V.NZS3404 1997-Channel Section
Verify the design capacity of a channel section per NZS 3404 1997.
Details
The member is a PFC250 section used in a 9 m simply supported span. The beam is loaded with a vertical load of 8.4 kN point load at 5m from start end, a 10 kN axial load at the mid-point, and a distributed load that decreases from 0.5 kN/m at the start down to 0.2 kN/m at the end. Steel grade is 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 = 421,000 mm3
The nominal section capacity in bending about Z axis, Msz = ϕfy×Zez
Msz = 300× 421,000/106 = 126.3 kN·m
ϕMsz = 0.9×126.3 = 113.67 kN·m
Section Bending Capacity About Y-Axis
Effective Section Modulus, Zey = 88,925 mm3
The nominal section capacity in bending about Z axis, Msy = ϕfy×Zey
Msy = 300× 88,925/106 = 26.68 kN·m
ϕMsy = 0.9×26.68 = 24.01 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 = 1×1×1×9,000 = 9,000 mmReference buckling moment, Mo
| [Ref : Clause 5.6.1.1 (c)] |
Mbx = αmαsMsx ≤ Msx
| Mbz = 1.352 × 0.281 × 126.3 = 48.0 kN·m ≤ (Msz, Msy)Max. | [Ref : Clause 5.6.1.1.1(a)] |
ϕMbz = 0.9×48.0 = 43.19 kN·m
Check for Shear
Shear Area of the section, Ay = d×tw = 250×8 = 2,000 mm2
Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×300×2,000 = 384 kN
| Vvn = 2×324/(0.9 + 1.2) = 308.6 kN | [Ref : Clause 5.11.2] |
ϕVy = 0.9×384 = 345.6 kN
Shear Area of the section, AZ = 2×bf× tf = 2×90×15 = 2,700 mm2
Section Shear Capacity (Along z axis),Vz = 0.6×fy×Az = 0.6×300×2,700 = 486 kN
ϕVz = 0.9×486 = 437.4 kN
Check for Axial Compression
Section Compression Capacity:
The flange slenderness, λeb = 5.9884 [Ref : Cl - 6.2.3.1]
Yield slender for flange, λeby = 14 [Ref : Table 6.2.4]
The web slenderness, λew = 30.125
Gross Area, Ag = 4,520 mm2
Net Area, An = 4,520 mm2
Form factor, Kf = Ae/Ag = 1
The nominal member section capacity for axial compression,
| Ns = Kf×An×fy = 1×4,520×300 = 1,356 kN | [Ref : Clause 6.2.1] |
| ϕNs = 0.9×1,356 = 1,220.4 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 = Lez/rz = 9,000 / 99.89 = 90.10
Geometrical Slenderness Ratio = Ley/ry = 9,000 / 28.37 = 317.2
Member slenderness,
| [Ref : Clause 6.3.3] |
| [Ref : Clause 6.3.3] |
αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 17.402
αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 5.970
| αb = 0.5 | [Ref : Table 6.3.3(2)] |
λz = λnz + αaz×αz = 107.4
λy = λny + αay×αb = 350.5
η = 0.31
η = 1.10
ξz = ((λz/90)2+ 1 + η)/(2×(λz/90)2) = 0.96
ξy = ((λy/90)2+ 1 + η)/(2×(λy/90)2) = 0.57
αcz= 0.493
αcy= 0.061
The nominal member capacity,
| Ncz= αcz×Ns =0.493×1,356 = 668.7 kN | [Ref : Clause 6.3.3] |
ϕNcz = 601.8 kN
The nominal member capacity,
| Ncy= αcy×Ns =0.061×1,356 = 82.72 kN | [Ref : Clause 6.3.3] |
ϕNcy = 74.44 kN
Nominal Section tension Capacity
[Ref : Clause 7.1]
Kte = 1.00
Nt1 = Ag×fy = 1,356 kN
Nt2 = 0.85×Kte×An×fu = 1,690.5 kN
| ϕNt = 0.9×1,356 = 1,220.4 kN | [Ref : Clause 5.6.1.1.1(a)] |
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| ϕMsz (kN·m) | 113.67 | 113.67 | none | |
| ϕMsy (kN·m) | 24.01 | 24.0098 | negligible | |
| ϕMbz (kN·m) | 43.19 | 42.9925 | negligible | |
| ϕVvy (kN) | 345.6 | 345.600 | none | |
| ϕNs (kN) | 1,220.4 | 1,220.4 | none | |
| ϕNcz (kN) | 601.8 | 601.8 | none | |
| ϕNcy (kN) | 74.44 | 74.74 | negligible | |
| ϕNt (kN) | 1,220.4 | 1,220.4 | 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-Channel Section.std is typically installed with the program.
