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Structural Applications of Ferritic Stainless Steels (SAFSS) RFSR-CT-2010-00026 (July 01, 2010 - June 30, 2013)
Work package 2: Structural performance of steel members
Deliverable 2.4: Report on parametric study and conclusions
Petr Hradil, Asko Tajla VTT, Technical Research Centre of Finland
Itsaso Arrayago, Marina Bock, Esther Real, Enrique Mirambell Departament d'Enginyeria de la Construcció,
Universitat Politècnica de Catalunya
Table of contents Overall buckling HRADIL, P., VTT-R-08483-12: Parametric study and conclusions, VTT research report Local buckling BOCK, M., REAL, E., MIRAMBELL, E., Report on parametric study and conclusions - Local buckling Web-crippling BOCK, M., REAL, E., MIRAMBELL, E., Parametric study and recommendations: Web-crippling
RESEARCH REPORT VTT-R-08438-12
Structural Applications of Ferritic Stainless Steels (SAFSS) WP2: Structural performance of steel members
Parametric study and conclusions
Authors: Petr Hradil
Confidentiality: Confidential until May 2014
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Preface The introduction of new material grades or fabrication methods in engineering structures always raises concerns about the validity of current design rules, especially those based on earlier material or member testing. One of the fundamental structural checks is the overall stability of beams and columns. In this report, a series of virtual buckling tests is calculated and compared to the Eurocode buckling curves. The main focus is on the applicability of ferritic steels that generally have different stress-strain behaviour than austenitic or duplex grades.
Espoo 11.12.2012
Authors
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Contents Preface ........................................................................................................................ 2
Abbreviations ............................................................................................................... 5
Introduction ............................................................................................................. 6 1 Cross-sections ........................................................................................................ 8 2
2.1 Welded I sections ............................................................................................ 8 2.2 Press-braked C sections ................................................................................. 9 2.3 Cold-rolled hollow sections ........................................................................... 11 2.4 Cross-sectional properties ............................................................................ 13
Material models .................................................................................................... 14 33.1 Initial modulus of elasticity ............................................................................ 14 3.2 Flat parts (basic) yield strength ..................................................................... 14 3.3 Nonlinear factor ............................................................................................. 14 3.4 Hardening rate .............................................................................................. 14 3.5 Model parameters ......................................................................................... 15 3.6 Residual stresses and work hardening from fabrication ................................ 16
Initial imperfections ............................................................................................... 22 44.1 Imperfections distribution .............................................................................. 22 4.2 Imperfections amplitude ................................................................................ 22
Utilization of the results ........................................................................................ 23 55.1 Basic calculations ......................................................................................... 25 5.2 Additional calculations .................................................................................. 26 5.3 Average material properties from tension tests ............................................. 26 5.4 Buckling curves plot ...................................................................................... 26 5.5 Nonlinear regression ..................................................................................... 27 5.6 Final buckling curves proposal ...................................................................... 27
Results ................................................................................................................. 28 66.1 Tension tests................................................................................................. 28
6.1.1 Welded I-sections .............................................................................. 29 6.1.2 Press-braked C sections .................................................................... 31 6.1.3 Cold-rolled hollow sections ................................................................ 33
6.2 Critical loads from buckling tests ................................................................... 34 6.3 Member lengths ............................................................................................ 38 6.4 Nondimensional slenderness ........................................................................ 38 6.5 Ultimate loads from buckling tests ................................................................ 39
6.5.1 Welded I sections ............................................................................... 40 6.5.2 Press-braked C sections .................................................................... 41 6.5.3 Cold-rolled hollow sections ................................................................ 42
6.6 Reduction factors .......................................................................................... 42 6.6.1 Minor axis flexural buckling of welded I sections ................................ 42 6.6.2 Major axis flexural buckling of welded I sections ................................ 43 6.6.3 Lateral-torsional buckling of welded I sections ................................... 44 6.6.4 Minor axis flexural buckling of press-braked C sections .................... 46 6.6.5 Torsional-flexural buckling of press-braked C sections ...................... 48 6.6.6 Minor axis flexural buckling of cold-rolled hollow sections ................. 50 6.6.7 Major axis flexural buckling of cold-rolled hollow sections ................. 52
6.7 Nonlinear regression ..................................................................................... 53
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Discussion ............................................................................................................ 55 77.1 Effect of material properties .......................................................................... 55 7.2 Effect of material thickness ........................................................................... 55 7.3 Effect of bending residual stress magnitude ................................................. 56 7.4 Effect of imperfection amplitude .................................................................... 57
Conclusions .......................................................................................................... 59 88.1 Recommendations ........................................................................................ 59
References ................................................................................................................ 62
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Abbreviations BSK 99 Swedish regulations for steel structures EN European standards FB Flexural buckling FEM Finite element method FSM Finite strip method GMNIA Geometrically and materially nonlinear analysis with imperfections LTB Lateral-torsional buckling TB Torsional buckling TFB Torsional-flexural buckling.
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Introduction 1Ferritic stainless steels are very competitive materials for load-bearing building structures, but they do not have such a long tradition as austenitic grades and a relatively low amount of experimental results from members is available to support design rules for such materials. The geometrically and materially nonlinear analysis on imperfect finite element models (GMNIA) has a great potential to simulate real experiments and, for instance, to computationally predict the buckling curve of a certain material and cross-section including the effects of fabrication such as enhanced strength and residual stress.
Series of numerical calculations were carried out to obtain parameters for overall buckling reduction calculation. Based on the material tests [1–9] review of available data [10], preliminary study [11, 12] and experiments [6] several important parameters were recognized that have to be taken into account by carrying out the parametric study.
(a) Buckling modes
The study covers flexural buckling (FB) to the major and minor axes, torsional-flexural buckling (TFB) and lateral-torsional buckling of beams (LTB). These modes are also recognised in Eurocode 3, where the reduction factors are given separately for compressed columns and members subjected to bending.
(b) Cross-sectional shapes and fabrication methods
Cold-formed open sections, hollow sections and welded open sections are the basic categories in Eurocode 3, Part 1-4. We selected cold-rolled (by circle-to-rectangle forming) hollow sections, press-braked open sections and welded I-sections in the present study because more detailed knowledge of the fabrication method was needed for accurate buckling strength prediction.
(c) Material nonlinearity
The value of the Ramberg-Osgood coefficient n is generally higher in ferritic steels (black markers in Figure 1) but it can decrease during fabrication. It should be noted that a higher nonlinear factor usually leads to a higher buckling strength.
(d) Strain hardening rate
The stress-strain relation beyond the yield point can be represented as the ratio of the ultimate stress σu or 1% proof stress σ1.0 and 0.2% proof stress σ0.2. This parameter does not significantly affect the buckling strength, but the lower hardening rate also means lower strength enhancement in corners, which can lead to differences in the average member strength. We extrapolated the collected experimental stress-strain curves to 40% strain and used the corresponding stress σ40 in Figure 1 instead of the real measured ultimate stress because the value of ultimate strain εu in the numerical models is always 40%. The lower limit of fu/fy ratio of stainless steels in Eurocode 3 is 1.1.
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(e) Design yield strength
The particular value of yield strength used in the member design does not significantly affect the buckling reduction factors, but it is essential to know to which of the following strengths it corresponds. Cold-formed profiles from sheets with virgin material strength σ0.2,v may have higher values of yield point in the flat parts σ0.2,f and corners σ0.2,c due to the fabrication. Therefore, the average yield strength fy,a can differ from the basic one fy,b and would require a new set of buckling curves.
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Cross-sections 2The study focuses on welded, press-braked and cold-rolled hollow sections. Sectional properties of welded I-sections were compared to the parameters of typical hot-rolled steel sections (IPE and HE). The selection of cold-formed cross-section geometrical properties was based on over 800 collected cross-sectional shapes from EN 1019-2, SCI database [13] and Stalatube Oy product range [14–16] in order to obtain buckling curves conservative for the most of typical cross-sections. The thickness of material in selected cross-sections is usually the higher bound of typical thin-walled structures because the effect of residual stresses and enhanced material properties, which is important in global buckling, and members with smaller material thickness may yield unsafe results.
2.1 Welded I sections
In case of welded I sections, the flexural buckling to both axes (FBx, FBy) was tested as well as lateral torsional buckling (LTB). The aspect ratio 3:1 (I 150x50x10x5) was used for minor axis buckling and lateral torsional buckling, and the ratio 1:1 (H 100x10x5) for major axis buckling (see Table 1).
As can be observed on Figure 1, Figure 2 and Table 1, the A/Wel ratio is always the higher bound of typical hot-rolled sections in the direction of buckling tests.
Figure 1. Area-to-section modulus about major axis in typical I sections.
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Figure 2. Area-to-section modulus about minor axis in typical I sections.
Collected experimental results [17–20] show that this ratio of tested I sections is between 0.47 and 1.54 cm-1 in minor axis buckling and 0.14 and 0.27 in major axis buckling. Although several special cross-sections were tested in compression where the A/Wel,x ratio was higher than 5 due to the higher width than height, these experiments were only stub column tests.
Table 1. Welded section parameters.
Basic Sections
H (mm)
B (mm)
tw (mm)
tf (mm)
A/Wel,x (cm-1)
A/Wel,y (cm-1)
WE3T5 150 50 5 10 0.21 1.97 WE1T5 100 100 5 10 0.28 0.72
Figure 3. Basic welded I sections.
2.2 Press-braked C sections
Press-braked C sections were tested in minor axis flexural buckling (FBy) and flexural torsional buckling (TFB). A/Wel ratio is also governing the imperfection factor in flexural buckling of lipped channels (see Figure 4) while in torsional
y
x
H
B
tw
t f
y
x
t f
tw B
H
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buckling the situation is not so clear. However, we will use this ratio for indication of the most suitable section as well (see Figure 5).
Figure 4. Area-to-section modulus about major axis in typical C sections.
Figure 5. Area-to-section modulus about minor axis in typical C sections.
Concerning rather limited deviation of C-section aspect ratios, we could use the same profile for both studies (see Table 2): Lipped channel 72x36x15x4 (aspect ratio 2:1, thickness 4 mm and average corner radius 6 mm).
Table 2. C sections parameters.
Basic Sections
H (mm)
B (mm)
C (mm)
t (mm)
A/Wel,x (cm-1)
A/Wel,y (cm-1)
ri/t Apb/A
PB2T4 72SAF 36 15 4 0.47 1.30 1.0 24%
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Figure 6. Basic press-braked C section.
2.3 Cold-rolled hollow sections
The rectangular hollow sections have been tested in major axis flexural buckling and minor axis flexural buckling. For each of the phenomena different cross-sectional parameters were selected. The highest ratio of cross-sectional area and elastic section modulus A/Wel was used (see Figure 7 and Figure 8). This ratio affects the imperfection factor directly, and therefore for the minor axis buckling (FBy) the most critical cross-section is with the highest aspect ratio, while the square hollow section was used in case of major axis buckling (FBx).
In buckling with eccentricity e the condition below should be fulfilled:
21 11
ele A Wχχ λ
⋅⋅ + = − ⋅
(1)
As can be seen on Figure 8, there are several cross-section with very high A/Wel ratio between 2.5 and 3.5 (the ratio is 3.4 for RHS 40x10x2). Such cross-sections were disregarded in our study because they are not typically used in engineering structures.
In the real experiments the A/Wel ratio is ranging from 0.15 to 1.0 in minor axis buckling and from 0.03 to 0.56 in major axis buckling. This data is collected from 193 minor axis flexural buckling experiments and 24 major axis flexural buckling experiments that are basis of Eurocode buckling curves described in the design manual commentary [20] and results published in [1, 2, 9, 21–27].
t
H
B
Cr
y
x
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Figure 7. Area-to-section modulus about major axis in typical cold-rolled hollow sections (SHS, RHS).
Figure 8. Area-to-section modulus about minor axis in typical cold-rolled hollow sections (SHS, RHS).
All the selected cross-sections have the average corner radius r = 6 mm and perimeter 192 mm. The ratios of internal corner radius and thickness ri/t and the corner area affected by work-hardening to the total cross-sectional area Acr/A chosen for the study are presented in Table 3.
Table 3. Hollow sections parameters.
Basic Sections
H (mm)
B (mm)
t (mm)
A/Wel.x (cm-1)
A/Wel.y (cm-1)
ri/t Acr/A
CR3T4 72 24 4 0.60 1.30 1.0 52% CR1T4 48 48 4 0.69 0.69 1.0 62%
Additional Sections
H (mm)
B (mm)
t (mm)
A/Wel.x (cm-1)
A/Wel.y (cm-1)
ri/t Acr/A
CR3T1 a) 72 24 1 1.02 0.54 5.5 30% CR3T2 a) 72 24 2 1.10 0.56 2.5 40%
a) used to study the effect of material thickness
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Figure 9. Basic cold-rolled hollow sections.
Only two cross-sections were used: RHS 72x24x4 (aspect ratio 3:1, thickness 4 mm) and SHS 48x4 (aspect ratio 1:1, thickness 4 mm) with the highest A/Wel ratio in their category (see Table 3).
2.4 Cross-sectional properties
The following properties (Table 4) were used for preliminary calculation of critical loads. Torsional properties were calculated using simplified cross sections (Figure 10) in CUTWP software [28].
Table 4. Cross-sectional properties of selected profile.
Basic Sections
A (mm2)
Ix (mm4)
Iy (mm4)
J (mm4)
Cw (mm6)
WE3T5 1700 6043330 209792 39167 1020830000 WE1T5 2400 4280000 - - - PB2T4 585.1 421331 91382 3121 107959000 CR3T4 662.8 - 61098 - - CR1T4 662.8 229034 - - -
Additional Sections
A (mm2)
Ix (mm4)
Iy (mm4)
J (mm4)
Cw (mm6)
CR3T1 a) 177.7 - - - - CR3T2 a) 347.4 - - - -
a) used to study the effect of material thickness
Figure 10. Cross-section simplification for TFB and LTB tests.
HB
t
r
y
x
H
B
t
y
xr
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Material models 3The effect of material nonlinearity and work-hardening from the fabrication is described by two important material parameters: the nonlinear factor n and the ratio of ultimate and yield strength fu/fy = σu/σ0.2.We used four groups of materials with different nonlinear factor n (groups A, B, C and D) varying from 5 to 40 and four levels of material hardening (groups 1, 1*, 2 and 2*) from 1.1 to 1.8. Their properties correspond to the basic materials in press-braked and welded sections and to the flat part materials in case of cold-rolled hollow sections. The initial modulus of elasticity E0 was always 200 GPa and the basic (flat parts) yield strength σ0.2 was selected as low as 250 MPa to produce conservative results. Stress-strain relationships are based on Mirambell and Real’s two stage model [5], where the ultimate strain εu and the second nonlinear parameter m are 0.4 and 3 respectively in all cases.
3.1 Initial modulus of elasticity
The average initial slope of stress-strain curve in stainless steels is approximately 200 GPa and it can be even decreased due to work hardening [6]. We used this value in the parametric study.
3.2 Flat parts (basic) yield strength
Basic yield strength fyb is equal to offset yield stress of the virgin material σ02,v in case of press-braked and welded sections. However, we used 0.2% proof stress of the flat parts σ02,f of cold-rolled hollow sections as the basic strength (fyf in the text) because it is the basis of Eurocode buckling curves [29] and due to lack of reliable models predicting strength enhancement in ferritic stainless steels [6]. This value can be provided by the producers and is also available in existing experimental studies. The yield strength variation has not significant influence on overall buckling [11], and therefore it can be as low as 250 MPa, which produces safe results.
3.3 Nonlinear factor
We used four groups of materials with different nonlinear factor n (Groups A, B, C and D) varying from 5 to 40.
Table 5. Nonlinear parameters n.
Basic Groups n valid for
A 5 5 ≤ n < 10 B 10 10 ≤ n < 20 C 20 20 ≤ n < 40 D 40 n ≥ 40
3.4 Hardening rate
In order to distinguish materials with almost ideally plastic behaviour and those with more significant hardening rate, two groups of materials were created with
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different σ10/σ02 (ratio of 1.0% proof and 0.2% proof stress) and σu/σ02 (ratio of ultimate and 0.2% proof stress).
Table 6. Hardening rate related to the 1.0% proof stress and ultimate strength.
Basic Groups 10 10 02σ σ σ= valid for 02u uσ σ σ= note
1 1.025 σ10 < 1.1σ02 1.1 EN ductility limit 2 1.100 σ10 ≥ 1.1σ02 1.4 -
Additional Groups σ10/σ02 valid for σu/σ02 Note
1* 1.050 - 1.2 - 2* 1.200 - 1.8 Material model limit
Two-stage material model was needed either Mirambell and Real’s [5] (with ultimate stress and strain) or Gardner’s [30] (with 1.0% proof stress) and several assumptions had to be made on the remaining parameters. If the second nonlinear parameter m is 3.0 in both cases, the engineering stress at 40% plastic strain can be obtained from Gardner’s model and inserted in Mirambell-Real’s model as an ultimate strain.
3.5 Model parameters
Sixteen different material models are described in Table 7.
Table 7. Model parameters.
Basic Models
E0 σ02 σ10 σu εu n m (GPa) (MPa) (MPa) (MPa)
Gro
up 1
A1 200 250 256.25 275 0.4 5 3 B1 200 250 256.25 275 0.4 10 3 C1 200 250 256.25 275 0.4 20 3 D1 200 250 256.25 275 0.4 40 3
Gro
up 2
A2 200 250 275 350 0.4 5 3 B2 200 250 275 350 0.4 10 3 C2 200 250 275 350 0.4 20 3 D2 200 250 275 350 0.4 40 3
Additional Models E0 σ02 σ10 σu εu n m
Gro
up1*
A1* 200 250 262.5 300 0.4 5 3 B1* 200 250 262.5 300 0.4 10 3 C1* 200 250 262.5 300 0.4 20 3 D1* 200 250 262.5 300 0.4 40 3
Gro
up2*
A2* 200 250 300 450 0.4 5 3 B2* 200 250 300 450 0.4 10 3 C2* 200 250 300 450 0.4 20 3 D2* 200 250 300 450 0.4 40 3
Two parameters of our numerical study (n and σ ) are plotted on Figure 11 together with results from material tests performed in VTT, UPC in Barcelona,
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Outokumpu and Acerinox. Green colour indicates austenitic steel grades, violet colour ferritic materials and blue marks represent duplex steels.
Figure 11. Comparison of selected models with real material tests.
It can be observed that several of the material models in this study are less important since they don’t represent typical stainless steel behaviour. Models such as C2*, D2 and D2* have significantly higher hardening ratio than simple Ramberg-Osgood curve while most of the tested materials have lower values of this parameter.
3.6 Residual stresses and work hardening from fabrication
The effect of work hardening was accounted for in the parametric study in form of enhanced material properties in corner areas of cold formed sections. Bending and membrane residual stresses and strains were considered where appropriate.
(a) Welded sections
Bending residual stresses are not significant in welded members; however, membrane stresses from welding have to be considered instead. The model for carbon steels from the Swedish standard BSK 99 that was proposed by Gardner and Cruise [31] for ferritic fabricated sections (see Figure 12) was used. Then the compressive stress is calculated to maintain the equilibrium as:
( )( )
2.25
0.5 2.25f w
c yf w
t tf
b h t tσ
+=
+ − + (2)
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Figure 12. Distribution of membrane residual stresses according to BSK 99.
The compressive stress was therefore 92.5 and 72.6 MPa in WE3T5 and WE1T5 sections respectively.
Figure 13. Distribution of membrane residual stresses in studied sections in longitudinal direction.
(b) Press-braked sections
In case of press-braked section, the enhanced yield strength was applied in corners only (corners area Apb) according to [32].
( )02,
02, 0.126
1.673 vc
ir t
σσ = (3)
Because the virgin material strength σ02,v corresponds to the basic yield strength fyb, we could calculate the average yield strength as proposed in the National Annex of BS EN 1993-1-4
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( )( )0.126
1.673yb pb pb
iya u
f A A Ar t
f fA
− +
= ≤ (4)
The increase of average yield strength depends on the share of corners in total cross-sectional area more than on the corner radius. In Figure 14 we assume that the internal corner radius ri varies between 0.5t and 3t.
Figure 14. Strength enhancements in press-braked sections.
Since the share of corners is typically lower than 25% (see Figure 15), the average yield strength did not exceed 300 MPa in the parametric study. Actually, the average yield strength was 290 MPa for ri/t = 1.0 and Apb/A = 24% as in PB2T4 cross-section.
Figure 15. Share of corners in typical press-braked sections.
Bending residual stresses 36% of fyb were inserted in corner areas and 15% of fyb in flats according to [31].
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Table 8. Enhanced material strength in flat parts and corners of press-braked sections.
Material σ02,f σu,f σ02,c σu,c models (MPa) (MPa) (MPa) (MPa)
Group 1 (A1-D1) 250 275 420 460 a) Group 1* (A1*-D1*) 250 300 420 460 a)
Group 2 (A2-D2) 250 350 420 460 a) Group 2* (A2*-D2*) 250 450 420 460 a)
a) no predictive model for ultimate strength in corners was available, therefore the maximum of flat part’s strength and the ductility limit is used
Figure 16. Materials and residual stresses in numerical models.
(c) Cold-rolled rectangular hollow sections
Cold-rolled sections enhanced area was extended 2t from corners (extended area Acr). Currently, there are several possible ways to implement strength enhancement as described in Figure 17. We used the approach B with the fixed flat parts yield strength 250 MPa and variable virgin material and corner strength.
37.5 MPa
fy = 250 MPa
-90 MPa
fy = 420 MPa
-37.5 MPa
90 MPa
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Figure 17. Calculation of enhanced yield strength in hollow sections.
In the following calculations we assumed that the initial modulus of elasticity, the ratio of ultimate and yield strength uσ , nonlinear parameters m and n, and the ultimate strain remain the same during the work hardening and therefore are applicable to the virgin material as well as work hardened faces and corners. Virgin material parameters were selected to match target flat parts strength 250 MPa.
Even though the enhanced material strength depends also on the nonlinear factor n, only one value was used for each group of materials that was approximately the average of results with different n factors (see Table 9). The values of other parameters presented in the table are valid for n = 5, but their variation is very small when the n factor increases.
coupon tests
Cruise (4)
coupon tests
Cruise (5)
full section tests
same value
same value
coupon tests
Rossi
Rossi
A
B
C
D
virgin material flat parts corners average
material
BS EN (6)
Cruise (5)
averaging
averaging (7)n/a
n/a
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Table 9. Calculation of enhanced material strength in hollow sections.
Virgin material parameters Group 1 (A1-D1)
Group 1* (A1*-D1*)
Group 2 (A2-D2)
Group 2* (A2*-D2*)
uσ 1.1 1.2 1.4 1.8
02,vσ 235 MPa 225 MPa 205 MPa 175 MPa
, 02,uu v vσ σ σ=
260 MPa 270 MPa 290 MPa 315 MPa
( )0
02,0 02,1 0,002v
v
EEn E σ
=+
21.0 GPa 20.22 GPa 18.59 GPa 16.09 GPa
Abdella’s material model [33]
Group 1 (A1-D1)
Group 1* (A1*-D1*)
Group 2 (A2-D2)
Group 2* (A2*-D2*)
02,2 02,
02,
vv
v
r Eεσ
= 0.284 0.281 0.274 0.264
02,02,
, 02,
* u vv
u v v
r Eε ε
σ σ−
=−
355.1 178.4 90.01 45.65
( )02,
, 1 * 1v
u v
EE
r m=
+ − 19.78 MPa 37.94 MPa 69.37 MPa 119.3 MPa
02,,
, 02,
u vu u v
u v v
r Eε ε
σ σ−
=−
0.334 0.335 0.336 0.338
1* ** 1
urp rr
−=
− 0.668 0.669 0.672 0.677
Rossi’s predictive model [34]
Group 1 (A1-D1)
Group 1* (A1*-D1*)
Group 2 (A2-D2)
Group 2* (A2*-D2*)
02, ,1
2 02,
v u v
v
Cr
ε σσ
=
0.0123 0.0134 0.0154 0.0196
( )( )
02, ,2 *
02,2 02,
* 1 v u vp
vu v
rC
r
ε σσε ε
−=
− 8.07 4.40 2.56 1.632
1 *pα = −
0.332 0.331 0.328 0.323 ,
02, 02,
1 22 2
u vf v
b d b dC Ct t
α
σσ σ
π π
= + + +
+
250 MPa 250 MPa 250 MPa 250 MPa
,02, 02,
1 22 2
ult vc v
i ir rC Ct t
α
σσ σ= +
+
265 MPa 275 MPa 290 MPa 325 MPa
Ultimate strengths
Group 1 (A1-D1)
Group 1* (A1*-D1*)
Group 2 (A2-D2)
Group 2* (A2*-D2*)
, 02,uu f fσ σ σ=
275 MPa 300 MPa 350 MPa 450 MPa
, 02,uu c cσ σ σ=
290 MPa 330 MPa 405 MPa 585 MPa
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Initial imperfections 4All of finite element models were perturbed prior to the arc-length non-linear calculation. The common approach was used that is described in the following chapters.
4.1 Imperfections distribution
Only global buckling modes were regarded in the geometrically and materially nonlinear FE analysis and therefore the initial imperfections were distributed according to the first overall buckling shape with positive critical load. The search for such shape can be unsuccessful for very low member slenderness; therefore we used constrained eigenvalue analysis [35] which provided results also for members where the local or distortional buckling dominated.
4.2 Imperfections amplitude
In the preliminary study, the fabrication tolerances L/750 were used as imperfection amplitude. Fabrication limits naturally contain also the deflections due to residual stresses. Since residual stresses are included in FE models this time, lower amplitude is needed that represents only the pure geometrical imperfections. We selected L/1500 which is widely used in similar studies and is also the basis of the European buckling curves in the Eurocodes [36].
Table 10. Imperfection amplitudes.
Basic imperfection amplitude
Cross-sections used
Materials used
L/1500 all all Additional imperfection
amplitudes Cross-sections
used Materials
used L/750 a) CR3T4 A2, C2 L/1000 a) CR3T4, PB2T4 A2 L/2000 a) CR3T4, PB2T4 A2
a) used to study the effect of initial imperfections
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Utilization of the results 5Over 1500 numerical calculations of models with shell elements, residual stress and nonlinear materials (mostly with two steps: eigenvalue analysis and arc-length Riks method [37] with initial imperfections) were carried out in this parametrical study. Software for automatic execution of virtual testing tool for Abaqus [38] and evaluation of the whole series of models was developed using scientific and numerical modules for Python [39]. It was also demonstrated that such study doesn’t require special computational power since all models were calculated on personal workstation with dual-core CPU and 3GB memory.
Figure 18. Flowchart of the buckling curves evaluation.
The recorded ultimate loads from buckling test simulations were recalculated to nondimensional reduction factors and plotted against nondimensional member slenderness (see Figure 18). These plots were compared to the standard Eurocode buckling curves [29] and experimental results.
Nondimensional slenderness
(basic strength)
Elastic critical load(Euler)
Design member length
Cornell University Thin-Walled Section Properies (CUTWP)
Linear Eigenvalue Analysis (LEA)
in Abaqus
Imperfection distribution
Elastic critical load(numerical)
Verification of the FE model
Nondimensional slenderness
(design strength)
Global nonlinear analysis (GMNIA)
in AbaqusUltimate load
Nondimensional reduction factor
(design strength)
Buckling curve(numerical)
Nonlinear regression analysis (NLRA)
in Python
Initial slenderness and imperfection factor
Buckling curve(Ayrton-Perry)
10 x for each buckling curve
Results of a single calculation
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Nonlinear regression (curve fitting) of Ayrton-Perry formula [40] was used to calculate (a) the initial slenderness λ0 and imperfection factor α or (b) the imperfection factor with given initial slenderness (0.2 or 0.4).
(1) Nondimensional slenderness λf(b)
Ten values are selected from 0.18 to 4.00. They are assumed to be valid in combination with the basic (or flat parts) strength.
(2) Elastic critical load (Euler) Fcr,E (Mcr,E)
Theory of elastic buckling is used to predict the value of the critical load. For compressed members:
, ( ), 2
( )
y f bcr E
f b
f AF
λ= (5)
Members subjected to bending are calculated either with plastic or elastic bending resistance:
, ( ) ( ), 2
( )
y f b el plcr E
f b
f WM
λ= (6)
(3) Design member length L
The final length of the member is calculated directly in simple (flexural buckling) cases (Eq. (7) or with CUTWP software in more complex (torsional buckling) cases using the iterative approach.
( ) ( )f b yf b crL i E f EI Nλ π π= ⋅ =
(7)
(4) Elastic critical load (numerical) Fcr,FEM (Mcr,FEM)
The critical load from the linear eigenvalue analysis (LEA) of the model with non-uniform distribution of material properties and residual stresses doesn’t have to be necessarily the same as the predicted one. Both results were compared, and when their difference was higher than 5%, the basic nondimensional slenderness was corrected using Eqs. (8) and (9).
( ) , ( ) ,f b y f b cr FEMf A Fλ =
(8)
( ) , ( ) ( ) ,f b y f b el pl cr FEMf W Mλ =
(9)
(5) Nondimensional slenderness (design strength) λv, λa
Each type of yield strength other than the basic one (virgin or average) to be used in design would require different buckling curves plot. Therefore the values of nondimensional slenderness were corrected accordingly using the approach from Eqs. (8) and (9).
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(6) Imperfection distribution
The shapes of initial imperfections were extracted from the results of LEA analysis and amplified to match selected amplitude in the node with highest displacement.
(7) Ultimate load Fult (Mult)
The peak loads in arc-length Riks analysis were recorded for each evaluated case. This is the common approach in geometrically and materially nonlinear analysis of imperfect model (GMNIA).
(8) Nondimensional reduction factor χ
The value of reduction factor has to correspond to the yield strength that is used in the design or higher to provide safe results. Therefore it is possible to create three sets of reduction factor-to-slenderness plots for fya (average strength), fyf(b) (flat faces, basic strength) and virgin material strength fyv of cold-rolled hollow sections.
ult
y
Ff A
χ = (10)
( )
ult
y el pl
Mf W
χ = (11)
5.1 Basic calculations
We have selected 5 basic cross-sections for evaluation of 7 different buckling modes. Calculation of single buckling curve is based on 10 different slenderness ratios in our study. Because enhanced material properties and residual stresses were used, each cross-section and material combination was tested also in tension (TT) to provide the average material behaviour. Each test was performed six times with different materials (see Table 11).
Table 11. Basic calculations.
Section Test Materials No. of calculations WE3T5 FBy A1-D1, A2-D2 80
LTB A1-D1, A2-D2 80 TT A1-D1, A2-D2 8
WE1T5 FBx A1-D1, A2-D2 80 TT A1-D1, A2-D2 8
PB2T4 FBy A1-D1, A2-D2 80 TFB A1-D1, A2-D2 80 TT A1-D1, A2-D2 8
CR3T4 FBy A1-D1, A2-D2 80 TT A1-D1, A2-D2 8
CR1T4 FBx A1-D1, A2-D2 80 TT A1-D1, A2-D2 8 Total: 760
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5.2 Additional calculations
Several models were created with different cross-sections or other parameters to test the sensitivity of buckling strength prediction on material thickness, initial bow imperfections or residual stress magnitude.
Table 12. The effect of material thickness.
Section Test Materials No. of calculations CR3T1 FBy A2 10 CR3T2 FBy A2 10
Total: 20
Table 13. The effect of initial bow imperfections.
Section Test Materials No. of calculations PB2T4 FBy A2, C2 40 CR3T4 FBy A2, C2 40
Total: 80
Table 14. The effect of residual stresses.
Section Test Materials No. of calculations PB2T4 TT A1-D1, A2-D2 8 CR3T4 FBy A2, C2 70
TT A1-D1, A2-D2 8 CR1T4 TT A1-D1, A2-D2 8
Total: 94
Additional 560 results from buckling calculations of material groups A1* to D1* and A2* to D2* are used to complete some of the presented studies with smaller steps in material hardening rate. These results are not presented in detail in the report.
5.3 Average material properties from tension tests
The load-displacement curves of tension tests of each cross-section and material provided the valuable information how the enhanced properties and residual stresses influence the average material behaviour. The average yield strength was compared to the predictive models, and also initial modulus of elasticity E0, non-linear factors n and m and the ultimate strength σu were obtained by the optimization of Ramberg-Osgood based material curves according to [6].
5.4 Buckling curves plot
The calculated ultimate load for each of FE models is used for calculation of non-dimensional reduction factor:
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ult
y
Ff A
χ = (12)
These factors are plotted against non-dimensional slenderness in the form of well-known buckling curves:
ycr fL iE
λπ
= (13)
Both calculations are based also on the yield strength of the material and this value has to be corresponding to the yield strength that is used in the design or higher to provide safe results. Therefore it is possible to create three sets of reduction factor-to-slenderness plots for fya (average strength), fyf(b) (flat faces, basic strength) and virgin material strength fyv of cold-rolled hollow sections.
5.5 Nonlinear regression
To obtain the analytical expression of the corresponding buckling curve, the non-linear regression was used with the variable parameters α (imperfections factor) and 0λ (initial slenderness).
5.6 Final buckling curves proposal
Results of non-linear regression of each of the curves are evaluated manually accounting for the effect of typical materials used in structures (materials A1 and D2* were usually disregarded) and a table of buckling curves parameters was proposed similar to the EN 1993-1-4 curves.
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Results 6Stress-strain curves from tensile tests of full sections are presented in this chapter as well as critical loads from eigenvalue analysis and results of GMNIA calculations in form of ultimate loads and nondimensional reduction factors. Curve-fitted parameters of Ayrton-Perry buckling curve are included at the end.
6.1 Tension tests
Because of the similarities of tensile test results, only three cross-sections are presented in Chapters 0, 6.1.2 and 6.1.3, the welded I section WE3T5, press-braked channel PB2T4 and cold-rolled CR3T4.
