V.NZS3404 1997-Tube Section Non Compact
Verify the design capacity of a pipe section per the NZS3404 1997 code.
Details
Verify the capacity of a PIP3239H member. Steel grade = 250 MPa. The simply supported span is 9 m with a 60 kN load at mid-span.
Validation
Section Classification
Evaluate the slenderness effects of the pipe member:
Section classification is non-compact ()
Section Bending Capacity About Z-Axis
Effective Section Modulus for a compact section:
Effective section modulus for a non-compact section:
The nominal section capacity in bending about Z axis, ϕMs = ϕfy×Ze
Ms = 250× 633.1×103/106 = 158.3 kN·m
ϕMsz = 0.9×158.3 = 142.4 kN·m
Member Bending Capacity
End restraint arrangement = LL
A twist restraint factor, Kt (SKT) = 1.00
Minor axis rotation restraints = Both
Lateral rotation restraint factor, Kr (SKR) = 1.0
Load Height factor, Kl, (LHT) = 1.00 [Ref : Table 5.6.3(2)]
Effective length = 1×1×1×9,000 = 9,000 mmαm = 1 | [Ref: Cl no -5.6.1.1 (b)] |
Reference buckling moment, Mo
αs = 1 | [Ref : Clause 5.6.1.1 (c)] |
Member bending capacity, Mbz
Mbz = αmαsMsz ≤ Msz
Mbz = 1 × 1 × 158.2 = 158.3 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×158.3 = 142.4 kN·m
Check for Shear
Nominal shear capacity, Vz, of a circular hollow section: [Ref. Cl no 5.11.4.2]
Vy = 0.36×fy×Ae = 0.36×250×6,290×10-3 = 566.1 kN
ϕVy = 0.9×566.1 = 509.5 kN
Nominal shear capacity, Vy, of a circular hollow section: [Ref. Cl no 5.12.2]
Design bending moment, M = 135 kN·m
0.75×ϕ×Ms ≤ M ≤ ϕ×Ms
0.75×142.4 = 106.8 kN·m
ϕVy = 0.9 × 386.9 = 348.3 kN
Check for Axial Capacity
Section Compression Capacity:
Gross Area, Ag = 6,290 mm2
The effective outside diameter is the minimum of de1, de2, and do:
The effective outside diameter = do = 323.9 mm
Net Area, An = 6,290 mm2
Form factor, Kf = Ae/Ag = 1.0
The nominal member section capacity for axial compression,
Ns = Kf×An×fy = 1.0×6,290×250 = 1,573 kN | [Ref : Clause 6.2.1] |
ϕNs = 0.9×1,573 = 1,415 kN |
Member Compression Capacity
Length of the member, L = 9,000 mm
Effective length factor for slenderness & buckling about minor Y- axis, Ky = 1.0
Effective length factor for slenderness & buckling about minor Z- axis, Kz = 1.0
Effective Length of member, Lez = 1.0×9,000 mm = 9,000 mm
Effective Length of member, Ley = 1.0×9,000 mm = 9,000 mm
Geometrical Slenderness Ratio = Ley/ry = Lez/rz = 9,000 / 112.3 = 80.13
Member slenderness,
[Ref : Clause 6.3.3] |
αb = -0.5 | [Ref : Table 6.3.3(2)] |
λ = λn + αa×αb = 70.48
η = 0.19
The nominal member capacity,
Ncy = Ncz= αcz×Ns =0.74×1,573 = 1,171 kN | [Ref : Clause 6.3.3] |
ϕNcy = ϕNcz = 1,054 kN
Nominal Section tension Capacity
[Ref : Clause 7.1]
Kte = 1.00
Nt1 = Ag×fy = 6,290 × 250×10-3 = 1,573 kN
Nt2 = 0.85×Kte×An×fu = 0.85(1.0)(6,290)(250×10-3) = 1,711 kN
ϕNt = 0.9×1,573 = 1,415 kN | [Ref : Clause 5.6.1.1.1(a)] |
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕMsz (kN·m) | 142.4 | 142.4352 | negligible | |
ϕMsy (kN·m) | 142.4 | 142.4352 | negligible | |
ϕMbz (kN·m) | 142.4 | 142.4352 | negligible | |
ϕVy (kN) | 348.3 | 348.022 | negligible | |
ϕVz (kN) | 509.5 | 509.16 | negligible | |
ϕNs (kN) | 1,415 | 1,414.3 | negligible | |
ϕNcz (kN) | 1,054 | 1,054 | none | |
ϕNcy (kN) | 1,054 | 1,054 | none | |
ϕNt (kN) | 1,415 | 1,415.3 | negligible |
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-Tube Section Non Compact.std is typically installed with the program.
