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} = \frac{B}{{2 t}_{f}} \sqrt{\frac{f_{y}}{250}} = \frac{198.8}{2(15.60)} \sqrt{\frac{300}{250}} = 6.98 < 8

Section flange classification is compact.

Evaluate the slenderness effects of the beam web:

λ_{e w} = \frac{d}{t_{w}} \sqrt{\frac{f_{y}}{250}} = \frac{501.8}{10.20} \sqrt{\frac{300}{250}} = 56.89 < 89

Section web classification is compact

Section Bending Capacity About Z-Axis

Effective Section Modulus, Z_ez = 2.37×10⁶ mm³

The nominal section capacity in bending about Z axis, M_sz = ϕf_y×Z_ez

M_sz = 300× 2.37 = 711 kN·m

ϕM_sz = 0.9×700 = 639.9 kN·m

Section Bending Capacity About Y-Axis

Effective Section Modulus, Z_ey = 341.6×10³ mm³

The nominal section capacity in bending about Z axis, M_sy = ϕf_y×Z_ey

M_sy = 300× 341.6×10³/10⁶ = 102.5 kN·m

ϕM_sy = 0.9×102.5 = 92.23 kN·m

Member Bending Capacity

End restraint arrangement = FF

A twist restraint factor, K_t (SKT) = 1.00

Minor axis rotation restraints = Both

Lateral rotation restraint factor, K_r (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} = \frac{1.7 M_{m}^{*}}{\sqrt{{(M_{2}^{*})}^{2} + {(M_{3}^{*})}^{2} + {(M_{4}^{*})}^{2}}} = \frac{1.7 \times 109.8}{\sqrt{{(3.383)}^{2} + {(-77.73)}^{2} + {(-7.246)}^{2}}} = 2.389 \leq 2.5

Reference buckling moment, M_o

M_{o} = \sqrt{\frac{π^{2} E I_{y}}{{L_{e}}^{2}} [G J + (\frac{π^{2} E I_{w}}{{L_{e}}^{2}})]} = 416.5 kN·m

α_{s} = 0.6 \{\sqrt{[{(\frac{M_{s x}}{M_{o a}})}^{2} + 3]} - (\frac{M_{s x}}{M_{o a}})\} = 0.435

[Ref : Clause 5.6.1.1 (c)]

M_bx = α_mα_sM_sx ≤ M_sx

M_bz = 2.389 × 0.435 × 416.5 = 711.0 kN·m ≤ (M_sz, M_sy)_Max.

[Ref : Clause 5.6.1.1.1(a)]

ϕM_bz = 0.9×711.0 = 639.9 kN·m

Check for Shear

Shear Area of the section, A_y = d×t_w = 533×10.2 = 5,437 mm²

Section Shear Capacity (Along Y axis), V_y = 0.6×f_y×A_y = 0.6×300×5,437 = 1,044 kN

ϕV_y = 0.9×1,044 = 939.4 kN

Shear Area of the section, A_Z = 2×b_f× t_f = 2×209×15.6 = 6,521 mm²

Section Shear Capacity (Along z axis),V_z = 0.6×f_y×A_z = 0.6×300×6,521 = 1,174 kN

ϕV_z = 0.9×1,174 = 1,056 kN

Check for Axial Compression

Section Compression Capacity:

The flange slenderness, λ_eb = 6.98 [Ref : Cl - 6.2.3.1]

Yield slender for flange, λ_eby = 16 [Ref : Table 6.2.4]

The web slenderness, λ_ew = 55.66

Gross Area, A_g = 11,800 mm²

Net Area, A_n = 11,800 mm²

Form factor, K_f = A_e/A_g = 0.92

The nominal member section capacity for axial compression,

N_s = K_f×A_n×f_y = 0.92×11,800×300 = 3,257 kN

[Ref : Clause 6.2.1]

ϕN_s = 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, K_y = 1.0

Effective length factor for slenderness & buckling about minor Z- axis, K_z= 1.0

Effective Length of member, L_ez = 1.0×9,000 mm = 9,000 mm

Effective Length of member, L_ey = 1.0×9,000 mm = 9,000 mm

r_z = √(554×10⁶ / 11,800) = 216.7

r_y = √(23.8×10⁶ / 11,800) = 44.91

Geometrical Slenderness Ratio = L_ez/r_z = 9,000 / 216.7 = 41.54

Geometrical Slenderness Ratio = L_ey/r_y = 9,000 / 44.91 = 200.4

Member slenderness,

λ_{n z} = \frac{L_{e z}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 41.54 \sqrt{1} \sqrt{\frac{300}{250}} = 43.57

