MPa Nfmm
12.23.2.2 Buckling in the strong inertia of the profile (along Y-Y)
The calculations are made in order to obtain the work ratio of the analyzed element. The work ratio of the element is calculated using the percentage of the design buckling resistance of the compressed element (Nb,Rd) from the compression force applied to the element (NEd). The design buckling resistance of the compressed member, Nb,Rd, is calculated according to Eurocode 3 1993-1-1-2005, Chapter 6.3.1.1.
% 100 100
,
≤
×
Rd b
N
EdN
(6.46)Cross-class classification is made according to Table 5.2
778 . 3 34
. 6
1 .
219 =
= mm
mm t
d
814 . 355 0 235
235 = =
= f
yε
381 . 46 814 . 0 50 80
778 .
34 ≤ ×
2= × =
= ε
d
It will be used the following buckling curve corresponding to Table 6.2:
The imperfection factor
α
corresponding to the appropriate buckling curve will be 0.21:The design buckling resistance of the compressed element is calculated using the next formula:
1
Coefficient corresponding to non-dimensional slenderness after the Y-Y axis
χ
coefficient corresponding to non-dimensional slendernessλ
will be determined from the relevant buckling curve according to:1 1
λ
the non-dimensional slenderness corresponding to Class 1, 2 and 3 cross-sections:1
The design buckling resistance of the compression member will be:
mm N N f mm
N A
M y y
Rd
b
950533 . 8
1
/ 355 4210
636 .
0
2 21
,
× × = × × =
= γ
χ
N N
Ed= 100000
% 520 . 10 8 100
. 950533
100000 100
,
=
×
=
× N
N N
N
Rd b
Ed
Finite elements modeling
■ Linear element: S beam,
■ 4 nodes,
■ 1 linear element.
Finite elements results
The appropriate non-dimensional slenderness The appropriate non-dimensional slenderness
χ
LTRatio of the design normal force to design buckling resistance in the strong inertia of the profile Column subjected to axial force
Adimensional - SNy
12.23.2.3 Reference results
Result name Result description Reference value
χ
yχ
ycoefficient corresponding to non-dimensional slendernessλ
y 0.636SN
y Ratio of the design normal force to design buckling resistance in thestrong inertia of the profile 0.1052
12.23.3Calculated results
Result name Result description Value Error
Xy coefficient corresponding to non-dimensional slenderness 0.635463 adim 0.0000 % SNy Ratio of the design normal force to design buckling
resistance in the strong inertia of the profile 0.105293 adim 0.0000 %
12.24 EC3 / NF EN 1993-1-1/NA - France: Verifying the lateral torsional buckling of a IPE300 beam (evaluated by SOCOTEC France - ref. Test 22)
Test ID: 5702 Test status: Passed
12.24.1Description
The test verifies the lateral torsional buckling of a IPE300 beam made of S235 steel.
The calculations are made according to Eurocode 3, French Annex.
12.24.2Background
Lateral torsional buckling verification for an unrestrained IPE300 beam subjected to axis bending efforts, made of S235 steel. The beam is simply supported. The beam is subjected to a uniform vertical load (10 000 N) applied constantly on the entire length. The dead load will be neglected.
This test was evaluated by the French control office SOCOTEC.
12.24.2.1 Model description
■ Reference: Guide d’evaluation Advance Design, EN 1993-1-1: 2005;
■ Analysis type: static linear (plane problem);
■ Element type: linear.
The following load case and load combination are used:
■ Exploitation loadings (category A): Q1 = -10 000 N,
■ The ultimate limit state (ULS) combination is: Cmax = 1 x Q
■ Cross section dimensions are in millimeters (mm).
Units
Metric System
Geometrical properties
S235 steel material is used. The following characteristics are used:
■ Yield strength fy = 235 MPa,
■ Longitudinal elastic modulus: E = 2.1 x 105 MPa.
Boundary conditions
The boundary conditions are described below:
■ Outer:
► Support at start point (x = 0) restrained in translation along X, Y and Z axis,
► Support at the end point (z = 3.00) restrained in translation along Y and Z axis and restrained rotation along X axis.
■ Inner: None.
Loading
The column is subjected to the following loadings:
■ External: Linear load From X=0.00m to X=5.00m: FZ = N = -10 000 N,
■ Internal: None.
12.24.2.2 Buckling in the strong inertia of the profile (along Y-Y)
The calculations are made in order to obtain the work ratio of the analyzed element. The work ratio of the element is calculated using the percentage of the design buckling moment resistance of the bended element (Mb,Rd) from the designed value moment (MEd) produced by the linear force applied to the element (NEd). The design buckling resistance of the compressed member, Nb,Rd, is calculated according to Eurocode 3 1993-1-1-2005, Chapter 6.3.1.1.