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6.1.1 Welded I-sections
Figure 19. Stress-strain diagrams of full-section tensile test results of welded profiles from materials A1 to C1.
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Figure 20. Stress-strain diagrams of full-section tensile test results of welded profiles from materials A2 to C2.
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6.1.2 Press-braked C sections
Figure 21. Stress-strain diagrams of full-section tensile test results of press-braked profiles from materials A1 to C1.
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Figure 22. Stress-strain diagrams of full-section tensile test results of press-braked profiles from materials A2 to C2.
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6.1.3 Cold-rolled hollow sections
Figure 23. Stress-strain diagrams of full-section tensile test results of cold-rolled profiles from materials A1 to C1.
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Figure 24. Stress-strain diagrams of full-section tensile test results of cold-rolled profiles from materials A2 to C2.
6.2 Critical loads from buckling tests
Critical loads were predicted analytically from Eq. (5) and (6) using the flat parts (basic) strength (Table 15).
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Table 15. Predicted critical loads Ncr with basic strength and E0 = 200 GPa.
case nondimensional slenderness
WE3T5 WE3T5 WE1T5 PB2T4 CR3T4 LTB FBy FBx FBx CR1T4
λ f(b) (kNm) (kN) (kN) (kN) (kN) 0 0.18 644.6 13600 19200 4680.8 5302.4 1 0.25 322.3 6800 9600 2340.4 2651.2 2 0.35 161.2 3400 4800 1170.2 1325.6 3 0.50 80.6 1700 2400 585.1 662.8 4 0.71 40.3 850 1200 292.6 331.4 5 1.00 20.1 425 600 146.3 165.7 6 1.41 10.1 212.5 300 73.1 82.8 7 2.00 5.0 106.3 150 36.6 41.4 8 2.83 2.5 53.1 75 18.3 20.7 9 4.00 1.3 26.6 37.5 9.1 10.4
More accurate prediction would need real material parameters such as the average material strength and elastic modulus obtained from the tensile tests (numerically in our case). This calculation was performed only for flexural buckling tests and the results are summarized in Table 16, Figure 25, Figure 26 and Figure 27.
Table 16. Predicted critical loads Ncr with average strength and E0 from tensile tests.
case PB2T4 CR3T4 CR1T4 (kN) (kN) (kN) 0 4417.5 3928.9 3978.4 1 2208.7 1964.4 1989.2 2 1104.4 982.2 994.6 3 552.2 491.1 497.3 4 276.1 245.6 248.7 5 138.0 122.8 124.3 6 69.0 61.4 62.2 7 34.5 30.7 31.1 8 17.3 15.3 15.5 9 8.6 7.7 7.8
Standard linear eigenvalue analysis (LEA) was used for obtaining imperfection distribution. This calculation returns also the value of elastic critical load that was compared to the prediction from Table 15 and Table 16 on Figure 25, Figure 26 and Figure 27.
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Table 17. Critical loads from basic buckling analysis.
case nondimensional slenderness
WE3T5 PB2T4 PB2T4 CR3T4 CR1T4 FBy FBy TFB FBy FBx
λ f(b) (kN) (kN) (kN) (kN) (kN) 0 0.18 (3027) (1726.9) (1631.6) (2530.2) (3808.3) 1 0.25 (2724) 1401.7 (1418.1) 1813.6 2145.4 2 0.35 (2599) 1002.0 1185.2 1047.9 1129.3 3 0.50 1573 566.2 615.0 561.9 579.9 4 0.71 828.0 294.8 310.9 291.0 293.8 5 1.00 421.6 149.5 155.4 147.9 147.9 6 1.41 212.1 75.2 76.7 74.6 74.2 7 2.00 106.3 37.7 37.8 37.5 37.2 8 2.83 53.2 18.9 18.8 18.8 18.7 9 4.00 26.6 9.4 9.3 9.4 9.3
The first buckling mode of very short members is, however, local or distortional, which does not yield preferred imperfection distribution. Therefore we used constrained LEA in such cases. Each group of nodes forming a cross-section was stiffened with triangular membrane elements that prevented geometrical changes in cross-sectional shape. The results of constrained LEA are presented in Table 18.
Table 18. Critical loads from constrained buckling analysis.
case nondimensional slenderness
PB2T4 PB2T4 CR3T4 CR1T4 FBy TFB FBy FBx
λ f(b) (kN) (kN) (kN) (kN) 0 0.18 1726.9 4270.1 3240.0 4186.0 1 0.25 1401.7 2415.2 1972.0 2315.4 2 0.35 1002.0 1284.6 1119.5 1220.3 3 0.50 566.2 663.0 603.9 628.8 4 0.71 294.8 332.0 315.1 316.7 5 1.00 149.5 165.8 160.6 159.6 6 1.41 75.2 82.1 81.3 79.2 7 2.00 37.7 40.4 40.9 39.7 8 2.83 18.9 20.1 20.4 19.72 9 4.00 9.4 10.0 10.2 9.9
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Figure 25. Comparison of predicted critical loads and FEM results.
Figure 26. Comparison of predicted critical loads and FEM results.
Figure 27. Comparison of predicted critical loads and FEM results.
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6.3 Member lengths
Member lengths correspond to the non-dimensional slenderness sequence
( ) 2n
f bλ = for n from -5 to 4. They are calculated directly from the equation (9) in case of flexural buckling (FBx and FBy), and the CUTWP software [28] was used for torsional buckling modes (TFB and LTB).
Table 19. Lengths of members in mm.
Calculation number λ f(b)
WE3T5 WE1T5 WE3T5 PB2T4 PB2T4 CR3T4 CR1T4 FBy FBx LTB FBy TFB FBy FBx
0 0.18 174 663 301 196 282 151 292 1 0.25 247 938 430 278 401 213 413 2 0.35 349 1327 618 393 576 302 584 3 0.50 493 1876 904 555 838 427 826 4 0.71 697 2653 1365 785 1251 603 1168 5 1.0 986 3752 2183 1111 1923 853 1652 6 1.4 1395 5307 3802 1570 2981 1207 2336 7 2.0 1973 7505 7170 2221 4477 1706 3304 8 2.8 2790 10613 14066 3141 6536 2413 4672 9 4.0 3945 15010 28000 4442 9390 3413 6607
The virgin material 0.2% stress was used for predicting critical loads, and therefore the final non-dimensional slenderness has to be recalculated with the yield strength used in the buckling curve plot.
6.4 Nondimensional slenderness
Since several different material strengths can be used in predicted buckling curves, corresponding slenderness had to be corrected. The corrected slenderness was used for example in case of virgin material properties of hollow sections (CR3T4 and CR1T4).
Table 20. Nondimensional slenderness of results using virgin strength.
case nondimensional
slenderness of flat parts
CR3T4 and CR1T4
A1-D1 A2-D2
λ f λv λv 0 0.18 0.17 0.16 1 0.25 0.24 0.23 2 0.35 0.34 0.32 3 0.50 0.48 0.45 4 0.71 0.69 0.64 5 1.00 0.97 0.91 6 1.41 1.37 1.28 7 2.00 1.94 1.81 8 2.83 2.74 2.56 9 4.00 3.88 3.62
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0
yvcrv
fLi E
λπ
= (14)
The calculation of slenderness related to the average strength in cross-section is based on the critical loads obtained either analytically or by FSM.
yaa
cr
AfN
λ = (15)
Table 21. Nondimensional slenderness of results using average strength.
case nondimensional
slenderness of flats (basic)
PB2T4 CR3T4 CR1T4
A1-D1 A2-D2 A1-D1 A2-D2
λ f(b) λa λa λa λa λa 0 0.18 0.19 0.18 0.18 0.18 0.19 1 0.25 0.27 0.25 0.26 0.25 0.26 2 0.35 0.38 0.36 0.37 0.36 0.37 3 0.50 0.54 0.51 0.52 0.51 0.52 4 0.71 0.77 0.72 0.74 0.72 0.74 5 1.00 1.08 1.02 1.04 1.02 1.05 6 1.41 1.53 1.44 1.47 1.44 1.48 7 2.00 2.17 2.03 2.08 2.04 2.10 8 2.83 3.07 2.87 2.94 2.88 2.96 9 4.00 4.34 4.06 4.16 4.07 4.19
6.5 Ultimate loads from buckling tests
The peak loads from non-linear analysis on imperfect numerical models are reported in Table 22, Table 23 and Table 24 for materials A1-D1 and A2-D2. The complete tables can be found in Appendix A: Ultimate loads.
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6.5.1 Welded I sections
Table 22. Results of GMNIA analysis of welded I sections.
case length (mm)
ultimate loads of minor axis flexural buckling tests (kN), section WE3T5 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 151 425.23 424.55 423.75 422.37 446.25 442.08 436.71 429.12 1 213 416.78 414.90 412.81 411.81 431.43 426.41 420.01 414.54 2 302 399.73 393.97 391.57 390.65 408.55 400.80 395.51 391.62 3 427 355.04 349.16 346.75 344.06 360.63 353.86 349.04 344.76 4 603 273.47 271.70 269.62 269.96 278.35 276.45 274.11 269.20 5 853 184.91 188.51 194.34 199.50 188.24 193.19 200.07 198.00 6 1207 114.43 120.90 126.94 133.34 116.94 124.34 131.40 132.40 7 1706 65.85 70.94 78.47 83.81 67.30 73.42 81.00 83.35 8 2413 35.95 39.98 44.45 46.07 36.69 41.37 45.39 45.99 9 3413 19.03 21.63 23.57 24.39 19.48 22.24 23.98 24.36
case length (mm)
ultimate loads of major axis flexural buckling tests (kN). section WE1T5 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 663 606.06 605.13 604.40 603.60 629.36 622.84 614.56 599.67 1 938 599.84 594.83 595.48 595.00 608.40 602.41 595.95 593.37 2 1327 576.74 576.30 578.81 578.99 582.33 577.37 575.08 574.79 3 1876 534.65 527.13 525.99 526.30 533.55 525.39 522.44 522.21 4 2653 429.24 431.47 433.51 434.60 428.63 431.58 433.37 432.27 5 3752 300.89 312.77 327.62 338.82 301.24 316.22 332.19 337.40 6 5307 189.80 208.15 228.45 243.06 191.71 211.68 232.89 242.22 7 7505 109.71 125.06 134.34 137.38 110.53 126.42 134.62 137.11 8 10613 59.32 59.32 68.34 68.59 59.57 59.57 68.03 68.56 9 15010 30.93 33.73 34.20 34.28 30.87 33.58 34.16 34.28
case length (mm)
ultimate loads of lateral-torsional buckling tests (kNm). section WE3T5 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 301 23.58 23.59 23.58 23.54 25.10 24.97 24.71 24.32 1 430 23.02 23.04 23.04 23.01 24.10 23.92 23.64 23.30 2 618 22.20 22.14 22.12 22.13 22.86 22.66 22.44 22.25 3 904 20.40 20.26 20.25 20.30 20.78 20.56 20.45 20.27 4 1365 16.74 16.92 17.09 17.14 16.94 17.00 17.10 17.14 5 2183 12.39 12.83 13.09 13.21 12.44 12.85 13.08 13.18 6 3802 8.00 8.26 8.43 8.54 8.01 8.26 8.42 8.52 7 7170 4.42 4.61 4.75 4.87 4.41 4.61 4.74 4.86 8 14066 2.27 2.48 2.56 2.59 2.28 2.48 2.56 2.59
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6.5.2 Press-braked C sections
Table 23. Results of GMNIA analysis of press-braked channels.
case length (mm)
ultimate loads of minor axis flexural buckling tests (kN), section PB2T4 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 196 167.05 166.91 166.80 166.60 170.63 172.27 167.86 169.01 1 278 162.58 162.51 162.65 162.75 166.32 165.26 164.07 162.81 2 393 155.32 155.86 156.85 157.68 157.44 156.83 156.73 157.05 3 555 142.78 145.07 147.55 149.09 143.21 144.95 147.21 148.42 4 785 120.80 126.19 130.73 134.08 120.74 126.07 130.42 133.52 5 1110 89.96 97.75 104.28 108.71 89.89 97.57 103.90 108.12 6 1570 57.72 63.34 66.39 67.63 57.63 63.29 66.28 67.54 7 2221 32.54 34.47 35.38 35.58 32.49 34.43 35.36 35.57 8 3141 17.00 17.72 17.94 17.99 16.98 17.71 17.93 17.98 9 4442 8.67 8.96 9.05 9.08 8.66 8.96 9.05 9.08
case length (mm)
ultimate loads of torsional-flexural buckling tests (kN). section PB2T4 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 282 173.88 173.54 173.26 172.91 179.17 178.10 176.66 174.62 1 401 171.63 170.92 170.74 170.71 174.78 173.13 171.76 170.71 2 576 166.10 165.80 166.58 167.16 167.68 166.34 166.40 166.53 3 838 154.56 155.82 157.26 158.22 154.87 155.70 157.01 157.54 4 1251 130.90 135.71 139.74 142.55 130.85 135.59 139.50 142.07 5 1926 96.51 103.71 109.49 113.27 96.44 103.58 109.20 112.80 6 2981 59.51 64.35 66.94 68.01 59.45 64.27 66.88 67.93 7 4477 32.42 33.92 34.36 34.41 32.38 33.93 34.35 34.43 8 6536 16.75 17.15 18.77 18.77 16.73 17.16 18.77 18.77 9 9390 8.52 8.66 8.66 8.66 8.52 8.66 8.66 8.66
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6.5.3 Cold-rolled hollow sections
Table 24. Results of GMNIA analysis of cold-rolled hollow sections.
case length (mm)
ultimate loads of minor axis flexural buckling tests (kN), section CR3T4 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 151 175.39 175.31 175.22 175.09 203.14 202.47 201.79 199.28 1 213 164.93 164.00 163.78 164.24 178.34 175.04 172.69 172.12 2 302 155.32 152.07 158.29 160.85 165.45 163.73 165.66 167.58 3 427 142.09 145.45 150.64 154.08 149.00 151.95 156.89 160.02 4 603 124.08 127.75 131.76 133.53 128.50 132.04 136.15 137.04 5 853 91.14 92.83 94.23 96.17 93.36 95.20 96.66 97.96 6 1207 54.87 56.03 57.06 57.72 55.73 56.95 58.05 58.60 7 1706 28.78 29.85 31.19 32.07 29.01 30.08 31.47 32.27 8 2413 14.40 15.29 16.44 17.08 14.63 15.49 16.51 17.10 9 3413 7.23 7.82 8.54 8.81 7.39 5.47 8.55 8.81
case length (mm)
ultimate loads of major axis flexural buckling tests (kN). section CR1T4 A1
(n = 5) B1
(n = 10) C1
(n = 20) D1
(n = 40) A2
(n = 5) B2
(n = 10) C2
(n = 20) D2
(n = 40) 0 292 175.86 175.79 175.72 175.59 207.12 207.01 205.77 203.46 1 413 163.80 163.04 163.47 164.50 178.90 175.99 174.26 173.97 2 584 154.09 155.25 157.92 160.30 166.35 165.55 167.06 169.00 3 826 141.38 144.40 148.81 151.57 150.14 152.53 156.73 159.36 4 1168 119.84 122.39 125.55 127.06 125.40 128.30 131.63 132.83 5 1652 87.86 89.83 91.28 91.92 91.33 93.20 94.71 95.38 6 2336 52.37 53.47 54.61 55.43 53.71 54.98 56.17 57.03 7 3304 28.48 29.54 30.76 31.58 29.15 30.26 31.44 32.17 8 4672 14.54 15.26 16.20 16.70 14.94 15.62 16.42 16.86 9 6607 7.43 7.88 8.45 8.67 7.65 5.41 8.52 8.72
6.6 Reduction factors
Calculated reduction factors are presented for the basic material models (A1-D1 and A2-D2) in this chapter. However, they were evaluated also for additional materials (A1*-D1* and A2*-D2*) in order to obtain curve-fitted parameters of buckling curves.
6.6.1 Minor axis flexural buckling of welded I sections
Table 25. Reduction factors of welded I sections minor axis flexural buckling (WE3T5).
case nondimensional slenderness
A1 (n = 5)
B1 (n = 10)
C1 (n = 20)
D1 (n = 40)
A2 (n = 5)
B2 (n = 10)
C2 (n = 20)
D2 (n = 40)
0 0.18 1.00 1.00 1.00 0.99 1.05 1.04 1.03 1.01 1 0.25 0.98 0.98 0.97 0.97 1.02 1.00 0.99 0.98 2 0.35 0.94 0.93 0.92 0.92 0.96 0.94 0.93 0.92 3 0.50 0.84 0.82 0.82 0.81 0.85 0.83 0.82 0.81 4 0.71 0.64 0.64 0.63 0.64 0.65 0.65 0.64 0.63 5 1.00 0.44 0.44 0.46 0.47 0.44 0.45 0.47 0.47 6 1.41 0.27 0.28 0.30 0.31 0.28 0.29 0.31 0.31 7 2.00 0.15 0.17 0.18 0.20 0.16 0.17 0.19 0.20 8 2.83 0.08 0.09 0.10 0.11 0.09 0.10 0.11 0.11 9 4.00 0.04 0.05 0.06 0.06 0.05 0.05 0.06 0.06
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Figure 28. Buckling curves of welded I sections minor axis flexural buckling tests (WE3T5).
6.6.2 Major axis flexural buckling of welded I sections
Table 26. Reduction factors of welded I sections major axis flexural buckling (WE1T5).
case nondimensional slenderness
A1 (n = 5)
B1 (n = 10)
C1 (n = 20)
D1 (n = 40)
A2 (n = 5)
B2 (n = 10)
C2 (n = 20)
D2 (n = 40)
0 0.18 1.01 1.01 1.01 1.01 1.05 1.04 1.02 1.00 1 0.25 1.00 0.99 0.99 0.99 1.01 1.00 0.99 0.99 2 0.35 0.96 0.96 0.96 0.96 0.97 0.96 0.96 0.96 3 0.50 0.89 0.88 0.88 0.88 0.89 0.88 0.87 0.87 4 0.71 0.72 0.72 0.72 0.72 0.71 0.72 0.72 0.72 5 1.00 0.50 0.52 0.55 0.56 0.50 0.53 0.55 0.56 6 1.41 0.32 0.35 0.38 0.41 0.32 0.35 0.39 0.40 7 2.00 0.18 0.21 0.22 0.23 0.18 0.21 0.22 0.23 8 2.83 0.10 0.10 0.11 0.11 0.10 0.10 0.11 0.11 9 4.00 0.05 0.06 0.06 0.06 0.05 0.06 0.06 0.06
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Figure 29. Buckling curves of welded I sections major axis flexural buckling tests (WE1T5).
6.6.3 Lateral-torsional buckling of welded I sections
Table 27. Reduction factors of welded I sections lateral-torsional buckling (WE3T5) elastic.
case nondimensional slenderness
A1 (n = 5)
B1 (n = 10)
C1 (n = 20)
D1 (n = 40)
A2 (n = 5)
B2 (n = 10)
C2 (n = 20)
D2 (n = 40)
0 0.18 1.17 1.17 1.17 1.17 1.25 1.24 1.23 1.21 1 0.25 1.14 1.14 1.14 1.14 1.20 1.19 1.17 1.16 2 0.35 1.10 1.10 1.10 1.10 1.13 1.12 1.11 1.10 3 0.50 1.01 1.01 1.01 1.01 1.03 1.02 1.02 1.01 4 0.71 0.83 0.84 0.85 0.85 0.84 0.84 0.85 0.85 5 1.00 0.61 0.64 0.65 0.66 0.62 0.64 0.65 0.65 6 1.41 0.40 0.41 0.42 0.42 0.40 0.41 0.42 0.42 7 2.00 0.22 0.23 0.24 0.24 0.22 0.23 0.24 0.24 8 2.83 0.11 0.12 0.13 0.13 0.11 0.12 0.13 0.13
Table 28. Reduction factors of welded I sections lateral-torsional buckling (WE3T5) plastic.
case nondimensional slenderness
A1 (n = 5)
B1 (n = 10)
C1 (n = 20)
D1 (n = 40)
A2 (n = 5)
B2 (n = 10)
C2 (n = 20)
D2 (n = 40)
0 0.18 1.03 1.03 1.03 1.03 1.10 1.09 1.08 1.07 1 0.25 1.01 1.01 1.01 1.01 1.06 1.05 1.04 1.02 2 0.35 0.97 0.97 0.97 0.97 1.00 0.99 0.98 0.98 3 0.50 0.89 0.89 0.89 0.89 0.91 0.90 0.90 0.89 4 0.71 0.73 0.74 0.75 0.75 0.74 0.75 0.75 0.75 5 1.00 0.54 0.56 0.57 0.58 0.55 0.56 0.57 0.58 6 1.41 0.35 0.36 0.37 0.37 0.35 0.36 0.37 0.37 7 2.00 0.19 0.20 0.21 0.21 0.19 0.20 0.21 0.21 8 2.83 0.10 0.11 0.11 0.11 0.10 0.11 0.11 0.11
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Figure 30. Buckling curves of welded I sections major axis flexural buckling tests (WE1T5) for materials A1-D1.
Figure 31. Buckling curves of welded I sections major axis flexural buckling tests (WE1T5) for materials A2-D2.
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6.6.4 Minor axis flexural buckling of press-braked C sections
Table 29. Reduction factors of press-braked channels minor axis flexural buckling (PB2T4).
case
nondimensional slenderness
A1 (n = 5) B1 (n = 10) C1 (n = 20) D1 (n = 40) fyb fya fyb fya fyb fya fyb fya
λb 250 MPa 294 MPa 250
MPa 294 MPa
250 MPa
294 MPa
250 MPa
294 MPa
0 0.18 1.14 0.97 1.14 0.97 1.14 0.97 1.14 0.97 1 0.25 1.11 0.95 1.11 0.95 1.11 0.95 1.11 0.95 2 0.35 1.06 0.90 1.07 0.91 1.07 0.91 1.08 0.92 3 0.50 0.98 0.83 0.99 0.84 1.01 0.86 1.02 0.87 4 0.71 0.83 0.70 0.86 0.73 0.89 0.76 0.92 0.78 5 1.00 0.62 0.52 0.67 0.57 0.71 0.61 0.74 0.63 6 1.41 0.39 0.34 0.43 0.37 0.45 0.39 0.46 0.39 7 2.00 0.22 0.19 0.24 0.20 0.24 0.21 0.24 0.21 8 2.83 0.12 0.10 0.12 0.10 0.12 0.10 0.12 0.10 9 4.00 0.06 0.05 0.06 0.05 0.06 0.05 0.06 0.05
case
nondimensional slenderness
A2 (n = 5) B2 (n = 10) C2 (n = 20) D2 (n = 40) fyb fya fyb fya fyb fya fyb fya
λb 250 MPa 294 MPa 250
MPa 294 MPa
250 MPa
294 MPa
250 MPa
294 MPa
0 0.18 1.17 0.99 1.18 1.00 1.15 0.98 1.16 0.98 1 0.25 1.14 0.97 1.13 0.96 1.12 0.95 1.11 0.95 2 0.35 1.08 0.92 1.07 0.91 1.07 0.91 1.07 0.91 3 0.50 0.98 0.83 0.99 0.84 1.01 0.86 1.01 0.86 4 0.71 0.83 0.70 0.86 0.73 0.89 0.76 0.91 0.78 5 1.00 0.61 0.52 0.67 0.57 0.71 0.60 0.74 0.63 6 1.41 0.39 0.34 0.43 0.37 0.45 0.39 0.46 0.39 7 2.00 0.22 0.19 0.24 0.20 0.24 0.21 0.24 0.21 8 2.83 0.12 0.10 0.12 0.10 0.12 0.10 0.12 0.10 9 4.00 0.06 0.05 0.06 0.05 0.06 0.05 0.06 0.05
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Figure 32. Buckling curves of press-braked channels minor axis flexural buckling tests (PB2T4) normalized to the basic material strength.
Figure 33. Buckling curves of press-braked channels minor axis flexural buckling tests (PB2T4) normalized to the average material strength.
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6.6.5 Torsional-flexural buckling of press-braked C sections
Table 30. Reduction factors of press-braked channels torsional-flexural buckling (PB2T4).
case
nondimensional slenderness
A1 (n = 5) B1 (n = 10) C1 (n = 20) D1 (n = 40) fyb fya fyb fya fyb fya fyb fya
λb 250 MPa 294 MPa 250
MPa 294 MPa
250 MPa
294 MPa
250 MPa
294 MPa
0 0.18 1.19 1.01 1.19 1.01 1.18 1.01 1.18 1.01 1 0.25 1.17 1.00 1.17 0.99 1.17 0.99 1.17 0.99 2 0.35 1.14 0.97 1.13 0.96 1.14 0.97 1.14 0.97 3 0.50 1.06 0.90 1.07 0.91 1.08 0.91 1.08 0.92 4 0.71 0.89 0.76 0.93 0.79 0.96 0.81 0.97 0.83 5 1.00 0.66 0.56 0.71 0.60 0.75 0.64 0.77 0.66 6 1.41 0.41 0.35 0.44 0.37 0.46 0.39 0.46 0.40 7 2.00 0.22 0.19 0.23 0.20 0.23 0.20 0.24 0.20 8 2.83 0.11 0.10 0.12 0.10 0.13 0.11 0.13 0.11 9 4.00 0.06 0.05 0.06 0.05 0.06 0.05 0.06 0.05
case
nondimensional slenderness
A2 (n = 5) B2 (n = 10) C2 (n = 20) D2 (n = 40) fyb fya fyb fya fyb fya fyb fya
λb 250 MPa 294 MPa 250
MPa 294 MPa
250 MPa
294 MPa
250 MPa
294 MPa
0 0.18 1.22 1.04 1.22 1.04 1.21 1.03 1.19 1.02 1 0.25 1.19 1.02 1.18 1.01 1.17 1.00 1.17 0.99 2 0.35 1.15 0.98 1.14 0.97 1.14 0.97 1.14 0.97 3 0.50 1.06 0.90 1.06 0.91 1.07 0.91 1.08 0.92 4 0.71 0.89 0.76 0.93 0.79 0.95 0.81 0.97 0.83 5 1.00 0.66 0.56 0.71 0.60 0.75 0.64 0.77 0.66 6 1.41 0.41 0.35 0.44 0.37 0.46 0.39 0.46 0.40 7 2.00 0.22 0.19 0.23 0.20 0.23 0.20 0.24 0.20 8 2.83 0.11 0.10 0.12 0.10 0.13 0.11 0.13 0.11 9 4.00 0.06 0.05 0.06 0.05 0.06 0.05 0.06 0.05
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Figure 34. Buckling curves of press-braked channels torsional-flexural buckling tests (PB2T4) normalized to the basic material strength.
Figure 35. Buckling curves of press-braked channels torsional-flexural buckling tests (PB2T4) normalized to the average material strength.
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6.6.6 Minor axis flexural buckling of cold-rolled hollow sections
Table 31. Reduction factors of cold-rolled hollow sections min. axis flexural buckling (CR3T4).
case
A1 (n = 5) B1 (n = 10) C1 (n = 20) D1 (n = 40) fyv fyf fya fyv fyf fya fyv fyf fya fyv fyf fya
235 MPa
250 MPa
258 MPa
235 MPa
250 MPa
258 MPa
235 MPa
250 MPa
258 MPa
235 MPa
250 MPa
258 MPa
0 1.13 1.06 1.03 1.13 1.06 1.03 1.12 1.06 1.03 1.12 1.06 1.02 1 1.06 1.00 0.97 1.05 0.99 0.96 1.05 0.99 0.96 1.05 0.99 0.96 2 1.00 0.94 0.91 0.98 0.92 0.89 1.02 0.96 0.93 1.03 0.97 0.94 3 0.91 0.86 0.83 0.93 0.88 0.85 0.97 0.91 0.88 0.99 0.93 0.90 4 0.80 0.75 0.73 0.82 0.77 0.75 0.85 0.80 0.77 0.86 0.81 0.78 5 0.59 0.55 0.53 0.60 0.56 0.54 0.60 0.57 0.55 0.62 0.58 0.56 6 0.35 0.33 0.32 0.36 0.34 0.33 0.37 0.34 0.33 0.37 0.35 0.34 7 0.18 0.17 0.17 0.19 0.18 0.17 0.20 0.19 0.18 0.21 0.19 0.19 8 0.09 0.09 0.08 0.10 0.09 0.09 0.11 0.10 0.10 0.11 0.10 0.10 9 0.05 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.05 0.05
case
A2 (n = 5) B2 (n = 10) C2 (n = 20) D2 (n = 40) fyv fyf fya fyv fyf fya fyv fyf fya fyv fyf fya
205 MPa
250 MPa
271 MPa
205 MPa
250 MPa
271 MPa
205 MPa
250 MPa
271 MPa
205 MPa
250 MPa
271 MPa
0 1.50 1.23 1.13 1.49 1.22 1.13 1.49 1.22 1.12 1.47 1.20 1.11 1 1.31 1.08 0.99 1.29 1.06 0.98 1.27 1.04 0.96 1.27 1.04 0.96 2 1.22 1.00 0.92 1.21 0.99 0.91 1.22 1.00 0.92 1.23 1.01 0.93 3 1.10 0.90 0.83 1.12 0.92 0.85 1.15 0.95 0.87 1.18 0.97 0.89 4 0.95 0.78 0.72 0.97 0.80 0.74 1.00 0.82 0.76 1.01 0.83 0.76 5 0.69 0.56 0.52 0.70 0.57 0.53 0.71 0.58 0.54 0.72 0.59 0.55 6 0.41 0.34 0.31 0.42 0.34 0.32 0.43 0.35 0.32 0.43 0.35 0.33 7 0.21 0.18 0.16 0.22 0.18 0.17 0.23 0.19 0.18 0.24 0.19 0.18 8 0.11 0.09 0.08 0.11 0.09 0.09 0.12 0.10 0.09 0.13 0.10 0.10 9 0.05 0.04 0.04 0.04 0.03 0.03 0.06 0.05 0.05 0.06 0.05 0.05
Figure 36. Hollow sections minor axis flexural buckling tests (CR3T4) to the virgin strength.
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Figure 37. Hollow sections min. axis flexural buckling tests (CR3T4) to the flat parts strength.
Figure 38. Hollow sections minor axis flexural buckling tests (CR3T4) to the average strength.
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6.6.7 Major axis flexural buckling of cold-rolled hollow sections
Table 32. Reduction factors of cold-rolled hollow sections maj. axis flexural buckling (CR1T4).
case
A1 (n = 5) B1 (n = 10) C1 (n = 20) D1 (n = 40) fyv fyf fya fyv fyf fya fyv fyf fya fyv fyf fya
235 MPa
250 MPa
258 MPa
235 MPa
250 MPa
258 MPa
235 MPa
250 MPa
258 MPa
235 MPa
250 MPa
258 MPa
0 1.13 1.06 1.02 1.13 1.06 1.02 1.13 1.06 1.02 1.13 1.06 1.02 1 1.05 0.99 0.95 1.05 0.98 0.95 1.05 0.99 0.95 1.06 0.99 0.96 2 0.99 0.93 0.90 1.00 0.94 0.90 1.01 0.95 0.92 1.03 0.97 0.93 3 0.91 0.85 0.82 0.93 0.87 0.84 0.96 0.90 0.87 0.97 0.91 0.88 4 0.77 0.72 0.70 0.79 0.74 0.71 0.81 0.76 0.73 0.82 0.77 0.74 5 0.56 0.53 0.51 0.58 0.54 0.52 0.59 0.55 0.53 0.59 0.55 0.54 6 0.34 0.32 0.30 0.34 0.32 0.31 0.35 0.33 0.32 0.36 0.33 0.32 7 0.18 0.17 0.17 0.19 0.18 0.17 0.20 0.19 0.18 0.20 0.19 0.18 8 0.09 0.09 0.08 0.10 0.09 0.09 0.10 0.10 0.09 0.11 0.10 0.10 9 0.05 0.04 0.04 0.05 0.05 0.05 0.05 0.05 0.05 0.06 0.05 0.05
case
A2 (n = 5) B2 (n = 10) C2 (n = 20) D2 (n = 40) fyv fyf fya fyv fyf fya fyv fyf fya fyv fyf fya
205 MPa
250 MPa
271 MPa
205 MPa
250 MPa
271 MPa
205 MPa
250 MPa
271 MPa
205 MPa
250 MPa
271 MPa
0 1.52 1.25 1.14 1.52 1.25 1.14 1.51 1.24 1.13 1.50 1.23 1.12 1 1.32 1.08 0.98 1.30 1.06 0.97 1.28 1.05 0.96 1.28 1.05 0.96 2 1.22 1.00 0.91 1.22 1.00 0.91 1.23 1.01 0.92 1.24 1.02 0.93 3 1.11 0.91 0.83 1.12 0.92 0.84 1.15 0.95 0.86 1.17 0.96 0.88 4 0.92 0.76 0.69 0.94 0.77 0.71 0.97 0.79 0.72 0.98 0.80 0.73 5 0.67 0.55 0.50 0.69 0.56 0.51 0.70 0.57 0.52 0.70 0.58 0.52 6 0.40 0.32 0.30 0.40 0.33 0.30 0.41 0.34 0.31 0.42 0.34 0.31 7 0.21 0.18 0.16 0.22 0.18 0.17 0.23 0.19 0.17 0.24 0.19 0.18 8 0.11 0.09 0.08 0.11 0.09 0.09 0.12 0.10 0.09 0.12 0.10 0.09 9 0.06 0.05 0.04 0.04 0.03 0.03 0.06 0.05 0.05 0.06 0.05 0.05
Figure 39. Hollow sections major axis flexural buckling tests (CR1T4) to the virgin strength.
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Figure 40. Hollow sections maj. axis flexural buckling tests (CR1T4) to the flat parts strength.
Figure 41. Hollow sections major axis flexural buckling tests (CR1T4) to the average strength.
