V.NZS3404 1997-I section
Verify the Design Capacity of I Section as per NZS3404 1997.
Details
Verify the Section bending capacity of an UB530X92.4. Span of the member = 9 m. Both ends of the member are simply supported.
- Concentrated in the Y direction: 84.5 kN (at a distance of 5m from the left support)
- Concentrated in the Z direction: 10 kN (at mid-span)
- Concentrated in the X direction: 10 kN (at mid-span)
Fy = 300 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 = 2.37×106 mm3
The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez
Msz = 300× 2.37 = 711 kN·m
ϕMsz = 0.9×700 = 639.9 kN·m
Section Bending Capacity About Y-Axis
Effective Section Modulus, Zey = 341.6×103 mm3
The nominal section capacity in bending about Z axis, Msy = ϕfy×Zey
Msy = 300× 341.6×103/106 = 102.5 kN·m
ϕMsy = 0.9×102.5 = 92.23 kN·m
Member Bending Capacity
End restraint arrangement = FF
A twist restraint factor, Kt (SKT) = 1.00
Minor axis rotation restraints = Both
Lateral rotation restraint factor, Kr (SKR) = 0.70
Load Height factor, Kl, (LHT) = 1.00 [Ref : Table 5.6.3(2)]
Effective length = 1×1×0.7×9,000 = 6,300 mmReference buckling moment, Mo
[Ref : Clause 5.6.1.1 (c)] |
Mbx = αmαsMsx ≤ Msx
Mbz = 2.389 × 0.435 × 416.5 = 711.0 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×711.0 = 639.9 kN·m
Check for Shear
Shear Area of the section, Ay = d×tw = 533×10.2 = 5,437 mm2
Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×300×5,437 = 1,044 kN
ϕVy = 0.9×1,044 = 939.4 kN
Shear Area of the section, AZ = 2×bf× tf = 2×209×15.6 = 6,521 mm2
Section Shear Capacity (Along z axis),Vz = 0.6×fy×Az = 0.6×300×6,521 = 1,174 kN
ϕVz = 0.9×1,174 = 1,056 kN
Check for Axial Compression
Section Compression Capacity:
The flange slenderness, λeb = 6.98 [Ref : Cl - 6.2.3.1]
Yield slender for flange, λeby = 16 [Ref : Table 6.2.4]
The web slenderness, λew = 55.66
Gross Area, Ag = 11,800 mm2
Net Area, An = 11,800 mm2
Form factor, Kf = Ae/Ag = 0.92
The nominal member section capacity for axial compression,
Ns = Kf×An×fy = 0.92×11,800×300 = 3,257 kN | [Ref : Clause 6.2.1] |
ϕNs = 0.9×3,257 = 2,931 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
rz = √(554×106 / 11,800) = 216.7
ry = √(23.8×106 / 11,800) = 44.91
Geometrical Slenderness Ratio = Lez/rz = 9,000 / 216.7 = 41.54
Geometrical Slenderness Ratio = Ley/ry = 9,000 / 44.91 = 200.4
Member slenderness,
[Ref : Clause 6.3.3] |
[Ref : Clause 6.3.3] |
αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 19.24
αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 9.60
αb = 0.0 | [Ref : Table 6.3.3(2)] |
λz = λnz + αaz×αz = 43.57
λy = λny + αay×αb = 210.1
η = 0.10
η = 0.64
ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 2.84
ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 0.65
αcz= 0.89
αcy= 0.16
The nominal member capacity,
Ncz= αcz×Ns =0.89×3,246 = 2,888 kN | [Ref : Clause 6.3.3] |
ϕNcz = 2,600 kN
The nominal member capacity,
Ncy= αcy×Ns =0.16×3,246 = 521.9 kN | [Ref : Clause 6.3.3] |
ϕNcy = 470 kN
Combined Bending and Axial
Section Combined Capacity (About Z-axis) ≤ Msz
Mrz =1.18×Msz×(1-N/ϕNsz) = 837.54 kN·m
Mrz =1.18×Msz×(1-N/ϕNsz) = 837.54 kN·m
ϕMrz = 639.90 kN·m [Ref : Cl -8.1.5]
Section Combined Capacity (About y-axis) ≤ Msy
Mrz =1.19×Msy×(1-(N/ϕNsy)2) = 121.96 kN·m
ϕMry = 92.239 kN·m [Ref : Cl -8.1.5]
Section Combined Capacity (Biaxial) [Ref : Cl -8.1.5]
λ = 1.4+(N/ϕNs) = 1.402
(Mz/ϕMrz)λ + (My/ϕMry)λ = 0.14
Member in-plane Capacity (Z-axis) Miz ≤ Mrz
Miz = Msz{[1-(1+ẞm/2)3](1-N/ϕNcz) + 1.18(1+ẞm/2)3√(1-N/ϕNcz)} = 709.63 kN·m