STAAD SPACE
*
* INPUT FILE: NZS3404_Channel_Section_Compact.STD
*
* REFERENCE : Hand Calculation
*
* OBJECTIVE : TO DETERMINE THE ADEQUACY OF CHANNEL 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+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 PFC250
*
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
1 CON GY -8.4
SELFWEIGHT Y -1
MEMBER LOAD
1 UNI X -10
1 TRAP Z -0.5 -2
PERFORM ANALYSIS
*
PARAMETER 1
CODE NZS3404 1997
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 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 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 PFC250 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.8.4.5.1 Governing Ratio: 46.122 *(FAIL) Governing Location: 2.250 m from Start. SECTION PROPERTIES ------------------ d: 250.0000 mm bf: 90.0000 mm tf: 15.0000 mm tw: 8.0000 mm Ag: 4520.0000 mm2 J: 238.0000E+03 mm4 Iw: 34.8250E+09 mm6 Iz: 45.1000E+06 mm4 Sz: 421.0000E+03 mm3 (plastic) Zz: 360.8000E+03 mm3 (elastic) rz: 99.8893E+00 mm Iy: 3.6400E+06 mm4 Sy: 107.0000E+03 mm3 (plastic) Zy: 59.2834E+03 mm3 (elastic) ry: 28.3780E+00 mm STAAD SPACE -- PAGE NO. 10 * 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 : 300.000 MPa [NZS3404 Table 2.1] fy, web : 320.000 MPa [NZS3404 Table 2.1] fu : 440.000 MPa [NZS3404 Table 2.1] SLENDERNESS: ACTUAL SLENDERNESS RATIO: 317.147 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 180.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.205 Critical Location : 4.500 m from Start. Mz* = -23.3483E+00 KNm Section Slenderness: Compact Zez = 421.0000E+03 mm3 ϕMsz = 113.6700E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 1.449 Critical Location : 1.500 m from Start. My* = 34.7977E+00 KNm Section Slenderness: Compact Zey = 88.9251E+03 mm3 ϕMsy = 24.0098E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.544 Critical Location : 4.500 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 9.00 m(F ) Mz* = -23.3483E+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 = 1.352 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 42.2526E+00 KNm [NZS3404 5.6.1.1.1(d)] αsz = 0.279 [NZS3404 5.6.1.1.1(c)] ϕMbz = 42.9225E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] STAAD SPACE -- PAGE NO. 11 * SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.017 Critical Location : 0.000 m from Start. Vy* = 5.7625E+00 KN ϕVvmy = 345.6000E+00 KN [NZS3404 5.12.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.016 Critical Location : 0.750 m from Start. Vz* = 4.0781E+00 KN ϕVvmz = 262.4400E+00 KN [NZS3404 5.12.2] STAAD SPACE -- PAGE NO. 12 * AXIAL ----- Section Compression Capacity Critical Load Case : 1* Critical Ratio : 0.074 Critical Location : 0.000 m from Start. N* = 90.0000E+00 KN Ae = 4.5200E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 1.000 [AS 4100 6.2.2] An = 4.5200E+03 mm2 ϕNs = 1.2204E+03 KN [NZS3404 6.2.1] Member Compression Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.150 Critical Location : 0.000 m from Start. N* = 90.0000E+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 = 98.699 [NZS3404 6.3.3] λ,z = 107.400 [NZS3404 6.3.3] ε,z = 0.959 [NZS3404 6.3.3] αc,z = 0.493 [NZS3404 6.3.3] ϕNcz = 0.6018E+3 KN [NZS3404 6.3.3] Member Compression Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 1.204 Critical Location : 0.000 m from Start. N* = 90.0000E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 9.00 m(U ) Ley = 9.00 m λn,y = 347.417 [NZS3404 6.3.3] λ,y = 350.403 [NZS3404 6.3.3] ε,y = 0.569 [NZS3404 6.3.3] αc,y = 0.061 [NZS3404 6.3.3] ϕNcy = 0.7474E+2 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 = 4.5200E+03 mm2 ϕNt = 1.2204E+03 KN [NZS3404 7.2] STAAD SPACE -- PAGE NO. 13 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.213 Critical Location : 4.500 m from Start. ϕMrz = 109.4786E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 1.554 Critical Location : 0.750 m from Start. ϕMry = 22.3867E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 1.689 Critical Location : 1.500 m from Start. γ = 1.461 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.222 Critical Location : 4.500 m from Start. ϕMiz = 105.1701E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 14.256 Critical Location : 2.250 m from Start. ϕMiy = 2.3263E+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 : 3.092 Critical Location : 2.250 m from Start. ϕMoz,c= 4.1587E+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 : 46.122 Critical Location : 2.250 m from Start. ********************************************************************************