V. NZS3404 1997-Tube Section Non Compact

Verify the design capacity of a pipe section per the NZS3404 1997 code.

Details

Verify the capacity of a PIP3239H member. Steel grade = 250 MPa. The simply supported span is 9 m with a 60 kN load at mid-span.

Validation

Section Classification

Evaluate the slenderness effects of the pipe member:

Section classification is non-compact ( )

Section Bending Capacity About Z-Axis

Effective Section Modulus for a compact section:

Effective section modulus for a non-compact section:

The nominal section capacity in bending about Z axis, ϕM_s = ϕf_y×Z_e

M_s = 250× 633.1×10³/10⁶ = 158.3 kN·m

ϕM_sz = 0.9×158.3 = 142.4 kN·m

Member Bending Capacity

End restraint arrangement = LL

A twist restraint factor, K_t (SKT) = 1.00

Minor axis rotation restraints = Both

Lateral rotation restraint factor, K_r (SKR) = 1.0

Load Height factor, Kl, (LHT) = 1.00 [Ref : Table 5.6.3(2)]

Effective length = 1×1×1×9,000 = 9,000 mm

α_m = 1

([Ref: Cl no -5.6.1.1 (b)])

Reference buckling moment, M_o

α_s = 1

([Ref : Clause 5.6.1.1 (c)])

Member bending capacity, M_bz

M_bz = α_mα_sM_sz ≤ M_sz

M_bz = 1 × 1 × 158.2 = 158.3 kN·m ≤ (M_sz, M_sy)_Max.

([Ref : Clause 5.6.1.1.1(a)])

ϕM_bz = 0.9×158.3 = 142.4 kN·m

Check for Shear

Nominal shear capacity, V_z , of a circular hollow section: [Ref. Cl no 5.11.4.2]

V_y = 0.36×f_y×A_e = 0.36×250×6,290×10^-3 = 566.1 kN

ϕV_y = 0.9×566.1 = 509.5 kN

Nominal shear capacity, V_y , of a circular hollow section: [Ref. Cl no 5.12.2]

Design bending moment, M = 135 kN·m

0.75×ϕ×M_s ≤ M ≤ ϕ×M_s

0.75×142.4 = 106.8 kN·m

ϕV_y = 0.9 × 386.9 = 348.3 kN

Check for Axial Capacity

Section Compression Capacity:

Gross Area, A_g = 6,290 mm²

The effective outside diameter is the minimum of d_e1 , d_e2 , and d_o :

The effective outside diameter = d_o = 323.9 mm

Net Area, A_n = 6,290 mm²

Form factor, K_f = A_e/A_g = 1.0

The nominal member section capacity for axial compression,

N_s = K_f×A_n×f_y = 1.0×6,290×250 = 1,573 kN

([Ref : Clause 6.2.1])

ϕN_s = 0.9×1,573 = 1,415 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

Geometrical Slenderness Ratio = L_ey/r_y = L_ez/r_z = 9,000 / 112.3 = 80.13

Member slenderness,

([Ref : Clause 6.3.3])

α_b = -0.5

([Ref : Table 6.3.3(2)])

λ = λ_n + α_a×α_b = 70.48

η = 0.19

The nominal member capacity,

N_cy = N_cz= α_cz×N_s =0.74×1,573 = 1,171 kN

([Ref : Clause 6.3.3] )

ϕN_cy = ϕN_cz= 1,054 kN

Nominal Section tension Capacity

[Ref : Clause 7.1]

K_te = 1.00

N_t1 = A_g×f_y = 6,290 × 250×10^-3 = 1,573 kN

N_t2 = 0.85×K_te×A_n×f_u = 0.85(1.0)(6,290)(250×10^-3) = 1,711 kN

ϕN_t = 0.9×1,573 = 1,415 kN

([Ref : Clause 5.6.1.1.1(a)])

Results

Table 1. Comparison of results
Result Type	Reference	STAAD.Pro	Difference
ϕM_sz (kN·m)	142.4	142.4352	negligible
ϕM_sy (kN·m)	142.4	142.4352	negligible
ϕM_bz (kN·m)	142.4	142.4352	negligible
ϕV_y (kN)	348.3	348.022	negligible
ϕV_z (kN)	509.5	509.16	negligible
ϕN_s (kN)	1,415	1,414.3	negligible
ϕN_cz (kN)	1,054	1,054	none
ϕN_cy (kN)	1,054	1,054	none
ϕN_t (kN)	1,415	1,415.3	negligible

STAAD.Pro Input File

The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\New Zealand\NZS3404 1997-Tube Section Non Compact.std is typically installed with the program.

