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:
Section flange classification is compact.
Evaluate the slenderness effects of the beam web:
Section web classification is compact
Section Bending Capacity About Z-Axis
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
Section Bending Capacity About Y-Axis
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, = 2.0 [Ref : Table 5.6.3(2)]
Effective length = 1×1×2×5,000 = 10,000 mmαm = 1.25
Reference buckling moment, Mo
[Ref : Clause 5.6.1.1 (c)] |
Mbx = αmαsMsx ≤ Msx
Mbz = 1.25 × 0.284 × 12.98 = 4.61 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×4.61 = 4.15 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,
[Ref : Clause 6.3.3] |
[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
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
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 2023\Samples \Verification Models\09 Steel Design\New Zealand\NZS3404 1997-Unequal Angle Section.std is typically installed with the program.
- 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 (<= 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] ********************************************************************************