V.NZS3404 1997-RHS Section
Verify the design capacity of a rectangular hollow section as per NZS3404 1997.
Details
Verify the section bending capacity of an HSST20x12x0.75 spanning 6 m. Steel grade is 250 MPa.
Validation
Section Classification
Evaluate the slenderness effects of the Y axis:
Section classification is compact.
Evaluate the slenderness effects of the Z axis:
Section classification is compact
Section Bending Capacity About Z-Axis
Effective Section Modulus, Zez = 4.425×106 mm3
The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez
Msz = 250× 4.425×106/106 = 1,106 kN·m
ϕMsz = 0.9×1,106 = 995.6 kN·m
Section Bending Capacity About Y-Axis
Effective Section Modulus, Zey = 3.114×106 mm3
The nominal section capacity in bending about Z axis, Msy = ϕfy×Zey
Msy = 250× 3.114×106/106 = 778.5 kN·m
ϕMsy = 0.9×778.5 = 700.7 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 = 1×1×1×6,000 = 6,000 mm| αm = 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 × 1,106 = 1,106 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×1,106 = 995.6 kN·m
Check for Axial Compression
Section Compression Capacity:
Gross Area, Ag = 26,774 mm2
Net Area, An = 26,774 mm2
Form factor, Kf = Ae/Ag = 1.0
The nominal member section capacity for axial compression,
| Ns = Kf×An×fy = 1.0×26,774×250 = 6,694 kN | [Ref : Clause 6.2.1] |
| ϕNs = 0.9×6,694 = 6,024 kN |
Member Compression Capacity
Length of the member, L = 6,000 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 = 1.0×6,000 mm = 6,000 mm
Effective Length of member, Ley = 1.0×6,000 mm = 6,000 mm
rz = √(911.5×106 / 26,774) = 184.5
ry = √411.2×106 / 26,774) = 123.9
Geometrical Slenderness Ratio = Lez/rz = 6,000 / 184.5 = 32.5
Geometrical Slenderness Ratio = Ley/ry = 6,000 / 123.9 = 48.4
Member slenderness,
| [Ref : Clause 6.3.3] |
| [Ref : Clause 6.3.3] |
αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 15.30
αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 20.07
| αb = -1.0 | [Ref : Table 6.3.3(2)] |
λz = λnz + αaz×αz = 17.22
λy = λny + αay×αb = 28.34
η = 0.012
η = 0.048
ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 14.33
ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 5.785
αcz= 0.988
αcy= 0.949
The nominal member capacity,
| Ncz= αcz×Ns =0.988×6,694 = 6,611 kN | [Ref : Clause 6.3.3] |
ϕNcz = 5,950 kN
The nominal member capacity,
| Ncy= αcy×Ns =0.949×6,694 = 6,353 kN | [Ref : Clause 6.3.3] |
ϕNcy = 5,717 kN
Nominal Section tension Capacity
[Ref : Clause 7.1]
Kte = 1.00
Nt1 = Ag×fy = 6,024 kN
Nt2 = 0.85×Kte×An×fu = 6,694 kN
| ϕNt = 0.9×6,694 = 6,024 kN | [Ref : Clause 5.6.1.1.1(a)] |
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| ϕMsz ( kN·m ) | 995.6 | 995.5142 | negligible | |
| ϕMsy ( kN·m ) | 700.7 | 700.547 | negligible | |
| ϕMbz ( kN·m ) | 995.6 | 995.5142 | negligible | |
| ϕNcz (kN) | 5,950 | 5,949 | negligible | |
|
ϕNcy (kN) |
5,717 | 5,719 | negligible | |
| ϕNs (kN) | 6,024 | 6,024.2 | negligible | |
| ϕNt (kN) | 6,024 | 6,024.2 | 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-RHS Section.std is typically installed with the program.