STAAD SPACE
*
*  INPUT FILE: NZS3404_Tube_Section_Non_Compact.STD
*
* REFERENCE : Hand Calculation
*
*  OBJECTIVE : TO DETERMINE THE ADEQUACY OF TUBE 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; 5 3 0 0; 6 6 0 0;
*
MEMBER INCIDENCES
1 1 5; 2 5 6; 3 6 4;
DEFINE PMEMBER
1 TO 3 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
*
UNIT MMS NEWTON
MEMBER PROPERTY INDIAN
1 TO 3 TABLE ST PIP3239H
*
UNIT METER KN
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 4 FIXED BUT FX MY MZ
PRINT ALL
*
LOAD 1 LOADTYPE None  TITLE LOAD CASE 1
MEMBER LOAD
2 CON GY -60
PERFORM ANALYSIS
PRINT ANALYSIS RESULTS
*
PARAMETER 1
CODE NZS3404 1997
BEAM 1 PMEMB 1
IST 2 PMEMB 1
SGR 6 PMEMB 1
SKL 1 PMEMB 1
SKR 1 PMEMB 1
SKT 1 PMEMB 1
TRACK 2 PMEMB 1
DUCT 3 PMEMB 1
GLD 1 PMEMB 1
CHECK CODE ALL
*
FINISH

STAAD.Pro Output

 STEEL DESIGN    
   ***NOTE : SGR NOT SPECIFIED OR "DEFAULT" SPECIFIED FOR MEMBER NO.      1.
   ***NOTE : BY DEFAULT "AS 1163 C250" WILL BE USED FOR HOLLOW SECTIONS.
   ***NOTE : SGR NOT SPECIFIED OR "DEFAULT" SPECIFIED FOR MEMBER NO.      2.
   ***NOTE : BY DEFAULT "AS 1163 C250" WILL BE USED FOR HOLLOW SECTIONS.
   ***NOTE : SGR NOT SPECIFIED OR "DEFAULT" SPECIFIED FOR MEMBER NO.      3.
   ***NOTE : BY DEFAULT "AS 1163 C250" WILL BE USED FOR HOLLOW SECTIONS.
 |----------------------------------------------------------------------------------|
 |  Member Number:      1                                                           |
 |  Member Section:  ST   PIP3239H        (AISC SECTIONS)                           |
 |  Status: PASS  Ratio:   0.647  Critical Load Case:     1  Location:       1.00   |
 |  Critical Condition: Cl.5.1                                                      |
 |  Critical Design Forces:  (Unit: KN    METE)                                     |
 |      FX:       0.000E+00 T     FY:     -30.000E+00      FZ:       0.000E+00      |
 |      MX:       0.000E+00       MY:       0.000E+00      MZ:      90.000E+00      |
 |----------------------------------------------------------------------------------|
 |----------------------------------------------------------------------------------|
 |  Member Number:      2                                                           |
 |  Member Section:  ST   PIP3239H        (AISC SECTIONS)                           |
 |  Status: PASS  Ratio:   0.970  Critical Load Case:     1  Location:       0.50   |
 |  Critical Condition: Cl.5.1                                                      |
 |  Critical Design Forces:  (Unit: KN    METE)                                     |
 |      FX:       0.000E+00 T     FY:      30.000E+00      FZ:       0.000E+00      |
 |      MX:       0.000E+00       MY:       0.000E+00      MZ:    -135.000E+00      |
 |----------------------------------------------------------------------------------|
      STAAD SPACE                                              -- PAGE NO.   12 
    *                                           
                       STAAD.PRO CODE CHECKING - NZS-3404-1997 (v1.0)
                     **************************************************
 |----------------------------------------------------------------------------------|
 |  Member Number:      3                                                           |
 |  Member Section:  ST   PIP3239H        (AISC SECTIONS)                           |
 |  Status: PASS  Ratio:   0.647  Critical Load Case:     1  Location:       0.00   |
 |  Critical Condition: Cl.5.1                                                      |
 |  Critical Design Forces:  (Unit: KN    METE)                                     |
 |      FX:       0.000E+00 T     FY:     -30.000E+00      FZ:       0.000E+00      |
 |      MX:       0.000E+00       MY:       0.000E+00      MZ:     -90.000E+00      |
 |----------------------------------------------------------------------------------|