6.7 Nonlinear regression
Four types of curve-fitting of Ayrton-Perry curve were used in the regression study. The general optimization with variable both α and λ0 parameters was used in all studies. Then three analyses were additionally carried out with fixed initial slenderness 0.2, 0.3, and 0.4. All results are presented in Appendix B: Regression results. Table 33 shows only maximum values of imperfection factors with fixed initial slenderness. This slenderness was selected according to the calculated reduction factors. Only in the case of cold-rolled hollow sections, all three options are presented since the results were very sensitive to the hardening ratio and more buckling curves are recommended with different initial slenderness. The table also shows the benefit of higher n factor that is most significant in press-braked sections.
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Table 33. Maximum imperfection factors for selected initial slenderness and buckling mode.
Basic or flat parts strength used λ0 α
n = 5 α
n = 10 α
n = 20 α
n = 40 Welded I section major axis flexural buckling,
WE1T5 0.2 0.54 0.52 0.49 0.48
Welded I section minor axis flexural buckling, WE3T5 0.2 0.72 0.78 0.71 0.72
Welded I section lateral-torsional buckling, WE3T5 0.4 0.82 0.76 0.73 0.69
Press-braked C-section minor axis flexural buckling, PB2T4 0.4 0.40 0.29 0.21 0.17
Press-braked C-section torsional-flexural buckling, PB2T4 0.2 0.19 0.14 0.10 0.08
Cold-rolled hollow section major axis flexural buckling, CR1T4
0.2 0.51 0.46 0.41 0.38 0.3 0.63 0.58 0.51 0.48 0.4 0.69 0.62 0.57 0.55
Cold-rolled hollow section major axis flexural buckling, CR3T4
0.2 0.45 0.44 0.37 0.35 0.3 0.56 0.54 0.47 0.44 0.4 0.62 0.62 0.57 0.55
Table 34. Maximum imperfection factors for selected initial slenderness and buckling mode.
Average strength used λ0 α
n = 5 α
n = 10 α
n = 20 α
n = 40 Press-braked C-section minor axis flexural buckling,
PB2T4 0.2 0.45 0.36 0.31 0.28
Press-braked C-section torsional-flexural buckling, PB2T4 0.2 0.30 0.24 0.21 0.19
Cold-rolled hollow section major axis flexural buckling, CR1T4 0.2 0.57 0.52 0.46 0.43
Cold-rolled hollow section major axis flexural buckling, CR3T4 0.2 0.49 0.50 0.44 0.41
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Discussion 7
7.1 Effect of material properties
Calculated reduction factors of welded open sections indicate that the flexural buckling to the major or minor axis corresponds to the EN 1993-1-4 buckling curves. Higher n values may yield in a slight improvement in buckling resistance for higher slenderness levels than 0.71. Lateral-torsional buckling tests resulted in good correlation to the EN 1993-1-4 when the plastic section modulus was used, and therefore are conservative in elastic design.
Basic strength can be used together with the EN 1993-1-4 buckling curve in case of flexural and torsional-flexural buckling of the press-braked C-sections (Figures 7 and 8), but the use of average strength provides unsafe results in the case of flexural buckling. For instance, the slenderness 1.0 with the average strength 250 MPa will change to 1.08 for the average strength 294 MPa, but the reduction factor in flexural buckling with material A1will drop from 0.61 to 0.52, which is lower than the EN 1993-1-4 design curve, where the reduction factor is 0.55. Results are not sensitive to the strain hardening rate, however significant improvement of predicted strength would be possible by increasing the nonlinear factor n. The results of the torsional-flexural buckling strength were rather conservative, but this could also be caused by the selection of the cross-sectional shape which was based on compression and bending resistance (particularly the A/W ratio).
The use of virgin material strength always provides conservative results in cold-rolled hollow sections especially at lower slenderness. A lower buckling strength prediction than the EN 1993-1-4 buckling curve was achieved using material models with a high strain hardening ratio (A1-D1 and A1*-D1*) and the flat parts strength (Figures 9 and 10). However, the results with an average strength are not sensitive to this ratio and they are always unsafe.
7.2 Effect of material thickness
The thickness of material is not related to the nondimensional buckling reduction factor, however, in our cases the ratios A/W were slightly modified by changing steel thickness and therefore small differences were expected. The effect of this change was tested for thickness t equal to 1, 2 and 4 mm, cold-rolled hollow section and material A2 (see Figure 42).
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Figure 42. Effect of material thickness.
As can be observed from Figure 42, the effect of thickness variation is insignificant in overall buckling; however, smaller values caused more of tested specimen fail in local or distortional buckling. In our case, 5 members failed in local buckling with 1 mm thickness, 2 failed with 2 mm thickness and only one failed with 1 mm thickness.
7.3 Effect of bending residual stress magnitude
Materials with highest and lowest nonlinearity (A2 and C2) were used to study the effect of bending residual stresses on the predicted buckling curve. Three scenarios were considered. Fully plastic through-thickness distribution (referred as 100% in Figure 43 and Figure 44) is the upper bound of the real stress from cold-forming and elastic distribution (50% in our study) is the lower bound. The last scenario was without bending residual stress (0%) as in annealed material.
Figure 43. Effect of residual stress on material A2 (n = 5).
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Figure 44. Effect of residual stress on material C2 (n = 20).
The relative difference of both curves in Figure 43 and Figure 44 is the ratio of reduction factors χ100%/ χ0% -1. This difference is typically positive in shorter members and negative at higher slenderness. The point where residual stress starts increasing buckling resistance is, however, not fixed and seems to be dependent on the material nonlinearity n.
7.4 Effect of imperfection amplitude
According to the Ayrton-Perry formula, the imperfection factor α can be expressed as:
0 yi E fAW
πα
γ= (16)
In the example on Figure 45 we assumed that the ratio A/W is 1.3, radius of gyration i = 9.6 mm and amplitude factor γ = L/e is 750, 1000, 1500 or 2000.
Figure 45. Theoretical effect of imperfection amplitude.
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In reality, however, the effect of imperfection amplitude is also affected by other factors, for instance by residual stress. This was simulated using finite element models with material C2 (n = 20) with and without bending residual stress. The selected amplitudes were L/750 and L/1500.
Figure 46. Effect of initial bow imperfections with residual stress.
Figure 47. Effect of initial bow imperfections without residual stress.
The relative difference of both curves in Figure 46 and Figure 47 is the ratio of reduction factors χ1500/χ750 -1. It can be observed that residual stress is decreasing the effect of imperfection amplitude in this case from about 10% to 6%.
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Conclusions 8Welded profiles were tested in major and minor axis flexural buckling and lateral-torsional buckling. The material model was uniform in the whole cross-section with the single material yield strength fy,b. The variation of strain hardening ratio fu/fy did not significantly affect the results and the effect of the nonlinear parameter n was also relatively small. Calculated results indicate that the current buckling curves for flexural buckling of welded open sections can be used with all materials.
Press-braked channels were tested in minor axis flexural and torsional-flexural buckling. The basic yield strength fy,b and the average strength fy,a were used in evaluation. The use of average strength would require the recalibration of the buckling curve in Eurocode, which is only valid in combination with the basic strength. Designers may also benefit from a higher nonlinear parameter n, which is typical in ferritic stainless steels.
Cold-rolled hollow sections were tested in minor and major axis flexural buckling. Virgin material strength fy,v, flat parts strength fy,f and average strength fy,a were used. While the application of virgin strength resulted in conservative results, average strength would require new buckling curves as in the case of press-braked sections. The situation was not so clear with flat parts strength, which is nowadays used in the design code. The calculations were very sensitive to the strain hardening ratio due to the differences in enhanced material yield strength prediction, and models containing materials such as ferritic steels with a lower fu/fy ratio produced lower strength than the Eurocode buckling curve, especially in lower slenderness ranges. Using the carbon steel buckling curve with the initial slenderness 0.2 would be more appropriate in such cases.
8.1 Recommendations
EN 1993-1-4: 2.1.2 (2) Ductility requirements
The ductility requirements in EN 1993-1-1 (clause 3.2.2) indicate that the yield strength has to be limited to minimum of Rp02 or 1/1.1 Rm. The parametric study respects this limit with the assumption that the total ultimate strain is not higher than 40%.
EN 1993-1-4: 2.1.3 (1) Material coefficients
We recommend a lower value of elastic modulus E for ferritic grades. A good estimation seems to be 200000 N/mm2, the same as in austenitic grades, if further studies do not suggest any better value. The recommendation is based on the review of available data [10] and experimental test in VTT [41].
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EN 1993-1-4: 5.1 (2) Partial factors
The safety factor γM1 for the resistance of members to instability assessed by member checks may be reviewed since it seems that it doesn’t account for the variability of measured elastic modulus E that was used in its evaluation.
EN 1993-1-4: 5.4.1 Buckling resistance of members
We recommend the definition of geometrical limits for cross-sections that are used in combination with the Eurocode buckling curves, because there are profiles available on the market that may have lower sectional resistance due to higher A/W ratio than tested in experiments and numerical calculations. The upper limits k used in experiments and numerical calculations are in Table 35.
A W k≤ (17)
Table 35. Upper limit of A/W ratio in cm-1 (EXP from collected experiments, FEM based on the numerical calculations).
Buckling mode Type of member kEXP kFEM
Flexural
Cold-formed open sections - 1.3 Hollow sections (major axis) 0.4 0.6 Hollow sections (minor axis) 1.0 1.3
Welded open sections (major axis) 0.2 0.3 Welded open sections (minor axis) 1.5 2.0
Torsional-flexural Cold-formed open sections 0.7 0.5 Other sections a) - -
Torsional All members a) - - a) These failure modes were not studied.
EN 1993-1-4: Table 5.3 Buckling curves
The original table of α and λ0 values (Table 36) may be extended by the additional parameters that will be valid when the average yield strength is used in the design either obtained by predictive modelling or full section testing. The basic values of initial slenderness and reduction factor are also reviewed. The recommendations are summarized in Table 37 based on results in Table 33.
Table 36. Values of α and λ0 for flexural, torsional and torsional-flexural buckling from Table 5.3 in EN 1993-1-4.
Buckling mode Type of member α 0λ
Flexural
Cold-formed open sections 0.49 0.4 Hollow sections 0.49 0.4
Welded open sections (major axis) 0.49 0.2 Welded open sections (minor axis) 0.76 0.2
Torsional and torsional-flexural All members 0.34 0.20
The numerical study indicates that the torsional-flexural buckling curves of tested lipped channels can have lower imperfection factor α, but regarding to the
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experiments in “Appendix C: Comparison with experiments”, we recommend to keep the Eurocode value at least for n smaller than 20.
Table 37. Recommended changes of the values of α and λ0 for flexural, torsional and torsional-flexural buckling when the basic strength is used.
Buckling mode Type of member α n > 5
α n > 10
α n > 20 0λ
Flexural
Cold-formed open sections 0.49 0.34 0.21 0.4 Hollow sections fu/fy ≥ 1.1 0.76 0.49 0.49 0.2 Hollow sections fu/fy ≥ 1.4 0.76 0.49 0.49 0.3 Hollow sections fu/fy ≥ 1.8 0.76 0.49 0.49 0.4
Welded open sections (major axis) 0.76 0.49 0.49 0.2 Welded open sections (minor axis) 0.76 0.76 0.76 0.2
Torsional-flexural Cold-formed open sections 0.34 0.34 0.21 0.2 Other sections a) 0.34 0.34 0.34 0.2
Torsional All members a) 0.34 0.34 0.34 0.2 a) Values were not verified.
In some cases designers may wish to take advantage of the higher average yield strength by taking the effect of enhanced material properties in cold-formed corners into account. This approach would, however, need lower nondimensional reduction factors. Recommended parameters for cold-formed open sections and hollow sections are in Table 38 based on results in Table 34.
Table 38. Recommended values of α and λ0 for flexural and torsional-flexural buckling when the average strength is used.
Buckling mode Type of member α n > 5
α n > 10
α n > 20
0λ
Flexural
Cold-formed open sections 0.49 0.49 0.34 0.2 Hollow sections (major axis) 0.76 0.76 0.49 0.2
Hollow sections (minor axis) 0.49 0.49 0.49 0.2
Torsional-flexural Cold-formed open sections 0.49 0.49 0.49 0.2
EN 1993-1-4: 5.4.3.1 (1) Lateral-torsional buckling curves
The imperfection factor αLT = 0.76 can be used for welded open sections if the nonlinear factor n ≥ 10. Higher values of α were observed in numerical models with n = 5 and therefore the curve has to be verified in such cases.
EN 1993-1-4: C.2 (2) c) True stress-strain curve
The equation is not relevant since finite element solvers may have different requirements on stress-strain input (e.g. Abaqus uses true plastic strain and its calculation is defined in the manual [42] as ( )ln 1pl
true nom true Eε ε σ= + − ). However, since it is a common mistake to switch engineering and true strain in modelling, the sentence can be modified to a more general form without formula.
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Appendix A: Ultimate loads
case length (mm)
ultimate loads of major axis flexural buckling tests (kN), section WE1T5 A1 B1 C1 D1 A1* B1* C1* D1*
0 663 606.1 612.7 629.4 673.0 605.1 610.0 622.8 657.8 1 938 599.8 599.1 608.4 631.6 594.8 597.5 602.4 614.9 2 1327 576.7 579.0 582.3 590.2 576.3 597.5 577.4 579.0 3 1876 534.7 536.3 533.6 537.7 527.1 527.2 525.4 526.2 4 2653 429.2 428.9 428.6 429.6 431.5 432.2 431.6 430.0 5 3752 300.9 300.9 301.2 300.1 312.8 312.6 316.2 311.2 6 5307 189.8 191.7 191.7 188.9 208.1 208.1 211.7 207.1 7 7505 109.7 109.6 110.5 109.4 125.1 125.0 126.4 124.3 8 10613 59.3 59.3 59.6 58.9 59.3 59.3 59.6 58.9 9 15010 30.9 30.9 30.9 30.7 33.7 33.7 33.6 33.6 A2 B2 C2 D2 A2* B2* C2* D2* 0 663 604.4 607.6 614.6 630.1 603.6 604.5 599.7 605.4 1 938 595.5 595.8 595.9 596.0 595.1 596.3 593.4 585.1 2 1327 578.8 577.5 575.1 573.2 579.0 578.4 574.8 566.1 3 1876 526.0 525.1 522.4 518.5 526.3 527.3 522.2 515.4 4 2653 433.5 432.6 433.4 429.7 434.6 432.3 432.3 427.3 5 3752 327.6 327.4 332.2 325.4 338.8 338.3 337.4 333.3 6 5307 228.5 228.3 232.9 225.6 243.1 242.7 242.2 237.4 7 7505 134.3 134.3 134.6 133.2 137.4 137.3 137.1 136.1 8 10613 68.3 68.3 68.0 68.1 68.6 68.6 68.6 68.1 9 15010 34.2 34.2 34.2 34.1 34.3 34.3 34.3 34.1
case length (mm)
ultimate loads of minor axis flexural buckling tests (kN), section WE3T5 A1 B1 C1 D1 A1* B1* C1* D1*
0 151 425.2 431.7 446.3 478.7 424.5 429.9 442.1 467.2 1 213 416.8 421.2 431.4 454.6 414.9 418.8 426.4 442.8 2 302 399.7 403.3 408.6 421.2 394.0 397.2 400.8 412.1 3 427 355.0 357.5 360.6 367.5 349.2 350.7 353.9 357.0 4 603 273.5 274.7 278.3 278.8 271.7 272.5 276.5 274.6 5 853 184.9 185.1 188.2 185.6 188.5 188.6 193.2 187.7 6 1207 114.4 114.4 116.9 114.5 120.9 120.9 124.3 120.2 7 1706 65.9 65.9 67.3 65.7 70.9 70.9 73.4 70.5 8 2413 35.9 35.9 36.7 35.7 40.0 40.0 41.4 39.7 9 3413 19.0 19.0 19.5 18.9 21.6 21.6 22.2 21.5 A2 B2 C2 D2 A2* B2* C2* D2* 0 151 423.8 428.2 436.7 450.9 422.4 425.3 429.1 432.5 1 213 412.8 415.7 420.0 427.6 411.8 413.1 414.5 414.4 2 302 391.6 393.5 395.5 397.6 390.6 391.8 391.6 388.4 3 427 346.8 347.8 349.0 350.9 344.1 344.8 344.8 340.8 4 603 269.6 270.7 274.1 270.1 270.0 270.3 269.2 267.0 5 853 194.3 194.1 200.1 191.8 199.5 199.3 198.0 195.8 6 1207 126.9 126.8 131.4 126.0 133.3 133.1 132.4 131.7 7 1706 78.5 78.3 81.0 77.4 83.8 83.7 83.3 81.7 8 2413 44.5 44.4 45.4 44.0 46.1 46.0 46.0 45.7 9 3413 23.6 23.6 24.0 23.4 24.4 24.4 24.4 24.1
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case length (mm)
ultimate loads of lateral torsional buckling (kNm), section WE3T5 A1 B1 C1 D1 A1* B1* C1* D1*
0 301 23.6 24.1 25.1 27.5 23.6 24.0 25.0 27.1 1 430 23.0 23.4 24.1 25.7 23.0 23.3 23.9 25.1 2 618 22.2 22.4 22.9 23.7 22.1 22.4 22.7 23.2 3 904 20.4 20.5 20.8 21.2 20.3 20.4 20.6 20.8 4 1365 16.7 16.8 16.9 17.1 16.9 16.9 17.0 17.1 5 2183 12.4 12.4 12.4 12.5 12.8 12.8 12.8 12.8 6 3802 8.0 8.0 8.0 8.0 8.3 8.3 8.3 8.3 7 7170 4.4 4.4 4.4 4.4 4.6 4.6 4.6 4.6 8 14066 2.3 2.3 2.3 2.3 2.5 2.5 2.5 2.5 9 28000 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.2 A2 B2 C2 D2 A2* B2* C2* D2* 0 301 23.6 23.9 24.7 26.2 23.5 23.8 24.3 25.1 1 430 23.0 23.3 23.6 24.3 23.0 23.2 23.3 23.4 2 618 22.1 22.3 22.4 22.6 22.1 22.2 22.3 22.1 3 904 20.3 20.3 20.4 20.4 20.3 20.3 20.3 20.1 4 1365 17.1 17.1 17.1 17.1 17.1 17.1 17.1 16.9 5 2183 13.1 13.1 13.1 13.0 13.2 13.2 13.2 13.1 6 3802 8.4 8.4 8.4 8.4 8.5 8.5 8.5 8.5 7 7170 4.7 4.7 4.7 4.7 4.9 4.9 4.9 4.8 8 14066 2.6 2.6 2.6 2.6 2.6 2.7 2.6 2.7 9 28000 1.4 1.4 1.4 1.4 1.6 1.6 1.6 1.6
case length (mm)
ultimate loads of minor axis flexural buckling tests (kN), section PB2T4 A1 B1 C1 D1 A1* B1* C1* D1*
0 196 167.1 168.9 170.6 182.8 166.9 168.6 172.3 180.6 1 278 162.6 163.7 166.3 172.0 162.5 163.4 165.3 169.1 2 393 155.3 155.9 157.4 159.9 155.9 156.3 156.8 157.5 3 555 142.8 142.8 143.2 143.8 145.1 145.0 144.9 144.6 4 785 120.8 120.8 120.7 120.5 126.2 126.2 126.1 125.4 5 1110 90.0 89.9 89.9 89.7 97.8 97.8 97.6 97.2 6 1570 57.7 57.7 57.6 57.5 63.3 63.3 63.3 63.0 7 2221 32.5 32.5 32.5 32.4 34.5 34.5 34.4 34.4 8 3141 17.0 17.0 17.0 16.9 17.7 17.7 17.7 17.7 9 4442 8.7 8.7 8.7 8.6 9.0 9.0 9.0 8.9 A2 B2 C2 D2 A2* B2* C2* D2* 0 196 166.8 168.2 167.9 176.9 166.6 167.5 169.0 171.4 1 278 162.7 163.2 164.1 165.4 162.8 162.9 162.8 162.2 2 393 156.8 156.8 156.7 156.2 157.7 157.6 157.1 155.3 3 555 147.6 147.5 147.2 146.3 149.1 149.0 148.4 146.7 4 785 130.7 130.6 130.4 129.8 134.1 133.9 133.5 132.3 5 1110 104.3 104.1 103.9 102.9 108.7 108.6 108.1 107.4 6 1570 66.4 66.4 66.3 66.1 67.6 67.6 67.5 67.2 7 2221 35.4 35.4 35.4 35.3 35.6 35.6 35.6 35.6 8 3141 17.9 17.9 17.9 17.9 18.0 18.0 18.0 18.0 9 4442 9.1 9.1 9.0 9.0 9.1 9.1 9.1 9.1
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case length (mm)
ultimate loads of torsional-flexural buckling tests (kN), section PB2T4 A1 B1 C1 D1 A1* B1* C1* D1*
0 282 173.9 175.5 179.2 187.7 173.5 175.0 178.1 185.2 1 401 171.6 172.7 174.8 179.7 170.9 171.6 173.1 176.1 2 576 166.1 166.6 167.7 169.7 165.8 166.0 166.3 166.7 3 838 154.6 154.7 154.9 155.1 155.8 155.8 155.7 155.4 4 1251 130.9 130.9 130.9 130.7 135.7 135.7 135.6 135.2 5 1926 96.5 96.5 96.4 96.3 103.7 103.7 103.6 103.2 6 2981 59.5 59.5 59.5 59.3 64.3 64.3 64.3 64.1 7 4477 32.4 32.4 32.4 32.3 33.9 33.9 33.9 33.9 8 6536 16.7 16.7 16.7 16.7 17.1 17.2 17.2 17.2 9 9390 8.5 8.5 8.5 8.5 8.7 8.7 8.7 8.7 A2 B2 C2 D2 A2* B2* C2* D2* 0 282 173.3 174.4 176.7 181.1 172.9 173.6 174.6 175.9 1 401 170.7 171.2 171.8 172.5 170.7 170.7 170.7 169.9 2 576 166.6 166.6 166.4 165.6 167.2 167.0 166.5 164.8 3 838 157.3 157.2 157.0 156.3 158.2 158.1 157.5 155.8 4 1251 139.7 139.7 139.5 139.0 142.5 142.4 142.1 140.7 5 1926 109.5 109.4 109.2 108.4 113.3 113.2 112.8 112.2 6 2981 66.9 66.9 66.9 66.7 68.0 68.0 67.9 67.7 7 4477 34.4 34.4 34.4 34.3 34.4 34.4 34.4 34.4 8 6536 18.8 18.8 18.8 18.8 18.8 18.8 18.8 18.8 9 9390 8.7 8.7 8.7 8.7 8.7 8.7 8.7 8.7
case length (mm)
ultimate loads of major axis flexural buckling tests (kN), section CR1T4 A1 B1 C1 D1 A1* B1* C1* D1*
0 292 175.9 186.0 207.1 257.0 175.8 186.1 207.0 255.8 1 413 163.8 169.5 178.9 201.0 163.0 168.1 176.0 194.3 2 584 154.1 158.9 166.4 183.1 155.2 159.5 165.6 178.9 3 826 141.4 144.9 150.1 161.5 144.4 #N/A 152.5 163.1 4 1168 119.8 122.1 125.4 132.7 122.4 124.7 128.3 136.0 5 1652 87.9 89.3 91.3 95.3 89.8 91.3 93.2 97.4 6 2336 52.4 52.9 53.7 55.3 53.5 54.1 55.0 56.7 7 3304 28.5 28.7 29.1 30.0 29.5 29.9 30.3 30.9 8 4672 14.5 14.7 14.9 15.4 15.3 15.4 15.6 16.0 9 6607 7.4 7.5 7.7 7.9 7.9 5.4 5.4 5.5 A2 B2 C2 D2 A2* B2* C2* D2* 0 292 175.7 185.8 205.8 252.4 175.6 185.5 203.5 244.5 1 413 163.5 167.8 174.3 188.3 164.5 168.6 174.0 185.0 2 584 157.9 161.7 167.1 178.5 160.3 164.0 169.0 179.0 3 826 148.8 152.2 156.7 166.6 151.6 154.9 159.4 168.3 4 1168 125.5 128.1 131.6 138.7 127.1 129.6 132.8 139.7 5 1652 91.3 92.6 94.7 99.2 91.9 93.4 95.4 99.5 6 2336 54.6 55.3 56.2 58.1 55.4 56.1 57.0 58.7 7 3304 30.8 31.1 31.4 31.9 31.6 31.9 32.2 32.6 8 4672 16.2 16.3 16.4 16.6 16.7 16.8 16.9 17.0 9 6607 8.5 8.5 8.5 8.5 8.7 8.7 8.7 8.7
70 (183)
RESEARCH REPORT VTT-R-08438-12
69 (78)
case length (mm)
ultimate loads of minor axis flexural buckling tests (kN), section CR3T4 A1 B1 C1 D1 A1* B1* C1* D1*
0 151 175.4 185.1 203.1 244.8 175.3 185.1 202.5 242.6 1 213 164.9 169.9 178.3 197.6 164.0 169.8 175.0 190.8 2 302 155.3 159.1 165.5 178.9 152.1 159.1 163.7 174.8 3 427 142.1 144.9 149.0 158.0 145.5 148.4 152.0 160.0 4 603 124.1 125.9 128.5 134.0 127.7 128.9 132.0 137.6 5 853 91.1 92.0 93.4 96.2 92.8 93.2 95.2 97.9 6 1207 54.9 55.2 55.7 56.5 56.0 56.3 56.9 57.7 7 1706 28.8 28.9 29.0 29.4 29.9 30.0 30.1 30.5 8 2413 14.4 14.5 14.6 14.9 15.3 15.4 15.5 15.6 9 3413 7.2 7.3 7.4 7.5 7.8 7.3 5.5 5.5 A2 B2 C2 D2 A2* B2* C2* D2* 0 151 175.2 185.1 201.8 239.8 175.1 185.1 199.3 #N/A 1 213 163.8 169.9 172.7 184.4 164.2 169.8 172.1 180.9 2 302 158.3 161.2 165.7 175.0 160.8 163.2 167.6 175.4 3 427 150.6 153.2 156.9 164.3 154.1 157.8 160.0 166.5 4 603 131.8 132.9 136.2 140.9 133.5 135.9 137.0 142.7 5 853 94.2 95.0 96.7 100.4 96.2 97.0 98.0 100.2 6 1207 57.1 57.5 58.0 58.7 57.7 58.2 58.6 59.4 7 1706 31.2 31.5 31.5 31.6 32.1 32.2 32.3 32.5 8 2413 16.4 16.5 16.5 16.5 17.1 17.0 17.1 17.0 9 3413 8.5 8.5 8.5 8.5 8.8 8.7 8.8 8.7
71 (183)
RESEARCH REPORT VTT-R-08438-12
70 (78)
Appendix B: Regression results
parameter regression results of major axis flexural buckling tests,
section WE1T5and basic strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.590 0.594 0.655 0.728 0.527 0.540 0.552 0.606 λ0 0.235 0.241 0.278 0.321 0.213 0.236 0.238 0.267
α (λ0 = 0.2) 0.544 0.540 0.539 0.534 0.512 0.497 0.504 0.516 α (λ0 = 0.3) 0.651 0.652 0.687 0.689 0.606 0.599 0.623 0.655 α (λ0 = 0.4) 0.575 0.583 0.714 0.835 0.536 0.545 0.607 0.721
A2 B2 C2 D2 A2* B2* C2* D2* α 0.463 0.468 0.457 0.485 0.418 0.425 0.420 0.432 λ0 0.197 0.198 0.195 0.194 0.180 0.184 0.168 0.149
α (λ0 = 0.2) 0.466 0.470 0.462 0.491 0.436 0.440 0.449 0.481 α (λ0 = 0.3) 0.549 0.554 0.549 0.591 0.511 0.516 0.522 0.552 α (λ0 = 0.4) 0.495 0.499 0.502 0.555 0.466 0.471 0.469 0.480
parameter regression results of minor axis flexural buckling tests,
section WE3T5 and basic strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.812 0.876 0.942 1.075 0.787 0.854 0.851 0.996 λ0 0.246 0.279 0.320 0.368 0.232 0.245 0.287 0.333
α (λ0 = 0.2) 0.721 0.706 0.674 0.673 0.726 0.779 0.674 0.718 α (λ0 = 0.3) 0.871 0.914 0.890 0.878 0.859 0.920 0.880 0.914 α (λ0 = 0.4) 0.709 0.853 1.037 1.165 0.685 0.835 0.933 1.154
A2 B2 C2 D2 A2* B2* C2* D2* α 0.750 0.775 0.761 0.866 0.712 0.721 0.749 0.778 λ0 0.221 0.238 0.252 0.279 0.211 0.218 0.228 0.228
α (λ0 = 0.2) 0.712 0.704 0.665 0.699 0.693 0.689 0.697 0.723 α (λ0 = 0.3) 0.836 0.864 0.846 0.913 0.809 0.815 0.850 0.894 α (λ0 = 0.4) 0.665 0.729 0.794 0.952 0.645 0.658 0.714 0.758
parameter regression results of lateral-torsional buckling tests,
section WE3T5 and basic strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.658 0.682 0.713 0.747 0.591 0.580 0.627 0.642 λ0 0.296 0.315 0.343 0.374 0.281 0.266 0.316 0.331
α (λ0 = 0.2) 0.513 0.507 0.494 0.482 0.483 0.511 0.472 0.476 α (λ0 = 0.3) 0.664 0.656 0.634 0.610 0.619 0.620 0.602 0.596 α (λ0 = 0.4) 0.760 0.800 0.819 0.803 0.705 0.740 0.760 0.763
A2 B2 C2 D2 A2* B2* C2* D2* α 0.549 0.561 0.574 0.586 0.529 0.537 0.541 0.550 λ0 0.273 0.284 0.296 0.300 0.269 0.274 0.277 0.265
α (λ0 = 0.2) 0.460 0.458 0.455 0.461 0.448 0.450 0.450 0.470 α (λ0 = 0.3) 0.586 0.583 0.580 0.586 0.569 0.572 0.573 0.598 α (λ0 = 0.4) 0.668 0.695 0.710 0.730 0.644 0.664 0.672 0.688
72 (183)
RESEARCH REPORT VTT-R-08438-12
71 (78)
parameter regression results of minor axis flexural buckling tests,
section PB2T4 and basic strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.414 0.416 0.419 0.424 0.264 0.263 0.265 0.271 λ0 0.417 0.417 0.420 0.422 0.382 0.380 0.380 0.378
α (λ0 = 0.2) 0.260 0.260 0.261 0.266 0.186 0.186 0.187 0.192 α (λ0 = 0.3) 0.316 0.316 0.317 0.321 0.222 0.223 0.224 0.231 α (λ0 = 0.4) 0.398 0.398 0.399 0.402 0.274 0.275 0.277 0.285
A2 B2 C2 D2 A2* B2* C2* D2* α 0.177 0.178 0.179 0.189 0.134 0.138 0.138 0.144 λ0 0.349 0.349 0.344 0.350 0.334 0.346 0.329 0.319
α (λ0 = 0.2) 0.136 0.137 0.139 0.145 0.108 0.108 0.111 0.118 α (λ0 = 0.3) 0.161 0.162 0.165 0.172 0.126 0.127 0.131 0.139 α (λ0 = 0.4) 0.196 0.198 0.200 0.210 0.153 0.154 0.158 0.169
parameter regression results of minor axis flexural buckling tests,
section PB2T4 and average strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.365 0.378 0.400 0.441 0.252 0.262 0.284 0.301 λ0 0.092 0.115 0.154 0.211 0.000 0.017 0.072 0.102
α (λ0 = 0.2) 0.450 0.448 0.441 0.431 0.362 0.361 0.360 0.363 α (λ0 = 0.3) 0.513 0.515 0.516 0.534 0.407 0.409 0.414 0.434 α (λ0 = 0.4) 0.456 0.463 0.474 0.584 0.372 0.377 0.388 0.450
A2 B2 C2 D2 A2* B2* C2* D2* α 0.176 0.183 0.190 0.211 0.132 0.136 0.142 0.150 λ0 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
α (λ0 = 0.2) 0.296 0.297 0.299 0.309 0.255 0.257 0.263 0.280 α (λ0 = 0.3) 0.329 0.332 0.336 0.356 0.282 0.284 0.291 0.310 α (λ0 = 0.4) 0.308 0.312 0.316 0.349 0.267 0.269 0.275 0.289
parameter regression results of torsional-flexural buckling tests,
section PB2T4 and basic strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.378 0.379 0.380 0.383 0.246 0.246 0.247 0.250 λ0 0.530 0.530 0.530 0.530 0.518 0.517 0.516 0.513
α (λ0 = 0.2) 0.188 0.188 0.189 0.190 0.131 0.131 0.132 0.135 α (λ0 = 0.3) 0.223 0.223 0.224 0.226 0.154 0.155 0.156 0.159 α (λ0 = 0.4) 0.273 0.273 0.274 0.277 0.187 0.187 0.189 0.193
A2 B2 C2 D2 A2* B2* C2* D2* α 0.171 0.172 0.172 0.182 0.142 0.142 0.142 0.143 λ0 0.513 0.513 0.508 0.512 0.538 0.533 0.525 0.502
α (λ0 = 0.2) 0.095 0.096 0.097 0.101 0.075 0.076 0.078 0.082 α (λ0 = 0.3) 0.111 0.112 0.114 0.118 0.088 0.089 0.091 0.096 α (λ0 = 0.4) 0.134 0.134 0.136 0.142 0.105 0.106 0.109 0.115
73 (183)
RESEARCH REPORT VTT-R-08438-12
72 (78)
parameter regression results of torsional-flexural buckling tests,
section PB2T4 and average strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.327 0.341 0.357 0.374 0.237 0.242 0.246 0.252 λ0 0.243 0.265 0.287 0.310 0.192 0.204 0.211 0.217
α (λ0 = 0.2) 0.299 0.298 0.296 0.296 0.241 0.240 0.241 0.244 α (λ0 = 0.3) 0.364 0.367 0.367 0.366 0.286 0.289 0.292 0.296 α (λ0 = 0.4) 0.391 0.422 0.442 0.455 0.303 0.321 0.339 0.352
A2 B2 C2 D2 A2* B2* C2* D2* α 0.180 0.182 0.183 0.185 0.148 0.150 0.150 0.149 λ0 0.150 0.156 0.153 0.136 0.114 0.119 0.105 0.054
α (λ0 = 0.2) 0.197 0.197 0.199 0.206 0.170 0.172 0.176 0.188 α (λ0 = 0.3) 0.231 0.233 0.237 0.246 0.199 0.201 0.206 0.220 α (λ0 = 0.4) 0.248 0.256 0.267 0.281 0.214 0.216 0.225 0.238
parameter regression results of major axis flexural buckling tests,
section CR1T4 and virgin strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.598 0.654 0.702 0.758 0.569 0.747 0.675 0.715 λ0 0.345 0.447 0.572 0.710 0.366 0.527 0.594 0.726
α (λ0 = 0.2) 0.421 0.360 0.285 0.216 0.381 0.355 0.265 0.200 α (λ0 = 0.3) 0.534 0.445 0.342 0.253 0.481 0.425 0.316 0.233 α (λ0 = 0.4) 0.675 0.574 0.426 0.304 0.615 0.527 0.389 0.279
A2 B2 C2 D2 A2* B2* C2* D2* α 0.577 0.636 0.650 0.653 0.600 0.629 0.625 0.621 λ0 0.416 0.511 0.614 0.734 0.451 0.526 0.618 0.733
α (λ0 = 0.2) 0.342 0.306 0.245 0.182 0.329 0.293 0.237 0.175 α (λ0 = 0.3) 0.428 0.370 0.290 0.211 0.406 0.353 0.280 0.203 α (λ0 = 0.4) 0.554 0.466 0.355 0.252 0.522 0.442 0.341 0.242
parameter regression results of major axis flexural buckling tests,
section CR1T4 and flat parts strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.560 0.578 0.610 0.638 0.514 0.514 0.560 0.595 λ0 0.244 0.297 0.370 0.475 0.249 0.343 0.376 0.490
α (λ0 = 0.2) 0.506 0.457 0.406 0.332 0.460 0.366 0.369 0.299 α (λ0 = 0.3) 0.634 0.581 0.510 0.405 0.575 0.466 0.463 0.364 α (λ0 = 0.4) 0.672 0.687 0.657 0.517 0.621 0.561 0.594 0.463
A2 B2 C2 D2 A2* B2* C2* D2* α 0.485 0.503 0.548 0.582 0.480 0.516 0.568 0.582 λ0 0.275 0.330 0.412 0.518 0.300 0.367 0.444 0.529
α (λ0 = 0.2) 0.409 0.370 0.329 0.277 0.381 0.346 0.316 0.272 α (λ0 = 0.3) 0.512 0.468 0.411 0.334 0.480 0.438 0.391 0.327 α (λ0 = 0.4) 0.573 0.570 0.532 0.419 0.551 0.554 0.503 0.408
74 (183)
RESEARCH REPORT VTT-R-08438-12
73 (78)
parameter regression results of major axis flexural buckling tests,
section CR1T4 and average strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.548 0.552 0.572 0.595 0.500 0.480 0.504 0.499 λ0 0.185 0.203 0.232 0.279 0.184 0.235 0.208 0.229
α (λ0 = 0.2) 0.566 0.548 0.531 0.493 0.518 0.444 0.494 0.468 α (λ0 = 0.3) 0.698 0.681 0.667 0.626 0.636 0.548 0.614 0.584 α (λ0 = 0.4) 0.704 0.706 0.716 0.745 0.653 0.597 0.656 0.648
A2 B2 C2 D2 A2* B2* C2* D2* α 0.469 0.462 0.457 0.432 0.463 0.454 0.446 0.411 λ0 0.207 0.211 0.211 0.198 0.233 0.235 0.227 0.188
α (λ0 = 0.2) 0.462 0.451 0.446 0.434 0.431 0.421 0.420 0.421 α (λ0 = 0.3) 0.568 0.556 0.550 0.534 0.533 0.521 0.519 0.515 α (λ0 = 0.4) 0.603 0.599 0.597 0.587 0.581 0.574 0.573 0.566
parameter regression results of minor axis flexural buckling tests,
section CR3T4 and virgin strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.525 0.573 0.663 0.756 0.452 0.630 0.653 0.712 λ0 0.349 0.449 0.593 0.721 0.338 0.470 0.622 0.733
α (λ0 = 0.2) 0.372 0.316 0.254 0.209 0.329 0.350 0.238 0.191 α (λ0 = 0.3) 0.466 0.390 0.304 0.244 0.413 0.422 0.282 0.223 α (λ0 = 0.4) 0.590 0.501 0.378 0.293 0.509 0.527 0.346 0.267
A2 B2 C2 D2 A2* B2* C2* D2* α 0.510 0.636 0.641 0.661 0.534 0.629 0.603 0.625 λ0 0.439 0.511 0.648 0.748 0.487 0.526 0.649 0.743
α (λ0 = 0.2) 0.289 0.306 0.227 0.176 0.271 0.293 0.214 0.173 α (λ0 = 0.3) 0.358 0.370 0.267 0.205 0.331 0.353 0.251 0.200 α (λ0 = 0.4) 0.460 0.466 0.323 0.244 0.421 0.442 0.304 0.238
parameter regression results of minor axis flexural buckling tests,
section CR3T4 and flat parts strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.496 0.513 0.537 0.573 0.420 0.535 0.482 0.535 λ0 0.243 0.290 0.351 0.448 0.210 0.297 0.354 0.465
α (λ0 = 0.2) 0.450 0.417 0.379 0.319 0.411 0.437 0.338 0.286 α (λ0 = 0.3) 0.561 0.525 0.474 0.392 0.503 0.539 0.423 0.351 α (λ0 = 0.4) 0.607 0.624 0.603 0.502 0.540 0.618 0.533 0.449
A2 B2 C2 D2 A2* B2* C2* D2* α 0.413 0.503 0.473 0.533 0.400 0.516 0.499 0.549 λ0 0.275 0.330 0.402 0.509 0.305 0.367 0.445 0.532
α (λ0 = 0.2) 0.351 0.370 0.295 0.257 0.317 0.346 0.279 0.251 α (λ0 = 0.3) 0.435 0.468 0.368 0.313 0.396 0.438 0.345 0.303 α (λ0 = 0.4) 0.494 0.570 0.471 0.395 0.461 0.554 0.443 0.380
75 (183)
RESEARCH REPORT VTT-R-08438-12
74 (78)
parameter regression results of minor axis flexural buckling tests,
section CR3T4 and average strength A1 B1 C1 D1 A1* B1* C1* D1*
α 0.480 0.490 0.519 0.554 0.401 0.506 0.443 0.469 λ0 0.186 0.201 0.236 0.273 0.137 0.207 0.202 0.229
α (λ0 = 0.2) 0.494 0.488 0.478 0.468 0.454 0.499 0.440 0.440 α (λ0 = 0.3) 0.608 0.604 0.599 0.591 0.548 0.600 0.543 0.548 α (λ0 = 0.4) 0.632 0.638 0.656 0.712 0.565 0.617 0.589 0.614
A2 B2 C2 D2 A2* B2* C2* D2* α 0.394 0.463 0.397 0.397 0.379 0.456 0.386 0.430 λ0 0.206 0.228 0.211 0.199 0.235 0.251 0.229 0.266
α (λ0 = 0.2) 0.389 0.436 0.388 0.398 0.353 0.407 0.363 0.377 α (λ0 = 0.3) 0.475 0.540 0.476 0.489 0.432 0.506 0.445 0.462 α (λ0 = 0.4) 0.516 0.587 0.525 0.544 0.482 0.563 0.499 0.575
76 (183)
RESEARCH REPORT VTT-R-08438-12
75 (78)
Appendix C: Comparison with experiments Collected experimental results were sorted by the cross-section and failure mode and then again (if necessary) by the material properties according to the proposed buckling curves. Therefore three graphs are used (Figure C1 to C3) for flexural buckling of hollow sections with different hardening ratio. Points are based on the measured elastic modulus E.
