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:
Section flange classification is non-compact.
Evaluate the slenderness effects of the beam web:
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
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
Member Bending Capacity
End restraint arrangement = FU
A twist restraint factor, Kt = 1.00
Lateral rotation restraint factor, Kr = 1.0
Load Height factor, Kl, = 1.00 [Ref : Table 5.6.3(2)]
Effective length = 1×1×1×5,000 = 5,000 mm
Reference buckling moment, Mo
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
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
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,
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,
The nominal member capacity,
The nominal member capacity,
Nominal Section tension Capacity Ref : Clause 7.1
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) | 34.74 | 34.6143 | 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 2024\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, Kt = 1 is specified by
SKT 1.0
(default value; Kt is calculated) - The lateral rotation restraint factor, Kr = 1.0 is specified by
SKR 1.0
(default value; Kr 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 (<= 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]
********************************************************************************