%
Cross-class classification is made according to Table 5.2
■ for beam web:
therefore the beam web is considered to be
Class 1
therefore the haunch is considered to be Class1
In conclusion, the section is considered to be Class 1
The buckling curve will be determined corresponding to Table 6.2:
2 150 2
300 = ≤
= mm
mm b
h
the buckling curve about Y-Y will be considered “a”The design buckling resistance moment against lateral-torsional buckling is calculated according the next formula:
, 1
M y y LT Rd b
f M W
γ
χ × ×
=
(6.55)Where:
χ
LTreduction factor for lateral-torsional buckling:1 1
2
2
≤
− Φ +
= Φ
LT LT LT
LT
λ
χ
(6.56)λ
LTthe non-dimensional slenderness corresponding:Mcr is the elastic critical moment for lateral-torsional buckling, is based on gross cross sectional properties and takes into account the loading conditions, the real moment distribution and the lateral restraints.
( ) ( ) ( )
according to EN 1993-1-1-AN France; AN.3 Chapter 2 Where:
E is the Young’s module: E=210000N/mm2 G is the share modulus: G=80770N/mm2
Iz is the inertia of bending about the minor axis Z: Iz=603.8 x104mm4 It is the torsional inertia: It=20.12x104mm4
IW is the warping inertia (deformation inertia moment): Iw=12.59x1010mm6 L is the beam length: L=5000mm
kz and kw are buckling coefficients
zg is the distance between the point of load application and the share center (which coincide with the center of gravity)
C1 and C2 are coefficients depending on the load variation over the beam length
If the bending moment is linear along the bar, if there are no transversal loads or if the transverse load is applied to the center, then C2xxg=0 and the Mcr formula become:
The C1 coefficient is chosen from the Table2 of the EN 1993-1-1-AN France; AN.3 Chapter 3.3:
kNm
therefore:
063
Finite elements modeling
■ Linear element: S beam,
■ 6 nodes,
■ 1 linear element.
Finite elements results
The steel calculation results can be found in the Shape Sheet window. The “Class” tab shows the classification of the cross section and the effective characteristics (not applicable in this case, as the cross section is class 1).
Lateral torsional buckling coefficient Simply supported beam subjected to bending efforts
Lateral torsional buckling coefficient
Elastic critical moment for lateral-torsional buckling Simply supported beam subjected to bending efforts
Mcr
12.24.2.3 Reference results
Result name Result description Reference value
χ
LT Lateral-torsional buckling coefficient [adim.] 0.621Mcr Elastic critical moment for lateral-torsional buckling [kNm] 130.61
12.24.3Calculated results
Result name Result description Value Error
XLT Lateral-torsional buckling coefficient 0.621588
adim 0.0947 %
Mcr Elastic critical moment for lateral-torsional buckling 130.699
kN*m 0.0681 %
12.25 EC3 / NF EN 1993-1-1/NA - France: Verifying the design plastic shear resistance of a rectangular hollow section beam (evaluated by SOCOTEC France - ref. Test 12)
Test ID: 5706 Test status: Passed
12.25.1Description
Verifies the design plastic shear resistance of a rectangular hollow section beam made of S275 steel.
The verification is made according to Eurocode 3 (EN 1993-1-1) French Annex.
12.25.2Background
Verifies the adequacy of a rectangular hollow section beam made of S275 steel to resist shear. Verification of the shear resistance at ultimate limit state is realised. The name of the cross-section is RC3020100 and can be found in the Advance Design OTUA library. The beam is simply supported and it is subjected to an uniformly distributed load (50 000 N/ml) applied at its top. The dead load will be neglected.
This test was evaluated by the French control office SOCOTEC.
12.25.2.1 Model description
■ Reference: Guide d’evaluation Advance Design, EN 1993-1-1: 2001;
■ Analysis type: static linear (plane problem);
■ Element type: linear.
The following load case and load combination are used:
■ Exploitation loadings (category A), Q:
► Fz = -50 000 N/ml,
■ The ultimate limit state (ULS) combination is: Cmax = 1 x Q
■ Cross section dimensions are in milimeters (mm).
Units
Metric System Geometry
Below are described the beam cross section characteristics:
■ Height: h = 300 mm,
Materials properties
S275 steel material is used. The following characteristics are used:
■ Yield strength fy = 275 MPa,
■ Longitudinal elastic modulus: E = 2.1 x 105 MPa.
Boundary conditions
The boundary conditions are described below:
■ Outer:
► Support at start point (x = 0) restrained in translation along X, Y and Z axis,
► Support at end point (x = 5.00) restrained in translation along Y, Z axis and restrained in rotation along X axis.
■ Inner: None.
Loading
The beam is subjected to the following loadings:
■ External:
► Uniformly distributed load: q = Fz = -50 000 N/ml,
■ Internal: None.