Figure C1. Proposed curve for hollow sections fu/fy ≥ 1.1 flexural buckling (α = 0.49, λ0 = 0.2, fy = fy,f(b)).
Figure C2. Proposed curve for hollow sections fu/fy ≥ 1.4 flexural buckling (α = 0.49, λ0 = 0.3, fy = fy,f(b)).
77 (183)
RESEARCH REPORT VTT-R-08438-12
76 (78)
Figure C3. Proposed curve for hollow sections fu/fy ≥ 1.8 flexural buckling (α = 0.49, λ0 = 0.4, fy = fy,f(b)).
Figure C4. Proposed curve for welded open sections major axis flexural buckling (α = 0.49, λ0 = 0.2).
78 (183)
RESEARCH REPORT VTT-R-08438-12
77 (78)
Figure C5. Proposed curve for welded open sections major axis flexural buckling (α = 0.76, λ0 = 0.2).
Figure C6. Proposed curve for open sections torsional-flexural buckling (α = 0.34, λ0 = 0.2).
79 (183)
RESEARCH REPORT VTT-R-08438-12
78 (78)
Figure C7. Proposed curve for open sections lateral-torsional buckling (α = 0.76, λ0,LT = 0.4).
80 (183)
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....................
....................
....................
....................
....................
....................
....................
....................
....................
or................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
....................
3 (6
3
....... 4
....... 5
....... 8
....... 8
..... 12
..... 13
..... 13
..... 14
..... 14
..... 15
..... 17
..... 19
..... 19
..... 24
..... 27
..... 32
..... 32
..... 33
..... 35
..... 36
..... 39
..... 45
..... 51
..... 54
..... 57
62)
83 (183)
1. In Thosefailurmakepost‐bucklconcesubjeto redessenstainl On thwithoare cplastihinge The sthe band sdepe(intercombcarbothesevaluesigniflimits For thexperclass benddifferto dif This rthreesteel previCentrinvessquarbendclass (stub
ntroductio
e cross‐sectire occurs at es up the cro‐buckling strling behavioept of effectected to a unduce the resnce a Winteless steel res
he other haout developicapable of reic moment ce without red
study of locaboundary betstocky sectind on the rnal or outstbined compron and staine limits werees are conseficantly due s as well as r
he case of mrimental res1 and 2 liming were derent bucklingfferent stress
report presee methods tohas also beously validare of Finlanstigation hare/rectanguling tests in 3 limit for i columns) as
on
ons classifiean average
oss section rerength, the wour of a plattive width, wniformly distsistance dueer curve andspectively.
nd, those seng any local eaching the capacity provduction of th
l buckling phtween slendons (class 1manufacturitand elemenression and nless steel ree developed ervative. Howto the receneduction fac
members in cults from stmits. Class lerived fromg factors whis gradients.
ents a numero ferritic staen considereated with exd has beenas considerar hollow ssquare/rectnternal and s well as clas
ed as slenderstress beloweaches the cwhole cross e has been which assumtributed stre to the effecd can be fou
ections that instability afull plastic vides the sehe resistance
henomenon der sections, 1‐3). These ling processnts) as well bending) anespectively.based on limwever, durinnt emergencctors have be
compressionub columns imits for me those propich were obt
rical investigainless steel ed for compxperimental used to med numericections, I‐setangular holloutstand els 2 and 1 lim
r (class 4) arw the yield critical stress section is ctaken into
mes that the ess, by applycts of local bund in EN19
can sustainare classifiedmoment arection with ee the section
involves the those that limits that d(cold‐formeas the stresnd can be foIt is importmited experng the last yce of stainleseen proposed
n the determand/or benembers in bposed for mtained from e
gation with tcross‐sectio
parison purpresults, de
model stub ccal results ections and low sectionslements andmits (4‐point
re characteristress. Onces, the plate bcapable to raccount in Etotal load ising a reductbuckling. This993‐1‐5 and
n a stress levas class 3 oe classified aenough rotatis classified
e assessmentare susceptidefine the ded or weldess gradient (ound in EN1tant to pointimental resuyears these ass steels andd by Gardne
mination of tding tests abending andmembers in elastic analy
he aim to asons. Austenitoses. An Abveloped by columns andfrom stub
channels wis. Those resd the reductibending test
zed becausee the most sbuckles localresist higherEurocodes bs carried by tion factor ρ s effective w EN1993‐1‐4
vel equals tor better. Whas 2 or betttion capacityas class 1.
t of class 3 lible to buckldifferent claed), the boufully compre1993‐1‐1 andt out that foults and theravailable datd more accurr and Theofa
he class 3 lind only ben combined compressiosis of perfec
ssess the apptic stainless aqus plug‐inthe VTT Ted 4‐point beb columns ithout lips aults has beeion factor fots).
e the fact thslender platelly but, due tr loads. The by considerina fictitious to the real width formul4 for carbo
o the yield hen those seter and whey to form a p
imit which de locally (class of the seundary condessed, bendd EN1993‐1or stainless refore the cuta have incrrately slendeanous (2008)
mit was basnding tests focompressio
on by considct plates subj
plicability of steel and c
n, which hasechnical Resending testscarried o
as well as 4en used to aor class 4 se
4 (6
4
at the e that to the post‐
ng the width width a is in n and
stress ctions n this plastic
efines ass 4), ection ditions ing or ‐4 for steel, urrent eased erness ).
ed on or the n and dering jected
these arbon s been search s. The ut in ‐point assess ctions
62)
84 (183)
2. A All stsectiodifferChanpoint
F
FigurThe sFerritproje(441)experfrom
0
20
40
60
80
100
120
140
vailable e
tub column on. Figure 2rent cross snels, circulat/3‐point ben
Figure 2.2 Num
e 2.2 plots tstainless steetic, Duplex aect is focused) are the drimental datthese tests
12
25
11
19
31
1
40
2
Cross sections
experimen
tests and 32.1 summariections: squr hollow secnding tests w
Figure
(a) mber of cross se
he different el types founnd Lean dupd on ferritic gdifferent fouta for stub cmight be fou
715
91
4 24 4
s according to s
ntal data
3‐point/4‐pozes all expeuare and rections CHS) awere gathere
2.1 Number of
ctions accordin
types of stand in the liteplex. Within egrades, it is iund grades.column testsund in Annex
426
stainless steel ty
int bending erimental rectangular hoand angles. Aed.
f cross sections
ng to stainless s
ainless steel terature are Aeach group dmportant to. Table 2.1 s and bendinx A.
ype
SHS
RHS
I‐section
Channel
CHS
Angle
0
10
20
30
40
50
60
tests foundsults found ollow sectionA total of 199
and test config
steel type. (a) st
that made uAustenitic, Hdifferent grao point out thand 2.2 s
ng tests resp
8
11
20
1
17
2
Cross sectio
d are presenin the literans (SHS and9 stub colum
guration
(b) tub columns. (b
p the differeigh Strengthdes are conshat 1.4003 (3ummarizes pectively. Fu
4
3
4
24
2
ns according to
nted througature considd RHS), I‐secmn tests and
b) bending tests
ent cross sech Austenitic (sidered. Sinc3Cr12) and 1all the ava
urther inform
4
38
2 22
6
stainless steel t
5 (6
5
h this dering ctions, 94 4‐
s.
ctions. (HSA), ce this 1.4509 ailable mation
type
SHS
RHS
I‐section
CHS
62)
85 (183)
Ra
Br
Ta
Bu
Ra
St
St
Yo
Liu
Ku
Yo
Ga
Yo
Ba
Ga
Th
Af
Ga
‐a) Not
Re
asmussen and
redenkamp and
alja and Salmi (
urgan et al. (20
asmussen (200
tangenberg (19
tangenberg (20
oung and Harto
u Young (2003)
uwamura (2003
oung and Liu (2
ardner and Net
oung and Lui (2
ardi and Kyriak
ardner, Talja an
heofanous and
fshan and Gard
ardner and Sali
available
eference
Hancock (1993
d Van den Berg
(1995)
000)
0)
999) ‐ ECSC (200
000) ‐ ECSC (200
ono (2002)
)
3)
2003)
thercot (2004a
2005)
kides (2006)
nd Badoo (200
Gardner (2009
dner (2011)
iba (2011)
Se
3a) SC
g (1995) I‐se
S
CC
RC
00) I‐seI‐se
00) I‐seC
C
S
SS
I‐seI‐seChChCCAA
R
) SRC
SSRR
C
6) SR
9) SR
RSS
I‐se
Table
ection Numof te
SHS 2CHS 2
ection 2
SHS 1
CHS 1CHS 2
RHS 3CHS 3
ection 3ection 1
ection 7CHS 7
CHS 3
SHS 4
SHS 6SHS 6ection 8ection 8annel 6annel 5CHS 5CHS 5Angle 6Angle 6
RHS 8
SHS 17RHS 16CHS 4
SHS 4SHS 2RHS 2RHS 1
CHS 15
SHS 4RHS 4
SHS 6RHS 2
RHS 4SHS 2SHS 2
ection 4
Total: 199 t
1.1 Stub colum
mber ests
Grad
1.430 1.430
1.400
1.430
1.454 1.443
1.430 1.430
1.430 1.446
7 1.4007 1.400
1.430
4 1.430
6 1.4306 1.4318 1.4308 1.4316 1.430 1.431 1.430 1.431
6 1.4306 1.431
8 1.430
7 1.4306 1.4304 1.430
4 1.446 ‐a)
1.446 ‐a)
5 1.441
4 1.4314 1.431
6 1.416 1.416
4 1.400 1.400 1.450
4 1.416
tests
mn test
e Materia
06 304L 06 304L
03 3Cr12
01 304
41 321 35 316L
06 304L 06 304L
01 304 62 2205
03 3Cr1203 3Cr12
01 304
01 304
01 304 18 301LN01 304 18 301LN01 304 18 301LN01 304 18 301LN01 304 18 301LN
01 304
01 304 01 304 01 304
62 2205 ‐a)
62 2205 ‐a)
10 SAF 250
18 301LN18 301LN
62 LDX21062 LDX210
03 3Cr1203 3Cr1209 441
62 LDX210
al Type
AustenitiAusteniti
2 Ferritic
Austeniti
AustenitiAusteniti
AustenitiAusteniti
AustenitiDuplex
2 Ferritic 2 Ferritic
Austeniti
Austeniti
AustenitiN Austeniti
AustenitiN Austeniti
AustenitiN Austeniti
AustenitiN Austeniti
AustenitiN Austeniti
Austeniti
AustenitiAustenitiAusteniti
Duplex HSA
Duplex HSA
07 Super dup
N AustenitiN Austeniti
01 Lean dupl01 Lean dupl
2 Ferritic 2 Ferritic
Ferritic
01 Lean dupl
6 (6
6
c c
c
c c
c c
c
c
c
c c c c c c c c c c
c
c c c
lex
c c
ex ex
ex
62)
86 (183)
‐a) Not
Rasmu
Talja a
Burgan
Gardn
Real a
Zhou a
Gardn
Theofa
Afshan
Gardn
available
Referen
ussen and Hanc
and Salmi (1995
n et al. (2000)
ner and Netherc
nd Mirambell (
and Young (200
ner, Talja and B
anous and Gard
n and Gardner
ner and Saliba (
ce
cock (1993b)
5)
cot (2004b)
(2005)
05)
adoo (2006)
dner (2010)
(2011)
2011)
Tab
Section
SHS CHS
SHS RHS
I‐section I‐section CHS CHS CHS CHS
SHS RHS
SHS RHS
SHS C
RHS C
I‐section
I‐section C
SHS RHS SHS RHS SHS RHS
SHS RHS
SHS RHS
RHS SHS SHS RHS SHS SHS
I‐section I‐section
le 1.2 Bending
Type of test
No
4‐point 4‐point
4‐point 4‐point
4‐point 4‐point 4‐point 4‐point 4‐point 4‐point
3‐point 3‐point
3‐point 3‐point
Continuous beam
Continuous beam 3‐point
Continuous beam
4‐point 4‐point 4‐point 4‐point 4‐point 4‐point
4‐point 4‐point
3‐point 3‐point
4‐point 4‐point 4‐point 3‐point 3‐point 3‐point
3‐point 4‐point
Total:
tests
Number of tests
Gr
1 1.41 1.4
3 1.46 1.4
9 1.43 1.44 1.44 1.41 1.42 1.4
5 1.44 1.4
1 1.41 1.4
1 1.4
1 1.4
1 1.4
1 1.4
4 1.44 1.42 1.42 1.42 ‐1 ‐
2 1.44 1.4
6 1.42 1.4
2 1.41 1.41 1.42 1.41 1.41 1.4
4 1.44 1.4
94 tests
ade Mater
4306 3044306 304
4301 3044301 304
4301 3044462 22054301 3044462 22054541 3214435 316
4301 3044301 304
4301 3044301 304
4301 304
4301 304
4306 304
4306 304
4301 3044301 3044462 22054462 2205‐a) ‐a) ‐a) ‐a) 4318 301L4318 301L
4162 LDX214162 LDX21
4003 3Cr14003 3Cr14509 4414003 3Cr14003 3Cr14509 441
4162 LDX214162 LDX21
rial Type
4L Austeni4L Austeni
4 Austeni4 Austeni
4 Austeni5 Duple4 Austeni5 Duple1 Austeni6L Austeni
4 Austeni4 Austeni
4 Austeni4 Austeni
4 Austeni
4 Austeni
4L Austeni
4L Austeni
4 Austeni4 Austeni5 Duple5 Duple
HSA HSA
LN AusteniLN Austeni
101 Lean dup101 Lean dup
12 Ferriti12 Ferriti1 Ferriti12 Ferriti12 Ferriti1 Ferriti
101 Lean dup101 Lean dup
7 (6
7
itic itic
itic itic
itic x itic x itic itic
itic itic
itic itic
itic
itic
itic
itic
itic itic x x
itic itic
plex plex
c c c c c c
plex plex
62)
87 (183)
3. Fo
3.1 S
TableGard
memthe mthe c
stresselemand i
ormulatio
Slenderness
es 3.1, 3.2 aner and The
bers in bendmaterial factcompressed
s ratio andents respectn figure 3.2 f
235
.
235
. 21000
on
s limits
and 3.3 preseofanous (2
ding and meor that mighpart express
d boundary tively and thefor stainless
For c
00 For s
Figure 3.1 Wid
sent the clas008) propos
mbers partiaht be obtainsed as a dec
conditions de width‐to thsteel.
carbon steel
stainless stee
dth‐to‐thicknes
ss section limsal (hereinaf
ally compresned accordincimal, kσ is
defined in tahickness rati
el
s ratios for com
mits in EN19fter G&T) fo
ssed respectg to equatiothe buckling
bles 3.5 ando is specified
mpression parts
993‐1‐4, ENor members
ively. Withinon 3.1, α is tg factor corr
3.6 for inted in figure 3.
s in EN1993‐1‐1
1993‐1‐1 ans in compre
n these tablethe percentaresponding t
rnal and out.1 for carbon
E
1
8 (6
8
nd the ession,
es, is age of to the
tstand n steel
q 3.1
62)
88 (183)
Internal
parts
Outstand flanges
Angles
Tubular
sections
Internal
parts
Tubular
sections
parts 1
2
3
1 Cold
forme
Weld
2 Cold
forme
Weld
3 Cold
forme
Weld
3 h: thlongeflang
sections
1
2
3
parts 1
2
3
sections
1
2
3
Figure 3.2 Wid
EN
/ tc/ tc/ tc
d ed /c
ed cd ed /c
ed /cd ed
/ tc
ed /c
he est ge
/h
2
t
b
/d
/d
/dTable
E
/c/c/c
/d
d
/dTab
dth‐to‐thicknes
N1993‐1‐4
7.25t
7.26t
7.30t
10t/
9t/
4.10t
4.9/ t
9.11t
11t/
9.11t
1.9t
h
250t/
270t/
290t/
3.1 slendernes
EN1993‐1‐4
0.56/ t
2.58t
8.74t
250t/
270t/
2280/ tble 3.2 slendern
s ratios for com
EN19
t/ct/ct/c
t/c
t/c
/ tc
/ tc
t/c
t/ct/h
t2
hb
t/d
t/d
t/dss limits for mem
EN1
/ tc/ tc/ tc
t/d
t/d
t/dness limits for m
mpression parts
993‐1‐1
33
38
42
9t
9t
10
10
14
14
15
5,11
250
270
290
mbers in compr
1993‐1‐1
72t
83t
124
250t
270t
290t
members in ben
s in EN1993‐1‐4
Gardner and
/c/c/c
/c
/c
/c
/c
/c
/c
t2
hb
/d
/d
/dression
Gardner and
/c/c/c
/d
/d
/ tdding
4
d Theofanous (2
33t/
35/ t
37/ t
9t/
9t/
10/ t
10/ t
14t/
14t/
5,11h
250t/
270t/
290t
d Theofanous (2
72/ t
76/ t
90/ t
250t/
270t/
2280t
9 (6
9
2008)
2008)
62)
89 (183)
Internal parts
1
2
3
Outstand flanges
(Tip in
compression)
1
2
3
Outstand flanges
(Tip in
ten
sion)
1
2
3
1
5.01
5.01
2
5.01
5.01
3
5.01
5.01
1
Cold formed
Welded
2
Cold formed
Welded
3
Cold formed
Welded
1
Cold formed
Welded
2
Cold formed
Welded
3
Cold formed
Welded
Tab
EN19
/ tc
/ tc
/ tc
/ tc
tc 15/
tc 15/
/ tc
/ tc
/ tc
/ tc
tc 18/
tc 16/
/ tc
/ tc
/ tc
/ tc
tc 18/
tc 16/ ble 3.3 slendern
993‐1‐4
113
308
28
113
320
1.29
k3.5
k3.5
10
9
4.10
4.9
k1.8
k7.6
10
9
4.10
4.9
k1.8
k7.6
ness limits for m
EN1
/ tc
/ tc
/ tc
/ tc
.0/ tc
62/ tc
/c
/c
/ tc
/ tc
tc /
tc /
/ tc
/ tc
/ tc
/ tc
tc /
tc / members in com
1993‐1‐1
113
396
36
t
113
456
5.41
33.067.
42
1
9
t
9
t
10
t
10
t
k21
k21
9
9
10
10
k21
k21mbined banding
Gardne
c
c
c
c
c
c
c
c
g and compress
er and Theofano
13
396/
tc
36
/ tc
13
420/
tc
38
/ tc
t 5.18/
t 5.18/
9
/ tc
9
/ tc
10
/ tc
10
/ tc
ktc 21/
ktc 21/
9
/ tc
9
/ tc
10
/ tc
10
/ tc
ktc 21/
ktc 21/ sion
10 (6
10
ous (2008)
1
1
k
k
k
k
k
k
62)
90 (183)
Table 3.5 kσ co
Table 3.6 kσ co
oefficient for int
oefficient for ou
ternal elements
utstand flanges
s
s
11 (6
11
62)
91 (183)
3.2 R
Table
p is
width
follow
‐b = b
‐b = b
‐b = b
‐b = c
‐b = h
‐b = h
And t
‐b = d
‐b = f
‐b = b
‐b = f
‐b = c
‐b = h
Internal
Outstand
p
Reduction fa
e 3.4 present
s the elemen
h which has
wing:
bw for webs;
b for interna
b‐3t for flang
c for outstan
h for equal‐l
h for unequa
the latter de
d for webs (e
flat element
b for interna
flat element
c for outstan
h for equal‐l
Cold form
ed
Welded
k
tb
4.28
actor for cla
ts the reduc
nt slenderne
different de
al flange elem
ges of RHS;
nd flanges;
eg angles;
al‐leg angles;
fines the rele
except RHS);
width for w
al flange elem
width for RH
nd flanges;
eg angles an
EN1993‐1
0772.0
p
2.01
p
2.01
p
Table
ass 4 sectio
tion factor
ss defined in
efinition in E
ments (excep
;
evant width
ebs of RHS, w
ments (excep
HS flanges, w
nd unequal‐le
‐4
1125.
2
p
1231
2
p
1242
2
p
3.4 Reduction
ons
for local bu
n equation 3
EN1993‐1‐5
pt RHS);
as:
which can co
pt RHS);
which can co
eg angles;
EN19
.0 p
1 fo
p
1 for
p
factor for local
uckling to ap
3.2. Whitin th
and EN1993
onservatively
nservatively
993‐1‐5
30552
p
or 67.0p
1188.0
2
p
r 748.0p
1188.0
2
p
l buckling (ρ fun
pply to class
his equation
3‐1‐4. The fo
y be taken as
be taken as
1
3
0
8
nction)
s 4 sections w
b is the rel
ormer stablis
s h‐2t;
b‐2t;
G&T (2008)
07.0772.02
pp
188.02
p
p
188.02
p
p
E
12 (6
12
where
levant
sh the
179
1
1
q 3.2
62)
92 (183)
3.3 C
The dunityHowe42 wh The d(see sfigure
p )
differ
3.4 C
Onceelem
,
,
Wherand ρFor m
,
,
,
Wherrespe
Comments o
definition of y should replever, for EN1hich produce
definition ofsection 3.2) aes 3.1 and 3
and c/tε ra
rent Eurocod
Cross‐sectio
e the cross‐seents in comp
. ∙
. ∙
re σ0.2 is theρ is the effecmembers in b
. ∙
. ∙
. ∙
re Wel and ectively, Weff
on the slen
class 3 limitlicate the va1993‐1‐5 whes a disconti
f the relevanas well as th.2). These d
atios for the
des.
on resistanc
ection is claspression mig
∙ .
e proof strestive width rebending:
Wpl are the
f is the elasti
derness lim
t is connectelue of the lihen ρ=1 the nuity in the f
nt width in Ee width‐to‐tiscrepancies
e same sect
ce
ssified as its ght be calcula
∙
ss, Ag is the eduction fun
e elastic andc section mo
mits and the
ed with the rmit as occurresult is a slformulation.
EN1993‐1‐5 hickness rats might deal
tion and aff
most slendeated as follow
For
gross‐cross nction (see ta
Fo
d plastic secodulus of the
e reduction
reduction funrs in both ENenderness li.
and EN1993io for outstain different
fect the com
er element, tws:
r class 1, 2 an
For class 4
section, Aeff
able 3.4).
or class 1 and
For class 3
For class 4
ction modulue effective‐cr
factor
nction and wN1993‐1‐4 amit of c/tε=
3‐1‐4 for RHnd flanges frelement sle
mparison of
the cross sec
nd 3 sections
sections
is the effec
d 2 sections
sections
sections
us of the grross section.
when ρ equand G&T pro=38.22 rathe
S/SHS is diffrom channelenderness va
f results bet
ction resista
s E
E
ctive cross‐se
E
E
E
ross‐cross se
13 (6
13
als the posal. r than
ferent ls (see alues (
tween
nce in
Eq. 3.3 Eq. 3.4
ection
Eq. 3.5 Eq. 3.6 Eq. 3.7
ection
62)
93 (183)
4. Pa
4.1 G Intern
Outst
Intern It is r
intern
Test c
arametric
Geometrica
nal parts:
tand parts a
nal radius
ecommende
nal radius of
configuratio
The specielement.
The specigross cro
c study da
l limitation
and stiffeners
ed to use a m
f cold‐formed
on (stub colu
imen should
imen shouldss‐section (im
tabase
s according
s:
minimum val
d sections:
mn test)
have a lengt
have a lengt
min).
g to EN1993
Table 4.1 C
ue for the
th of at least
th less than
3‐1‐4
t
0.5 1 401.5 2 2.5 3 4 5
Cross‐section lim
In
stiff
buckl
sizes
If c
sho
2t fo
2.5t
t 3 times the
20 times the
hw<
200 00 (slenderness
600 (400) 800 (400) 1000 (400) 1200 (400) 1600 (400) 2000 (400)
mitations specif
order to pro
feners and to
ing of the sti
of stiffeners
the followi
0.2 c/
0.1 d/
c/b < 0.2 or d
uld be ignor
or austenitic
t for duplex s
e width of the
e least radius
s limit)
fied in EN1993‐
ovide sufficie
o avoid prim
iffeners itsel
s should be w
ing ranges:
/b 0.6
/b 0.3
d/b < 0.1 the
red (c=0 or d
c
stainless stee
e widest plat
s of gyration
14 (6
14
‐1‐4
ent
mary
lf, the
within
lip
=0).
els.
te
of its
62)
94 (183)
4.2 M It wathe m
Nonli
It walocal valuecarbononlithe ait is pnew 100 wwith austemate
Materials
as proposed most conveni
inear factor
Project Name
A1 B1 C1
(A1*) (B1*) (C1*) A2 B2 C2
(A2*) (B2*) (C2*)
s found in thbuckling be
e of n, is cloon steel. Fernear factor pplicability oproposed to cmaterials wiwere also ada n value
enitics, ferriterials conside
Label
M1 M3 M5 M7 M2 M4 M6 M8 C1 C2 C3 C4
to consider ient variation
Group A B C
E0 σ0
200 25200 25200 25200 25200 25200 25200 25200 25200 25200 25200 25200 25
he preliminahaviour as wose to austerritic stainlebetween auof both EN19consider maith the samedded to poinequals to 2tics and carered in this p
E0 σ0.2
200 250 200 250 200 250 200 250 200 250 200 250 200 250 200 250 200 250 200 250 200 250 200 250
Table 4.3 M
3 nonlinearns according
n 5 10 20
.2 σ1.0
0 2560 2560 2560 262.20 262.20 262.20 2750 2750 2750 3000 3000 300
Table 4.2 Ma
ry study thawell as both nitic stainlesss steel dispstenitic and993‐1‐4 and terials A ande mechanicant out the n20. Figures rbon steel cparametric st
σ1.0 σu
256 275 262.2 300 275 350 300 450 256 275 262.2 300 275 350 300 450 256 275 262.2 300 275 350 300 450
Material param
r factors andg to the studi
Hard
σu
275 275 275
300 300 300
350 350 350 450 450 450
aterial paramet
at the nonlin yield and uss steel wheplay a less r carbon steeG&T proposd B to develoal properties nonlinear pa4.1‐4.3 shoconsidered rtudy are pres
εu n m
0.4 5 0.4 5 0.4 5 0.4 5 0.4 10 0.4 10 0.4 10 0.4 10 0.4 100 0.4 100 0.4 100 0.4 100
meters considere
d four hardeied phenome
ening rate
εu
0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4
ters proposed
ear factor haultimate streereas group rounded streel. Mainly, tsal to ferriticop the parambut with a rameter inflow the stresrespectively.sented in Ta
m σu /σ0.2 A
3 1.1 3 1.2 3 1.4 3 1.8 3 1.1 3 1.2 3 1.4 3 1.8 3 1.1 3 1.2 3 1.4 3 1.8
ed in the param
ening rates aena (see tab
Group 1 (1*) 2 (2*)
n m
5 10 20 5 10 20 5 10 20 5 10 20
as a relativelss. Group A,C has a simess‐strain rehe aim of thc stainless stemetric study. nonlinear pauence even ss‐strain relaThe key pa
ble 4.3
Assumed type o
AusteniticAusteniticAusteniticAusteniticFerritic Ferritic Ferritic Ferritic Carbon Carbon Carbon Carbon
metric study
and then comle 4.2):
σ1.0/σ01.025 (1.05) 1.1 (1.20)
m σu /σ0.
