V. EC3 - Pipe Section with Conc Load
Verify the adequacy of a circular hollow section used as a beam subject to concentrated loads per EN 1993-1-1:2005 (no national annex used).
Details
The member is a 6 m long beam with pinned ends. The beam supports 10kN concentrated loads at the third points. The steel is grade S275. The section is a European 114.3X8CHS.
Section Properties
- A = 26.7 cm2
- Outer diameter = 114.3 mm
- t = 8 mm
- Iz = Iy = 379 cm4
- Zz = Zy = 90.6 cm3
- Cw = 0 cm6
Partial safety factors:
ΓM0 = 1.0
ΓM1 = 1.0
ΓM2 = 1.25
Validation
Section Classification
As per Table 5.2:
d / t = 114.3 / 8 = 14.3 < 50×ε2 = 50 (0.924)2 = 42.7
Hence, this is a Class 1 section.
Slenderness Ratio
The slenderness ratio = kL / r = 1 × 6,000 / 37.68 = 159.3
Axial Tension
Determine axial tension capacity per Cl. 6.2.3.
The tensile capacity is the minimum of Npl,Rd and Nu,Rd, thus: Nt,Rd = 567.1 kN.
No axial tension in section, so by observation no need to check ratio.
Axial Compression
Determine axial compression capacity per Cl. 6.2.4 for a Class 1 section.
Next, check the flexural buckling resistance per Cl. 6.3.1.3:
From Table 6.1: the imperfection factor, ɑ = 0.21.
where= | ||
= | ||
= |
ƛ = 1.834
The compression capacity is the minimum of Nc,Rd and Nb,Rd, thus: Nc,Rd = 191.7 kN.
No axial compression in section, so by observation no need to check ratio.
Bending Capacity
Maximum bending moment in the section (center third of span): MEd = 20.0 kN·m.
Check for bending capacity per Cl. 6.2.5:
For a Class 1 section:
Ratio per Eq. 6.12: MEd / Mc,Rd = 20.0 / 24.92 = 0.803
Shear Capacity
Maximum shear in the section: VEd = 10 kN
Check for shear capacity per Cl. 6.2.6 for plastic design (Class 1):
Ratio per Eq. 6.17: VEd / Vc,Rd = 10.0 / 26.9 = 0.037Lateral Torsional Buckling
where= | ||
= | ||
= | ||
= | ||
= | ||
= |
Therefore,
For CHS sections, χLT = 1.0.
Ratio per Eq. 6.12: MEd / Mb,Rd = 20.0 / 24.92 = 0.803
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Section Class | Class 1 | Class 1 | none | |
Slenderness Ratio | 159.3 | 159.3 | none | |
Tension Capacity (kN) | 567.1 | 567.1 | none | |
Compression Capacity (kN) | 191.7 | 191.7 | none | |
Moment Capacity (kN·m) | 24.92 | 24.9 | negligible | |
Shear Area (cm2) | 17.0 | 16.99 | negligible | |
Shear Capacity (kN) | 269.9 | 269.9 | none | |
MB (kN·m) | 24.92 | 24.9 | negligible | |
Ratio per Cl. 6.2.5 | 0.803 | 0.803 | none | |
Ratio per Cl. 6.2.6 (Y) | 0.037 | 0.037 | none | |
Ratio per Cl. 6.3.2 LTB | 0.803 | 0.803 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2023\Samples \Verification Models\09 Steel Design\Europe\EC3 - Pipe Section with Conc Load.std is typically installed with the program.
- Symmetric point loads about mid-span: CMM 5
- Use Cl. 6.3.2.2 to determine χLT: MTH 1
- The values of C1 1.0 and C2 1.0 are specified.
- The values of Fy and Fu are specified directly using PY 275000 and FU 295000.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 07-May-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 6 0 0;
MEMBER INCIDENCES
1 1 2;
DEFINE MATERIAL START
ISOTROPIC STEEL
E 2.05e+08
POISSON 0.3
DENSITY 76.8195
ALPHA 1.2e-05
DAMP 0.03
END DEFINE MATERIAL
MEMBER PROPERTY EUROPEAN
1 TABLE ST 114.3X8CHS
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 PINNED
LOAD 1 LOADTYPE None TITLE LOAD CASE 1
MEMBER LOAD
1 CON GY -10 2
1 CON GY -10 4
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
C1 1 ALL
C2 1 ALL
CMM 5 ALL
MTH 1 ALL
FU 295000 ALL
PY 275000 ALL
TRACK 2 ALL
CHECK CODE ALL
PRINT MEMBER PROPERTIES ALL
FINISH
STAAD.Pro Output
STAAD.PRO CODE CHECKING - EN 1993-1-1:2005 ******************************************** NATIONAL ANNEX - NOT USED PROGRAM CODE REVISION V1.14 BS_EC3_2005/1 STAAD PLANE -- PAGE NO. 3 ALL UNITS ARE - KN METE (UNLESS OTHERWISE Noted) MEMBER TABLE RESULT/ CRITICAL COND/ RATIO/ LOADING/ FX MY MZ LOCATION ======================================================================= 1 ST 114.3X8CHS (EUROPEAN SECTIONS) PASS EC-6.2.5 0.803 1 0.00 0.00 20.00 2.00 ======================================================================= MATERIAL DATA Grade of steel = USER Modulus of elasticity = 205 kN/mm2 Design Strength (py) = 275 N/mm2 SECTION PROPERTIES (units - cm) Member Length = 600.00 Gross Area = 26.70 Net Area = 26.70 z-axis y-axis Moment of inertia : 379.000 379.000 Plastic modulus : 90.600 90.600 Elastic modulus : 66.317 66.317 Shear Area : 16.998 16.998 Radius of gyration : 3.768 3.768 Effective Length : 600.000 600.000 DESIGN DATA (units - kN,m) EUROCODE NO.3 /2005 Section Class : CLASS 1 Squash Load : 734.25 Axial force/Squash load : 0.000 GM0 : 1.00 GM1 : 1.00 GM2 : 1.25 z-axis y-axis Slenderness ratio (KL/r) : 159.3 159.3 Compression Capacity : 191.7 191.7 Tension Capacity : 567.1 567.1 Moment Capacity : 24.9 24.9 Reduced Moment Capacity : 24.9 24.9 Shear Capacity : 269.9 269.9 BUCKLING CALCULATIONS (units - kN,m) Lateral Torsional Buckling Moment MB = 24.9 co-efficients C1 & K : C1 =1.000 K =1.0, Effective Length= 6.000 Lateral Torsional Buckling Curve : Compression buckling curves: z-z: Curve a y-y: Curve a STAAD PLANE -- PAGE NO. 4 CRITICAL LOADS FOR EACH CLAUSE CHECK (units- kN,m): CLAUSE RATIO LOAD FX VY VZ MZ MY EC-6.2.5 0.803 1 0.0 10.0 0.0 20.0 0.0 EC-6.2.6-(Y) 0.037 1 0.0 10.0 0.0 0.0 0.0 Torsion has not been considered in the design. _________________________ ************** END OF TABULATED RESULT OF DESIGN **************