V.NZS3404 1997-Tube Section Compact
Verify the design capacity of a PIPX80 section per the NZS3404 1997 code.
Details
Verify the bending capacity of a PIPX80 member. Steel grade = 250 MPa. The simply supported span is 9 m with a 8.4 kN load at 5 m from the left support.
Validation
Section Classification
Evaluate the slenderness effects of the pipe member:
Section classification is compact
Section Bending Capacity About Z-Axis
Effective Section Modulus, Zez = 508×103 mm3
The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez
Msz = 250× 508×103/106 = 127 kN·m
ϕMsz = 0.9×127 = 114.3 kN·m
The pipe is symmetric, thus ϕMsy = ϕMsz
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)] |
Mbx = αmαsMsx ≤ Msx
Mbz = 1 × 1 × 127 = 127 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×127 = 114.3 kN·m
Check for Shear
Section Shear Capacity (Along Y axis), Vy = 0.36×fy×Ag = 0.36×250×7,677 = 691 kN
ϕVy = 0.9×691 = 622 kN
The pipe is symmetric, thus ϕVz = ϕVy
Check for Axial Compression
Section Compression Capacity:
Gross Area, Ag = 7,677 mm2
Net Area, An = 7,677 mm2
Form factor, Kf = Ae/Ag = 1.0
The nominal member section capacity for axial compression,
Ns = Kf×An×fy = 1.0×7,677×250 = 1,919 kN | [Ref : Clause 6.2.1] |
ϕNs = 0.9×1,919 = 1,727 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
ry = rz = √(41.62×106 / 7,677) = 73.63
Geometrical Slenderness Ratio = Ley/ry = Lez/rz = 9,000 / 73.63 = 122.2
Member slenderness,
[Ref : Clause 6.3.3] |
αa = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 15.10
αb = -1.0 | [Ref : Table 6.3.3(2)] |
λ = λn + αa×αb = 107.1
η = 0.3
ξy = ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 1
αcy = αcz = 0.495
The nominal member capacity,
Ncy = Ncz= αcz×Ns =0.495×1,919 = 950 kN | [Ref : Clause 6.3.3] |
ϕNcy = ϕNcz = 855 kN
Nominal Section tension Capacity
[Ref : Clause 7.1]
Kte = 1.00
Nt1 = Ag×fy = 7,677 × 250×10-3 = 1,919 kN
Nt2 = 0.85×Kte×An×fu = 0.85(1.0)(7,677)(250×10-3) = 1,631 kN
ϕNt = 0.9×1,919 = 1,727 kN | [Ref : Clause 5.6.1.1.1(a)] |
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕMsz (kN·m) | 114.3 | 114.2998 | negligible | |
ϕMbz (kN·m) | 114.3 | 114.2998 | negligible | |
ϕVy (kN) | 622 | 622.9 | negligible | |
ϕNs (kN) | 1,727 | 1,727.4 | negligible | |
ϕNcy (kN) | 855 | 854.7 | negligible | |
ϕNt (kN) | 1,727 | 1,727.4 | 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 Compact.std is typically installed with the program.
STAAD SPACE
*
* INPUT FILE: NZS3404_Tube_Section_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
*
MEMBER PROPERTY AMERICAN
1 TO 3 TABLE ST PIPX80
*
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 -8.4
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
CHECK CODE PMEMB 1
*
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 PIPX80 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.5.1 Governing Ratio: 0.165 (PASS) Governing Location: 4.500 m from Start. SECTION PROPERTIES ------------------ OD: 219.0750 mm t: 11.8110 mm Ag: 7677.4033 mm2 J: 83.2463E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 41.6231E+06 mm4 Sz: 507.9990E+03 mm3 (plastic) Zz: 379.9899E+03 mm3 (elastic) rz: 73.6309E+00 mm Iy: 41.6231E+06 mm4 Sy: 507.9990E+03 mm3 (plastic) Zy: 379.9899E+03 mm3 (elastic) ry: 73.6309E+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: 122.231 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 400.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.165 Critical Location : 4.500 m from Start. Mz* = -18.9000E+00 KNm Section Slenderness: Compact Zez = 507.9990E+03 mm3 ϕMsz = 114.2998E+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: Compact Zey = 507.9990E+03 mm3 ϕMsy = 114.2998E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.165 Critical Location : 4.500 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 9.00 m(F ) Mz* = -18.9000E+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 = 2.6123E+03 KNm [NZS3404 5.6.1.1.1(d)] αsz = 1.000 [NZS3404 5.6.1.1.1(c)] ϕMbz = 114.2998E+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 : 0.007 Critical Location : 0.000 m from Start. Vy* = 4.2000E+00 KN ϕVvmy = 622.9389E+00 KN [NZS3404 5.12.2] 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 ϕVvmz = 622.9389E+00 KN [NZS3404 5.12.2] 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 = 7.6774E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 7.6774E+03 mm2 ϕNs = 1.7274E+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 = -1.00 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 122.231 [NZS3404 6.3.3] λ,z = 107.130 [NZS3404 6.3.3] ε,z = 0.961 [NZS3404 6.3.3] αc,z = 0.495 [NZS3404 6.3.3] ϕNcz = 0.8547E+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 )- 9.00 m(U ) Ley = 9.00 m λn,y = 122.231 [NZS3404 6.3.3] λ,y = 107.130 [NZS3404 6.3.3] ε,y = 0.961 [NZS3404 6.3.3] αc,y = 0.495 [NZS3404 6.3.3] ϕNcy = 0.8547E+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 = 7.6774E+03 mm2 ϕNt = 1.7274E+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 : 0.165 Critical Location : 4.500 m from Start. ϕMrz = 114.2998E+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 = 114.2998E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.165 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 : 0.165 Critical Location : 4.500 m from Start. ϕMiz = 114.2998E+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 = 114.2998E+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. ********************************************************************************