3 1.1 3 1.1 3 1.1 3 1.2 3 1.2 3 1.2 3 1.4 3 1.4 3 1.4 3 1.8 3 1.8 3 1.8
ly influence , which has milar behavioelationship whis study is aeel and ther Additionallyarameter eqmore than ationship foarameters o
of steel
c c c c
15 (6
15
mbine
0.2
2
in the a low our to with a assess efore, y, four ual to those or the of the
62)
95 (183)
100
150
200
250
300
350
σ(M
Pa)
100
150
200
250
300
350
σ(M
Pa)
100
150
200
250
300
350
σ(M
Pa)
Figu
Figu
Figure
0
0
0
0
0
0
0 0
0 0
0
0
0
0
0
0
0
re 4.1 Material
ure 4.2 Materia
4.3 Material b
0.01 0
0.01 0
0.01 0
l behaviour of t
al behaviour of
ehaviour of the
0.02 0
ε (%)
0.02 0
ε (%)
0.02 0
ε (%)
the austenitics
the ferritics (n=
e carbon steel (
0.03 0
0.03 0
0.03 0
(n=5)
=10)
n=100)
.04 0.
.04 0.
.04 0.
05
M7
M5
M3
M1
.05
M8
M6
M4
M2
.05
C4
C3
C2
C1
16 (6
16
62)
96 (183)
4.3 C The nomethe sp
SHS:
*ri<2t
RHS:
I‐sect
Chan
H
Cross‐sectio
cross‐sectioenclature depecimen.
RHS and SHS
h x b x t x(S1): 40x4(S2): 40x4(S4): 40x4(S5): 55x5(S6): 65x6(S7): 65x6(S8): 70x7(S9): 70x7(S10): 90x
t
(R1): 80x6(R2): 80x6(R3): 80x6
tions: b (I (I (I (I (I
(I
nnels: h (C (C (C (C (C (C
R
t
ri
rm
ons and spe
on dimensioefined in figu
S sections Figure 4
x ri 40x2x4 40x3x4* 40x3x6 55x1.5x3.5 65x1.5x3.5 65x1.75x3.5 70x1.5x3.5 70x1.75x3.5 x90x1.75x3.5
60x1.75x3.5 60x2x4 60x2.25x4.5
f x hw x tf x tw1): 100x50x32): 100x50x23): 100x50x24): 80x40x3x5): 80x40x2.6): 80x40x3.
x b x t x ri C1): 40x30x2C2): 40x30x3C3): 60x30x3C4): 60x35x3C5): 80x40x3C6): 80x40x3
h
b
B
cimen dime
ons consideure 4.4. The a
.4 Definition of
5
w 3x3 2.5x3 2x3 x3 .75x3 .25x3
2x4 3x6 3x6 3x6 3.25x6.5 3x6
h H
ensions
ered are salphanumer
Channelsf symbols for co
(S11)(S12)(S13)(S14)(S15)(S16)(S17)(S18)(S19)(S19)
(R4): (R5):
(I7): 8(I8): 7(I9): 7(I10)(I11)(I12)
(C7): (C8): (C9): (C10)(C11)
b
rm
ri
R
tw
B
pecified as ical code be
onsidered cross
): 90x90x2x4): 100x100x2): 100x100x2): 100x100x2): 100x100x3): 100x100x3): 110x110x2): 120x120x2): 130x130x2):140x140x2x
80x60x3x480x60x3x
80x40x3.5x370x40x3.25x70x40x3x3.5: 70x40x3.75: 100x80x5.5: 100x80x6x4
100x50x3x6100x50x4x8120x60x3x6): 140x60x5x): 160x70x5x
tf
h
follows atween brack
Is‐sections
4 2x4 2.25x4.5 2.5x5 3x4* 3x6 2x4 2x4 2x4 x4
3.5 x3.5 5 5x4 5x4 4
6 8 6 x10 x10
H hw
according tokets is the la
‐sections
tw
bf
a
17 (6
17
o the bel of
w tf
62)
97 (183)
For s
large
was k
Total
564
Total
tub column
st plate that
kept constan
of numeric
simulations
of numeric
tests the le
t makes up t
nt and equals
al stub colu
cal 4‐point b
ngth of all t
he cross‐sec
s to 1000mm
mns: (19SHS
bending test
he specimen
ction wherea
m.
S + 5RHS + 1
ts: (19SHS +
ns have been
as for the 4‐p
12I‐section +
+ 3RHS) ∙ 12
n set to kee
point bendin
+ 11Channel
materials =
p three time
ng test, the l
s) ∙ 12mater
264 simula
18 (6
18
es the
ength
rials =
ations
62)
98 (183)
5. Pa The rdifferdetersectiohas bthe re
5.1 H The rultimconstratio asses1‐5 (EgraphEN19respowith
Fi
Nu
,nu
m/A
·σ0.
2
arametric
results from rent cross‐srmine the reons and Chabeen used toeduction fac
Hollow sect
results obtamate responstituent elemc/tε where ss the currenEC‐1‐1) as weh as G&T. Th993‐1‐4, 37 onse of the tstrain harde
For stockthe ultimwhere th
The bordthe class Theofano
Despite tlimit for c
igure 5.1 Assess
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0 5
c study. Re
the parameections are esistance of tannels respeco assess classtor ρ.
ions (SHS a
ined in the se (Nu,num/Aent in the crc representsnt class 3 limell as the newhe value of ein G&T propthree materining. The ma
ky sections wmate response ultimate re
der that sepa3 limit, is q
ous (hereinaf
the material carbon steel
sment of class 3
10 15 20
esults from
etric study apresented
these specimctively. As ms 3 limit for
nd RHS)
parametric ∙σ0.2) is ploross‐section s the flat parit for internaw limit propach limit is dposal and 4ials studied: ain conclusio
with the same of the speesponse incr
arates both quite conservfter “G&T”) p
behaviour sis not a suita
3 slenderness li
0 25 30
AustenitEC-1-4 (
m stub co
are shown inseparately.
mens can be mentioned bmembers (in
study are sotted agains(h in RHS anrt (c=B‐2tw‐2al elements osed in Garddisplayed in 2 in EN1993austenitics ons that can
me σu, the greecimen. This reases for hig
behaviors spvative providproposal.
similarities bable border
imits for fully c
35 40 45
c/tε
ics (n=5)(30.7)
olumn test
n this sectionDetails of found in Annefore, the renternal and o
shown in figt the slendd either h or2ri or H‐2tf‐2of both EN1dner and Thethe legend i3‐1‐5. The f(n=5), ferritibe drawn fro
eater the notendency is gher n values
pecified in Eding a more
etween ferrfor ferritics.
ompressed hol
50 55 60
Ferritics (n=G&T (37)
ts
n where thethe relevannex B, C andesults from soutstand) in
gure 5.1 wherness of tr b in SHS) reri). The aim 993‐1‐4 (EC‐eofanous (20n brackets aigure highligcs (n=10) anom figure 5.1
onlinear parareversed fos.
N1993‐1‐4, efficient de
itics and car
low sections (in
65 70 7
10) CaEC
e results for nt parameted D for SHS/Rstub column compressio
here the secthe most slepresented bof this graph‐1‐4) and EN008) labeled and worths 3ghts the diffnd carbon (n1 are:
ameter, the or slender se
which estabesign Gardne
rbon steel, C
nternal elemen
75 80 85
arbon (n=100)C-1-1 (42)
19 (6
19
the 3 ers to RHS, I‐n tests on and
ctional ender by the h is to 1993‐in the 30.7 in ferent n=100)
lower ctions
blishes er and
Class 3
ts)
90
62)
99 (183)
In figjust tcalcuultimstressof eit
consi
The f
F
0
0
0
0
0
0
0
1
1
1
1
1
1
ρ
ure 5.2, the those that alated accord
mate numerics, Ac is the arther the web
dering the fl
, .⁄
4 ∙ ∙, .⁄
2
following rem
The redubut provi
The propconsiderethis propvalue ma
The reduthe carbo
Both ENinternal eto ferritic
Figure 5.2 Asse
0.30
0.40
0.50
0.60
0.70
0.80
0.90
.00
.10
.20
.30
.40
.50
0.4
AusEC-
real reductiare susceptiding to equacal load obtrea of the cob (cweb) or fl
lat part (b =c
2 ∙
2 ∙ ∙
marks are wo
ction factor des a safe de
posed curveed in this paposal was caterial was ab
uction factoron steel cons
1993‐1‐4 anelements (SHc stainless ste
ssment of the r
0.6
stenitics (n=5)-1-4 (0.541)
on factor ρ ible to bucktion 5.1 andained in theorners, t is thange (cflange)
c).
∙
orth to point
proposed inesign for all t
by G&T is arametric stlibrated conbout 6.
r proposed isidered here
nd G&T desHS/RHS) subjeel.
reduction funct
) CarbonG&T (0
has been plokle locally (cd 5.2 for SHSe stub columhe correspon). The elem
t up from figu
EN1993‐1‐4the material
not a suitaudy (n=5). Hsidering exp
n EN1993‐1in (n=100) b
sign procedujected to uni
tion for fully co
0.8λp
n (n=100)0.651)
otted againsclass 4). ThiS and RHS remn test simunding thickneent slendern
ure 5.2:
4 is conservas considered
able reductiHowever, it perimental re
‐5 provides ut cannot be
ures to evaiform compr
mpressed hollo
1.0
Ferritic n=EC-1-5 (0
t the elemenis reduction espectively wulation, σ0.2 ess and c refeness has bee
tive for highd in this para
on factor fois importantesults in wh
the most efe applied to f
luate the eession could
ow sections (int
1.2
=100.673)
nt slenderne factor has where Nu,num is the yield ers to the flaen determin
E
E
h n value matametric study
or the austet to mentionich the aver
fficient desigferritics.
effective widd be safely ap
ternal elements
20 (6
20
ess for been is the proof at part ned by
q 5.1
q 5.2
terials y.
enitics n that rage n
gn for
dth of pplied
s)
1.4
62)
100 (183)
Figurslend(Nu,nu
form
differ Figur
slendfollowment
Figure
Nu
,nu
m/N
u,R
k
es 5.3‐5.6 aderness migh
um) ‐ultimate
ulations, aga
rent b value
e 5.3 comp
derness has wed procedutioned:
Current E
G&T propthe unityto a 4%.
For slendtendency
Both EN1internal eto ferritic
e 5.3 Compariso
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1
EN19G&T; EC-1-
re presenteht affect the theoretic
ainst the ele
s that are m
pares curren
been deterure to calib
EN1993‐1‐4 p
posal providy (see conclu
der sectionsy is reversed
1993‐1‐4 anelements (SHc stainless ste
on of analytical 1‐4 an
0.2 0.3
93-1-4 (flat); nn=5
-4 (0.541)
d with the ae results. Tal load (Nu
ement slend
entioned be
nt EN1993‐1
rmined with rate G&T p
provides safe
e some valusions from f
s, the highefor stocky se
d G&T desiHS/RHS) subjeel.
ultimate loads nd G&T proposa
0.4 0.5
=5 EGG
aim of evaluThe figures
u,Rk), which
derness, p ,
low follow th
1‐4 with G&
the flat paroposal. The
e results for
ues in slendefigure 5.2). T
er the n vaections.
ign procedujected to uni
obtained accoal. λp determin
0.6 0.7 0
EN1993-1-4 (flaG&T; n=10G&T (0.651)
uating how tshow the rais determi
, estimated
he nomencla
&T proposal
art of the se following
any materia
er sections wThe maximum
lue, the gre
res to evaluiform compr
rding to the limed with the flat
0.8 0.9 1.
at); n=10
the definitioatio ultimatined accord
with differe
ature of figur
l. In this ca
ection (b =cconclusions
l of this stud
with a ratio m overpredic
eater the co
uate the caression could
mits and reductit parts.
.0 1.1 1.2
EN1993-1G&T; n=10EC-1-5 (0.
on of the elete numericading to diff
ent b values
re 4.4.
ase, the ele
c) which waare worth
dy.
Nu,num/Nu,Rk ction has be
onservatism
rrying capacd be safely ap
ion factors of E
1.3 1.4
-4 (flat); n=10000.673)
21 (6
21
ement l load ferent
s. The
ement
as the to be
below een up
. This
city of pplied
N1993‐
λp
(flat)
0
62)
101 (183)
Figur
relevthe lepresefollow
Figure1
Nu
,nu
m/N
u,R
k
e 5.4 compa
ant width (begend with tents the samwing remark
The fact
therefore
side.
For slend
shows thhorizonta10% less
Both prois conside
e 5.4 Compariso1‐4. λp determin
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1
EN19EN19EC-1
ares the resu
b =H‐2t or B‐the word ‘flame compariss can be des
of consider
e reduces th
der sections,
he percentagal translationconservative
cedures can ered the des
on of analytical ned with either
0.2 0.3
993-1-4 (bar); n993-1-4 (flat); n-4 (0.541)
lts that EN19
‐2t) is considat’ in brackeon but withcribed:
ing the flat
e value of
where pge of conservn, when the e.
be safely apign is more e
ultimate loads r the flat parts o
0.4 0.5
n=5 En=5 E
G
993‐1‐4 prov
dered. In theets whereas h no distinct
part, which
p , produc
is used to d
vatism betwflat part is c
pplied to ferefficient.
obtained accoor the relevant
0.6 0.7
EN1993-1-4 (bEN1993-1-4 (flG&T (0.651)
vide when ei
e figure, the the latter wion between
h is shorter
ces a transla
determine th
ween both prconsidered t
rritic stainles
rding to the limwidth. Distinct
0.8 0.9 1
bar); n=10lat); n=10
ther the flat
former resuwith the wordn the differe
than the re
tion of the
e reduction
rocedures. Athe theoretic
ss steel but w
mits and reductiion is made bet
1.0 1.1 1.2
EN1993-1EN1993-1EC-1-5 (0
t part (b =c)
ults are labeld ‘bar’. Figuent materials
elevant widt
results to th
factor, the
Additionally tcal load is u
when the fla
ion factors of Etween materia
2 1.3 1.4
1-4 (bar); n=101-4 (flat)0.673)
22 (6
22
or the
lled in re 5.5 s. The
h and
he left
graph
to the p to a
at part
N1993‐ls.
λp
00
62)
102 (183)
Figure
Finallused consimark
the eis wodesigThe nconse
Figure
Nu
,nu
m/N
u,R
kN
u,n
um
/Nu
,Rk
e 5.5 Compariso1‐4. λp deter
ly, figure 5.6to evaluatdering eithekers) wherea
lement slendorth to mentgn. However,numerical reervative due
e 5.6 Compariso
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1EN1993-1-EC-1-4 (0.
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1EN1993-1-4EC-1-4 (0.5
on of analytical mined with eith
6 presents a cte the croser the flat as EN1993‐1‐
derness has tion that the, there is a smesults of th to the stres
on of analytical
0.2 0.3-4 (bar); n=5,1541)
0.2 0.34 (bar); n=5,10541)
ultimate loads her the flat par
comparison ss‐section repart (light b‐5 has applie
been calculae fact of consmall region wese specimes‐strain beha
ultimate loads 1‐4
0.4 0.50,100 EN
G&
0.4 0.50 EN
G&
obtained accorts or the releva
of EN1993‐1esistance inblue filled med to carbon
ated considesidering thiswhere the foens, which aviour of this
obtained acco4 and EN1993‐1
0.6 0.71993-1-4 (flat)
&T (0.651)
0.6 0.7N1993-1-4 (flat&T (0.651)
rding to the limant width. No d
1‐4 and EN19n austeniticsmarkers) or n steel (n=10
ering a relevas relevant wiormulation sehave a coms material (s
rding to the lim1‐5.
0.8 0.9 1); n=5,10,100
0.8 0.9 1); n=5,10
mits and reductiistinction betw
993‐1‐5. EN1s (n=5) andthe relevan00). Accordi
ant width of dth provideeems to be u
mmon C4 maee figure 4.3
mits and reducti
1.0 1.1 1.2Series1EC-1-5 (0
1.0 1.1 1.2EN1993EC-1-5 (
ion factors of Eween materials
1993‐1‐4 hasd ferritics (nt width (unng to EN199
b =H‐3t or Bs a more effup to a 2% uaterial, migh3).
ion factors of E
2 1.3 1.4
0.673)
2 1.3 1.43-1-5; n=100(0.673)
23 (6
23
N1993‐
s been (n=10) nfilled 93‐1‐5
B‐3t. It ficient nsafe. ht are
N1993‐
λp
λp
62)
103 (183)
5.2 I‐ The rultimby thbehavis to EN19labeleworthand 1the tharde
0
0
0
0
0
1
1
1
1
1
1
Nu
,nu
m/A
·σ0
.2
‐sections
results obtamate responshe ratio c/tεviour by theassess the c
993‐1‐5 (EC‐1ed in the grahs 11 for we14 in both Ghree materiening. The m
For stockthe ultim
This tendfor highe
The bordthe class which cocold formsteel.
In additio(carbon s
Figure 5.7 Ass
.50
.60
.70
.80
.90
.00
.10
.20
.30
.40
.50
0AusEC-
ined in the se (Nu,num/A∙σε. The dimee flange and current class1‐1) as wellaph as G&T. elded elemeG&T proposaals studied:
main conclusi
ky sections wate response
dency is rever n values.
er that sepa3 limit, is quncluded thamed outstand
on, it is impsteel limit) se
essment of clas
5
Fully c
stenitics n=5-1-4-W (11)
parametric σ0.2) is plottensions of thall I‐section s 3 limit for as the newThe value onts in EN199l and EN199austenitics (ons that can
with the same of the spec
ersed for sle
arates both buite conservat there is nod members
portant to peems to be o
ss 3 slendernes
10
compressed sec
Ferritics EC-1-4-C
study are sed against thhe I‐sectionswebs were outstand el
w limit propof each limit 93‐1‐4, 11.9 93‐1‐5. The f(n=5), ferritin be drawn fr
me σu, the grecimen.
nder section
behaviours sative provido evidence toand propose
point up thaoptimal.
ss limits for fully
ctions‐outstand
n=10CF (11.9)
shown in fighe slendernes were set designed as ements of bosed in Garis displayed for cold‐for
figure highligcs (n=10) anrom figure 5
eater the no
ns where the
specified in Eing a more eo propose ded to adopt
at G&T limit
y compressed I
15
d parts (I‐section
Carbon n=100G&T (14)
gure 5.7 whess of the flto control tclass 1. The both EN1993rdner and Thin the legenrmed elemenghts the diffend carbon (n.7 are:
onlinear para
e ultimate re
EN1993‐1‐4, efficient desiifferent limitcarbon stee
t proposal f
‐sections (outst
20
n)
0 SerieEC-1
here the secange represthe local bu aim of this 3‐1‐4 (EC‐1‐4heofanous (nd in bracketnts in EN199erent responn=100) with
ameter, the
esponse incr
which estabign G&T prots for weldel limit to sta
for stainless
tand elements)
25 c/tes9-1 (14)
24 (6
24
ctional ented ckling graph 4) and (2008) ts and 93‐1‐4 nse of strain
lower
reases
blishes posal, ed and ainless
steel
)
tε
62)
104 (183)
In figreducnumethe wand 3
The f
Figur(Nu,Rk
slend
width The f
ρ
gure 5.8, the ction factor erical load oweb thicknes3.2
, .⁄
following rem
The reduproposedefficient d
Both ENoutstand be safely
Figure 5.8 Ass
es 5.9 and 5
k), which is
derness, p ,
h for outstan
following rem
Both EN1
G&T provefficient d
For both Nu,Rk ratio
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.00 0
Austen
EC-1-4
real reductihas been cabtained in ths, tf is the fla
2 ∙ ∙4 ∙ ∙
marks are wo
uction factord curve by Gdesign with a
1993‐1‐4 anelements (fapplied to fe
sessment of cla
5.10 show ths determine
, estimated
nd elements
marks are wo
1993‐1‐4 and
vides with ledesign.
formulationo. Moreover,
0.20 0.40
nitics n=5
4-W (0.589)
ion factor ρalculated acche stub coluange thickne
∙
orth to point
r proposed G&T, which all the data l
nd G&T desflanges fromerritic stainle
ss 3 reduction f
e ratio ultimed according
with b =c. E
of I‐sections
orth to point
d G&T propos
ess conserva
ns, the great, this tenden
0.60 0.8
Ferritics n
EC-1-4-CF
has been plocording to eumn test simess and cf is t
t up from figu
in EN1993‐1is the samlocated on th
sign procedum I‐sections) ess steel.
factors for fully
mate numericg to differe
Eurocodes sh
s.
t up from figu
sal provide s
ative results
ter the nonncy is also gre
80 1.00
=10
F (0.637)
otted againsequation 5.3mulation, σ0.2
he outstand
ure 5.8:
1‐4 is quite e as carbonhe safe side (
ures to evasubjected to
y compressed I‐
cal load (Nu,n
ent formula
how consiste
ures 5.9 and
safe results f
(slender se
linear parameater for hig
1.20 1.40
Carbon n=100
G&T (0.748)
st the flange where Nu,nu
is the yield flange acco
conservativn steel one, (above the ρluate the eo uniform co
‐sections (outst
num) ‐ultimatations, agai
ency by defi
5.10:
or any mate
ctions) and
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1.60 1
0 Ser
EC
slenderness
um is the ultproof stressrding to figu
E
ve and againprovides a
ρ curve). effective widompression
tand elements)
te theoreticanst the ele
ining the rel
rial.
therefore a
reater the Nnesses.
1.80 2.00
ries7
C-1-5 (0.748)
25 (6
25
s. This timate s, tw is re 3.1
q 5.3
n, the more
dth of could
al load ement
levant
more
Nu,num/
λp
62)
105 (183)
Figure
Fig
0
1
1
1
1
1
1
Nu
,nu
m/N
u,R
kN
u,n
um
/Nu
,Rk
EE
It could bthe load compress
e 5.9 Compariso
gure 5.10 Comp
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1
EN1993-1-G&T; n=5EC-1-4-W
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1N1993-1-4; n=5,C-1-4-W (0.589)
be concludecarrying ca
sion could be
on of analytical 1‐4 and G
parison of analyEN199
0.2 0.3 0
-4; n=5
(0.589)
0.2 0.310 EN
) EC
d that Both apacity of oe safely appl
ultimate loads G&T proposal. D
ytical ultimate l93‐1‐4 and EN1
0.4 0.5 0.6
EN1993-1-4;G&T; n=10EC-1-4-CF (0
0.4 0.5 0.6N1993-1-4; n=10C-1-4-CF (0.638)
EN1993‐1‐4outstand eleied to ferriti
obtained accoDistinction betw
loads obtained 1993‐1‐5 (the sa
0.7 0.8
; n=10 EG
0.638) E
6 0.7 0.800 EN) EC
4 and G&T dments (I‐secc stainless st
rding to the limween the three
according to thame of G&T pro
0.9 1.0 1
EN1993-1-4; nG&T; n=100EC-1-5 (0.748)
0.9 1.0N1993-1-5/G&T; C-1-5 (0.748)
esign procedctions) subjeteel.
mits and reductimaterials
he limits and reoposal)
1.1 1.2 1.3
=100 SerSer
) G&
1.1 1.2 1.3n=100 Ser
G&
dures to evaected to un
ion factors of E
eduction factors
1.4 1.5 λries13ries12
&T (0.748)
3 1.4 1.5ries3
&T (0.748)
26 (6
26
aluate niform
N1993‐
s of
λp
λp
62)
106 (183)
5.3 C The rsectiorepre1‐1 (bucklgraphand Elabeleworthand 1the thardethosewidthwidthconse In fig
slend
respeis theproofthe fl
The f
Channels
results obtaional ultimatesented by th(c=B‐t‐ri) resling behavioh is to assessEN1993‐1‐5 ed in the grahs 11 for we14 in both Ghree materiening. The me mentionedh‐to‐thicknesh‐to‐thickneservative (see
gures 5.13 a
derness, pectevely. Thie ultimate nf stress, Ac islat part of th
, .⁄
2 ∙
following rem
The reduagain, themore effi
When thresults ar
Both ENoutstand safely ap
ined in the te response he ratio c/tεspectively. Tur by the flas the curren(EC‐1‐1) as waph as G&T. elded elemeG&T proposaals studied: main conclusid for I‐sectioss ratio resuss ratio is cae figure 5.11)
and 5.14, th
, determine
s reduction fnumerical loas the area of e web and c
∙∙
marks are wo
ction functioe proposed icient design
e flange slere less conse
1993‐1‐4 anelements (fplied to ferri
parametric s(Nu,num/A∙σ0 where c hasThe dimensionge and all tt class 3 limwell as the nThe value onts in EN199l and EN199austenitics (ions that canns but it is wults in a horialculated acc).
he real redu
ed according
factor has bead obtained the corners,
f is the flat p
∙
orth to point
on proposedcurve by G& with all the
nderness is rvative and t
nd G&T deslanges from itic stainless
study are sh
0.2) is plottes been calcuons of the the webs weit for outstanew limit proof each limit 93‐1‐4, 11.9 93‐1‐5. The f(n=5), ferritin be drawn fworth to meizontal transcording to E
uction factor
g to EN199
een calculate in the stub, tw is the wepart of the ou
t up in figure
d in EN1993‐&T, which is data located
determinedtherefore it
sign proceduchannels) susteel.
hown in figud against thlated accordchannels wre designed nd elementsoposed in Gais displayed for cold‐for
figure highligcs (n=10) anfrom figures ention that tslation of theN1993‐1‐4 t
r ρ has bee
3‐1‐4 (b =B
ed accordingb column teseb thickness,utstand flang
s 5.13 and 5
1‐4 is more the same asd on the safe
d according seems that i
ures to evaubjected to u
ures 5.11 andhe slenderneding to eithewere set to as class 1 ors of both ENardner and Tin the legenrmed elemenghts the diffend carbon (n5.11 and 5.1he fact of dee results andthe class thr
en plotted a
) and EN19
g to equationst simulationtf is the flange.
.14:
conservatives carbon steee side (above
to EN1993‐1s more suita
luate the euniform com
d 5.12 wheress of the fr Part 1‐4 (ccontrol ther 2. The aim oN1993‐1‐4 (ETheofanous (nd in bracketnts in EN199erent responn=100) with 12 are in lineefining a diffd therefore ree limit is u
against the f
993‐1‐1 (b =
n 5.4 where n, σ0.2 is thenge thickness
E
econservativel one, prove the ρ curve
1‐1 (flat parable.
effective widmpression cou
27 (6
27
re the flange =B) or local of this C‐1‐4) (2008) ts and 93‐1‐4 nse of strain e with ferent if the
unduly
flange
=B‐t‐ri)
Nu,num e yield s, cw is
q 5.4
ve and ides a e).
rt) the
dth of uld be
62)
107 (183)
Figur
Figur
N/A
·σ
re 5.11 Assessm
re 5.12 Assessm
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0
Nu
,nu
m/A
·σ0
.2
Auste
EC-1
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0
Nu
,nu
m/A
σ0.
2
Auste
EC-1-4
ment of class 3 sthi
ment of class 3 sthi
5
enitics n=5
-4-W (11)
5
nitics n=5
4-W (11)
slenderness limckness ratio ca
slenderness limckness ratio ca
1
Ferritics n=
EC-1-4-CF
10
Ferritics n=
EC-1-4-CF
mit for fully comlculated accord
mit for fully comlculated accord
0
=10 C
F (11.9) G
0
10 Ca
(11.9) G&
mpressed Channding to EN1993‐
mpressed Channding to EN1993‐
15
arbon n=100
G&T (14)
15
arbon n=100
&T (14)
nels (outstand e‐1‐4
nels (outstand e‐1‐1
20
Series9
EC-1-1
20
Series9
EC-1-1
elements). Wid
elements). Wid
25 c/t(Part 19
(14)
25 c/t(Part 19
(14)
28 (6
28
th‐to‐
th‐to‐
tε1-4)
tε1-1)
62)
108 (183)
F
F
Figurslend(Nu,nu
form
differ
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8ρ
0
0
0
1
1
1
1
1
ρ
igure 5.13 Asse
igure 5.14 Asse
es 5.15‐5.17derness migh
um) ‐ultimate
ulations, aga
rent b value
40
60
80
00
20
40
60
80
0.00 0.20Austeniti
EC-1-4-W
.40
.60
.80
.00
.20
.40
.60
.80
0.00 0.20Austenit
EC-1-4-
essment of classdeterm
essment of classdeter
7 are presentht affect thee theoretic
ainst the ele
s that are m
0 0.40ics
W (0.589)
0 0.40tics
-W (0.589)
s 3 reduction fumined with the
s 3 reduction furmined with the
ted with thee results. Thal load (Nu
ement slend
entioned be
0.60 0.80Ferritics
EC-1-4-CF (
0.60 0.80Ferritics
EC-1-4-CF (
unctions for fule full width acco
unctions for fule flat part acco
e aim of evalhese figures
u,Rk), which
derness, p ,
low follow th
1.00 1Ca
0.637) G&
1.00C
(0.637) G
ly compressed ording to EN199
ly compressed rding to EN199
luating how show the ris determi
, estimated
he nomencla
1.20 1.40arbon
&T (0.748)
1.20 1.40arbon
&T (0.748)
Channels (outs93‐1‐4.
Channels (outs3‐1‐1.
the definitioratio ultimatined accord
with differe
ature of figur
1.60 1Series
EC-1-5
1.60 1Series
EC-1-
stand flanges). λ
stand flanges). λ
on of the elete numericading to diff
ent b values
re 4.4.
.80 2.00(Part 1s7
5 (0.748)
1.80 2.00(Part s7
-5 (0.748)
29 (6
29
λp
λp
ement l load ferent
s. The
λp 1‐4)
λp 1‐1)
62)
109 (183)
Figur
slendfollowment
FigEN1
FigurdifferdistinEN19resistfilled steel
consithe re
0
1
1
1
1
1
1
Nu
,nu
m/N
u,R
k
e 5.15 com
derness has wed procedutioned:
Both EN1
G&T provefficient d
It could bthe load compress
gure 5.15 Comp1993‐1‐4 and G
e 5.16 preserent relevantnction betwe993‐1‐4 and tance in ausmarkers) or(n=100). A
dering a releeduction fac
0.90
.00
.10
.20
.30
.40
.50
0.0 0.1
EN1993-1-G&T; n=5EC-1-4-W
mpares curre
been determure to calib
1993‐1‐4 and
vides with ledesign.
be concludecarrying ca
sion could be
parison of analyG&T proposal. λ
ents how thet widths witeen the diff EN1993‐1‐stenitics (n=5r the full widAccording to
evant width tor of EN199
0.2 0.3 0
-4; n=5
(0.589)
ent EN1993‐
mined with trate G&T p
d G&T propos
ess conserva
d that Both apacity of oe safely appl
ytical ultimate lλp determined w
di
horizontal th no distinctferent mate5. EN1993‐5) and ferritdth (unfilled o EN1993‐1
of b =c=B‐t‐93‐1‐5 provid
.4 0.5 0.6
EN1993-1-4; G&T; n=10EC-1-4-CF (0
‐1‐4 with G
the flat partroposal. The
sal provide s
ative results
EN1993‐1‐4outstand eleied to ferriti
loads obtained with the flat paifferent materia
translation otion betweeerials. Finally1‐4 has betics (n=10) cmarkers) w
1‐5 the ele
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0.7 0.8
n=10 EG
0.638) E
&T proposa
t of the secte following
safe results f
(slender se
4 and G&T dements (chac stainless st
according to thrt according toals
f the results n materials sy, figure 5.1en used toonsidering ehereas EN19ment slend
th to mentioore efficient r
0.9 1.0 1
EN1993-1-4; n=G&T; n=100EC-1-1 (0.748)
al. In this ca
tion (b =B‐t‐conclusions
or any mate
ctions) and
esign procednnels) subjeteel.
he limits and reEN1993‐1‐1. D
due to the fsame compa16 presents o evaluate teither the fla993‐1‐5 has erness has
on that the faresults.
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=100 SerSerG&T
ase, the ele
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rial.
therefore a
dures to evaected to un
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fact of considarison but wa comparisthe cross‐seat part (lightapplied to cbeen calcu
act of consid
1.4 1.5
(Parties13ies12T (0.748)
30 (6
30
ement
as the to be
more
aluate niform
s of ween
dering ith no son of ection t blue arbon ulated
dering
λp
t 1-1)
62)
110 (183)
FigEN1
Fig
Nu
,nu
m/N
u,R
kN
u,n
um
/Nu
,Rk
E
E
gure 5.15 Comp1993‐1‐4. λp de
gure 5.16 Comp
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1
EN199
EC-1-4
0.90
1.00
1.10
1.20
1.30
1.40
1.50
0.0 0.1
EN1993-1-4(B);
EC-1-4-W (0.589
parison of analytermined with
parison of analy
0.2 0.3
3-1-4(B); n=5,10
4-CF (0.638)
0.2 0.3
n=5,10 E
9) E
ytical ultimate leither the flat p
ytical ultimate lEN1993
0.4 0.5 0.
