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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.

Loads:
  • 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:

λ e f = B 2 t f f y 250 = 198.8 2(15.60) 300 250 = 6.98 < 8

Section flange classification is compact.

Evaluate the slenderness effects of the beam web:

λ e w = d t w f y 250 = 501.8 10.20 300 250 = 56.89 < 89

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 mm
α m = 1.7 M m * ( M 2 * ) 2 + ( M 3 * ) 2 + ( M 4 * ) 2 = 1.7 × 109.8 ( 3.383 ) 2 + ( -77.73 ) 2 + ( -7.246 ) 2 = 2.389 2.5

Reference buckling moment, Mo

M o = π 2 E I y L e 2 G J + π 2 E I w L e 2 = 416.5  kN·m
α s = 0.6 M s x M o a 2 + 3 - M s x M o a = 0.435 [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,

λ n z = L e z r k f f y 250 = 41.54 1 300 250 = 43.57 [Ref : Clause 6.3.3]
λ n y = L e y r k f f y 250 = 200.4 1 300 250 = 210.1 [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

Table 1. Comparison of 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 CONNECT Edition\Samples\ Verification Models\09 Steel Design\New Zealand\NZS 3404 1997\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
PRINT ALL
*
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
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
*
PARAMETER 2
CODE NZS3404 1997
TRACK 2 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

 STEEL DESIGN    
   NOTE : SGR NOT SPECIFIED OR "DEFAULT" SPECIFIED FOR PMEMBER NO.      1.
   NOTE : BY DEFAULT "AS/NZS 3679.1 300" WILL BE USED FOR ROLLED SECTIONS.
   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
 |----------------------------------------------------------------------------------|
 |  PMember Number:      1                                                          |
 |  Member Section:  ST   UB530X92.4      (AISC SECTIONS)                           |
 |  Status: PASS  Ratio:   0.852  Critical Load Case:     1  Location:       1.00   |
 |  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    ]     |
 | ϕVvy  =     939.444E+00 KNm     ϕVvz  =       1.056E+03 KNm     [Cl.5.12.3 ]     |
 | 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]     |
 |----------------------------------------------------------------------------------|