V. NZS3404 1997-UB Section
Verify the Design Capacity of I Section as per NZS3404 1997.
Details
Verify the section bending capacity of an UB530X92.4. The member is used in a 15 m simply supported span..
Validation
Section Classification
Evaluate the slenderness the beam flanges:
λef =(B/2tf) ×√(fy/250) = 198.8/ (2×15.60)×√ (300/250) = 6.98 < 8
Flange is compact.
Evaluate the slenderness of the beam web:
λew =(d/tw) ×√(fy/250) = 501.80/10.20×√(300/250) =53.89 < 89
Web is compact.
Bending Capacity
Section Bending Capacity About Strong Axis
Effective section modulus, Zez = 2.37(10)6 mm3
The nominal section capacity in bending about the Z axis, Msz = ϕfy×Zez
Msz = 0.9 × 300 × 2.37 = 639.9 kN·m
Section Bending Capacity About Weak Axis
Effective section modulus, Zey = 341.6(10)3 mm3
The nominal section capacity in bending about the Y axis, Msy = ϕfy×Zey
Msy = 0.9 × 300 × 341.6 (10)-3 = 92.24 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) = 1
Load Height factor, Kl,(LHT) = 1.00 (Table 5.6.3(2) of NZS3404:1997)
Effective length = 1×1×1×15,000 = 15,000 mm
Design Bending Moment, Mm = 160.8 kN·m
Quarter Point Moment of segment, M2 = -72.443 kN·m
Mid-Point Moment of segment, M3 = -2.267 kN·m
Quarter Point Moment of segment, M4 = 72.499 kN·m
Therefore, αm = 2.5
Reference Buckling Moment, Mo
| [Ref. cl 5.6.1.1(c)] |
Mbz = αmαsMsx ≤ Msx = 2.5 × 0.157 × 71 = 279.1 kN·m
ϕMbz = 251.2 kN·m
Check for Shear
Shear Area of the section, Ay = d×tw = 533.0×10.2 = 5,436.6 mm2
Section Shear Capacity (Along Y axis), Vy = 0.6×fy×Ay = 0.6×320×5,436.6=1,044 kN
ΖVy = 0.9×1,044 = 939.4 kN
Shear Area of the section, AZ = 2× bf× tf = 2×209×15.6 = 6,520.8 mm2
Section Shear Capacity (Along z axis), Vz = 0.6×fy×Az = 0.6×300×6,520.8 = 1,174 kN
ϕVz = 1,056 kN
Check for Axial Compression
Section Compression Capacity
The flange slenderness, λeb = 6.98 [Ref : Cl no - 6.2.3.1]
Yield slender for flange, λeby = 16.00 [Ref : Table 6.2.4]
The web slenderness, λew = 55.66
Yield slender for web, λeby = 45
Effective Width, be=209 mm
Effective Depth, DE=405.7 mm
Gross Area, Ag = 11,800 mm2
Net Area, An = 10,820 mm2
Form factor, Kf = Ae/Ag = 0.917
The nominal member section capacity for axial compression ,
| Ns = Kf×An×fy = 0.917×10,819.8×300 = 3,246 kN | [Ref : Cl no - 6.2.1] |
| ϕNs = 0.9×3,246 = 2,920 kN | [Ref : Cl no - 6.2.1] |
Member Compression Capacity
Effective length factor for slenderness & buckling about minor Y- axis, Ky =1.00
Effective length factor for slenderness & buckling about minor Z- axis, Kz =1.00
Effective Length of member, Lez = 15,000 mm
Effective Length of member, Ley = 15,000 mm
Geometrical Slenderness Ratio = 69.23
Geometrical Slenderness Ratio = 334.0
Member slenderness, λnz = (Le/r)×√(kf)×√(fy/250) [Ref : Cl no - 6.3.3.]