- The hot-rolled residual stress category is specified using IST 2
- The steel grade is specified using SGR 0
STAAD PLANE
*
* INPUT FILE: NZS3404_Frame 2.STD
*
* REFERENCE : Hand Calculation
*
* OBJECTIVE : TO DETERMINE THE ADEQUACY OF TUBE,HSST SHAPE PER
* THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 21-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 6 0; 3 8 6 0; 4 8 0 0;
*
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
DEFINE PMEMBER
2 PMEMBER 1
1 PMEMBER 2
3 PMEMBER 3
*
*
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 INDIAN
2 TABLE ST TUB1251256
*
MEMBER PROPERTY AMERICAN
1 3 TABLE ST HSST20X12X0.75
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 FIXED
4 PINNED
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
PMEMBER LOAD
1 UNI Y -10
2 UMOM GZ 25
3 TRAP GZ 4 6
3 CON Y 10 0.1 0
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
IST 2 PMEMB 1 TO 3
TRACK 2 PMEMB 1 TO 3
SGR 0 PMEMB 1 TO 3
CHECK CODE PMEMB 2 3
*
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0) ************************************************** AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE FOR Y UP :- 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 2 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 HSST20X12X0.75 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.8.4.4.1 Governing Ratio: 0.090 (PASS) Governing Location: 0.000 m from Start. SECTION PROPERTIES ------------------ d: 508.0000 mm b: 304.8000 mm t: 17.7292 mm Ag: 26774.1387 mm2 J: 924.0338E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 911.5469E+06 mm4 Sz: 4.4245E+06 mm3 (plastic) Zz: 3.5888E+06 mm3 (elastic) rz: 184.5150E+00 mm Iy: 411.2367E+06 mm4 Sy: 3.1135E+06 mm3 (plastic) Zy: 2.6984E+06 mm3 (elastic) ry: 123.9333E+00 mm STAAD PLANE -- PAGE NO. 4 * 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: 48.413 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 180.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.090 Critical Location : 0.000 m from Start. Mz* = -89.2106E+00 KNm Section Slenderness: Compact Zez = 4.4245E+06 mm3 ϕMsz = 995.5142E+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 = 3.1135E+06 mm3 ϕMsy = 700.5470E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.090 Critical Location : 0.000 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 6.00 m(F ) Mz* = -89.2106E+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 = 6.00 m [NZS3404 5.6.3] αm = 1.000 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 41.0351E+03 KNm [NZS3404 5.6.1.1.1(d)] αsz = 1.000 [NZS3404 5.6.1.1.1(c)] ϕMbz = 995.5142E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] STAAD PLANE -- PAGE NO. 5 * SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.001 Critical Location : 0.000 m from Start. Vy* = 1.1125E+00 KN ϕVvmy = 2.1765E+03 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 = 1.2893E+03 KN [NZS3404 5.12.2] STAAD PLANE -- PAGE NO. 6 * AXIAL ----- Section Compression Capacity Critical Load Case : 1* Critical Ratio : 0.007 Critical Location : 0.000 m from Start. N* = 40.2237E+00 KN Ae = 26.7741E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 26.7741E+03 mm2 ϕNs = 6.0242E+03 KN [NZS3404 6.2.1] Member Compression Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.007 Critical Location : 0.000 m from Start. N* = 40.2237E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 6.00 m(U ) Lez = 6.00 m αb = -1.00 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 32.518 [NZS3404 6.3.3] λ,z = 17.215 [NZS3404 6.3.3] ε,z = 14.331 [NZS3404 6.3.3] αc,z = 0.988 [NZS3404 6.3.3] ϕNcz = 0.5949E+4 KN [NZS3404 6.3.3] Member Compression Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.007 Critical Location : 0.000 m from Start. N* = 40.2237E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 6.00 m(U ) Ley = 6.00 m λn,y = 48.413 [NZS3404 6.3.3] λ,y = 28.343 [NZS3404 6.3.3] ε,y = 5.785 [NZS3404 6.3.3] αc,y = 0.949 [NZS3404 6.3.3] ϕNcy = 0.5719E+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 = 26.7741E+03 mm2 ϕNt = 6.0242E+03 KN [NZS3404 7.2] STAAD PLANE -- PAGE NO. 7 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.090 Critical Location : 0.000 m from Start. ϕMrz = 995.5142E+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 = 700.5470E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.034 Critical Location : 0.000 m from Start. γ = 1.407 