# 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

$αm=1.7Mm×(M1*)2+(M2*)2+(M3*)2≤2.5$
$αm=1.7×160.8(-72.44)2+(-2.267)2+(72.5)2=2.66$

Therefore, αm = 2.5

Reference Buckling Moment, Mo

 $αs=0.6MsxMoa2+3-MsxMoa=0.157$ [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 = λnzaxαb = 72.62

λy = λnyayαb = 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

Table 1. Comparison of results
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

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\09 Steel Design\New Zealand\NZS 3404 1997\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
*
SELFWEIGHT Y -1
23 49 FY -200
46 49 FX 200
36 49 FZ -200
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


 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:-
---------     -------------     ---------------
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 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:   216.6775E+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
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]
BENDING
-------
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    ]
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 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 (&lt;= ϕMsz)      [NZS3404 5.6.1.1.1(a)]
STAAD SPACE                                              -- PAGE NO.   23
*
SHEAR
-----
Section Shear Capacity (along Y-axis)
Critical Ratio     :   0.071
Critical Location  :   5.015 m from Start.
Vy*  =    66.8261E+00 KN
ϕVvy =   939.4444E+00 KN                 [NZS3404 5.11.2]
Section Shear Capacity (along Z-axis)
Critical Ratio     :   0.002
Critical Location  :  10.015 m from Start.
Vz*  =     2.4943E+00 KN
ϕVvz =     1.0564E+03 KN                 [NZS3404 5.11.2]
STAAD SPACE                                              -- PAGE NO.   24
*
AXIAL
-----
Section Compression Capacity
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]
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]
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 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
------------------------
Critical Ratio     :   0.257
Critical Location  :   5.015 m from Start.
ϕMrz  =   639.9001E+00 KNm               [NZS3404 8.3.2]
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 Ratio     :   0.271
Critical Location  :   9.985 m from Start.
γ     =     1.426                         [NZS3404 8.3.4]
Critical Ratio     :   0.267
Critical Location  :   5.015 m from Start.
ϕMiz  =   616.9343E+00 KNm               [NZS3404 8.4.2]
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 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 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 Ratio     :   0.000
Critical Location  :   0.000 m from Start.
Member Biaxial Capacity (Compression)
Critical Ratio     :   1.918
Critical Location  :  10.015 m from Start.
STAAD SPACE                                              -- PAGE NO.   26
*
SEISMIC PROVISIONS
------------------
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]
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 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 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 Ratio     : N/A
Critical Location  : N/A
Status           =   Passed              [NZS3404 12.4.1.2]
Section Symmetry Requirement
Critical Ratio     : N/A
Critical Location  : N/A
Status           =   Passed              [NZS3404 12.5.2]
Min Web Thickness Requirement for Beam
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 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 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 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