λnz = 69.23×√1×√(300/250)= 72.62
Member slenderness, λny =(Ley/r)×√(kf)×√(fy/250) [Ref : Cl no - 6.3.3]
λny = 334×√1×√(300/250)= 350.35
αaz = 2,100×(λnz - 13.5)/(λnz2 - 15.3λnz + 2,050) = 19.984
αay = 2,100×(λny - 13.5)/(λny2 - 15.3λny + 2,050) = 5.923
| αb = 0.00 | [Ref : table 6.3.3(2)] |
λz = λnz+αaxαb = 72.62
λy = λny+αayαb = 350.35
η = 0.19
η = 1.10
ξz = ((λz/90)2+1+η)/(2×(λz/90)2) = 1.42
ξy = ((λy/90)2+1+η)/(2×(λy/90)2) = 0.57
| αcz=0.731 | [Ref : Cl no - 6.3.3] |
| αcy=0.061 | [Ref : Cl no - 6.3.3] |
The nominal member capacity, Ncz= αcz ×Ns [Ref : Cl no - 6.3.3]
Ncz= αcz ×Ns =0.731×3,246 =2,373 kN
ϕNcz= 2,136 kN
The nominal member capacity, Ncy= αcy ×Ns [Ref : Cl no - 6.3.3]
Ncy= αcy ×Ns =0.061×3,246 = 198.9 kN
ϕNcy= 178.96 KN
Nominal Section Tension Capacity
Ref. Cl 7.1
Kte= 1.00
Nt1 = Ag×fy = 3,540 kN
Nt2 = 0.85×Kte×An×fu = 4,413 kN
ϕNt = 3,186 kN [Ref : Cl no -5.6.1.1.1(a)]
Results
| Result Type | Reference | STAAD.Pro | Difference | Comments |
|---|---|---|---|---|
| ϕMsz (kN·m) | 639.9 | 639.9001 | negligible | |
| ϕMsy (kN·m) | 92.24 | 92.2392 | negligible | |
| ϕMbz (kN·m) | 251.2 | 251.3427 | negligible | |
|
ϕVy (kN)
|
939.4 | 939.4444 | negligible | |
| ϕVz (kN) | 1,056 | 1,056.4 | negligible | |
| ϕNs (kN) | 2,920 | 2,921.3 | negligible | |
| ϕNcz (kN) | 2,136 | 2,136 | none | |
| ϕNcy (kN) | 178.96 | 179.0 | negligible | |
| ϕNt (kN) | 3,186 | 3,186.0 | 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-UB Section.std is typically installed with the program.
STAAD SPACE
*
* INPUT FILE: NZS3404_Frame.STD
*
* REFERENCE : Hand Calculation
*
* OBJECTIVE : TO DETERMINE THE ADEQUACY OF UB,UC SHAPE PER
* THE NZS3404-1997 CODE
*
START JOB INFORMATION
ENGINEER DATE 16-Feb-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 0 5 0; 3 5 5 0; 4 5 0 0; 5 10 5 0; 6 10 0 0; 7 0 10 0; 8 5 10 0;
9 10 10 0; 10 0 15 0; 11 5 15 0; 12 10 15 0; 13 0 0 5; 14 0 5 5; 15 5 5 5;
16 5 0 5; 17 10 5 5; 18 10 0 5; 19 0 10 5; 20 5 10 5; 21 10 10 5; 22 0 15 5;
23 5 15 5; 24 10 15 5; 25 0 0 10; 26 0 5 10; 27 5 5 10; 28 5 0 10; 29 10 5 10;
30 10 0 10; 31 0 10 10; 32 5 10 10; 33 10 10 10; 34 0 15 10; 35 5 15 10;
36 10 15 10; 37 0 0 15; 38 0 5 15; 39 5 5 15; 40 5 0 15; 41 10 5 15;
42 10 0 15; 43 0 10 15; 44 5 10 15; 45 10 10 15; 46 0 15 15; 47 5 15 15;
48 10 15 15; 49 5 10 18;
*
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4; 4 3 5; 5 5 6; 6 2 7; 7 3 8; 8 5 9; 9 7 8; 10 8 9; 11 7 10;
12 8 11; 13 9 12; 14 10 11; 15 11 12; 16 2 14; 17 3 15; 18 5 17; 19 7 19;
20 8 20; 21 9 21; 22 10 22; 23 11 23; 24 12 24; 25 13 14; 26 14 15; 27 15 16;
28 15 17; 29 17 18; 30 14 19; 31 15 20; 32 17 21; 33 19 20; 34 20 21; 35 19 22;
36 20 23; 37 21 24; 38 22 23; 39 23 24; 40 14 26; 41 15 27; 42 17 29; 43 19 31;
44 20 32; 45 21 33; 46 22 34; 47 23 35; 48 24 36; 49 25 26; 50 26 27; 51 27 28;