[Ref : Clause 6.3.3]

λ_{n y} = \frac{L_{e y}}{r} \sqrt{k_{f}} \sqrt{\frac{f_{y}}{250}} = 200.4 \sqrt{1} \sqrt{\frac{300}{250}} = 210.1

[Ref : Clause 6.3.3]

α_az = 2,100×(λ_nz - 13.5)/(λ_nz² - 15.3λ_nz + 2,050) = 19.24

α_ay = 2,100×(λ_ny - 13.5)/(λ_ny² - 15.3λ_ny + 2,050) = 9.60

α_b = 0.0

[Ref : Table 6.3.3(2)]

λ_z = λ_nz + α_az×α_z = 43.57

λ_y = λ_ny + α_ay×α_b = 210.1

η = 0.10

η = 0.64

ξ_z = ((λ_z/90)²+ 1 + η)/(2×(λ_z/90)²) = 2.84

ξ_y = ((λ_y/90)²+ 1 + η)/(2×(λ_y/90)²) = 0.65

α_cz= 0.89

α_cy= 0.16

The nominal member capacity,

N_cz= α_cz×N_s =0.89×3,246 = 2,888 kN

[Ref : Clause 6.3.3]

ϕN_cz= 2,600 kN

The nominal member capacity,

N_cy= α_cy×N_s =0.16×3,246 = 521.9 kN

[Ref : Clause 6.3.3]

ϕN_cy = 470 kN

Combined Bending and Axial

Section Combined Capacity (About Z-axis) ≤ M_sz

M_rz =1.18×M_sz×(1-N/ϕN_sz) = 837.54 kN·m

ϕM_rz = 639.90 kN·m [Ref : Cl -8.1.5]

Section Combined Capacity (About y-axis) ≤ M_sy

M_rz =1.19×M_sy×(1-(N/ϕN_sy)²) = 121.96 kN·m

ϕM_ry = 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

(M_z/ϕM_rz)λ + (M_y/ϕM_ry)λ = 0.14

Member in-plane Capacity (Z-axis) M_iz ≤ M_rz

M_iz = M_sz{[1-(1+ẞm/2)3](1-N/ϕN_cz) + 1.18(1+ẞm/2)3√(1-N/ϕN_cz)} = 709.63 kN·m

ϕM_iz = 638.67 kN·m

Member in-plane Capacity (y-axis) M_iy ≤ M_ry [Ref : Cl - 8.4.4.2.2]

M_sy{[1-(1+ẞm/2)3](1-Ny/ϕN_cy) + 1.18(1+ẞm/2)3√(1-Ny/ϕN_cy)} = 101.40 kN·m

ϕM_iy =91.26 kN·m

Member Out- of- plane Capacity (Tension) [Ref : Cl - 8.4.4.2]

M_ozt = M_bz(1 + N/ϕN_t) =712.12 kN·m

Nominal out-plane member moment capacity,M_ozt = 711.00 kN·m

ϕM_ozt = 639.90 kN·m

Member Out-of-plane Capacity(Compression) M_oz ≤ M_rz [Ref : Cl - 8.4.4.1]

M_oz = M_bz(1 - N/ϕN_cy) = 703.43 kN·m

ϕM_ozc = 633.09 kN·m

Member Biaxial Capacity (Compression)

M_cz = 709.63 kN·m

ϕM_cz = 638.67 kN·m

(M_z/ϕM_cz)1.4+(M_y/ϕM_iy)1.4 = 0.139

Member Biaxial Capacity (tension)

M_tx = 711.00 kN·m

ϕM_tx = 639.90 kN·m

(M_z/ϕM_tz)1.4+(M_y/ϕM_ry)1.4 = 0.116

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
ϕM_sz ( kN·m )	639.9	639.9001	Negligible
ϕM_sy ( kN·m )	92.23	92.2392	Negligible
ϕM_bz ( kN·m )	639.9	639.900	None
ϕV_y (kN)	939.4	939.4	None
ϕV_z (kN)	1,056	1,056.4	Negligible
ϕN_s (kN)	2,931	2,921.3	Negligible
ϕN_cz (kN)	2,600	2,599	None
ϕN_cy (kN)	470	469.7	None
ϕM_rz ( kN·m )	639.900	639.900	None
ϕM_ry ( kN·m )	92.239	92.239	None
ϕM_iz ( kN·m )	638.7849	638.7849	None
ϕM_iy ( kN·m )	91.2744	91.2744	None
ϕM_ozc ( kN·m )	633.09	633.09	None
ϕM_ozt ( 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\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]     |
 |----------------------------------------------------------------------------------|