V.NZS3404 1997-Angle section compact
Verify the design capacity of compact angle section as per NZ3404 1997.
Details
The member is an A150X150X19 section used in a 5 m cantilever member. The cantilever is loaded with a 2 kN point load at the free end. Steel grade is 280 MPa.
Validation
Section Classification
Section classification is compact.
Section Bending Capacity About Z-Axis
Effective Section Modulus, Zez = 110,960 mm3
The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez
Msz = 280× 110,960/106 = 31.07 kN·m
ϕMsz = 0.9×31.07 = 27.962 kN·m
Section Bending Capacity About Y-Axis
Effective Section Modulus, Zey = 248,967 mm3
The nominal section capacity in bending about Z axis, Msy = ϕfy×Zey
Msy = 280× 248,967/106 = 69.71 kN·m
ϕMsy = 0.9×69.71 = 62.74 kN·m
Member Bending Capacity
End restraint arrangement = FU
A twist restraint factor, Kt = 1.0
Minor axis rotation restraints = Both
Lateral rotation restraint factor, Kr = 1.0
Load Height factor, Kl, (LHT) = 1.00 [Ref : Table 5.6.3(2)]
Effective length = 1×1×0.7×9,000 = 6,300 mmαm = 1.25 [Table 5.6.2]
Reference buckling moment, Mo
| [Ref : Clause 5.6.1.1 (c)] |
Mbx = αmαsMsy ≤ Msy
| Mbz = 1.25 × 0.780 × 69.71 = 67.98 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×67.98 = 61.17 kN·m
Check for Shear
Shear Area of the section, Ay = d×tw = 150×19 = 2,850 mm2
Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×280×2,850 = 478 kN
| Vvn = 2×478/(0.9 + 1.2) = 456 kN | [Ref : Clause 5.11.2] |
ϕVy = 0.9×456 = 410.4 kN
Shear Area of the section, AZ = bf× tf = 150×19 = 2,850 mm2
Section Shear Capacity (Along z axis),Vz = 0.6×fy×Az = 0.6×280×2,850 = 478 kN
Vvn = 2×478/(0.9 + 1.2) = 456 kN
ϕVz = 456×0.9 = 410.4 kN
Check for Axial Compression
Section Compression Capacity:
Gross Area, Ag = 5,360 mm2
Net Area, An = 5,360 mm2
Form factor, Kf = Ae/Ag = 1
The nominal member section capacity for axial compression,
Ns = Kf×An×fy = 1×5,360×280 = 1500.8 kN
| ϕNs = 0.9×1500.8 = 1,350.7 kN | [Ref : Clause 6.2.1] |
Member Compression Capacity
Length of the member, L = 5,000 mm
Effective length factor for slenderness & buckling about minor Y- axis, Ky = 1.00
Effective length factor for slenderness & buckling about minor Z- axis, Kz = 1.00
Effective Length of member, Lez = 5,000 mm
Effective Length of member, Ley = 5,000 mm
Geometrical Slenderness Ratio = Lez/rz = 5,000 / 29.3 = 170.648
Geometrical Slenderness Ratio = Ley/ry = 5,000 / 57.362 = 87.166
Member slenderness,
| [Ref : Clause 6.3.3] |
| [Ref : Clause 6.3.3] |
αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 10.999
αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 18.077
| αb = 0.5 | [Ref : Table 6.3.3(2)] |
λz = λnz + αaz×αz = 186.097
λy = λny + αay×αb = 101.286
η = 0.563
η = 0.286
ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 0.683
ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 1.008
αcz= 0.201
αcy= 0.532
The nominal member capacity,
| Ncz= αcz×Ns =0.201×1,500.8 = 301.388 kN | [Ref : Clause 6.3.3] |
ϕNcz = 271.3 kN
The nominal member capacity,
| Ncy= αcy×Ns =0.532×1,500.8 = 798.946 kN | [Ref : Clause 6.3.3] |
ϕNcy = 719.1 kN
Nominal Section tension Capacity
[Ref : Clause 7.1]
Kte = 1.00
Nt1 = Ag×fy = 1,500.8 kN
Nt2 = 0.85×Kte×An×fu = 2,004.6 kN
| ϕNt = 1,350.7 kN | [Ref : Clause 5.6.1.1.1(a)] |
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| ϕMsz (kN·m) | 27.962 | 27.9620 | none | |
| ϕMsy (kN·m) | 62.74 | 62.7397 | negligible | |
| ϕMbz (kN·m) | 61.17 | 61.0794 | negligible | |
| ϕVy (kN) | 410.4 | 410.4 | none | |
| ϕVz (kN) | 410.4 | 410.4 | none | |
| ϕNs (kN) | 1,350.7 | 1,350.7 | none | |
| ϕNcz (kN) | 271.3 | 271.2 | negligible | |
| ϕNcy (kN) | 719.1 | 719.1 | none | |
| ϕNt (kN) | 1,350.7 | 1,350.7 | 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 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_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 A150X150X19
*
CONSTANTS
BETA 45 ALL
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
IST 2 PMEMB 1
SGR 0 PMEMB 1
PBRACE TOP 0 FR 1 U PMEMB 1
PBRACE BOTTOM 0 FR 1 U PMEMB 1