ϕMiz = 638.67 kN·m
Member in-plane Capacity (y-axis) Miy ≤ Mry [Ref : Cl - 8.4.4.2.2]
Msy{[1-(1+ẞm/2)3](1-Ny/ϕNcy) + 1.18(1+ẞm/2)3√(1-Ny/ϕNcy)} = 101.40 kN·m
ϕMiy =91.26 kN·m
Member Out- of- plane Capacity (Tension) [Ref : Cl - 8.4.4.2]
Mozt = Mbz(1 + N/ϕNt) =712.12 kN·m
Nominal out-plane member moment capacity,Mozt = 711.00 kN·m
ϕMozt = 639.90 kN·m
Member Out-of-plane Capacity(Compression) Moz ≤ Mrz [Ref : Cl - 8.4.4.1]
Moz = Mbz(1 - N/ϕNcy) = 703.43 kN·m
ϕMozc = 633.09 kN·m
Member Biaxial Capacity (Compression)
Mcz = 709.63 kN·m
ϕMcz = 638.67 kN·m
(Mz/ϕMcz)1.4+(My/ϕMiy)1.4 = 0.139
Member Biaxial Capacity (tension)
Mtx = 711.00 kN·m
ϕMtx = 639.90 kN·m
(Mz/ϕMtz)1.4+(My/ϕMry)1.4 = 0.116
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
ϕMsz ( kN·m ) | 639.9 | 639.9001 | Negligible | |
ϕMsy ( kN·m ) | 92.23 | 92.2392 | Negligible | |
ϕMbz ( kN·m ) | 639.9 | 639.900 | None | |
ϕVy (kN) | 939.4 | 939.4 | None | |
ϕVz (kN) | 1,056 | 1,056.4 | Negligible | |
ϕNs (kN) | 2,931 | 2,921.3 | Negligible | |
ϕNcz (kN) | 2,600 | 2,599 | None | |
ϕNcy (kN) | 470 | 469.7 | None | |
ϕMrz ( kN·m ) | 639.900 | 639.900 | None | |
ϕMry ( kN·m ) | 92.239 | 92.239 | None | |
ϕMiz ( kN·m ) | 638.7849 | 638.7849 | None | |
ϕMiy ( kN·m ) | 91.2744 | 91.2744 | None | |
ϕMozc ( kN·m ) | 633.09 | 633.09 | None | |
ϕMozt ( kN·m ) | 639.900 | 639.900 | 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-I section.std is typically installed with the program.
STAAD SPACE
*
* INPUT FILE: NZS3404_I_Section.STD
*
* REFERENCE : Hand Calculation
*
* OBJECTIVE : TO DETERMINE THE ADEQUACY OF A UB 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;
*
MEMBER INCIDENCES
1 1 4;
*
DEFINE PMEMBER
1 PMEMBER 1
*
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+008
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-005
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 UB530X92.4
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 4 FIXED
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -84 5
SELFWEIGHT Y -1
MEMBER LOAD
1 CON GX 10
1 CON GZ 10
*
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
MAIN 1 PMEMB 1
TRACK 1 PMEMB 1
DUCT 1 PMEMB 1
GLD 1 PMEMB 1
PBCRES ZZ 0 T 1 T PMEMB 1
PBCRES YY 0 T 1 T PMEMB 1
PBRACE TOP 0 FR 1 FR PMEMB 1
PBRACE BOTTOM 0 FR 1 FR 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 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 |----------------------------------------------------------------------------------| | PMember Number: 1 | | Member Section: ST UB530X92.4 (AISC SECTIONS) | | Status: PASS Ratio: 0.852 Critical Load Case: 1 Location: 0.00 | | Critical Condition: T.12.4 | | Critical Design Forces: (Unit: KN METE) | | FX: -5.000E+00 T FY: 39.108E+00 FZ: -5.000E+00 | | MX: 0.000E+00 MY: 11.250E+00 MZ: 89.082E+00 | |----------------------------------------------------------------------------------| | ϕMsz = 639.900E+00 KNm ϕMsy = 92.239E+00 KNm [Cl.5.1 ] | | ϕMbz = 639.900E+00 KNm [Cl.5.1 ] | | ϕVvmy = 939.444E+00 KNm ϕVvmz = 1.056E+03 KNm [Cl.5.12.2 ] | | ϕNs = 2.921E+03 KN [Cl.6.1 ] | | ϕNcz = 2.599E+03 KN ϕNcy = 469.708E+00 KN [Cl.6.1 ] | | ϕNt = 3.186E+03 KN [Cl.7.1 ] | | ϕMrz = 639.900E+00 KNm ϕMry = 92.239E+00 KNm [Cl.8.3.2.2] | | ϕMiz = 638.785E+00 KNm ϕMiy = 91.274E+00 KNm [Cl.5.3.2.4] | | ϕMozc = 633.088E+00 KNm ϕMozt = 639.900E+00 KNm [Cl.8.4.4.1] | | ϕMcz = 633.088E+00 KNm [Cl.8.4.5.1] | | ϕMtz = 639.900E+00 KNm [Cl.8.4.5.1] | |----------------------------------------------------------------------------------|