Critical Ratio     :   0.000
Critical Location  :   0.000 m from Start.
STAAD SPACE                                              -- PAGE NO.    8
*
SEISMIC PROVISIONS
------------------
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]
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 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 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 Ratio     : N/A
Critical Location  : N/A
Status           =   Passed              [NZS3404 12.4.1.2]
Section Symmetry Requirement
Critical Ratio     : N/A
Critical Location  : N/A
Status           =   Passed              [NZS3404 12.5.2]
Min Web Thickness Requirement for Beam
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 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 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 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