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.090 Critical Location : 0.000 m from Start. ϕMiz = 995.5142E+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 = 695.6196E+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 : 0.090 Critical Location : 0.000 m from Start. ϕMoz,c= 988.5120E+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. ******************************************************************************** AXIS NOTATION FOR ANY SECTION OTHER THAN ST ANGLE FOR Y UP :- 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 STAAD PLANE -- PAGE NO. 8 * MEMBER DESIGN OUTPUT FOR PMEMBER 3 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 HSST20X12X0.75 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.8.4.4.1 Governing Ratio: 0.053 (PASS) Governing Location: 0.000 m from Start. SECTION PROPERTIES ------------------ d: 508.0000 mm b: 304.8000 mm t: 17.7292 mm Ag: 26774.1387 mm2 J: 924.0338E+06 mm4 Iw: 0.0000E+00 mm6 Iz: 911.5469E+06 mm4 Sz: 4.4245E+06 mm3 (plastic) Zz: 3.5888E+06 mm3 (elastic) rz: 184.5150E+00 mm Iy: 411.2367E+06 mm4 Sy: 3.1135E+06 mm3 (plastic) Zy: 2.6984E+06 mm3 (elastic) ry: 123.9333E+00 mm 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: 48.413 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 180.000 BENDING ------- Section Bending Capacity (about Z-axis) STAAD PLANE -- PAGE NO. 9 * Critical Load Case : 1* Critical Ratio : 0.053 Critical Location : 0.000 m from Start. Mz* = 52.3655E+00 KNm Section Slenderness: Compact Zez = 4.4245E+06 mm3 ϕMsz = 995.5142E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.022 Critical Location : 6.000 m from Start. My* = 15.6295E+00 KNm Section Slenderness: Compact Zey = 3.1135E+06 mm3 ϕMsy = 700.5470E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.053 Critical Location : 0.000 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 6.00 m(F ) Mz* = 52.3655E+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 = 6.00 m [NZS3404 5.6.3] αm = 1.000 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 41.0351E+03 KNm [NZS3404 5.6.1.1.1(d)] αsz = 1.000 [NZS3404 5.6.1.1.1(c)] ϕMbz = 995.5142E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.004 Critical Location : 0.500 m from Start. Vy* = 8.8875E+00 KN ϕVvmy = 2.1765E+03 KN [NZS3404 5.12.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.013 Critical Location : 6.000 m from Start. Vz* = 16.2009E+00 KN ϕVvmz = 1.2893E+03 KN [NZS3404 5.12.2] STAAD PLANE -- PAGE NO. 10 * AXIAL ----- Section Compression Capacity Critical Load Case : 1* Critical Ratio : 0.007 Critical Location : 0.000 m from Start. N* = 39.7763E+00 KN Ae = 26.7741E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 26.7741E+03 mm2 ϕNs = 6.0242E+03 KN [NZS3404 6.2.1] Member Compression Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.007 Critical Location : 0.000 m from Start. N* = 39.7763E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 6.00 m(U ) Lez = 6.00 m αb = -1.00 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 32.518 [NZS3404 6.3.3] λ,z = 17.215 [NZS3404 6.3.3] ε,z = 14.331 [NZS3404 6.3.3] αc,z = 0.988 [NZS3404 6.3.3] ϕNcz = 0.5949E+4 KN [NZS3404 6.3.3] Member Compression Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.007 Critical Location : 0.000 m from Start. N* = 39.7763E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 6.00 m(U ) Ley = 6.00 m λn,y = 48.413 [NZS3404 6.3.3] λ,y = 28.343 [NZS3404 6.3.3] ε,y = 5.785 [NZS3404 6.3.3] αc,y = 0.949 [NZS3404 6.3.3] ϕNcy = 0.5719E+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 = 26.7741E+03 mm2 ϕNt = 6.0242E+03 KN [NZS3404 7.2] STAAD PLANE -- PAGE NO. 11 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.053 Critical Location : 0.000 m from Start. ϕMrz = 995.5142E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.022 Critical Location : 6.000 m from Start. ϕMry = 700.5470E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.020 Critical Location : 0.000 m from Start. γ = 1.407 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.053 Critical Location : 0.000 m from Start. ϕMiz = 989.0403E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.022 Critical Location : 6.000 m from Start. ϕMiy = 695.8025E+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 : 0.053 Critical Location : 0.000 m from Start. ϕMoz,c= 988.5899E+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 : 0.021 Critical Location : 0.000 m from Start.