52 27 29; 53 29 30; 54 26 31; 55 27 32; 56 29 33; 57 31 32; 58 32 33; 59 31 34;
60 32 35; 61 33 36; 62 34 35; 63 35 36; 64 26 38; 65 27 39; 66 29 41; 67 31 43;
68 32 44; 69 33 45; 70 34 46; 71 35 47; 72 36 48; 73 37 38; 74 38 39; 75 39 40;
76 39 41; 77 41 42; 78 38 43; 79 39 44; 80 41 45; 81 43 44; 82 44 45; 83 43 46;
84 44 47; 85 45 48; 86 46 47; 87 47 48; 88 44 49;
DEFINE PMEMBER
22 46 70 PMEMBER 1
19 43 67 PMEMBER 2
16 40 64 PMEMBER 3
20 44 68 PMEMBER 4
17 41 65 PMEMBER 5
24 48 72 PMEMBER 6
21 45 69 PMEMBER 7
18 42 66 PMEMBER 8
1 6 11 PMEMBER 9
25 30 35 PMEMBER 10
49 54 59 PMEMBER 11
73 78 83 PMEMBER 12
88 PMEMBER 13
*
*
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
2 4 9 10 14 TO 24 26 28 33 34 38 TO 48 50 52 57 58 62 TO 72 74 76 81 82 86 -
87 TO 88 TABLE ST UB530X92.4
1 3 5 TO 8 11 TO 13 25 27 29 TO 32 35 TO 37 49 51 53 TO 56 59 TO 61 73 75 -
77 TO 80 83 TO 85 TABLE ST UC310X158
*
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 4 6 13 16 18 25 28 30 37 40 42 FIXED
*
MEMBER RELEASE
2 4 9 10 14 TO 24 26 28 33 34 38 39 50 52 57 58 62 63 74 76 81 82 86 -
87 START MY MZ
2 4 9 10 14 15 26 28 33 34 38 39 50 52 57 58 62 TO 66 68 69 71 72 74 76 81 -
82 86 87 END MY MZ
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
SELFWEIGHT Y -1
JOINT LOAD
23 49 FY -200
46 49 FX 200
36 49 FZ -200
MEMBER LOAD
20 44 68 88 UNI Y -50
26 88 CMOM GZ -30
88 CON GZ 20
*
PERFORM ANALYSIS
*
PRINT ANALYSIS RESULTS
*
PRINT MEMBER FORCES
*
PARAMETER 1
CODE NZS3404 1997
BEAM 1 PMEMB 5 13
DMAX 1.5 PMEMB 5 13
DMIN 0.4 PMEMB 5 13
IST 2 PMEMB 5 13
LHT 1 PMEMB 5 13
NSC 1 PMEMB 5 13
NSF 1 PMEMB 5 13
RATIO 1 PMEMB 5 13
SGR 0 PMEMB 5 13
SKL 1 PMEMB 5 13
SKR 1 PMEMB 5 13
SKT 1 PMEMB 5 13
TMAIN 400 PMEMB 5 13
TRACK 2 PMEMB 5 13
TSP 0 PMEMB 5 13
DUCT 1 PMEMB 5
GLD 1 PMEMB 5
CHECK CODE PMEMB 5
*
FINISH
STAAD.Pro Output
STEEL DESIGN ***NOTE : SGR NOT SPECIFIED OR "DEFAULT" SPECIFIED FOR PMEMBER NO. 5. ***NOTE : BY DEFAULT "AS/NZS 3679.1 300" WILL BE USED FOR ROLLED SECTIONS. STAAD SPACE -- PAGE NO. 21 * 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 5 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 UB530X92.4 (AISC SECTIONS) Governing Load Case: 1* Governing Criteria: Cl.12.8.3.1.1 Governing Ratio: 14.910 *(FAIL) Governing Location: 10.015 m from Start. SECTION PROPERTIES ------------------ d: 532.9999 mm bf: 209.0000 mm tf: 15.6000 mm tw: 10.2000 mm Ag: 11800.0000 mm2 J: 775.0001E+03 mm4 Iw: 1.5886E+12 mm6 Iz: 554.0001E+06 mm4 Sz: 2.3700E+06 mm3 (plastic) Zz: 2.0788E+06 mm3 (elastic) rz: 216.6776E+00 mm Iy: 23.8000E+06 mm4 Sy: 355.0000E+03 mm3 (plastic) Zy: 227.7512E+03 mm3 (elastic) ry: 44.9105E+00 mm STAAD SPACE -- PAGE NO. 22 * 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: 333.998 LOAD: 1 LOC.