V. EC3 - Tube Section with UDL
Verify the adequacy of a tube section used as a beam subject to a uniform load per EN 1993-1-1:2005 (no national annex used).
Details
The member is a 5 m long beam with fixed ends. The member is subject to a 10 kN/m uniform load. The steel is grade S275. The section is a European TUB1201205.
Section Properties
- A = 22.9 cm2
- Depth, D = 120 mm
- Width, B = 120 mm
- t = 5 mm
- Iz = Iy = 503 cm4
- Zz = Zy = 97.6 cm3
- Cw = 0 cm6
Partial safety factors:
Validation
Section Classification
As per Table 5.2:
Hence, this is a Class 1 section.
Slenderness Ratio
The slenderness ratio = kL / r = 1 × 5,000 / 46.87 = 106.7
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 = 630.0 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.
The compression capacity is the minimum of Nc,Rd and Nb,Rd , thus: Nc,Rd = 322.4 kN.
No axial compression in section, so by observation no need to check ratio.
Bending Capacity
Maximum bending moment in the section (at fixed supports): MEd = 20.83 kN·m.
Check for bending capacity per Cl. 6.2.5:
For a Class 1 section:
Ratio per Eq. 6.12: MEd / Mc,Rd = 20.83 / 26.84 = 0.776
Shear Capacity
Maximum shear in the section (at fixed supports): VEd = 25 kN
Check for shear capacity per Cl. 6.2.6 for plastic design (Class 1):
Lateral Torsional Buckling
Therefore,
From Table 6.4, buckling curve d
is used. From Table 6.3, ɑLT =
0.76 for buckling curve d.
As per Cl. 6.3.2.1, tube sections are not susceptible to lateral-torsional buckling, so χLT = 1.0.
Ratio per Eq. 6.12: MEd / Mb,Rd = 20.83 / 26.84 = 0.776
Results
Result Type | Reference | STAAD.Pro | Difference | Comments |
---|---|---|---|---|
Shear Area (cm2) | 11.45 | 11.45 | none | |
Section Class | Class 1 | Class 1 | none | |
Slenderness Ratio | 106.7 | 106.7 | none | |
Tension Capacity (kN) | 630.0 | 629.8 | negligible | |
Compression Capacity (kN) | 322.4 | 322.4 | none | |
Moment Capacity (kN·m) | 26.84 | 26.8 | negligible | |
Shear Capacity (kN) | 181.8 | 181.8 | none | |
Mcr (kN·m) | 904.6 | 905.7 | negligible | |
MB (kN·m) | 26.84 | 26.8 | negligible | |
Ratio per Cl. 6.2.5 | 0.776 | 0.776 | none | |
Ratio per Cl. 6.2.6 (Y) | 0.138 | 0.138 | none | |
Ratio per Cl. 6.3.2 LTB | 0.776 | 0.776 | none |
STAAD.Pro Input
The file C:\Users\Public\Public Documents\STAAD.Pro 2024\Samples \Verification Models\09 Steel Design\Europe\EC3 - Tube Section with UDL.std is typically installed with the program.
- Fixed end supports with a uniform load:
CMM 2
- Fixed end supports:
CMN 0.5
- Use Cl. 6.3.2.2 to determine χLT
:
MTH 1
- The values of
C1 1.0
andC2 1.0
are specified. - The values of Fy
and Fu
are
specified directly using
PY 275000
andFU 295000
.
STAAD PLANE
START JOB INFORMATION
ENGINEER DATE 04-May-21
END JOB INFORMATION
INPUT WIDTH 79
UNIT METER KN
JOINT COORDINATES
1 0 0 0; 2 5 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 TUB1201205
CONSTANTS
MATERIAL STEEL ALL
SUPPORTS
1 2 FIXED
LOAD 1 LOADTYPE Dead TITLE LOAD CASE 1
MEMBER LOAD
1 UNI GY -10
PERFORM ANALYSIS
PARAMETER 1
CODE EN 1993-1-1:2005
C1 1 ALL
C2 1 ALL
CMM 2 ALL
CMN 0.5 ALL
MTH 1 ALL
PY 275000 ALL
FU 450000 ALL
KC 0 ALL
TRACK 2 ALL
CHECK CODE 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 TUB1201205 (EUROPEAN SECTIONS)
PASS EC-6.2.5 0.776 1
0.00 0.00 20.83 0.00
=======================================================================
MATERIAL DATA
Grade of steel = USER
Modulus of elasticity = 205 kN/mm2
Design Strength (py) = 275 N/mm2
SECTION PROPERTIES (units - cm)
Member Length = 500.00
Gross Area = 22.90 Net Area = 22.90
z-axis y-axis
Moment of inertia : 503.000 503.000
Plastic modulus : 97.600 97.600
Elastic modulus : 83.833 83.833
Shear Area : 11.450 11.450
Radius of gyration : 4.687 4.687
Effective Length : 500.000 500.000
DESIGN DATA (units - kN,m) EUROCODE NO.3 /2005
Section Class : CLASS 1
Squash Load : 629.75
Axial force/Squash load : 0.000
GM0 : 1.00 GM1 : 1.00 GM2 : 1.25
z-axis y-axis
Slenderness ratio (KL/r) : 106.7 106.7
Compression Capacity : 322.4 322.4
Tension Capacity : 629.8 629.8
Moment Capacity : 26.8 26.8
Reduced Moment Capacity : 26.8 26.8
Shear Capacity : 181.8 181.8
BUCKLING CALCULATIONS (units - kN,m)
Lateral Torsional Buckling Moment MB = 26.8
co-efficients C1 & K : C1 =1.000 K =0.5, Effective Length= 5.000
Lateral Torsional Buckling Curve : CURVE d
Elastic Critical Moment for LTB, Mcr = 905.7
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 0.776 1 0.0 25.0 0.0 20.8 0.0
EC-6.2.6-(Y) 0.138 1 0.0 25.0 0.0 20.8 0.0
Torsion has not been considered in the design.
_________________________
************** END OF TABULATED RESULT OF DESIGN **************