0,100
0.4 0.5 0
EN1993-1-4(flat)
EC-1-4-CF (0.63
loads obtained part (flat) or th
loads obtained 3‐1‐4 and EN19
.6 0.7 0.8
EN1993-1-1(flat)
EC-1-5 (0.748)
0.6 0.7 0.8
); n=5,10 E
38) E
according to the full width (B)
according to th993‐1‐5.
0.9 1.0
); n=5,10,100
0.9 1.0
EN1993-1-1(flat)
EC-1-5 (0.748)
he limits and re. No distinction
he limits and re
1.1 1.2 1
EC-1-4-W
G&T (0.74
1.1 1.2 1
; n=100 Se
G
eduction factorsn between mate
eduction factors
.3 1.4 1.5
W (0.589)
48)
1.3 1.4 1.5
eries3
&T (0.748)
31 (6
31
s of erials
s of
λp
λp
62)
111 (183)
6. Pa The rSHS/Rthesebendcomp
6.1 C The a4‐poiMu,nu
sectioflat pdimewher
Figur
6.2 C The rultimconstratio asses1‐5 (EgraphEN19
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
Nu
,nu
m/A
·σ0
.2 a
nd
Mu
,nu
m/W
el,y·σ
0.2
arametric
results fromRHS are pree specimensing tests hapression.
Class 3 slend
assessment ont bending
m/Wel,y∙σ0.2) aon (h in RHS part (c=B‐2twnsions but sreas bending
re 6.1 Assessme
Class 2 slend
results obtamate responstituent elemc/tε where ss the currenEC‐1‐1) as weh as G&T. Th993‐1‐4, 35
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
0 5AustenitiAustenitiEC-1-4 (
c study. Re
m the paramesented. Det can be fouave been u
der limit
of class 3 limtests. Figureagainst the sand either h
w‐2ri or H‐2tsubjected tog tests as (BD
ent of class 3 sl
der limit
ined in the se (Mu,num/Went in the crc representsnt class 2 limell as the newhe value of ein G&T prop
10 15 20ics-SC (n=5)ics-BD (n=5)30.7)
esults from
etric study atails of the und in Anneused to asse
it might be te 6.1 plots tslenderness h or b in SHStf‐2ri). The s a different
D).
enderness limicolumns and
parametric Wpl,y∙σ0.2) is pross‐section s the flat parit for internaw limit propach limit is dposal and 3
0 25 30FeFeG&
m 4‐point
are shown irelevant parex E. As meness class 2
tackled consthe ultimateof the most ) representespecimens dtest. Stub c
ts for fully com4‐point bendin
study are splotted again(h in RHS anrt (c=B‐2tw‐2al elements osed in Garddisplayed in 8 in EN1993
35 40 45erritics-SC (n=erritics-BD (n=&T (37)
t bending
in this sectiorameters to ntioned befoand 1 limi
idering resule response oslender con
ed by the ratidisplayed precolumns are
mpressed hollowng tests results
shown in fignst the slend either h or2ri or H‐2tf‐2of both EN1dner and Thethe legend i3‐1‐5. The f
5 50 5510)10)
tests
on where thdetermine
ore, the rest for memb
ts from bothof both test stituent elemio c/tε whereesent the salabeled in t
w sections (inte
gure 6.2 whderness of tr b in SHS) reri). The aim 993‐1‐4 (EC‐eofanous (20n brackets aigure highlig
60 65 70Carbon-SCarbon-BEC-1-1 (4
he results fothe resistan
sults from 4bers (intern
h stub colum(Nu,num/A∙σ0ment in the e c represename cross‐sethe legend a
rnal elements)
here the secthe most slepresented bof this graph‐1‐4) and EN008) labeled and worths 2ghts the diff
0 75 80SC (n=100)BD (n=100)42)
32 (6
32
or the nce of ‐point nal) in
mn and
.2 and cross‐nts the ection as (SC)
. Stub
ctional ender by the h is to 1993‐in the 26.7 in ferent
c/tε
62)
112 (183)
respowith
Fi
6.3 C
Whenreduccapacsectioflat pinternlimit each EN19mate
The rcurva
Mpl, ain eq
M an
Mu
,nu
m/W
pl,y
·σ0.
2
onse of the tstrain harde
The bordproviding
Despite tlimit for c
igure 6.2 Assess
Class 1 slend
n the cross‐ction of the city (R) againon (h in RHS part (c=B‐2twnal elementproposed inlimit is displ
993‐1‐5 and erials studied
rotational caature at the p
and pl is the. 6.2. The m
d eqs. 6.4 an
1
0.40
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
0 5
Auste
EC-1-
three materining. The ma
er that sepag a more effi
the material carbon steel
sment of class 2
der limit
‐section presresistance, tnst the the sand either h‐2ri or H‐2tf‐s of both ENn Gardner anlayed in the G&T propo
d: austenitics
apacity has point at whic
e elastic curvmoment‐curv
nd 6.5 for .
10 15 2
nitics (n=5)
-4 (26.7)
ials studied: ain conclusio
rates both bcient design
behaviour sis not a suita
2 slenderness li
sents enougthe section isslenderness oh or b in SHS‐2ri). The aimN1993‐1‐4 (nd Theofanolegend in brosal. The figs (n=5), ferrit
been quantch the falling
vature corresature respon
All the param
20 25 30
austenitics ons that can
behaviors spefor stainless
similarities bable border
imits for fully c
gh rotation cs classified aof the most ) representem of this grapEC‐1‐4) and ous (2008) larackets and wgure highlightics (n=10) an
tified accordg branch of t
sponding to nse of the sp
meters of th
35 40 4
Ferritics (n=1
G&T (35)
(n=5), ferritibe drawn fro
ecified in ENs steel the G&
etween ferrfor ferritics.
ompressed hol
capacity to as class 1. Figslender con
ed by the ratiph is to asseEN1993‐1‐5
abeled in theworths 25.7 hts the diffend carbon (n
ding to eq. 6he moment–
Mpl as illustrpecimens wa
ese equation
45 50 55
0)
cs (n=10) anom figure 6.2
1993‐1‐4 is q&T proposal.
itics and car
low sections (in
form a plasgure 6.3 presstituent elemio c/tε wheress the curren5 (EC‐1‐1) ase graph as Gin EN1993‐1erent respo=100) with s
6.1 where –curvature c
rated in figuras calculated
ns are define
60 65 7
Carbon
EC-1-1
nd carbon (n2 are:
quite conser.
rbon steel, C
nternal elemen
stic hinge wsents the roment in the e c represennt class 1 lims well as theG&T. The va1‐4 and 33 innse of the strain harden
u is the seccurve falls be
re 6.4 and ded using eq. 6
ed in figure 6
E
70 75 80
n (n=100)
1 (38)
33 (6
33
n=100)
vative
Class 2
ts)
ithout tation cross‐nts the mit for e new lue of n both three ning.
ctional elow
efined 6.3 for
6.5.
q 6.1
c/tε
62)
113 (183)
EN19propoadop
Fi
4
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0
M/M
pl
993‐1‐4 doesosed in Bildted. The ma
The borconserva
The equivproposed
igure 6.3 Assess
Figure 6.4 De
/2 ∙3
84
2
0.00
3.00
6.00
9.00
12.00
15.00
0
R
Aust
EC-1
1 2 3
κplRotation
s not defined et al. (198in conclusion
rder that stive.
valent carbod in Gardner
sment of class 1
efinition of rota
5 10
enitics (n=5)
1-4 (25.7)
4 5
κ/κpl
n capacity R
e any rotatio89) Sedlacekns that can b
separates b
on steel limitand Theofan
1 slenderness li
tional capacity
15 20
6 7 8
onal capacitk and Feldmbe drawn fro
both behavi
t may be sanous (2008).
imits for fully c
y
25 30
Ferritics (n=1
G&T (33)
9 10
ty requirememann (1995)om figure 6.3
ors specifie
fely adopted
ompressed hol
Figure 6.5 4‐p
35 40
0)
L1
ent and the) for carbon are:
ed in EN19
d for ferritic
low sections (in
point bending te
45 50
Carbon
EC-1-1
L2
u1 u
ms
P/2
erefore, the n steel (R=3
993‐1‐4 is
c stainless st
nternal elemen
est configuratio
E
E
E
E
55 60 c
(n=100)
(33)
L3
u2
P/2
34 (6
34
value ) was
quite
eel as
ts)
on
q 6.2
q 6.3
q 6.4
q 6.5
c/tε
62)
114 (183)
7. Fe The o
in tab
Br
St
Af
The a
alrea
limits
Afshan
erritic sta
only tests fou
bles 7.1 and
Re
redenkamp and
tangenberg (20
fshan and Gard
assessment o
dy presented
s proposed in
Referen
n and Gardner
inless stee
und in the lit
7.2 for stub
eference
d Van den Berg
000) ‐ ECSC (200
dner (2011)
of the class li
d in Afshan a
n Gardner an
ce
(2011)
el in expe
terature in fe
columns and
Se
g (1995) I‐se
00) I‐seC
RSS
Table
Tab
imits conside
and Gardner
nd Theofano
Section
RHS SHS SHS RHS SHS SHS
erimental
erritic stainle
d bending te
ection Numof te
ection 2
ection 7CHS 7
RHS 4SHS 2SHS 2
Total: 24/199 t
7.1 Stub colum
le 7.2 Bending
ering these f
r (2013) whe
ous provides
Type of test
No
4‐point 4‐point 4‐point 3‐point 3‐point 3‐point
Total:
tests
ess steels cro
sts respectiv
mber ests
Grad
1.400
7 1.4007 1.400
4 1.400 1.400 1.450
tests
mn test
tests
ferritic stainle
re the main
a more effic
Number of tests
Gr
2 1.41 1.41 1.42 1.41 1.41 1.4
94 tests
oss‐sections a
vely.
e Materia
03 3Cr12
03 3Cr1203 3Cr12
03 3Cr1203 3Cr1209 441
ess steel dat
conclusions
ient design.
ade Mater
4003 3Cr14003 3Cr14509 4414003 3Cr14003 3Cr14509 441
are summari
al Type
2 Ferritic
2 Ferritic 2 Ferritic
2 Ferritic 2 Ferritic
Ferritic
ta has been
are that the
rial Type
12 Ferriti12 Ferriti1 Ferriti12 Ferriti12 Ferriti1 Ferriti
35 (6
35
ized
c c c c c c
62)
115 (183)
Refe
AshraAshrabased AfshaAfshaElem AfshaAfshasteel AfshaAfshaHollo BardiBardipart I Bild eBild, Sapplic5 of E BredeBredeSectio BurgaBurgacompResea EN 19Euroc EN 19EN 19for bu EN 19EN 1Supp GardGardCivil a
erences
af et al. (200af, M., Gardnd on deform
an and Gardnan, S. and ents. Journa
an and Gardnan, S. and Gdesign. 4th In
an and Gardnan, S. and Gow Sections.
i and Kyriakidi, F.C. and KyI:Experiment
et al. (1989) S., Roik, K., Scability of anEurocode 3,
enkamp andenkamp, P. on Columns.
an et al. (200an, B.A., Baparison betwarch (2000).
990 (2004) code 0 (2004
993‐1‐1 (200993‐1‐1. Euruildings.
993‐1‐4 (2001993‐1‐4. Eulementary ru
ner (2002) ner, L. (202)and Environm
8) ner, L. and Nation capaci
ner (2011) Gardner, L.l of Structur
ner (2012) Gardner, L. (nternational
ner (2013) ardner, L. (2Journal of St
des (2006) yriakides, S. ts. Internatio
Sedlacek, G.,nalysis modePart 1.1, Aac
van den BerJ. and van d. Journal of C
00) adoo, N.R., ween EurocoVol 54, 51‐7
4): Basis of st
06) rocode 3 (20
06) urocode 3 (ules for stain
). A new appmental Engin
ethercot, D. ty. Journal o
(2011). Teal Engineerin
2012). The Stainless Ste
2013). Expertructural Eng
(2006). Plastonal Journal
Stutzki, C. aels in Eurocodchen. 1989.
rg (1995) den Berg, G.Construction
Gilsenan, Kode 3, Part 73.
tructural des
006): Design
(2006): Desinless steel. C
proach to stneering, Imp
A. (2008). Stof Structural
esting of Feng (2011), AS
Continuous eel Experts S
rimental Studgineering (20
tic buckling oof Mechanic
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. J. (1995). Tal Steel Rese
.A. Structur1.4 and tes
sign.
of steel stru
ign of steelCEN.
tructural staerial College
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Strength MSeminar – De
dy of Cold‐F011), ASCE. V
of circular tucal Sciences (
macher, R. Th1. Backgroun
The Strengthearch (1995)
al design ot results. Jo
uctures ‐ Par
l structures
inless steel e London, Lo
inless steel d‐ASCE. Vol. 1
ess Steel T
ethod for stecember 201
ormed FerriVol. 139 (5), 7
ubes under a(2006). Vol. 4
he b/t‐ratios nd Documen
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f stainless surnal of Co
rt 1.1: Gener
‐ Part 1.4:
design. Ph.Dndon.
design: Resis134(3), 402‐4
Tubular Stru
tructural sta12, Ascot.
itic Stainless717‐728.
axial compre48(8), 830‐84
controlling tnt 5.02 for ch
ss Steel Built1‐144.
steel membnstructional
ral rules and
: General r
D. thesis, De
36 (6
36
stance 411.
ctural
ainless
s Steel
ssion‐41.
the hapter
t‐up I‐
bers – Steel
d rules
ules ‐
ept. of
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116 (183)
GardGardEngin GardGardstainl GardGardMate1291 GardGardMem60(9) GardGard2011 GardGardstainl1216 GardGarddesigVol. 1 KuwaKuwa(2003 Liu anLiu, Ymem RasmRasmmem RasmRasmmem
ner (2008) ner, L. (2008neers ‐ Struct
ner et al. (20ner, L., Taljaless steel. Th
ner and Nethner, L. and Nerial and cros‐1318.
ner and Nethner, L. and N
mber behavio), 1319–1332
ner and Salibner, L. and S. Budapest, H
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amura (2003amura, H. (23). Vol. 3(3),
nd Young (20Y. and Younbers Journal
mussen and Hmussen, K.J.Rbers. I: Colu
mussen and Hmussen, K.J.Rbers II: Beam
8). The Conttures and Bu
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hercot (2004Nethercot, Dss‐ sectional
hercot (2004Nethercot, Dour of colum2.
ba (2011) Saliba, N. (20Hungary.
ofanous (200Teofanous, Mements. Jou
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). Influence Journal of S
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s steel hollowel Research (
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e hollow sec9(2), 165‐177
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Institution o
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w sections‐P(2004). Vol.
w sections, Pearch (2004
ss steel. Euro
of local bucklVol. 64(11),
the behaviouDynamics (2
s. Steel Struc
ction compre7.
less steel tu9(8), 2349–2
less steel tu8), 2368–238
37 (6
37
of Civil
tenitic
Part 1: 60(9),
Part 2: ). Vol.
osteel
ling in 1207‐
ur and 2011).
ctures
ession
ubular 367.
ubular 86.
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117 (183)
RasmRasmConst Real aReal, struct SedlaSedlaEurocAach StangStangsheetatain StangStangDeve Talja Talja,VTT R TheoTheostainl TheoTheostainl Zhou ZhouThin‐ YounYounColum YounYounStruc
mussen (2000mussen, K. (tructional St
and MirambE. and Mirtures (2005)
acek and Feldacek, G. and code 3, Part en. 1995.
genberg (199genberg, H. Wting made ofless steel in
genberg (200genberg, H. lopment of t
and Salmi (1, A. and SalmResearch Not
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g and Liu (20g, B. and Lmns. Journal
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99) WP3.5S.02. Cf stainless stconstruction
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1995) mi, P. (1995). tes 1619. Esp
Gardner (200and Gardnellow section
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2005). Flexu65‐1475.
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. Ferritic sttainless steel
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09) er, L. (2009columns. En
10) r, L. (2010).l of Construc
). Tests of c5). Vol. 43(9),
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ural behavio
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. Experimentctional Steel
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s steel weldeProject (2000
el. Report ttion
l RHS beamsical Research
and numerictructures (20
tal and numResearch (20
stainless ste337.
tigation of ol. 129(2), 16
ed high stre38‐1745.
ubular struct
ess steel be
icability of af Eurocode 3
ed I‐sections0): Developm
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, columns anh Centre of F
cal modellin009). Vol. 31(
merical studie010). Vol. 66
eel tubular f
Cold‐Forme9‐176.
ngth stainles
ctures. Journ
eams. Engine
analysis mod3, Part 1.1,
s and cold foment of the
C Project (2
nd beam‐colFinland, 1995
g of lean d(12), 3047‐3
es of lean d6(6), 816‐825
flexural mem
ed Stainless
ss steel. Jour
38 (6
38
nal of
eering
els in
ormed use of
2000):
umns. 5.
duplex 058.
duplex 5.
mbers.
Steel
rnal of
62)
118 (183)
A
In
T
Annex A
n this annex, expe
a) Afshan andb) Gardner ac) Gardner, Td) Kuwamurae) Liu Young f) Rasmusseng) Rasmussenh) Talja and Si) Theofanouj) Young andk) Young andl) Bredenkamm) Gardner an) Stangenbeo) Stangenbe
Tables A1‐A3 gathe
erimental availabl
d Gardner (2011) nd Nethercot (20Talja and Badoo (2a (2003) (2003) n and Hancock (1n (2000) Salmi (1995) us and Gardner (2d Liu (2003) d Lui (2005) mp and Van den Bnd Saliba (2011) erg (1999) erg (2000)
er the relevant va
e data found in th
04a) 2006)
993a)
2009)
Berg (1995)
ariables for SHS/R
he literature is pr
RHS, I‐sections and
esented. The follo
d channels respec
owing articles we
ctively.
re considered:
39 (62)
339
119 (183)
Ref. Section type
a)
RHS RHS RHS RHS SHS SHS SHS SHS
b)
SHS SHSHS SHSHS SHSHS SHSHS SHSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSSHS SHSRHS RHRHS RHRHS RHRHS RHRHS RHRHS RHRHS RHSRHS RHSRHS RHRHS RHRHS RH
Reference gr
120×80×3‐1 3C120×80×3‐2 3C60×40×3‐1 3C60×40×3‐2 3C80×80×3‐1 3C80×80×3‐2 3C60×60×3‐1 460×60×3‐2 4
HS80x80x4‐SC1 3HS80x80x4‐SC2 3HS80x80x4‐SC3 3S80x80x4‐ASC1 3S80x80x4‐ASC2 3S100x100x2‐SC1 3S100x100x2‐SC2 3S100x100x3‐SC1 3S100x100x3‐SC2 3S100x100x4‐SC1 3S100x100x4‐SC2 3S100x100x6‐SC1 3S100x100x6‐SC2 3S100x100x8‐SC1 3S100x100x8‐SC2 3S150x150x4‐SC1 3S150x150x4‐SC2 3HS60x40x4‐SC1 3HS60x40x4‐SC2 3HS120x80x3‐SC1 3HS120x80x3‐SC2 3HS120x80x6‐SC1 3HS120x80x6‐SC2 3S150x100x4‐SC1 3S150x100x4‐SC2 3HS100x50x2‐SC1 3HS100x50x2‐SC2 3HS100x50x3‐SC1 3
rade L (mm) H (mm
Cr12 362 119.Cr12 362.2 120Cr12 122.1 59.9Cr12 122.1 59.9Cr12 242 80.1Cr12 242 80.1441 182.2 60.5441 182.2 60.5
304 400.2 79.8304 399.9 80.1304 399.4 80.1304 400.4 79.5304 399.8 79.7304 400.5 100.304 400.2 99.9304 400 100.304 399.8 100.304 399.8 99.8304 400.4 99.7304 399.8 100.304 399.6 100.304 399.1 100.304 400 100.304 449.9 150.304 450.7 150.304 180.3 60304 179.6 60304 359.9 120.304 360 120304 360.1 119.304 360.1 120304 450.4 149.304 450 149.304 300.6 99.8304 299.8 99.8304 299.9 100.
Measured dimensio
m) B (mm) t (mm)
9 80 2.84 0 80 2.83 9 40 2.81 9 40 2.81 1 80.1 2.83 1 80.1 2.82 5 60.5 2.98 5 60.6 2.9
8 79.9 3.68 1 80.1 3.82 1 79.9 3.83 5 79.7 3.77 7 79.6 3.68 2 100 1.91 9 100 1.91 1 100.3 2.87 1 100.1 2.84 8 99.9 3.84 7 99.8 3.83 1 100.1 5.94 2 100.1 5.92 3 100.7 7.97 1 100.7 7.97 4 149.9 3.79 2 150 3.74
40 3.83 40 3.82
1 80.2 2.93 0 80.2 2.91 9 80.4 5.85 0 80.3 5.85 9 99.9 3.82 9 99.9 3.83 8 49.8 1.85 8 50 1.84 1 50.1 2.89
ons
ri (mm) A (mm2)
3.7 1077.9 13.9 1074.3 13.19 508.1 3.19 508 3.67 850.8 3.43 849.1 2.9 662.1 3.1 654.8
4.6 1080 4.4 1124 4.4 1125 4.1 1105 4.4 1080 1.3 743 1.3 739 1.5 1101 1.5 1089 4.5 1431 4.5 1426 5.8 2147 5.8 2153 8 2785 8 2781 5.8 2167 16 2139 12.9 675 2.9 675 4.6 1109 14.6 1100 17 2107 17 2108 15.6 1799 15.6 1805 12.3 529 2.3 529 3.1 811
Mid‐section dime
h (mm)
b (mm)
t (mm
117.06 77.16 2.8117.17 77.17 2.857.09 37.19 2.857.09 37.19 2.877.27 77.27 2.877.28 77.28 2.857.52 57.52 2.957.60 57.70 2.9
76.12 76.22 3.676.28 76.28 3.876.27 76.07 3.875.73 75.93 3.776.02 75.92 3.698.29 98.09 1.997.99 98.09 1.997.23 97.43 2.897.26 97.26 2.895.96 96.06 3.895.87 95.97 3.894.16 94.16 5.994.28 94.18 5.992.33 92.73 7.992.13 92.73 7.9146.61 146.11 3.7146.46 146.26 3.756.17 36.17 3.856.18 36.18 3.8117.17 77.27 2.9117.09 77.29 2.9114.05 74.55 5.8114.15 74.45 5.8146.08 96.08 3.8146.07 96.07 3.897.95 47.95 1.897.96 48.16 1.897.21 47.21 2.8
ensions M
m)rm
(mm) E
(GPa)
84 5.12 216 83 5.32 216 81 4.60 219.381 4.60 219.383 5.09 210 82 4.84 210 98 4.39 218.390 4.55 218.3
68 6.44 186.682 6.31 186.683 6.32 186.677 5.99 206.368 6.24 206.391 2.26 201.391 2.26 201.387 2.94 195.884 2.92 195.884 6.42 191.383 6.42 191.394 8.77 198.492 8.76 198.497 11.99 202.497 11.99 202.479 7.70 206 74 7.87 206 83 4.82 192.882 4.81 192.893 6.07 209.391 6.06 209.385 9.93 194.585 9.93 194.582 7.51 205.883 7.52 205.885 3.23 208 84 3.22 208 89 4.55 203.6
40 (62)
aterial properties
σ0.2 (MPa)
σu (MPa)
n
423 472 10423 472 10454 475 7.454 475 7431 447 8431 447 8519 534 7519 534 7
457 706 5457 706 5457 706 5261 11261 11382 675 6.382 675 6.388 691 5.388 691 5.465 713 5.465 713 5.501 715 5.501 715 5.328 653 6.328 653 6.314 659 6.314 659 6.489 705 3.489 705 3.419 739 4.419 739 4.509 714 5.509 714 5.297 663 8297 663 8403 707 6.403 707 6.479 716 4.
4
Stub column testresults
n Nu,exp (kN)
δu (mm)
0.2 449 1.16 0.2 441 1.19 8 278 2.18 .8 271 2.12 .7 392 1.42 .7 389 1.49 .8 376 1.92 .8 370 1.94
5 727 7.4 5 714 7.2 5 711 7.7 1.5 309 8.6 1.5 335 7.1 .6 197 1.1 .6 189 0.9 .6 489 2.2 .6 496 2.3 .7 779 4 .7 774 4 .2 1513 13.4 .2 1507 13.5 .4 1630 29 .4 1797 38.2 .8 726 1.7 .8 713 1.6 .9 492 6.7 .9 497 6.7 .1 452 1.6 .1 447 1.6 .3 1459 7.8 .3 1465 7.9 8 660 2.5 8 659 2.3 .9 182 1.2 .9 181 1.3 .2 407 1.8
40
t
)
120 (183)
Ref. Section type
RHS RHRHS RH
b) RHS RHRHS RHRHS RH
c)
SHS RSHS RHRHS RRHS RSHS RHSHS RHSRHS RHSRHS RHS
d)
SHS SHS SHS SHS SHS SHS SHS SHS SHS SHS SHS SHS
e)
SHS SHS SHS SHS
f) SHS SHS
g) RHS RHS RHS
h) SHS
i) SHS 1
Reference gr
HS100x50x3‐SC2 3HS100x50x4‐SC1 3HS100x50x4‐SC2 3HS100x50x6‐SC1 3HS100x50x6‐SC2 3
RHS80x80x3‐A 30HS100x100x3‐A 30HS120x80x3‐A 30HS140x60x3‐A 30S80x80x3‐C850 30100x100x3‐C850 30S120x80x3‐C850 30S140x60x3‐C850 30
SC‐2□1 1.4SC‐2□2 1.4SC‐2□3 1.4SC‐2□4 1.4SC‐2□5 1.4SC‐2□6 1.4SC‐4□1 1.4SC‐4□2 1.4SC‐4□3 1.4SC‐4□4 1.4SC‐4□5 1.4SC‐4□6 1.4
S1L0360 3S1L0360R 3S2L0360 3S2L0360R 3
S1SC1 3S1SC2 3
R1SC1 3R2SC1 3R3SC1 3
RHS ‐1 CC‐1 3
00x100x4‐SC1 1.4
rade L (mm) H (mm
304 300 100.304 300.4 99.7304 300.6 99.8304 300 100.304 300.1 100
01LN 400 80.201LN 398 10001LN 400 12001LN 403 139.01LN 398 80.401LN 399 100.01LN 400 120.01LN 400 140
4301 150 50.84301 225 75.34301 300 100.34301 375 125.84301 450 1514301 600 200.54318 150 50.54318 225 75.54318 300 100.14318 375 125.54318 451 151.14318 600 200.0
304 360 69.9304 360 69.9304 358.5 70304 358.5 70
04L 300 80.404L 298 79.7
04L 300 84.704L 300 64.904L 300 50.7
304 399 59.5
4162 400 102
Measured dimensio
m) B (mm) t (mm)
1 50 2.89 7 49.9 3.73 8 49.8 3.68 1 50.1 5.95 0 50.1 5.96
2 80.1 3.07 0 100.1 3.06 0 79.9 3.09 7 60.4 3.10 4 80.1 3.05 3 100.1 3.05 5 80.7 3.07 0 60.4 3.04
88 50.88 2.9053 75.33 2.89 38 100.38 2.88 88 125.88 2.87 1 151 2.86558 200.58 2.8458 50.58 2.96 5 75.55 2.98 15 100.15 2.93553 125.53 2.98 13 151.13 2.95505 200.05 2.96
9 70.1 1.91 9 70.2 1.93
70 4.86 69.9 4.91
4 80.4 3 7 79.7 3
7 38 2.95 9 38.9 2.92 7 25 3.03
7 59.76 5
2 101 3.93
ons
ri (mm) A (mm2)
3.1 811 3.6 1026 3.6 1014 5.6 1558 5.5 1559
4 930 2.75 1168 4 1172 14.5 1168 13 936 3 1166 4 1163 14 1151 1
7.59 515.09 5.41 813.74 5.62 1104.365.43 1399.7 16.135 1686.01 16.155 2264.81 14.04 542.22 3.32 855.15 4.065 1132.493.02 1450.67 13.845 1760.28 14.04 2346.08 1
1.9 512 1.9 516 4.1 1213 4.1 1223
2.5 908.2 2.5 899.8
3.55 663.7 4.58 541.8 2.47 401.3
3.5 999
3.8 1495.2
Mid‐section dime
h (mm)
b (mm)
t (mm
97.21 47.11 2.895.97 46.17 3.796.12 46.12 3.694.15 44.15 5.994.04 44.14 5.9
77.13 77.03 3.096.94 97.04 3.0116.91 76.81 3.0136.60 57.30 3.177.35 77.05 3.097.25 97.05 3.0117.43 77.63 3.0136.96 57.36 3.0
47.98 47.98 2.972.44 72.44 2.897.50 97.50 2.8123.01 123.01 2.8148.14 148.14 2.8197.74 197.74 2.847.62 47.62 2.972.57 72.57 2.997.22 97.22 2.9122.55 122.55 2.9148.18 148.18 2.9197.09 197.09 2.9
67.99 68.19 1.967.97 68.27 1.965.14 65.14 4.865.09 64.99 4.9
77.40 77.40 3.076.70 76.70 3.0
81.75 35.05 2.961.98 35.98 2.947.67 21.97 3.0
54.57 54.76 5.0
98.07 97.07 3.9
ensions M
m)rm
(mm) E
(GPa)
89 4.55 203.673 5.47 208 68 5.44 208 95 8.58 187.296 8.48 187.2
07 5.53 187.506 4.28 195 09 5.55 199.510 6.05 196.505 4.53 173 05 4.53 183.507 5.54 190 04 5.52 186
91 9.05 203 89 6.86 203 88 7.06 203 87 6.87 203 87 7.57 203 85 7.58 203 96 5.52 206 98 4.81 206 94 5.53 206 98 4.51 206 96 5.32 206 96 5.52 206
91 2.86 195 93 2.87 195 86 6.53 194 91 6.56 194
00 4.00 194 00 4.00 194
95 5.03 92 6.04 03 3.99
00 6.00 192
93 5.77 198.8
41 (62)
aterial properties
σ0.2 (MPa)
σu (MPa)
n
479 716 4.471 702 5.471 702 5.605 754 5.605 754 5.
505 834.5 5483 806 5.5501 841 5.8478 847 5.6617 1024.5 4.6541 942.5 4.555 970.5 4.523 997 5.4
249 249 249 249 249 249 497 497 497 497 497 497
337 636 4337 636 4444 688 5444 688 5
420 695 395 695
569 3.3
586 761 9
4
Stub column testresults
n Nu,exp (kN)
δu (mm)
.2 415 1.8
.2 626 3.5
.2 627 3.7
.7 1217 9.3
.7 1217 9.8
5 598 55 609 85 595 65 560 65 755 .8 656 .6 645 45 642
241 282.38 323.15 353.84 363.91 364.83 377.45 459.41 468.73 480.49 482.95 511.87
4 194 4 193.1 5 825.3 5 843.9
485 471
357 355 297
39 801
9 1022 3.63
41
t
)
121 (183)
Ref. Section type
SHS 1SHS SHS SHS
i) SHS RHS RHS
j)
RHS RHS RHS RHS RHS RHS RHS RHS
k)
SHS SHS SHS SHS SHS SHS RHS RHS RHS
Reference gr
00x100x4‐SC2 1.480x80x4‐SC1 1.480x80x4‐SC2 1.460x60x3‐SC1 1.460x60x3‐SC2 1.480x40x4‐SC1 1.480x40x4‐SC2 1.4
R1L0360 3R1L0360R 3R2L0360 3R2L0360R 3R3L0360 3R3L0360R 3R4L0360 3R4L0360R 3
40x40x2 1.440x40x2a 1.450x50x1.5 1.450x50x1.5a 1.4150x150x3 H150x150x6 H140x80x3 1.4160x80x3 1.4200x110x4 H
Table
rade L (mm) H (mm
4162 400 1034162 319.7 80.54162 332.2 804162 239.8 604162 240 604162 239.9 79.54162 237.8 79.5
304 258.5 120304 359.5 120304 359 119.304 359 119.304 360 119.304 359.5 120.304 360 120.304 359 119.
