Verify the bending and compression capacity of a pipe section for bending and compression
per the AS4100:2020 code.
Reference
Standards Australia Committee BD-001. Steel structures AS 4100-2020.
Homebush, NSW. 2020.
Problem
A 9 m long, simply supported beam has a pipe cross section. The pipe outer diameter
is 300 mm OD and the thickness is 2.5 mm. The member is subjected to a 8.4 kN
vertical concentrated load at midspan along with a 25 kN axial force. The steel is
grade AS/NZS 1163 C450.
Material Properties
From references # 1:
Yield strength, fy = 450
MPa
Modulus of elasticity, E = 200,000
MPa
Shear modulus, G = 80,000 MPa
Calculations
Design Forces
Mz = ¼ PL = ¼ (8.4) (9) = 18.9 kN·m
Vy = ½ (8.4) = 4.2 kN
Fx = 25
kN
Section Properties
Outer diameter, D = 300 mm
Thickness, t = 2.5 mm
Inner diameter, d = 300 - 2× 2.5 = 295
mm
Gross area of section,
Moment of inertia,
Radius of gyration,
Elastic section modulus,
Plastic section modulus,
Torsional moment of inertia,
Warping constant, Iw = 0
(hollow, closed section)
Section Slenderness
(5.2.2)
λe > λey = 120, thus
the section is slender.
Bending Capacity
The effective section modulus:
The nominal moment capacity:
Ms = Zefy =
128.4× 450 ×(10)-3 = 57.8 kN·m
ϕMs = 0.90 (57.8) = 52.0
kN·m
Capacity ratio for bending about the z axis:
The moment modification
factor:
(5.6.1.1
(iii))
where
Mm
=
The maximum moment, Mz = 18.9
kN·m
M1
=
The moment at the ¼ point along the span, =
9.45 kN·m
M2
=
The moment at mid-span, = 18.9
kN·m
M3
=
The moment at the ¾ point along the span, =
9.45 kN·m
Assume that the length coefficients,
kt,
kl, and
kr are all equal 1.0.
Therefore, le = L = 9,000
mm
(5.6.1.1 (3))
The slenderness reduction factor:
(5.6.1.1 (2))
Both αm and
αsz are greater than
1.0, therefore ϕMbz = ϕMs = 52.0
kN·m
Nominal Section Capacity
The effective outside diameter, where λey =
82 per Table 6.2.4 :
The effective inner diameter, de = 148.8 - 2 ×
2.5 = 179.8 mm. The effective area of the section:
The file C:\Users\Public\Public Documents\STAAD.Pro
2024\Samples\Verification Models\09 Steel Design\Australia\AS4100 2020 - CHS Bending and Compression.std is typically installed with the program.
The 9 m physical member is modelled using three 3 m long analytical
segments
STAAD SPACE
START JOB INFORMATION
ENGINEER DATE 14-Jun-17
END JOB INFORMATION
INPUT WIDTH 79
*
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 3 0 0; 3 6 0 0; 4 9 0 0;
*
MEMBER INCIDENCES
1 1 2; 2 2 3; 3 3 4;
DEFINE PMEMBER
1 TO 3 PMEMBER 1
START USER TABLE
TABLE 1
UNIT METER KN
PIPE
PIP300X2.5
0.3 0.295 1 1
END
*
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
1 TO 3 UPTABLE 1 PIP300X2.5
CONSTANTS
MATERIAL STEEL ALL
*
SUPPORTS
1 PINNED
4 FIXED BUT FX MY MZ
PRINT ALL
*
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
2 CON GY -8.4
JOINT LOAD
4 FX -25
*
PERFORM ANALYSIS
*
PRINT ANALYSIS RESULTS
*
PARAMETER 1
CODE AS4100 2020
SGR 4 PMEMB 1
TRACK 2 PMEMB 1
CHECK CODE PMEMB ALL
*
FINISH
STAAD.Pro Output
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
ALL UNITS ARE IN - KN MET UNLESS OTHERWISE Noted
**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 [AS4100 Table 3.4]
3. (#) next to Young's modulus E indicates that its value is not 200000 MPa as per AS4100 1.4.