DUCT 2 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 A150X150X19 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Governing Ratio: 0.811 (PASS) Governing Location: 0.000 m from Start. SECTION PROPERTIES ------------------ d: 150.0000 mm b: 150.0000 mm t: 19.0000 mm Ag: 5360.0000 mm2 J: 644.9868E+03 mm4 Iw: 1.0569E+09 mm6 Iz: 4.6015E+06 mm4 Sz: 134.6263E+03 mm3 (plastic) Zz: 165.9782E+03 mm3 (elastic) rz: 29.3000E+00 mm Iy: 17.6365E+06 mm4 Sy: 265.6150E+03 mm3 (plastic) Zy: 73.9736E+03 mm3 (elastic) ry: 57.3620E+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 : 280.000 MPa [NZS3404 Table 2.1] fy, web : 280.000 MPa [NZS3404 Table 2.1] fu : 440.000 MPa [NZS3404 Table 2.1] SLENDERNESS: ACTUAL SLENDERNESS RATIO: 170.648 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 400.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.253 Critical Location : 0.000 m from Start. Mz* = -7.0711E+00 KNm Section Slenderness: Compact Zez = 110.9604E+03 mm3 ϕMsz = 27.9620E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.113 Critical Location : 0.000 m from Start. My* = -7.0711E+00 KNm Section Slenderness: Compact Zey = 248.9673E+03 mm3 ϕMsy = 62.7397E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.116 Critical Location : 0.000 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(FR)- 5.00 m(U ) Mz* = 7.0711E+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 = 137.6171E+00 KNm [NZS3404 5.6.1.1.1(d)] αsy = 0.779 [NZS3404 5.6.1.1.1(c)] ϕMby = 61.0794E+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 : 0.003 Critical Location : 0.000 m from Start. Vy* = 1.4142E+00 KN ϕVvmy = 410.4000E+00 KN [NZS3404 5.12.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.003 Critical Location : 0.000 m from Start. Vz* = 1.4142E+00 KN ϕVvmz = 410.4000E+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 = 5.3600E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 5.3600E+03 mm2 ϕNs = 1.3507E+03 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(U )- 5.00 m(U ) Lez = 5.00 m αb = 0.50 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 180.597 [NZS3404 6.3.3] λ,z = 186.097 [NZS3404 6.3.3] ε,z = 0.683 [NZS3404 6.3.3] αc,z = 0.201 [NZS3404 6.3.3] ϕNcz = 0.2712E+3 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(U )- 5.00 m(U ) Ley = 5.00 m λn,y = 92.248 [NZS3404 6.3.3] λ,y = 101.286 [NZS3404 6.3.3] ε,y = 1.008 [NZS3404 6.3.3] αc,y = 0.532 [NZS3404 6.3.3] ϕNcy = 0.7191E+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 = 5.3600E+03 mm2 ϕNt = 1.3507E+03 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 : 0.253 Critical Location : 0.000 m from Start. ϕMrz = 27.9620E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.113 Critical Location : 0.000 m from Start. ϕMry = 62.7397E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.366 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 : 0.253 Critical Location : 0.000 m from Start. ϕMiz = 27.9620E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.113 Critical Location : 0.000 m from Start. ϕMiy = 62.7397E+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 : 0.811 Critical Location : 5.000 m from Start. λsz = 7.30 [NZS3404 12.5.1.1] λez = 9.00 [NZS3404 Table 12.5] Section Slenderness (Bending about Y-axis) Critical Load Case : 1* Critical Ratio : 0.811 Critical Location : 0.000 m from Start. λsy = 7.30 [NZS3404 12.5.1.1] λey = 9.00 [NZS3404 Table 12.5] Max Specific Yield Stress Critical Load Case : 1* Critical Ratio : 0.778 Critical Location : 0.000 m from Start. Fy,actual = 280.00 Fy,limit = 360.00 [NZS3404 Table 12.4(1)] Max Actual Yield Ratio (Fy/Fu) Critical Load Case : 1* Critical Ratio : 0.795 Critical Location : 0.000 m from Start. Fy/Fu,actual = 0.64 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 : 0.089 Critical Location : 0.000 m from Start. tw,actual = 19.00 tw,min = 1.69 [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 = 0.70 [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 = 0.00 NoL = 372.4033E+00 KN λEYC = 2.01 N*/ϕNs - actual = 0.00 N*/ϕNs - limit = 0.05 [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 : 0.253 Critical Location : 0.000 m from Start. Mz* = -7.0711E+00 KN ϕMsvz= 27.9620E+00 KN [NZS3404 12.10.3.1] Shear-Z + Bend-Y Interaction Critical Load Case : 1* Critical Ratio : 0.113 Critical Location : 0.000 m from Start. My* = 7.0711E+00 KN ϕMsvy= 62.7397E+00 KN [NZS3404 12.10.3.1] ********************************************************************************