4462 300 40.14462 300 40.14462 300 50.14462 300 50HSA 600 150.HSA 601 150.4462 600 1404462 600 160.HSA 600 196.
e A.1 Geometrical dim
Measured dimensio
m) B (mm) t (mm)
3 102 3.97 5 80 3.88
80 3.81 60 3.09 60 3.17
5 39 3.76 5 39.6 3.81
0 40 1.96 0 40 1.93 8 40 5.3 6 40.1 5.27 8 79.8 2.78 1 79.9 2.81 2 80.3 5.98 9 80.5 6.03
1 39.9 1.9451 40 1.9471 50.3 1.584
50.3 1.5485 150.5 2.7966 150.2 5.8550 78.8 3.0751 80.8 2.8692 108.5 4.01
mensions, material pro
ons
ri (mm) A (mm2)
3.9 1524.7 3.8 1147.4 3.6 1125 2.3 683 2.1 700.4 3.5 799.8 4.3 808.8
3.1 598 13.1 590 13.7 1523 13.7 1515 13.9 1056 13.9 1066 16.5 2159 16.5 2172 1
1.8 288 1.8 289 1.5 295 1.5 289 4.6 1607 15.3 3382 17 1258 16.3 1305 19.1 2291 1
operties and experim
Mid‐section dime
h (mm)
b (mm)
t (mm
99.03 98.03 3.976.62 76.12 3.876.19 76.19 3.856.91 56.91 3.056.83 56.83 3.175.74 35.24 3.775.69 35.79 3.8
118.04 38.04 1.9118.07 38.07 1.9114.50 34.70 5.3114.33 34.83 5.2117.02 77.02 2.7117.29 77.09 2.8114.22 74.32 5.9113.87 74.47 6.0
38.16 37.96 1.938.15 38.05 1.948.52 48.72 1.548.45 48.75 1.5147.70 147.70 2.8144.75 144.35 5.8136.93 75.73 3.0157.23 77.93 2.8192.19 104.49 4.0
ental results from stu
ensions M
m)rm
(mm) E
(GPa)
97 5.89 198.888 5.74 199.981 5.51 199.909 3.85 209.817 3.69 209.876 5.38 199.581 6.21 199.5
96 4.08 198 93 4.07 198 30 6.35 194 27 6.34 194 78 5.29 193 81 5.31 193 98 9.49 194 03 9.52 194
95 2.77 216 95 2.77 216 58 2.29 200 55 2.27 200 80 6.00 189 86 8.23 194 08 8.54 212 87 7.73 208 01 11.11 200
ub columns test in SH
42 (62)
aterial properties
σ0.2 (MPa)
σu (MPa)
n
586 761 9679 773 6.679 773 6.755 839 6755 739 6734 817 10734 817 10
350 649 5350 649 5424 676 5424 676 5366 648 5366 648 5443 678 5443 678 5
707 827 4707 827 4622 770 5622 770 5448 699 4497 761 3486 736 6536 766 5503 961 4
HS/RHS
4
Stub column testresults
n Nu,exp (kN)
δu (mm)
9 1037 4.01 .5 923 4.13 .5 915 3.88 6 613 4.09 6 616 3.69 0.1 709 4.33 0.1 710 4.12
5 187.8 5 184.7 5 969.8 5 994.7 5 404.6 5 413.1 5 1414.1 5 1387.8
4 245.3 4 238 5 174.7 5 177.6 4 408.6 3 1927.4 6 558.2 5 537.3 4 957
42
t
)
122 (183)
Reference Refere
d)
SC‐2CSC‐2CSC‐2CSC‐2CSC‐2CSC‐2CSC‐4CSC‐4CSC‐4CSC‐4CSC‐4C
ence grade L (mm
C1 1.4301 150 C2 1.4301 240 C3 1.4301 300 C3A 1.4301 300 C4 1.4301 450 C5 1.4301 150 C1 1.4318 150 C2 1.4318 240.5C3 1.4318 300 C3A 1.4318 300 C4 1.4318 450.5
Table A
Measu) H (mm) B (mm)
49.75 24.83 80.3 39.58 100.45 49.98 101.1 49.6 150.4 49.68 50.25 49.48 50.25 25.03
80.05 39.98 100.45 50.05 100.45 50.05
150.5 50
A.2 Geometrical dime
ured dimensions tw (mm) tf (mm) r i2.93 2.71 2.92 2.63 2.93 2.62 2.93 2.62 2.92 2.63 2.92 2.81 3.02 2.79 3.02 2.74 3.02 2.73 3.01 2.71 3.02 2.73
ensions, material pro
i (mm) A (mm2) h (m
4.07 257.5 464.08 431.24 773.07 555.46 973.07 555.16 983.08 698.65 144.08 403.7 473.98 267.41 472.98 450.52 773.48 571.18 972.99 570.37 973.98 721.02 14
operties and experime
Mid‐section dimenmm) b (mm) t (mm
6.82 23.365 2.827.38 38.12 2.787.52 48.515 2.788.17 48.135 2.787.48 48.22 2.787.33 48.02 2.867.23 23.52 2.917.03 38.47 2.887.43 48.54 2.887.44 48.545 2.867.48 48.49 2.88
ental results from stu
nsions Materiam) rm (mm) E (GPa)
2 5.54 203 8 5.54 203 8 4.54 203 8 4.54 203 8 4.54 203 6 5.54 203 1 5.49 206 8 4.49 206 8 4.99 206 6 4.49 206 8 5.49 206
b columns test in Cha
43 (62)
al properties Stub co) σ0.2 (MPa) Nu,exp
249 106249 134249 146249 140249 15249 125497 186497 229497 233497 229497 228
annels
olumn test results (kN) δu (mm)
6.04 4.18 6.23 0.43 56 .02 6.16 .72 .78 .61 .19
43
123 (183)
Ref.
l) 141
m)
I‐I‐I‐2I‐2
d)
n) I
I‐160I
o)
Reference g
40x70x3.5x4.5 1.180x90x6x4.5 1.
‐200x140x6x6 1.‐200x140x8x6 1.200x140x10x8 1.200x140x12x8 1.
SC‐2H1 1.SC‐2H2 1.SC‐2H3 1.SC‐2H4 1.SC‐2H5 1.SC‐2H6 1.SC‐2H7 1.SC‐2H8 1.SC‐4H1 1.SC‐4H2 1.SC‐4H3 1.SC‐4H4 1.SC‐4H5 1.SC‐4H6 1.SC‐4H7 1.SC‐4H8 1.
I‐160x80‐SC 1.‐160x160‐SC 1.0x160DUPLEX‐SC 1.‐320x160‐SC 1.
ISC 140x80 1.ISC 140x100 1.ISC 140x120 1.ISC 160x100 1.ISC 140x140 1.ISC 180x100 1.ISC 200x100 1.
rade L (mm) H (m
4003 345 1404003 345 181
4162 600.35 214.4162 600.33 217.4162 600.28 219.4162 600.15 224.
4301 150 50.4301 300 504301 300 101.4301 300 1014301 300 1014301 450 1504301 600 2004301 600 2014318 150 51.4318 300 51.4318 300 1014318 300 102.4318 300 1004318 450 151.4318 600 201.4318 600 201
4301 451 1584301 447 1594462 449 1604301 894 32
4003 399.5 1394003 399.5 1404003 399 1384003 503 164003 509 1394003 504 1784003 504 199
Table A
Measured dime
mm) bf (mm) tw (mm
0.7 69.6 3.491.4 88.8 4.65
.29 138.89 6.01
.14 139.04 5.98
.85 139 8.03
.49 139.29 8.14
.9 49.9 2.960 98.9 2.94.25 49.7 2.931.3 75.2 2.931.2 99.7 2.920.9 99.6 2.950.7 100.15 2.931.1 150.4 2.95.3 49.3 3.01.6 99.2 3.011.3 50.25 3.01.05 74.8 2.990.3 99.7 3.02.25 99.5 3.02.95 100.1 3.021.4 149.75 3.01
8.8 79.5 69.1 160.75 60.5 160.7 6.80 160.3 6
9.1 79.2 60.8 99.55 68.9 119.6 60 99.3 69.5 139.25 68.2 100.2 69.5 99.15 6
A.3 Geometrical dime
nsions (mm)
m) tf (mm) a (mm)
9 4.65 5 6.18
1 6.12 5 8 8.04 5 3 10.35 6 4 12.68 6
6 2.95 4 2.93 3 2.94 3 2.94 2 2.93 5 2.93 3 2.93 5 2.94 1 3.04 1 2.99 1 3.03 9 3.02 2 3.03 2 3.03 2 3.01 1 3.02
9.86 3 9.94 3
10.06 3 9.84 3
6 4 6 4 6 4 6 4 6 4 6 4 6 4
ensions, material prop
Mid‐
A (mm2) hw (mm)
69.6 88.8
2914 138.893438 139.044476 139 5153 139.29
427.14 49.9 709.33 98.9 571.2 49.7 721.76 75.2 862.63 99.7 1011.52 99.6 1156.79 100.151460.25 150.4435.39 49.3 729.57 99.2 591.19 50.25738.86 74.8 887.82 99.7 1041.44 99.5 1194.31 100.11491.06 149.75
2430 79.5 4040 160.754370 160.74990 160.3
1713 79.2 1967.4 99.552196.6 119.62079.6 99.3 2436 139.252199.6 100.22314.8 99.15
perties and experime
‐section dimensions (
bf (mm) tw (mm)
136.05 3.49 175.22 4.65
208.17 6.01 209.1 5.98 209.5 8.03 211.81 8.14
47.95 2.96 47.07 2.94 98.31 2.93 98.36 2.93 98.27 2.92 147.97 2.95 197.77 2.93 198.16 2.95 48.26 3.01 48.61 3.01 98.27 3.01 99.03 2.99 97.27 3.02 148.22 3.02 198.94 3.02 198.38 3.01
148.94 6 149.16 6 150.44 6.8 310.16 6
133.1 6 134.8 6 132.9 6 154 6 133.5 6 172.2 6 193.5 6
ntal results from stub
(mm)
tf (mm) E (GPa)
4.65 196.21 6.18 196.75
6.12 193.5 8.04 199.68 10.35 211.68 12.68 204.71
2.95 203 2.93 203 2.94 203 2.94 203 2.93 203 2.93 203 2.93 203 2.94 203 3.04 206 2.99 206 3.03 206 3.02 206 3.03 206 3.03 206 3.01 206 3.02 206
9.86 200.61 9.94 198 10.06 202 9.84 199.91
6 220 6 220 6 220 6 220 6 220 6 220 6 220
b columns test in I‐sec
44 (62)
Material properties
σ0.2 (MPa) σu (MPa
365.65 487.61348.18 463.77
516 727.5508.19 727.5502.07 753.85471.44 724.07
235 235 235 235 235 235 235 235 440 440 440 440 440 440 440 440
299.35 614.86300 612.90
522.45 761.01302.54 618.27
345 479 345 479 345 479 345 479 345 479 345 479 345 479
ctions
Stub coluresu
a) n Nu,exp (kN)
449 689.5
10.7 1473 11.64 1849
11.89 2540 10.67 2978
152.76 192.81 171.08 199.94 203.37 207.72 206.07 231.41 253.36 289.65 279.53 309.9 323.35 310.11 311.48 359.71
5.68 885 5.53 1440 5.22 2590 6.02 1430
10.3 680 10.3 788 10.3 871 10.3 789 10.3 902 10.3 811 10.3 827
44
umn test ults δu (mm)
5.7 6.5 3.3 6.2 5.7 6.3 4.9
124 (183)
Ann
nex B
Specimen
(
S1M1 S1M3 S1M5 S1M7
S2M1 S2M3 S2M5 S2M7
S3M1 S3M3 S3M5 S3M7
S4M1 S4M3 S4M5 S4M7
S5M1 S5M3 S5M5 S5M7
S6M1 S6M3 S6M5 S6M7
S7M1 S7M3 S7M5 S7M7
S8M1 S8M3 S8M5 S8M7
S9M1 S9M3 S9M5 S9M7
S10M1 S10M3 S10M5 S10M7
S11M1 S11M3 S11M5 S11M7
S12M1 S12M3 S12M5 S12M7
S13M1 S13M3 S13M5 S13M7
S14M1 S14M3
Cross
h mm)
b (mm) (
40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40
55 55 55 55 55 55 55 55
65 65 65 65 65 65 65 65
65 65 65 65 65 65 65 65
70 70 70 70 70 70 70 70
70 70 70 70 70 70 70 70
90 90 90 90 90 90 90 90
90 90 90 90 90 90 90 90
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100
s‐section prope
t mm)
rm (mm) (
2 5.00 2 5.00 2 5.00 2 5.00
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2.25 5.63 2.25 5.63 2.25 5.63 2.25 5.63
2.5 6.25 2.5 6.25 2.5 6.25 2.5 6.25
3 5.50 3 5.50
erties
ri mm)
Ag (mm)
4 302.834 302.834 302.834 302.83
4 451.674 451.674 451.674 451.67
6 441.376 441.376 441.376 441.37
3.5 319.063.5 319.063.5 319.063.5 319.06
3.5 379.063.5 379.063.5 379.063.5 379.06
3.5 441.863.5 441.863.5 441.863.5 441.86
3.5 409.063.5 409.063.5 409.063.5 409.06
3.5 476.863.5 476.863.5 476.863.5 476.86
3.5 616.863.5 616.863.5 616.863.5 616.86
4 702.834 702.834 702.834 702.83
4 782.834 782.834 782.834 782.83
4.5 878.274.5 878.274.5 878.274.5 878.27
5 973.175 973.175 973.175 973.17
4 1171.674 1171.67
Material
σu (MPa)
n
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
7 275 5 7 300 5
Numerica
Nu,num
(kN) εcr
81.17 0.60483.79 0.60489.46 0.60499.65 0.604
123.33 1.29128.12 1.29138.88 1.29161.35 1.29
120.56 1.39125.24 1.39135.89 1.39158.37 1.39
82.77 0.24582.88 0.24583.92 0.24585.69 0.245
85.90 0.20686.21 0.20687.36 0.20686.11 0.206
114.64 0.278114.64 0.278114.85 0.278115.58 0.278
89.76 0.19190.49 0.19191.32 0.19189.13 0.191
120.08 0.258120.19 0.258120.29 0.258115.90 0.258
121.34 0.200120.19 0.200120.08 0.200120.29 0.200
158.76 0.262158.13 0.262158.34 0.262161.07 0.262
161.81 0.235161.81 0.235161.81 0.235161.81 0.235
199.42 0.298199.31 0.298200.05 0.298199.10 0.298
245.77 0.369241.44 0.369237.20 0.369245.14 0.369
311.41 0.524313.54 0.524
al results
r σcr,num
(MPa)
476 2015.87 476 2015.87 476 2015.87 476 2015.87
923 4307.67 923 4307.67 923 4307.67 923 4307.67
969 4656.33 969 4656.33 969 4656.33 969 4656.33
524 594.52 524 594.52 524 594.52 524 594.52
623 423.04 623 423.04 623 423.04 623 423.04
878 571.86 878 571.86 878 571.86 878 571.86
108 363.96 108 363.96 108 363.96 108 363.96
851 492.40 851 492.40 851 492.40 851 492.40
039 296.87 039 296.87 039 296.87 039 296.87
215 388.37 215 388.37 215 388.37 215 388.37
566 314.21 566 314.21 566 314.21 566 314.21
864 398.19 864 398.19 864 398.19 864 398.19
928 492.37 928 492.37 928 492.37 928 492.37
468 699.57 468 699.57
45 (6
45
62)
125 (183)
Specimen
(
S14M5 S14M7
S15M1 S15M3 S15M5 S15M7
S16M1 S16M3 S16M5 S16M7
S17M1 S17M3 S17M5 S17M7
S18M1 S18M3 S18M5 S18M7
S19M1 S19M3 S19M5 S19M7
R1M1 R1M3 R1M5 R1M7
R2M1 R2M3 R2M5 R2M7
R3M1 R3M3 R3M5 R3M7
R4M1 R4M3 R4M5 R4M7
R5M1 R5M3 R5M5 R5M7
S1M2 S1M4 S1M6 S1M8
S2M2 S2M4 S2M6 S2M8
S3M2 S3M4 S3M6 S3M8
S4M2 S4M4 S4M6
Cross
h mm)
b (mm) (
100 100 100 100
100 100 100 100 100 100 100 100
110 110 110 110 110 110 110 110
120 120 120 120 120 120 120 120
130 130 130 130 130 130 130 130
140 140 140 140 140 140 140 140
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40
55 55 55 55 55 55
s‐section prope
t mm)
rm (mm) (
3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
2 5.00 2 5.00 2 5.00 2 5.00
2.25 5.63 2.25 5.63 2.25 5.63 2.25 5.63
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
2 5.00 2 5.00 2 5.00 2 5.00
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
1.5 4.25 1.5 4.25 1.5 4.25
erties
ri mm)
Ag (mm)
4 1171.674 1171.67
6 1161.376 1161.376 1161.376 1161.37
4 862.834 862.834 862.834 862.83
4 942.834 942.834 942.834 942.83
4 1022.834 1022.834 1022.834 1022.83
4 1102.834 1102.834 1102.834 1102.83
3.5 476.863.5 476.863.5 476.863.5 476.86
4 542.834 542.834 542.834 542.83
4.5 608.274.5 608.274.5 608.274.5 608.27
4 811.674 811.674 811.674 811.67
6 801.376 801.376 801.376 801.37
4 302.834 302.834 302.834 302.83
4 451.674 451.674 451.674 451.67
6 441.376 441.376 441.376 441.37
3.5 319.063.5 319.063.5 319.06
Material
σu (MPa)
n
7 350 5 7 450 5
7 275 5 7 300 5 7 350 5 7 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 5 300 5 350 5 450 5
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10
Numerica
Nu,num
(kN) εcr
322.06 0.524333.98 0.524
309.60 0.533311.83 0.533320.25 0.533332.92 0.533
161.18 0.214160.86 0.214160.34 0.214160.02 0.214
160.91 0.196160.38 0.196160.91 0.196160.27 0.196
160.71 0.180160.61 0.180160.18 0.180160.29 0.180
161.87 0.167161.87 0.167161.87 0.167161.54 0.167
116.00 0.26116.32 0.26116.52 0.26116.63 0.26
140.49 0.347141.75 0.347143.12 0.347147.00 0.347
161.68 0.440163.05 0.440167.69 0.440172.86 0.440
219.07 0.768224.50 0.768234.19 0.768253.36 0.768
216.62 0.792221.63 0.792233.02 0.792253.04 0.792
81.06 0.60483.69 0.60488.73 0.60498.81 0.604
123.22 1.29128.01 1.29138.66 1.29161.03 1.29
120.56 1.39125.14 1.39135.57 1.39157.51 1.39
82.15 0.24581.52 0.24582.04 0.245
al results
r σcr,num
(MPa)
468 699.57 468 699.57
374 711.65 374 711.65 374 711.65 374 711.65
406 259.47 406 259.47 406 259.47 406 259.47
611 217.90 611 217.90 611 217.90 611 217.90
095 185.59 095 185.59 095 185.59 095 185.59
798 159.98 798 159.98 798 159.98 798 159.98
651 441.83 651 441.83 651 441.83 651 441.83
722 578.70 722 578.70 722 578.70 722 578.70
086 734.77 086 734.77 086 734.77 086 734.77
878 1281.30 878 1281.30 878 1281.30 878 1281.30
213 1320.22 213 1320.22 213 1320.22 213 1320.22
476 2015.87 476 2015.87 476 2015.87 476 2015.87
923 4307.67 923 4307.67 923 4307.67 923 4307.67
969 4656.33 969 4656.33 969 4656.33 969 4656.33
524 594.52 524 594.52 524 594.52
46 (6
46
62)
126 (183)
Specimen
(
S4M8
S5M2 S5M4 S5M6 S5M8
S6M2 S6M4 S6M6 S6M8
S7M2 S7M4 S7M6 S7M8
S8M2 S8M4 S8M6 S8M8
S9M2 S9M4 S9M6 S9M8
S10M2 S10M4 S10M6 S10M8
S11M2 S11M4 S11M6 S11M8
S12M2 S12M4 S12M6 S12M8
S13M2 S13M4 S13M6 S13M8
S14M2 S14M4 S14M6 S14M8
S15M2 S15M4 S15M6 S15M8
S16M2 S16M4 S16M6 S16M8
S17M2 S17M4 S17M6 S17M8
S18M2 S18M4 S18M6 S18M8
Cross
h mm)
b (mm) (
55 55
65 65 65 65 65 65 65 65
65 65 65 65 65 65 65 65
70 70 70 70 70 70 70 70
70 70 70 70 70 70 70 70
90 90 90 90 90 90 90 90
90 90 90 90 90 90 90 90
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
110 110 110 110 110 110 110 110
120 120 120 120 120 120 120 120
130 130 130 130 130 130 130 130
s‐section prope
t mm)
rm (mm) (
1.5 4.25
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2.25 5.63 2.25 5.63 2.25 5.63 2.25 5.63
2.5 6.25 2.5 6.25 2.5 6.25 2.5 6.25
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
erties
ri mm)
Ag (mm)
3.5 319.06
3.5 379.063.5 379.063.5 379.063.5 379.06
3.5 441.863.5 441.863.5 441.863.5 441.86
3.5 409.063.5 409.063.5 409.063.5 409.06
3.5 476.863.5 476.863.5 476.863.5 476.86
3.5 616.863.5 616.863.5 616.863.5 616.86
4 702.834 702.834 702.834 702.83
4 782.834 782.834 782.834 782.83
4.5 878.274.5 878.274.5 878.274.5 878.27
5 973.175 973.175 973.175 973.17
4 1171.674 1171.674 1171.674 1171.67
6 1161.376 1161.376 1161.376 1161.37
4 862.834 862.834 862.834 862.83
4 942.834 942.834 942.834 942.83
4 1022.834 1022.834 1022.834 1022.83
Material
σu (MPa)
n
450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
7 275 10 7 300 10 7 350 10 7 450 10
7 275 10 7 300 10 7 350 10 7 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
Numerica
Nu,num
(kN) εcr
82.04 0.245
91.22 0.20691.22 0.20690.49 0.20691.01 0.206
113.91 0.278114.22 0.278114.01 0.278114.85 0.278
94.03 0.19193.93 0.19193.93 0.19193.41 0.191
119.03 0.258117.68 0.258118.20 0.258117.57 0.258
131.69 0.200131.69 0.200131.48 0.200131.69 0.200
164.01 0.262164.12 0.262164.22 0.262161.81 0.262
167.79 0.235167.90 0.235167.79 0.235169.05 0.235
208.38 0.298208.27 0.298208.27 0.298208.27 0.298
240.80 0.369240.70 0.369241.65 0.369247.04 0.369
308.74 0.524310.77 0.524317.80 0.524325.89 0.524
307.68 0.533309.60 0.533316.41 0.533322.48 0.533
173.15 0.214173.78 0.214173.25 0.214172.52 0.214
176.60 0.196176.60 0.196176.28 0.196175.64 0.196
176.76 0.180176.66 0.180176.66 0.180175.80 0.180
al results
r σcr,num
(MPa)
524 594.52
623 423.04 623 423.04 623 423.04 623 423.04
878 571.86 878 571.86 878 571.86 878 571.86
108 363.96 108 363.96 108 363.96 108 363.96
851 492.40 851 492.40 851 492.40 851 492.40
039 296.87 039 296.87 039 296.87 039 296.87
215 388.37 215 388.37 215 388.37 215 388.37
566 314.21 566 314.21 566 314.21 566 314.21
864 398.19 864 398.19 864 398.19 864 398.19
928 492.37 928 492.37 928 492.37 928 492.37
468 699.57 468 699.57 468 699.57 468 699.57
374 711.65 374 711.65 374 711.65 374 711.65
406 259.47 406 259.47 406 259.47 406 259.47
611 217.90 611 217.90 611 217.90 611 217.90
095 185.59 095 185.59 095 185.59 095 185.59
47 (6
47
62)
127 (183)
Specimen
(
S19M2 S19M4 S19M6 S19M8
R1M2 R1M4 R1M6 R1M8
R2M2 R2M4 R2M6 R2M8
R3M2 R3M4 R3M6 R3M8
R4M2 R4M4 R4M6 R4M8
R5M2 R5M4 R5M6 R5M8
S1C1 S1C2 S1C3 S1C4
S2C1 S2C2 S2C3 S2C4
S3C1 S3C2 S3C3 S3C4
S4C1 S4C2 S4C3 S4C4
S5C1 S5C2 S5C3 S5C4
S6C1 S6C2 S6C3 S6C4
S7C1 S7C2 S7C3 S7C4
S8C1 S8C2 S8C3 S8C4
S9C1
Cross
h mm)
b (mm) (
140 140 140 140 140 140 140 140
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40
40 40 40 40 40 40 40 40
55 55 55 55 55 55 55 55
65 65 65 65 65 65 65 65
65 65 65 65 65 65 65 65
70 70 70 70 70 70 70 70
70 70 70 70 70 70 70 70
90 90
s‐section prope
t mm)
rm (mm) (
2 5.00 2 5.00 2 5.00 2 5.00
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
2 5.00 2 5.00 2 5.00 2 5.00
2.25 5.63 2.25 5.63 2.25 5.63 2.25 5.63
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
2 5.00 2 5.00 2 5.00 2 5.00
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
1.5 4.25 1.5 4.25 1.5 4.25 1.5 4.25
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
1.75 4.38
erties
ri mm)
Ag (mm)
4 1102.834 1102.834 1102.834 1102.83
3.5 476.863.5 476.863.5 476.863.5 476.86
4 542.834 542.834 542.834 542.83
4.5 608.274.5 608.274.5 608.274.5 608.27
4 811.674 811.674 811.674 811.67
6 801.376 801.376 801.376 801.37
4 302.834 302.834 302.834 302.83
4 451.674 451.674 451.674 451.67
6 441.376 441.376 441.376 441.37
3.5 319.063.5 319.063.5 319.063.5 319.06
3.5 379.063.5 379.063.5 379.063.5 379.06
3.5 441.863.5 441.863.5 441.863.5 441.86
3.5 409.063.5 409.063.5 409.063.5 409.06
3.5 476.863.5 476.863.5 476.863.5 476.86
3.5 616.86
Material
σu (MPa)
n
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 10 300 10 350 10 450 10
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100
Numerica
Nu,num
(kN) εcr
178.65 0.167178.54 0.167178.32 0.167177.56 0.167
115.58 0.26115.69 0.26115.69 0.26115.79 0.26
140.18 0.347138.81 0.347138.39 0.347142.91 0.347
160.74 0.440160.74 0.440165.79 0.440168.53 0.440
219.28 0.768224.18 0.768231.32 0.768252.72 0.768
216.41 0.792221.20 0.792231.00 0.792250.49 0.792
80.85 0.60482.53 0.60484.21 0.60486.31 0.604
123.01 1.29126.52 1.29133.87 1.29143.03 1.29
120.24 1.39123.97 1.39131.31 1.39142.28 1.39
82.57 0.24582.36 0.24581.73 0.24579.65 0.245
96.54 0.20696.33 0.20694.97 0.20692.89 0.206
114.43 0.278114.33 0.278113.39 0.278110.25 0.278
102.79 0.191102.79 0.191101.85 0.19199.66 0.191
122.80 0.258122.28 0.258120.81 0.258117.99 0.258
150.41 0.200
al results
r σcr,num
(MPa)
798 159.98 798 159.98 798 159.98 798 159.98
651 441.83 651 441.83 651 441.83 651 441.83
722 578.70 722 578.70 722 578.70 722 578.70
086 734.77 086 734.77 086 734.77 086 734.77
878 1281.30 878 1281.30 878 1281.30 878 1281.30
213 1320.22 213 1320.22 213 1320.22 213 1320.22
476 2015.87 476 2015.87 476 2015.87 476 2015.87
923 4307.67 923 4307.67 923 4307.67 923 4307.67
969 4656.33 969 4656.33 969 4656.33 969 4656.33
524 594.52 524 594.52 524 594.52 524 594.52
623 423.04 623 423.04 623 423.04 623 423.04
878 571.86 878 571.86 878 571.86 878 571.86
108 363.96 108 363.96 108 363.96 108 363.96
851 492.40 851 492.40 851 492.40 851 492.40
039 296.87
48 (6
48
62)
128 (183)
Specimen
(
S9C2 S9C3 S9C4
S10C1 S10C2 S10C3 S10C4
S11C1 S11C2 S11C3 S11C4
S12C1 S12C2 S12C3 S12C4
S13C1 S13C2 S13C3 S13C4
S14C1 S14C2 S14C3 S14C4
S15C1 S15C2 S15C3 S15C4
S16C1 S16C2 S16C3 S16C4
S17C1 S17C2 S17C2 S17C4
S18C1 S18C2 S18C3 S18C4
S19C1 S19C2 S19C3 S19C4
R1C1 R1C2 R1C3 R1C4
R2C1 R2C2 R2C3 R2C4
R3C1 R3C2 R3C3 R3C4
R4C1 R4C2
Cross
h mm)
b (mm) (
90 90 90 90 90 90
90 90 90 90 90 90 90 90
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
110 110 110 110 110 110 110 110
120 120 120 120 120 120 120 120
130 130 130 130 130 130 130 130
140 140 140 140 140 140 140 140
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60 80 60 80 60
80 60 80 60
s‐section prope
t mm)
rm (mm) (
1.75 4.38 1.75 4.38 1.75 4.38
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2.25 5.63 2.25 5.63 2.25 5.63 2.25 5.63
2.5 6.25 2.5 6.25 2.5 6.25 2.5 6.25
3 5.50 3 5.50 3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
2 5.00 2 5.00 2 5.00 2 5.00
1.75 4.38 1.75 4.38 1.75 4.38 1.75 4.38
2 5.00 2 5.00 2 5.00 2 5.00
2.25 5.63 2.25 5.63 2.25 5.63 2.25 5.63
3 5.50 3 5.50
erties
ri mm)
Ag (mm)
3.5 616.863.5 616.863.5 616.86
4 702.834 702.834 702.834 702.83
4 782.834 782.834 782.834 782.83
4.5 878.274.5 878.274.5 878.274.5 878.27
5 973.175 973.175 973.175 973.17
4 1171.674 1171.674 1171.674 1171.67
6 1161.376 1161.376 1161.376 1161.37
4 862.834 862.834 862.834 862.83
4 942.834 942.834 942.834 942.83
4 1022.834 1022.834 1022.834 1022.83
4 1102.834 1102.834 1102.834 1102.83
3.5 476.863.5 476.863.5 476.863.5 476.86
4 542.834 542.834 542.834 542.83
4.5 608.274.5 608.274.5 608.274.5 608.27
4 811.674 811.67
Material
σu (MPa)
n
300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
7 275 1007 300 1007 350 1007 450 100
7 275 1007 300 1007 350 1007 450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100350 100450 100
275 100300 100
Numerica
Nu,num
(kN) εcr
148.95 0.200142.67 0.200147.28 0.200
178.71 0.262178.92 0.262176.72 0.262172.94 0.262
194.15 0.235193.62 0.235192.78 0.235189.63 0.235
225.24 0.298224.92 0.298221.87 0.298217.23 0.298
252.23 0.369250.01 0.369247.78 0.369243.45 0.369
311.30 0.524311.51 0.524309.49 0.524302.25 0.524
308.96 0.533308.64 0.533308.10 0.533300.44 0.533
201.81 0.214191.00 0.214200.45 0.214198.35 0.214
201.29 0.196200.98 0.196199.92 0.196199.28 0.196
198.70 0.180198.38 0.180197.20 0.180195.60 0.180
198.27 0.167198.16 0.167197.73 0.167196.85 0.167
122.07 0.26121.65 0.26120.08 0.26117.99 0.26
140.18 0.347140.91 0.347139.55 0.347135.98 0.347
160.10 0.440160.21 0.440160.31 0.440157.05 0.440
218.33 0.768220.35 0.768
al results
r σcr,num
(MPa)
039 296.87 039 296.87 039 296.87
215 388.37 215 388.37 215 388.37 215 388.37
566 314.21 566 314.21 566 314.21 566 314.21
864 398.19 864 398.19 864 398.19 864 398.19
928 492.37 928 492.37 928 492.37 928 492.37
468 699.57 468 699.57 468 699.57 468 699.57
374 711.65 374 711.65 374 711.65 374 711.65
406 259.47 406 259.47 406 259.47 406 259.47
611 217.90 611 217.90 611 217.90 611 217.90
095 185.59 095 185.59 095 185.59 095 185.59
798 159.98 798 159.98 798 159.98 798 159.98
651 441.83 651 441.83 651 441.83 651 441.83
722 578.70 722 578.70 722 578.70 722 578.70
086 734.77 086 734.77 086 734.77 086 734.77
878 1281.30 878 1281.30
49 (6
49
62)
129 (183)
Specimen
(
R4C3 R4C4
R5C1 R5C2 R5C3 R5C4
Cross
h mm)
b (mm) (