(MET): 0.000 ALLOWABLE SLENDERNESS RATIO: 180.000 BENDING ------- Section Bending Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.257 Critical Location : 5.015 m from Start. Mz* = 164.5103E+00 KNm Section Slenderness: Compact Zez = 2.3700E+06 mm3 ϕMsz = 639.9001E+00 KNm [NZS3404 Cl.5.1 ] Section Bending Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.291 Critical Location : 10.015 m from Start. My* = -26.8162E+00 KNm Section Slenderness: Compact Zey = 341.6269E+03 mm3 ϕMsy = 92.2392E+00 KNm [NZS3404 Cl.5.1 ] Member Bending Capacity Critical Load Case : 1* Critical Ratio : 0.655 Critical Location : 5.015 m from Start. Crtiical Flange Segment: Location (Type): 0.00 m(F )- 15.00 m(F ) Mz* = 164.5103E+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 = 15.00 m [NZS3404 5.6.3] αm = 2.500 [NZS3404 5.6.1.1.1(b)(iii)] Mo = 127.0231E+00 KNm [NZS3404 5.6.1.1.1(d)] αsz = 0.157 [NZS3404 5.6.1.1.1(c)] ϕMbz = 251.3427E+00 KNm (<= ϕMsz) [NZS3404 5.6.1.1.1(a)] STAAD SPACE -- PAGE NO. 23 * SHEAR ----- Section Shear Capacity (along Y-axis) Critical Load Case : 1* Critical Ratio : 0.071 Critical Location : 5.015 m from Start. Vy* = 66.8261E+00 KN ϕVvmy = 939.4444E+00 KN [NZS3404 5.12.2] Section Shear Capacity (along Z-axis) Critical Load Case : 1* Critical Ratio : 0.002 Critical Location : 10.015 m from Start. Vz* = 2.4943E+00 KN ϕVvmz = 1.0564E+03 KN [NZS3404 5.12.2] STAAD SPACE -- PAGE NO. 24 * AXIAL ----- Section Compression Capacity Critical Load Case : 1* Critical Ratio : 0.039 Critical Location : 10.015 m from Start. N* = 114.4841E+00 KN Ae = 10.8198E+03 mm2 [NZS3404 6.2.3 / 6.2.4] kf = 0.917 [AS 4100 6.2.2] An = 11.8000E+03 mm2 ϕNs = 2.9213E+03 KN [NZS3404 6.2.1] Member Compression Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.054 Critical Location : 10.015 m from Start. N* = 114.4841E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 15.00 m(U ) Lez = 15.00 m αb = 0.00 [NZS3404 Table 6.3.3(1)/6.3.3(2)] λn,z = 72.617 [NZS3404 6.3.3] λ,z = 72.617 [NZS3404 6.3.3] ε,z = 1.416 [NZS3404 6.3.3] αc,z = 0.731 [NZS3404 6.3.3] ϕNcz = 0.2136E+4 KN [NZS3404 6.3.3] Member Compression Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.640 Critical Location : 10.015 m from Start. N* = 114.4841E+00 KN Unbraced Segment: Location (Type): 0.00 m(U )- 15.00 m(U ) Ley = 15.00 m λn,y = 350.351 [NZS3404 6.3.3] λ,y = 350.351 [NZS3404 6.3.3] ε,y = 0.569 [NZS3404 6.3.3] αc,y = 0.061 [NZS3404 6.3.3] ϕNcy = 0.1790E+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 = 11.8000E+03 mm2 ϕNt = 3.1860E+03 KN [NZS3404 7.2] STAAD SPACE -- PAGE NO. 25 * COMBINED BENDING AND AXIAL ------------------------ Section Combined Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.257 Critical Location : 5.015 m from Start. ϕMrz = 639.9001E+00 KNm [NZS3404 8.3.2] Section