- PMember : 1
|-----------------------------------------------------------------------------|
| PMember No: 1 PROFILE: ST PIP300X2.5 (UPT) |
| STATUS: PASS RATIO: 0.475 LOADCASE: 1* |
| LOCATION: 0.00 CRITERIA: SLENDERNESS |
| FX: 25.0000 C VY: 4.20000 VZ: 0.00000 |
| MX: 0.00000 MY: 0.00000 MZ: 0.00000 |
|-----------------------------------------------------------------------------|
| SLENDERNESS |
| Actual Slenderness : 85.563 |
| Allowable Slenderness: 180.000 |
|-----------------------------------------------------------------------------|
| SECTION PROPERTIES (Unit:mm) |
| Ag : 2.3366E+03 Azz : 1.0000E+06 Ayy : 1.0000E+06 |
| Izz : 25.8519E+06 Iyy : 25.8519E+06 J : 51.7038E+06 |
| Szz : 221.2647E+03 Syy : 221.2647E+03 Iw : 0.0000E+00 |
| Zzz : 172.3461E+03 Zyy : 172.3461E+03 |
| rz : 105.1858E+00 ry : 105.1858E+00 |
|-----------------------------------------------------------------------------|
| Material PROPERTIES (Unit:MPa) |
| Material Standard : AS 1163 |
| Nominal Grade : 450 |
| Residual Stress Category : HW (Heavily welded longitudinally) |
| E (#) : 205.0000E+03 G : 80.00E+03 |
| Fy(Flange): 450.0000E+00 Fy(Web): 450.0000E+00 Fu: 500.0000E+00|
|-----------------------------------------------------------------------------|
| Actual Member Length: 9.000 |
| Design Parameters |
| KZ : 1.00 KY : 1.00 NSF 1.00 PHI 0.90 |
| SKL: 1.00 SKT: 1.00 SKR 1.00 |
|-----------------------------------------------------------------------------|
| SECTION CLASSIFICATION |
| Z - Axis : Slender Y - Axis : Slender |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 13
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL TENSION |
|-----------------------------------------------------------------------------|
| Section Tension Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 893.7369E+00 0.000 Cl:7.2 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 2.3366E+03mm^2 Correction Factor (Kt) : 1.00|
|-----------------------------------------------------------------------------|
| CHECKS FOR AXIAL COMPRESSION |
|-----------------------------------------------------------------------------|
| Section Compression Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 25.0000E+00 580.0117E+00 0.043 Cl:6.2.1 1* 0.00 |
| Intermediate Results : |
| Net Area (An) : 2.3366E+03mm^2 |
| Effective Area (Ae) : 1.4321E+03mm^2 Ref : Cl. 6.2.3 / 6.2.4 |
| Form Factor (Kf) : 0.613 Ref : Cl. 6.2.2 |
|-----------------------------------------------------------------------------|
| Member Compression Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 25.0000E+00 391.9326E+00 0.064 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Lez): 9.00 m |
| ab : -0.5000 Table 6.3.3(1)/6.3.3(2) |
| ln,z : 89.8718 AS 4100, 6.3.3 |
| aa,z : 18.3253 AS 4100, 6.3.3 |
| l,z : 80.7091 AS 4100, 6.3.3 |
| h,z : 0.2191 AS 4100, 6.3.3 |
| x,z : 1.2580 AS 4100, 6.3.3 |
| ac,z : 0.6757 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
| Member Compression Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 25.0000E+00 391.9326E+00 0.064 Cl:6.3.3 1* 0.00 |
| Intermediate Results : |
| Effective Length (Ley): 9.00 m |
| ab : -0.5000 Table 6.3.3(1)/6.3.3(2) |
| ln,y : 89.8718 AS 4100, 6.3.3 |
| aa,y : 18.3253 AS 4100, 6.3.3 |
| l,y : 80.7091 AS 4100, 6.3.3 |
| h,y : 0.2191 AS 4100, 6.3.3 |
| x,y : 1.2580 AS 4100, 6.3.3 |
| ac,y : 0.6757 AS 4100, 6.3.3 |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 14