STAAD SPACE
*
* INPUT FILE: NZS3404_Tube_Section_Non_Compact.STD
*
* REFERENCE : Hand Calculation
*
* OBJECTIVE : TO DETERMINE THE ADEQUACY OF TUBE SHAPE PER
* THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 03-Jan-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 4 9 0 0; 5 3 0 0; 6 6 0 0;
*
MEMBER INCIDENCES
1 1 5; 2 5 6; 3 6 4;
DEFINE PMEMBER
1 TO 3 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
*
UNIT MMS NEWTON
MEMBER PROPERTY INDIAN
1 TO 3 TABLE ST PIP3239H
*
UNIT METER KN
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 PINNED
4 FIXED BUT FX MY MZ
PRINT ALL
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
2 CON GY -60
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
*
PARAMETER 1
CODE NZS3404 1997
BEAM 1 PMEMB 1
IST 2 PMEMB 1
SGR 6 PMEMB 1
SKL 1 PMEMB 1
SKR 1 PMEMB 1
SKT 1 PMEMB 1
TRACK 2 PMEMB 1
DUCT 3 PMEMB 1
GLD 1 PMEMB 1
CHECK CODE PMEMB ALL
*
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0) ************************************************** AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE:- STAAD.Pro NZS3404 Spec. Description --------- ------------- --------------- X/x Z/z Longitudinal axis of section Y/y Y/y Minor principal axis of section Z/z X/x Major 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 PIP3239H (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: T.12.4 Governing Ratio: 0.977 (PASS) Governing Location: 0.000 m from Start. SECTION PROPERTIES ------------------ OD: 323.9000 mm t: 6.3000 mm Ag: 6290.0005 mm2 J: 158.5800E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 79.2900E+06 mm4 Sz: 636.0001E+03 mm3 (plastic) Zz: 489.5957E+03 mm3 (elastic) rz: 112.2752E+00 mm Iy: 79.2900E+06 mm4 Sy: 636.0001E+03 mm3 (plastic) Zy: 489.5957E+03 mm3 (elastic) ry: 112.2752E+00 mm STAAD SPACE -- PAGE NO. 13 * MATERIAL PROPERTIES ------------------- Material Standard : AS 1163 Nominal Grade : 250 Residual Stress Category : HR (Hot-rolled) E (#) : 204999.984 MPa [NZS3404 1.4] G : 80000.000 MPa [NZS3404 1.4] fy, flange : 250.000 MPa [NZS3404 Table 2.1] fy, web : 250.000 MPa [NZS3404 Table 2.1] fu : 320.000 MPa [NZS3404 Table 2.1] SLENDERNESS: ACTUAL SLENDERNESS RATIO: 80.160 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 400.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.948 Critical Location : 4.500 m from Start. Mz* = -135.0000E+00 KNm Section Slenderness: Noncompact Zez = 633.0454E+03 mm3 ϕMsz = 142.4352E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. My* = 0.0000E+00 KNm Section Slenderness: Noncompact Zey = 633.0454E+03 mm3 ϕMsy = 142.4352E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.948 Critical Location : 4.500 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 9.00 m(F ) Mz* = -135.0000E+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 = 9.00 m [NZS3404 5.6.3] αm = 1.000 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 4.9763E+03 KNm [NZS3404 5.6.1.1.1(d)] αsz = 1.000 [NZS3404 5.6.1.1.1(c)] ϕMbz = 142.4352E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] STAAD SPACE -- PAGE NO. 14 * SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.086 Critical Location : 4.500 m from Start. Vy* = 30.0000E+00 KN ϕVvy = 348.0229E+00 KN [NZS3404 5.11.