Combined Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.291 Critical Location : 10.015 m from Start. ϕMry = 92.2392E+00 KNm [NZS3404 8.3.3] Section Combined Capacity (Biaxial) Critical Load Case : 1* Critical Ratio : 0.271 Critical Location : 9.985 m from Start. γ = 1.426 [NZS3404 8.3.4] Member In-plane Capacity (about Z-axis) Critical Load Case : 1* Critical Ratio : 0.267 Critical Location : 5.015 m from Start. ϕMiz = 616.9343E+00 KNm [NZS3404 8.4.2] Member In-plane Capacity (about Y-axis) Critical Load Case : 1* Critical Ratio : 0.806 Critical Location : 10.015 m from Start. ϕMiy = 33.2658E+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 : 1.150 Critical Location : 5.015 m from Start. ϕMoz,c= 143.1029E+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 : 1.918 Critical Location : 10.015 m from Start. STAAD SPACE -- PAGE NO. 26 * SEISMIC PROVISIONS ------------------ Section Slenderness (Bending about Z-axis) Critical Load Case : 1* Critical Ratio : 0.776 Critical Location : 0.000 m from Start. λsz = 6.98 [NZS3404 12.5.1.1] λez = 9.00 [NZS3404 Table 12.5] Section Slenderness (Bending about Y-axis) Critical Load Case : 1* Critical Ratio : 0.776 Critical Location : 0.000 m from Start. λsy = 6.98 [NZS3404 12.5.1.1] λey = 9.00 [NZS3404 Table 12.5] Max Specific Yield Stress Critical Load Case : 1* Critical Ratio : 0.833 Critical Location : 0.000 m from Start. Fy,actual = 300.00 Fy,limit = 360.00 [NZS3404 Table 12.4(1)] Max Actual Yield Ratio (Fy/Fu) Critical Load Case : 1* Critical Ratio : 0.852 Critical Location : 0.000 m from Start. Fy/Fu,actual = 0.68 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 : 0.679 Critical Location : 0.000 m from Start. tw,actual = 10.20 tw,min = 6.92 [NZS3404 12.7.2] Max Axial Force Limit for Column (a) Critical Load Case : 1* Critical Ratio : 0.078 Critical Location : 10.015 m from Start. N*/ϕNs - actual = 0.04 N*/ϕNs - limit = 0.50 [NZS3404 Table 12.8.1] Max Axial Force Limit for Column (b) Critical Load Case : 1* Critical Ratio : 14.910 Critical Location : 10.015 m from Start. b m = 0.00 NoL = 214.0169E+00 KN λEYC = 3.89 N*/ϕNs - actual = 0.04 N*/ϕNs - limit = 0.00 [NZS3404 12.8.3.1(b)] Max Axial Force Limit for Column (c) Critical Load Case : 1* Critical Ratio : 0.202 Critical Location : 10.015 m from Start. Ng*/ϕNs - actual = 0.04 Ng*/ϕNs - limit = 0.19 [NZS3404 12.8.3.1(c)] Shear-Y + Bend-Z Interaction Critical Load Case : 1* Critical Ratio : 0.253 Critical Location : 5.015 m from Start. Mz* = -161.9652E+00 KN ϕMsvz= 639.9001E+00 KN [NZS3404 12.10.3.1] Shear-Z + Bend-Y Interaction Critical Load Case : 1* Critical Ratio : 0.151 Critical Location : 9.985 m from Start. My* = -13.9665E+00 KN ϕMsvy= 92.2392E+00 KN [NZS3404 12.10.3.1] ********************************************************************************