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR SHEAR |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 306.6043E+00 0.000 Cl:5.11.2 1* 0.25 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmz) : 306.6043E+00 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| Section Shear Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 4.2000E+00 306.6043E+00 0.014 Cl:5.11.2 1* 0.25 |
| Intermediate Results : |
| Combined Shear Capacity (fVvmy) : 306.6043E+00 Ref : 5.12.3 |
|-----------------------------------------------------------------------------|
| CHECKS FOR BENDING |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Z - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 18.9000E+00 52.0261E+00 0.363 Cl:5.2.1 1* 4.50 |
| Intermediate Results : |
| Eff. Section Modulus (Zez): 128.4595E-06 |
|-----------------------------------------------------------------------------|
| Section Bending Capacity: Y - Axis |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 0.0000E+00 52.0261E+00 0.000 Cl:5.2.1 1* 4.50 |
| Intermediate Results : |
| Eff. Section Modulus (Zey): 128.4595E-06 |
|-----------------------------------------------------------------------------|
| Member Bending Capacity: |
| DEMAND CAPACITY RATIO REFERENCE L/C LOC |
| 18.9000E+00 52.0261E+00 0.363 Cl:5.6.1.1(a) 1* 4.50 |
| Intermediate Results : |
| Twist Restraint Factor (kt) : 1.00 Table 5.6.3(1) |
| Load Height Factor (kl) : 1.00 Table 5.6.3(2) |
| Lat. Rot. Restraint Factor (kr) : 1.00 Table 5.6.3(3) |
| Effective Length (le) : 9.00 5.6.3 |
| Moment Modification Factor (am) : 1.39 5.6.1.1(a)(iii) |
| Reference Buckling Moment (Mo) : 1.6343E+03 5.6.1.2(a) |
| Slenderness Reduction Factor(asz) : 1.018 5.6.1.1(a)(iv) |
|-----------------------------------------------------------------------------|
STAAD SPACE -- PAGE NO. 15
STAAD.Pro CODE CHECKING - ( AS4100-2020 )
************************************************
|-----------------------------------------------------------------------------|
| CHECKS FOR COMBINED INTERACTION |
|-----------------------------------------------------------------------------|
| Section Combined Capacity: |
| RATIO REFERENCE L/C LOC |
| 0.406 Cl 8.3.4 1* 4.50 |
| Intermediate Results : |
| Axial Capacity (fNs/fNt) : 580.0117E+00 8.3.1 |
| Section Moment Capacity (fMsz) : 52.0261E+00 5.2.1 |
| Section Moment Capacity (fMsy) : 52.0261E+00 5.2.1 |
| Reduced Section Moment Capacity (fMrz) : 49.7836E+00 8.3.2 |
| Reduced Section Moment Capacity (fMry) : 49.7836E+00 8.3.3 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: In-plane |
| RATIO REFERENCE L/C LOC |
| 0.388 Cl:8.4.2.2 1* 4.50 |
| Intermediate Results : |
| Axial Capacity (fNcz) : 391.9326E+00 8.4.2.2 |
| Axial Capacity (fNcy) : 391.9326E+00 8.4.2.2 |
| Moment Capacity (fMiz) : 48.7075E+00 8.4.2.2 |
| Moment Capacity (fMiy) : 48.7075E+00 8.4.2.2 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Out-of-plane(Comp) |
| RATIO REFERENCE L/C LOC |
| 0.388 Cl:8.4.4.1 1* 4.50 |
| Intermediate Results : |
| Axial Capacity (fNcy) : 391.9326E+00 8.4.4.1 |
| Moment Capacity (fMbz) : 52.0261E+00 8.4.4.1 |
| Moment Capacity (fMozc) : 48.7075E+00 8.4.4.1 |
|-----------------------------------------------------------------------------|
| Member Combined Capacity: Biaxial(Comp) |
| RATIO REFERENCE L/C LOC |
| 0.266 Cl:8.4.5.1 1* 4.50 |
| Intermediate Results : |
| Moment Capacity (fMcz) : 48.7075E+00 8.4.5.1 |
| Moment Capacity (fMiy) : 48.7075E+00 8.4.5.1 |
|-----------------------------------------------------------------------------|