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. Vz* = 0.0000E+00 KN ϕVvz = 509.1619E+00 KN [NZS3404 5.11.2] STAAD SPACE -- PAGE NO. 15 * 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 = 6.2859E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 0.999 [AS 4100 6.2.2] An = 6.2900E+03 mm2 ϕNs = 1.4143E+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 )- 9.00 m(U ) Lez = 9.00 m αb = -0.50 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 80.134 [NZS3404 6.3.3] λ,z = 70.478 [NZS3404 6.3.3] ε,z = 1.467 [NZS3404 6.3.3] αc,z = 0.745 [NZS3404 6.3.3] ϕNcz = 0.1054E+4 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 )- 9.00 m(U ) Ley = 9.00 m λn,y = 80.134 [NZS3404 6.3.3] λ,y = 70.478 [NZS3404 6.3.3] ε,y = 1.467 [NZS3404 6.3.3] αc,y = 0.745 [NZS3404 6.3.3] ϕNcy = 0.1054E+4 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 = 6.2900E+03 mm2 ϕNt = 1.4153E+03 KN [NZS3404 7.2] STAAD SPACE -- PAGE NO. 16 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.948 Critical Location : 4.500 m from Start. ϕMrz = 142.4352E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMry = 142.4352E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.948 Critical Location : 4.500 m from Start. γ = 1.400 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.948 Critical Location : 4.500 m from Start. ϕMiz = 142.4352E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. ϕMiy = 142.4352E+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 ϕNoz = 0.0000E+00 KN [NZS3404 8.4.4.1.2] ϕMoz,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. ϕMoz,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. 17 * SEISMIC PROVISIONS ------------------ Section Slenderness (Bending about Z-axis) Critical Load Case : 1* Critical Ratio : 0.791 Critical Location : 0.000 m from Start. λsz = 51.41 [NZS3404 12.5.1.1] λez = 65.00 [NZS3404 Table 12.5] Section Slenderness (Bending about Y-axis) Critical Load Case : 1* Critical Ratio : 0.791 Critical Location : 0.000 m from Start. λsy = 51.41 [NZS3404 12.5.1.1] λey = 65.00 [NZS3404 Table 12.5] Max Specific Yield Stress Critical Load Case : 1* Critical Ratio : 0.694 Critical Location : 0.000 m from Start. Fy,actual = 250.00 Fy,limit = 360.00 [NZS3404 Table 12.4(1)] Max Actual Yield Ratio (Fy/Fu) Critical Load Case : 1* Critical Ratio : 0.977 Critical Location : 0.000 m from Start. Fy/Fu,actual = 0.78 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 : 0.489 Critical Location : 0.000 m from Start. tw,actual = 6.30 tw,min = 3.08 [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 = 0.80 [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 = 1.9806E+03 KN λEYC = 0.89 N*/ϕNs - actual = 0.00 N*/ϕNs - limit = 0.26 [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 = 0.78 [NZS3404 12.8.3.1(c)] Shear-Y + Bend-Z Interaction Critical Load Case : 1* Critical Ratio : 0.948 Critical Location : 4.500 m from Start. Mz* = 135.0000E+00 KN ϕMsvz= 142.4352E+00 KN [NZS3404 12.10.3.1] Shear-Z + Bend-Y Interaction Critical Load Case : 1* Critical Ratio : 0.000 Critical Location : 0.000 m from Start. My* = 0.0000E+00 KN ϕMsvy= 142.4352E+00 KN [NZS3404 12.10.3.1] ********************************************************************************