80 60 80 60
80 60 80 60 80 60 80 60
Table B.1 Pa
s‐section prope
t mm)
rm (mm) (
3 5.50 3 5.50
3 7.50 3 7.50 3 7.50 3 7.50
arametric study
erties
ri mm)
Ag (mm)
4 811.674 811.67
6 801.376 801.376 801.376 801.37
y results for hol
Material
σu (MPa)
n
350 100450 100
275 100300 100350 100450 100
llow sections. S
Numerica
Nu,num
(kN) εcr
221.52 0.768222.16 0.768
215.98 0.792218.11 0.792218.86 0.792219.18 0.792
Stub columns
al results
r σcr,num
(MPa)
878 1281.30 878 1281.30
213 1320.22 213 1320.22 213 1320.22 213 1320.22
50 (6
50
62)
130 (183)
Ann
nex C
Specimen
I1M1 I1M3 I1M5 I1M7
I2M1 I2M3 I2M5 I2M7
I3M1 I3M3 I3M5 I3M7
I4M1 I4M3 I4M5 I4M7
I5M1 I5M3 I5M5 I5M7
I6M1 I6M3 I6M5 I6M7
I7M1 I7M3 I7M5 I7M7
I8M1 I8M3 I8M5 I8M7
I9M1 I9M3 I9M5 I9M7
I10M1 I10M3 I10M5 I10M7
I11M1 I11M3 I11M5 I11M7
I12M1 I12M3 I12M5 I12M7
I1M2 I1M4 I1M6 I1M8
I2M2 I2M4
Cross‐
bf (mm)
hw (mm)
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
70 40 70 40 70 40 70 40
70 40 70 40 70 40 70 40
70 40 70 40 70 40 70 40
100 80 100 80 100 80 100 80
100 80 100 80 100 80 100 80
100 50 100 50 100 50 100 50
100 50 100 50
‐section proper
tf (mm)
tw (mm)
3 3 3 3 3 3 3 3
2.5 3 2.5 3 2.5 3 2.5 3
2 3 2 3 2 3 2 3
3 3 3 3 3 3 3 3
2.75 3 2.75 3 2.75 3 2.75 3
3.25 3 3.25 3 3.25 3 3.25 3
3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5
3.25 3.5 3.25 3.5 3.25 3.5 3.25 3.5
3 3.5 3 3.5 3 3.5 3 3.5
3.75 4 3.75 4 3.75 4 3.75 4
5.5 4 5.5 4 5.5 4 5.5 4
6 4 6 4 6 4 6 4
3 3 3 3 3 3 3 3
2.5 3 2.5 3
rties
Ag (mm) (M
741 741 741 741 4
642.5 642.5 642.5 642.5 4
544 544 544 544 4
591 591 591 591 4
551.75 551.75 551.75 551.75 4
630.25 630.25 630.25 630.25 4
687.75 687.75 687.75 687.75 4
583.625583.625583.625583.625 4
549.5 549.5 549.5 549.5 4
670 670 670 670 4
1398 1398 1398 1398 4
1496 1496 1496 1496 4
741 741 741 741 4
642.5 642.5
Material
σu MPa)
n N(
275 5 18300 5 18350 5 18450 5 18
275 5 14300 5 14350 5 14450 5 14
275 5 10300 5 10350 5 11450 5 11
275 5 15300 5 15350 5 15450 5 16
275 5 14300 5 14350 5 14450 5 15
275 5 16300 5 16350 5 16450 5 17
275 5 18300 5 18350 5 19450 5 20
275 5 15300 5 15350 5 16450 5 17
275 5 14300 5 14350 5 15450 5 16
275 5 17300 5 18350 5 19450 5 21
275 5 37300 5 38350 5 39450 5 42
275 5 40300 5 41350 5 43450 5 48
275 10 18300 10 18350 10 18450 10 17
275 10 14300 10 14
Numerical r
u,num
kN) εcr
80.97 0.4175481.89 0.4175482.60 0.4175485.14 0.41754
45.15 0.3254444.94 0.3254445.15 0.3254445.25 0.32544
08.69 0.2347409.30 0.2347410.61 0.2347411.93 0.23474
52.86 0.5202154.38 0.5202158.24 0.5202162.20 0.52021
41.69 0.4614942.91 0.4614945.65 0.4614950.93 0.46149
64.63 0.5825965.44 0.5825969.93 0.5825979.32 0.58259
80.85 0.705983.80 0.705990.54 0.705904.82 0.7059
53.82 0.7092756.98 0.7092763.91 0.7092777.48 0.70927
43.52 0.636645.55 0.636651.95 0.636662.40 0.6366
78.81 0.9346483.80 0.9346494.41 0.9346413.08 0.93464
72.90 1.109882.35 1.109896.83 1.109829.80 1.1098
02.22 1.268513.55 1.268539.30 1.268587.19 1.2685
80.37 0.4175480.67 0.4175480.06 0.4175479.96 0.41754
47.07 0.3254447.28 0.32544
results
σcr,num
(MPa)
4 556.72 4 556.72 4 556.72 4 556.72
4 433.92 4 433.92 4 433.92 4 433.92
4 312.99 4 312.99 4 312.99 4 312.99
1 867.02 1 867.02 1 867.02 1 867.02
9 769.15 9 769.15 9 769.15 9 769.15
9 970.98 9 970.98 9 970.98 9 970.98
9 1176.50 9 1176.50 9 1176.50 9 1176.50
7 1350.99 7 1350.99 7 1350.99 7 1350.99
6 1212.57 6 1212.57 6 1212.57 6 1212.57
4 1780.27 4 1780.27 4 1780.27 4 1780.27
8 1479.73 8 1479.73 8 1479.73 8 1479.73
5 1691.33 5 1691.33 5 1691.33 5 1691.33
4 556.72 4 556.72 4 556.72 4 556.72
4 433.92 4 433.92
51 (6
51
62)
131 (183)
Specimen
I2M6 I2M8
I3M2 I3M4 I3M6 I3M8
I4M2 I4M4 I4M6 I4M8
I5M2 I5M4 I5M6 I5M8
I6M2 I6M4 I6M6 I6M8
I7M2 I7M4 I7M6 I7M8
I8M2 I8M4 I8M6 I8M8
I9M2 I9M4 I9M6 I9M8
I10M2 I10M4 I10M6 I10M8
I11M2 I11M4 I11M6 I11M4
I12M2 I12M4 I12M6 I12M8
I1C1 I1C2 I1C3 I1C4
I2C1 I2C2 I2C3 I2C4
I3C1 I3C2 I3C3 I3C4
I4C1 I4C2 I4C3
Cross‐
bf (mm)
hw (mm)
100 50 100 50
100 50 100 50 100 50 100 50
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
70 40 70 40 70 40 70 40
70 40 70 40 70 40 70 40
70 40 70 40 70 40 70 40
100 80 100 80 100 80 100 80
100 80 100 80 100 80 100 80
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
80 40 80 40 80 40
‐section proper
tf (mm)
tw (mm)
2.5 3 2.5 3
2 3 2 3 2 3 2 3
3 3 3 3 3 3 3 3
2.75 3 2.75 3 2.75 3 2.75 3
3.25 3 3.25 3 3.25 3 3.25 3
3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5
3.25 3.5 3.25 3.5 3.25 3.5 3.25 3.5
3 3.5 3 3.5 3 3.5 3 3.5
3.75 4 3.75 4 3.75 4 3.75 4
5.5 4 5.5 4 5.5 4 5.5 4
6 4 6 4 6 4 6 4
3 3 3 3 3 3 3 3
2.5 3 2.5 3 2.5 3 2.5 3
2 3 2 3 2 3 2 3
3 3 3 3 3 3
rties
Ag (mm) (M
642.5 642.5 4
544 544 544 544 4
591 591 591 591 4
551.75 551.75 551.75 551.75 4
630.25 630.25 630.25 630.25 4
687.75 687.75 687.75 687.75 4
583.625583.625583.625583.625 4
549.5 549.5 549.5 549.5 4
670 670 670 670 4
1398 1398 1398 1398 4
1496 1496 1496 1496 4
741 741 741 741 4
642.5 642.5 642.5 642.5 4
544 544 544 544 4
591 591 591
Material
σu MPa)
n N(
350 10 14450 10 14
275 10 11300 10 11350 10 11450 10 11
275 10 15300 10 15350 10 15450 10 15
275 10 13300 10 14350 10 14450 10 14
275 10 16300 10 16350 10 16450 10 17
275 10 18300 10 18350 10 18450 10 19
275 10 15300 10 15350 10 16450 10 17
275 10 14300 10 14350 10 15450 10 15
275 10 17300 10 18350 10 19450 10 21
275 10 37300 10 38350 10 39450 10 42
275 10 40300 10 41350 10 43450 10 48
275 100 18300 100 18350 100 18450 100 17
275 100 15300 100 15350 100 15450 100 15
275 100 12300 100 12350 100 12450 100 12
275 100 15300 100 15350 100 15
Numerical r
u,num
kN) εcr
47.07 0.3254446.87 0.32544
11.93 0.2347411.72 0.2347411.62 0.2347411.12 0.23474
52.45 0.5202153.87 0.5202153.57 0.5202157.63 0.52021
37.94 0.4614942.00 0.4614943.22 0.4614942.51 0.46149
62.79 0.5825964.93 0.5825968.81 0.5825975.44 0.58259
80.03 0.705983.40 0.705989.72 0.705992.98 0.7059
53.71 0.7092757.28 0.7092763.10 0.7092772.69 0.70927
43.22 0.636646.06 0.636651.13 0.636658.64 0.6366
79.01 0.9346483.50 0.9346493.70 0.9346411.34 0.93464
72.70 1.109882.15 1.109894.88 1.109826.10 1.1098
02.32 1.268512.21 1.268538.16 1.268582.25 1.2685
85.44 0.4175484.63 0.4175482.29 0.4175478.03 0.41754
58.44 0.3254458.04 0.3254456.31 0.3254452.55 0.32544
27.82 0.2347427.51 0.2347426.60 0.2347424.98 0.23474
50.93 0.5202151.34 0.5202151.54 0.52021
results
σcr,num
(MPa)
4 433.92 4 433.92
4 312.99 4 312.99 4 312.99 4 312.99
1 867.02 1 867.02 1 867.02 1 867.02
9 769.15 9 769.15 9 769.15 9 769.15
9 970.98 9 970.98 9 970.98 9 970.98
9 1176.50 9 1176.50 9 1176.50 9 1176.50
7 1350.99 7 1350.99 7 1350.99 7 1350.99
6 1212.57 6 1212.57 6 1212.57 6 1212.57
4 1780.27 4 1780.27 4 1780.27 4 1780.27
8 1479.73 8 1479.73 8 1479.73 8 1479.73
5 1691.33 5 1691.33 5 1691.33 5 1691.33
4 556.72 4 556.72 4 556.72 4 556.72
4 433.92 4 433.92 4 433.92 4 433.92
4 312.99 4 312.99 4 312.99 4 312.99
1 867.02 1 867.02 1 867.02
52 (6
52
62)
132 (183)
Specimen
I4C4
I5C1 I5C2 I5C3 I5C4
I6C1 I6C2 I6C3 I6C4
I7C1 I7C2 I7C3 I7C4
I8C1 I8C2 I8C3 I8C4
I9C1 I9C2 I9C3 I9C4
I10C1 I10C2 I10C3 I10C4
I11C1 I11C2 I11C3 I11C4
I12C1 I12C2 I12C3 I12C4
Cross‐
bf (mm)
hw (mm)
80 40
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
70 40 70 40 70 40 70 40
70 40 70 40 70 40 70 40
70 40 70 40 70 40 70 40
100 80 100 80 100 80 100 80
100 80 100 80 100 80 100 80
Table C.1
‐section proper
tf (mm)
tw (mm)
3 3
2.75 3 2.75 3 2.75 3 2.75 3
3.25 3 3.25 3 3.25 3 3.25 3
3.5 3.5 3.5 3.5 3.5 3.5 3.5 3.5
3.25 3.5 3.25 3.5 3.25 3.5 3.25 3.5
3 3.5 3 3.5 3 3.5 3 3.5
3.75 4 3.75 4 3.75 4 3.75 4
5.5 4 5.5 4 5.5 4 5.5 4
6 4 6 4 6 4 6 4
1 Parametric stu
rties
Ag (mm) (M
591 4
551.75 551.75 551.75 551.75 4
630.25 630.25 630.25 630.25 4
687.75 687.75 687.75 687.75 4
583.625583.625583.625583.625 4
549.5 549.5 549.5 549.5 4
670 670 670 670 4
1398 1398 1398 1398 4
1496 1496 1496 1496 4
udy results for
Material
σu MPa)
n N(
450 100 14
275 100 14300 100 14350 100 13450 100 13
275 100 16300 100 16350 100 16450 100 16
275 100 17300 100 17350 100 18450 100 18
275 100 15300 100 15350 100 15450 100 15
275 100 14300 100 14350 100 14450 100 14
275 100 17300 100 18350 100 18450 100 18
275 100 36300 100 37350 100 37450 100 37
275 100 39300 100 40350 100 41450 100 41
I‐sections. Stub
Numerical r
u,num
kN) εcr
47.89 0.52021
40.17 0.4614940.48 0.4614939.87 0.4614936.21 0.46149
62.69 0.5825963.00 0.5825963.10 0.5825960.65 0.58259
79.01 0.705979.62 0.705980.85 0.705981.15 0.7059
52.90 0.7092753.31 0.7092754.22 0.7092755.24 0.70927
42.51 0.636643.12 0.636643.72 0.636643.93 0.6366
77.58 0.9346480.85 0.9346481.66 0.9346483.40 0.93464
69.51 1.109873.83 1.109876.19 1.109877.94 1.1098
98.92 1.268507.26 1.268513.55 1.268519.11 1.2685
b columns
results
σcr,num
(MPa)
1 867.02
9 769.15 9 769.15 9 769.15 9 769.15
9 970.98 9 970.98 9 970.98 9 970.98
9 1176.50 9 1176.50 9 1176.50 9 1176.50
7 1350.99 7 1350.99 7 1350.99 7 1350.99
6 1212.57 6 1212.57 6 1212.57 6 1212.57
4 1780.27 4 1780.27 4 1780.27 4 1780.27
8 1479.73 8 1479.73 8 1479.73 8 1479.73
5 1691.33 5 1691.33 5 1691.33 5 1691.33
53 (6
53
62)
133 (183)
Ann
nex D
Specimen
C1M1 C1M3 C1M5 C1M7
C2M1 C2M3 C2M5 C2M7
C3M1 C3M3 C3M5 C3M7
C4M1 C4M3 C4M5 C4M7
C5M1 C5M3 C5M5 C5M7
C6M1 C6M3 C6M5 C6M7
C7M1 C7M3 C7M5 C7M7
C8M1 C8M3 C8M5 C8M7
C9M1 C9M3 C9M5 C9M7
C10M1 C10M3 C10M5 C10M7
C11M1 C11M3 C11M5 C11M7
C1M2 C1M4 C1M6 C1M8
C2M2 C2M4 C2M6 C2M8
C3M2 C3M4
n
Cross
H (mm)
B (mm)
40 30 40 30 40 30 40 30
40 30 40 30 40 30 40 30
60 30 60 30 60 30 60 30
60 35 60 35 60 35 60 35
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
120 60 120 60 120 60 120 60
140 60 140 60 140 60 140 60
160 70 160 70 160 70 160 70
40 30 40 30 40 30 40 30
40 30 40 30 40 30 40 30
60 30 60 30
s‐section prope
) tw
(mm) tf
(mm)
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3.25 3.253.25 3.253.25 3.253.25 3.25
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
3 3 3 3 3 3 3 3
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
3 3 3 3
erties
)Ag
(mm) (
183.42 183.42 183.42 183.42
262.69 262.69 262.69 262.69
322.69 322.69 322.69 322.69
352.69 352.69 352.69 352.69
476.21 476.21 476.21 476.21
442.69 442.69 442.69 442.69
562.69 562.69 562.69 562.69
733.66 733.66 733.66 733.66
682.69 682.69 682.69 682.69
1196.351196.351196.351196.35
1396.351396.351396.351396.35
183.42 183.42 183.42 183.42
262.69 262.69 262.69 262.69
322.69 322.69
Material
σu (MPa)
n N(
275 5 5300 5 5350 5 5450 5 5
275 5 7300 5 7350 5 7450 5 8
275 5 8300 5 9350 5 9450 5 10
275 5 9300 5 9350 5 10450 5 11
275 5 13300 5 13350 5 13450 5 14
275 5 12300 5 12350 5 12450 5 13
275 5 14300 5 14350 5 14450 5 15
275 5 20300 5 2350 5 21450 5 21
275 5 15300 5 15350 5 15450 5 15
275 5 33300 5 33350 5 34450 5 36
275 5 38300 5 38350 5 39450 5 40
275 10 5300 10 5350 10 5450 10 5
275 10 7300 10 7350 10 7450 10 8
275 10 8300 10 9
Numerical r
Nu,num
(kN) εcr
50.71 0.2694551.04 0.2694552.36 0.2694554.89 0.26945
73.81 0.6224675.79 0.6224679.75 0.6224688.22 0.62246
89.87 0.7001491.85 0.7001496.69 0.7001401.53 0.70014
98.12 0.5690699.88 0.5690603.07 0.5690610.44 0.56906
32.33 0.6071134.53 0.6071137.39 0.6071146.74 0.60711
22.65 0.5141924.08 0.5141927.27 0.5141931.45 0.51419
49.38 0.4069 48.17 0.4069 49.27 0.4069 50.59 0.4069
03.61 0.73495206.8 0.7349513.62 0.7349519.01 0.73495
58.62 0.3368 58.62 0.3368 59.39 0.3368 58.51 0.3368
31.87 0.9702335.06 0.9702346.28 0.9702367.18 0.97023
84.34 0.8252782.58 0.8252792.26 0.8252702.16 0.82527
50.6 0.2694550.93 0.2694551.92 0.2694553.57 0.26945
73.7 0.6224675.68 0.6224679.2 0.6224687.34 0.62246
89.87 0.7001491.85 0.70014
results
σcr,num
(MPa)
5 945.44 5 945.44 5 945.44 5 945.44
6 2243.10 6 2243.10 6 2243.10 6 2243.10
4 1637.75 4 1637.75 4 1637.75 4 1637.75
6 1331.13 6 1331.13 6 1331.13 6 1331.13
1 1054.70 1 1054.70 1 1054.70 1 1054.70
9 890.37 9 890.37 9 890.37 9 890.37
559.31 559.31 559.31 559.31
5 1020.76 5 1020.76 5 1020.76 5 1020.76
383.82 383.82 383.82 383.82
3 958.25 3 958.25 3 958.25 3 958.25
7 709.91 7 709.91 7 709.91 7 709.91
5 945.44 5 945.44 5 945.44 5 945.44
6 2243.10 6 2243.10 6 2243.10 6 2243.10
4 1637.75 4 1637.75
54 (6
54
62)
134 (183)
Specimen
C3M6 C3M8
C4M2 C4M4 C4M6 C4M8
C5M2 C5M4 C5M6 C5M8
C6M2 C6M4 C6M6 C6M8
C7M2 C7M4 C7M6 C7M8
C8M2 C8M4 C8M6 C8M8
C9M2 C9M4 C9M6 C9M8
C10M2 C10M4 C10M6 C10M8
C11M2 C11M4 C11M6 C11M8
C1C1 C1C2 C1C3 C1C4
C2C1 C2C2 C2C3 C2C4
C3C1 C3C2 C3C3 C3C4
C4C1 C4C2 C4C3 C4C4
C5C1 C5C2 C5C3 C5C4
C6C1 C6C2 C6C3
n
Cross
H (mm)
B (mm)
60 30 60 30
60 35 60 35 60 35 60 35
80 40 80 40 80 40 80 40
80 40 80 40 80 40 80 40
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
120 60 120 60 120 60 120 60
140 60 140 60 140 60 140 60
160 70 160 70 160 70 160 70
40 30 40 30 40 30 40 30
40 30 40 30 40 30 40 30
60 30 60 30 60 30 60 30
60 35 60 35 60 35 60 35
80 40 80 40 80 40 80 40
80 40 80 40 80 40
s‐section prope
) tw
(mm) tf
(mm)
3 3 3 3
3 3 3 3 3 3 3 3
3.25 3.253.25 3.253.25 3.253.25 3.25
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
3 3 3 3 3 3 3 3
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3 3 3 3 3 3 3 3
3.25 3.253.25 3.253.25 3.253.25 3.25
3 3 3 3 3 3
erties
)Ag
(mm) (
322.69 322.69
352.69 352.69 352.69 352.69
476.21 476.21 476.21 476.21
442.69 442.69 442.69 442.69
562.69 562.69 562.69 562.69
733.66 733.66 733.66 733.66
682.69 682.69 682.69 682.69
1196.351196.351196.351196.35
1396.351396.351396.351396.35
183.42 183.42 183.42 183.42
262.69 262.69 262.69 262.69
322.69 322.69 322.69 322.69
352.69 352.69 352.69 352.69
476.21 476.21 476.21 476.21
442.69 442.69 442.69
Material
σu (MPa)
n N(
350 10 9450 10 1
275 10 9300 10 9350 10 1450 10 10
275 10 13300 10 13350 10 13450 10 14
275 10 12300 10 12350 10 12450 10 12
275 10 14300 10 14350 10 14450 10 14
275 10 20300 10 20350 10 21450 10 21
275 10 16300 10 16350 10 16450 10 16
275 10 33300 10 33350 10 34450 10 36
275 10 38300 10 38350 10 38450 10 39
275 100 4300 100 5350 100 5450 100 4
275 100 7300 100 7350 100 7450 100 7
275 100 8300 100 8350 100 9450 100 9
275 100 9300 100 9350 100 9450 100 9
275 100 1300 100 13350 100 13450 100 12
275 100 12300 100 12350 100 12
Numerical r
Nu,num
(kN) εcr
96.25 0.70014102.3 0.70014
98.01 0.5690699.88 0.56906102.3 0.5690608.13 0.56906
32.22 0.6071133.87 0.6071136.62 0.6071143.66 0.60711
22.43 0.5141923.53 0.5141925.95 0.5141927.93 0.51419
47.62 0.4069 48.94 0.4069 49.38 0.4069 47.95 0.4069
03.61 0.7349506.25 0.7349511.31 0.7349517.03 0.73495
64.12 0.3368 64.12 0.3368 64.01 0.3368 63.13 0.3368
31.43 0.9702333.85 0.9702344.74 0.9702360.36 0.97023
83.46 0.8252781.59 0.8252785.22 0.8252791.27 0.82527
49.83 0.2694550.38 0.2694550.49 0.2694549.17 0.26945
73.48 0.6224674.47 0.6224675.35 0.6224676.12 0.62246
88.99 0.7001489.76 0.7001490.64 0.7001491.41 0.70014
97.46 0.5690697.9 0.5690697.79 0.5690697.57 0.56906
130.9 0.6071131.45 0.6071131.56 0.6071129.47 0.60711
21.33 0.5141921.55 0.5141921.44 0.51419
results
σcr,num
(MPa)
4 1637.75 4 1637.75
6 1331.13 6 1331.13 6 1331.13 6 1331.13
1 1054.70 1 1054.70 1 1054.70 1 1054.70
9 890.37 9 890.37 9 890.37 9 890.37
559.31 559.31 559.31 559.31
5 1020.76 5 1020.76 5 1020.76 5 1020.76
383.82 383.82 383.82 383.82
3 958.25 3 958.25 3 958.25 3 958.25
7 709.91 7 709.91 7 709.91 7 709.91
5 945.44 5 945.44 5 945.44 5 945.44
6 2243.10 6 2243.10 6 2243.10 6 2243.10
4 1637.75 4 1637.75 4 1637.75 4 1637.75
6 1331.13 6 1331.13 6 1331.13 6 1331.13
1 1054.70 1 1054.70 1 1054.70 1 1054.70
9 890.37 9 890.37 9 890.37
55 (6
55
62)
135 (183)
Specimen
C6C4
C7C1 C7C2 C7C3 C7C4
C8C1 C8C2 C8C3 C8C4
C9C1 C9C2 C9C3 C9C4
C10C1 C10C2 C10C3 C10C4
C11C1 C11C2 C11C3 C11C4
n
Cross
H (mm)
B (mm)
80 40
100 50 100 50 100 50 100 50
100 50 100 50 100 50 100 50
120 60 120 60 120 60 120 60
140 60 140 60 140 60 140 60
160 70 160 70 160 70 160 70
Table C.2
s‐section prope
) tw
(mm) tf
(mm)
3 3
3 3 3 3 3 3 3 3
4 4 4 4 4 4 4 4
3 3 3 3 3 3 3 3
5 5 5 5 5 5 5 5
5 5 5 5 5 5 5 5
2 Parametric st
erties
)Ag
(mm) (
442.69
562.69 562.69 562.69 562.69
733.66 733.66 733.66 733.66
682.69 682.69 682.69 682.69
1196.351196.351196.351196.35
1396.351396.351396.351396.35
tudy results for
Material
σu (MPa)
n N(
450 100 11
275 100 15300 100 15350 100 14450 100 14
275 100 20300 100 20350 100 20450 100 1
275 100 18300 100 1350 100 17450 100 17
275 100 32300 100 32350 100 3450 100 32
275 100 38300 100 38350 100 37450 100 36
channels. Stub
Numerical r
Nu,num
(kN) εcr
18.58 0.51419
52.02 0.4069 51.25 0.4069 49.38 0.4069 45.86 0.4069
01.74 0.7349502.18 0.7349501.96 0.73495199.1 0.73495
80.73 0.3368 180.4 0.3368 77.65 0.3368 75.23 0.3368
27.69 0.9702328.13 0.9702328.9 0.9702324.39 0.97023
80.82 0.8252780.49 0.8252777.96 0.8252768.83 0.82527
b columns
results
σcr,num
(MPa)
9 890.37
559.31 559.31 559.31 559.31
5 1020.76 5 1020.76 5 1020.76 5 1020.76
383.82 383.82 383.82 383.82
3 958.25 3 958.25 3 958.25 3 958.25
7 709.91 7 709.91 7 709.91 7 709.91
56 (6
56
62)
136 (183)
Ann
Spec
S3M1S3M3S3M5S3M7
S2M1S2M3S2M5S2M7
S1M1S1M3S1M5S1M7
R5MR5MR5MR5M
R4MR4MR4MR4M
R3MR3MR3MR3M
S15MS15MS15MS15M
S14MS14MS14MS14M
S4M1S4M3S4M5S4M7
S6M1S6M3S6M5S6M7
S8M1S8M3S8M5S8M7
S13MS13MS13MS13M
S5M1S5M3S5M5S5M7
S12MS12MS12MS12M
nex E
imen
C
My,p
(KNm
1 1.343 1.345 1.347 1.34
1 1.253 1.255 1.257 1.25
1 1.113 1.115 1.117 1.11
1 5.603 5.605 5.607 5.60
1 5.713 5.715 5.717 5.71
1 4.283 4.285 4.287 4.28
M1 10.7M3 10.7M5 10.7M7 10.7
M1 10.8M3 10.8M5 10.8M7 10.8
1 1.623 1.625 1.627 1.62
1 2.663 2.665 2.667 2.66
1 3.103 3.105 3.107 3.10
M1 9.03M3 9.03M5 9.03M7 9.03
1 2.293 2.295 2.297 2.29
M1 8.16M3 8.16M5 8.16M7 8.16
Cross‐section pr
pl m)
My,el (KNm)
4 1.19 4 1.19 4 1.19 4 1.19
5 1.10 5 1.10 5 1.10 5 1.10
1 0.98 1 0.98 1 0.98 1 0.98
0 4.81 0 4.81 0 4.81 0 4.81
1 4.91 1 4.91 1 4.91 1 4.91
8 3.68 8 3.68 8 3.68 8 3.68
76 9.51 76 9.51 76 9.51 76 9.51
89 9.64 89 9.64 89 9.64 89 9.64
2 1.44 2 1.44 2 1.44 2 1.44
6 2.36 6 2.36 6 2.36 6 2.36
0 2.74 0 2.74 0 2.74 0 2.74
3 7.99 3 7.99 3 7.99 3 7.99
9 2.02 9 2.02 9 2.02 9 2.02
6 7.22 6 7.22 6 7.22 6 7.22
roperties
pl (Rad) 7.01E‐05 7.01E‐05 7.01E‐05 7.01E‐05
7.07E‐05 7.07E‐05 7.07E‐05 7.07E‐05
7.07E‐05 7.07E‐05 7.07E‐05 7.07E‐05
3.64E‐05 3.64E‐05 3.64E‐05 3.64E‐05
3.63E‐05 3.63E‐05 3.63E‐05 3.63E‐05
3.63E‐05 3.63E‐05 3.63E‐05 3.63E‐05
2.83E‐05 2.83E‐05 2.83E‐05 2.83E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
5.14E‐05 5.14E‐05 5.14E‐05 5.14E‐05
4.35E‐05 4.35E‐05 4.35E‐05 4.35E‐05
4.04E‐05 4.04E‐05 4.04E‐05 4.04E‐05
2.83E‐05 2.83E‐05 2.83E‐05 2.83E‐05
4.35E‐05 4.35E‐05 4.35E‐05 4.35E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
Numerical
Mu,num (KNm)
1.48 1.55 1.70 2.00
1.36 1.42 1.55 1.81
1.20 1.24 1.33 1.51
6.14 6.33 6.76 7.60
6.11 6.33 6.91 7.78
4.55 4.67 4.89 5.34
11.32 11.51 11.93 12.62
11.47 11.72 12.07 12.80
1.66 1.68 1.73 1.81
2.72 2.76 2.83 2.96
3.13 3.17 3.22 3.35
9.16 9.20 9.42 9.78
2.24 2.26 2.26 2.31
7.99 7.90 8.17 8.26
Results
R MM
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
19.33 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
8.366 19.612 111.86 1>20 1
3.4663 13.84 14.724 16.533 1
4.4 14.685 16.215 19.07 1
3.35 13.63 14.48 16.34 1
2.646 13.06 13.14 14.33 1
2.17 12.61 12.927 14.236 1
1.78 11.87 12.51 14.23 1
‐ 1‐ 1‐ 1
1.618 1
‐ 1‐ 1
1.21 11.62 1
Rati
u,num/My,el
Mu,nu
My,p
1.24 1.111.30 1.161.43 1.271.68 1.50
1.23 1.091.29 1.141.41 1.241.65 1.46
1.22 1.081.26 1.121.36 1.201.54 1.36
1.27 1.091.32 1.131.41 1.211.58 1.36
1.24 1.071.29 1.111.38 1.181.55 1.33
1.24 1.061.27 1.091.33 1.141.45 1.25
1.19 1.051.21 1.071.25 1.111.33 1.17
1.19 1.051.22 1.081.25 1.111.33 1.18
1.15 1.021.17 1.031.20 1.061.26 1.12
1.15 1.021.17 1.041.20 1.061.26 1.11
1.14 1.011.16 1.021.18 1.041.22 1.08
1.15 1.011.15 1.021.18 1.041.22 1.08
1.11 0.981.12 0.991.12 0.991.14 1.01
1.11 0.981.09 0.971.13 1.001.14 1.01
ios
um/
pl Sectionclass
1 2 or 1 6 2 or 1 7 2 or 1 0 2 or 1
9 2 or 1 4 2 or 1 4 2 or 1 6 2 or 1
8 2 or 1 2 2 or 1 0 2 or 1 6 2 or 1
9 2 or 1 3 2 or 1 1 2 or 1 6 2 or 1
7 2 or 1 1 2 or 1 8 2 or 1 3 2 or 1
6 2 or 1 9 2 or 1 4 2 or 1 5 2 or 1
5 2 or 1 7 2 or 1 1 2 or 1 7 2 or 1
5 2 or 1 8 2 or 1 1 2 or 1 8 2 or 1
2 2 or 1 3 2 or 1 6 2 or 1 2 2 or 1
2 2 or 1 4 2 or 1 6 2 or 1 1 2 or 1
1 2 or 1 2 2 or 1 4 2 or 1 8 2 or 1
1 2 or 1 2 2 or 1 4 2 or 1 8 2 or 1
8 3 9 3 9 3 1 2 or 1
8 3 7 3 0 2 or 1 1 2 or 1
57 (6
57
n
62)
137 (183)
S10MS10MS10MS10M
S7M1S7M3S7M5S7M7
S11MS11MS11MS11M
S9M1S9M3S9M5S9M7
S16MS16MS16MS16M
S17MS17MS17MS17M
S18MS18MS18MS18M
S19MS19MS19MS19M
S3C1S3C2S3C3S3C4
S2C1S2C2S2C3S2C4
S1C1S1C2S1C3S1C4
R5C1R5C2R5C3R5C4
R4C1R4C2R4C3R4C4
R3C1R3C2R3C3R3C4
S15CS15CS15CS15C
S14C
M1 5.88M3 5.88M5 5.88M7 5.88
1 2.663 2.665 2.667 2.66
M1 7.28M3 7.28M5 7.28M7 7.28
1 5.173 5.175 5.177 5.17
M1 8.84M3 8.84M5 8.84M7 8.84
M1 10.5M3 10.5M5 10.5M7 10.5
M1 12.3M3 12.3M5 12.3M7 12.3
M1 14.4M3 14.4M5 14.4M7 14.4
1 1.342 1.343 1.344 1.34
1 1.252 1.253 1.254 1.25
1 1.112 1.113 1.114 1.11
1 5.602 5.603 5.604 5.60
1 5.712 5.713 5.714 5.71
1 4.282 4.283 4.284 4.28
C1 10.7C2 10.7C3 10.7C4 10.7
C1 10.8
8 5.20 8 5.20 8 5.20 8 5.20
6 2.35 6 2.35 6 2.35 6 2.35
8 6.45 8 6.45 8 6.45 8 6.45
7 4.57 7 4.57 7 4.57 7 4.57
4 7.83 4 7.83 4 7.83 4 7.83
4 9.34 4 9.34 4 9.34 4 9.34
9 10.98 9 10.98 9 10.98 9 10.98
40 12.76 40 12.76 40 12.76 40 12.76
4 1.19 4 1.19 4 1.19 4 1.19
5 1.10 5 1.10 5 1.10 5 1.10
1 0.98 1 0.98 1 0.98 1 0.98
0 4.81 0 4.81 0 4.81 0 4.81
1 4.91 1 4.91 1 4.91 1 4.91
8 3.68 8 3.68 8 3.68 8 3.68
76 9.51 76 9.51 76 9.51 76 9.51
89 9.64
3.14E‐05 3.14E‐05 3.14E‐05 3.14E‐05
4.04E‐05 4.04E‐05 4.04E‐05 4.04E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
3.14E‐05 3.14E‐05 3.14E‐05 3.14E‐05
2.57E‐05 2.57E‐05 2.57E‐05 2.57E‐05
2.35E‐05 2.35E‐05 2.35E‐05 2.35E‐05
2.17E‐05 2.17E‐05 2.17E‐05 2.17E‐05
2.01E‐05 2.01E‐05 2.01E‐05 2.01E‐05
7.01E‐05 7.01E‐05 7.01E‐05 7.01E‐05
7.07E‐05 7.07E‐05 7.07E‐05 7.07E‐05
7.07E‐05 7.07E‐05 7.07E‐05 7.07E‐05
3.64E‐05 3.64E‐05 3.64E‐05 3.64E‐05
3.63E‐05 3.63E‐05 3.63E‐05 3.63E‐05
3.63E‐05 3.63E‐05 3.63E‐05 3.63E‐05
2.83E‐05 2.83E‐05 2.83E‐05 2.83E‐05
2.82E‐05
5.67 5.73 5.72 5.84
2.52 2.53 2.54 2.59
6.65 6.64 6.67 6.77
4.58 4.56 4.60 4.67
7.53 7.57 7.57 7.76
8.58 8.59 8.61 8.68
9.54 9.65 9.75 9.83
10.74 10.66 10.83 10.92
1.47 1.53 1.65 1.79
1.35 1.40 1.49 1.58
1.19 1.22 1.28 1.32
6.08 6.25 6.45 6.59
6.21 6.39 6.60 6.74
4.54 4.60 4.65 4.66
11.31 11.36 11.37 11.30
11.51
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
9.1427 19.7 1
10.64 111.834 1
3.2189 13.5546 13.7976 14.0045 1
3.852 1
1.09 0.961.10 0.981.10 0.971.12 0.99
1.07 0.951.08 0.951.08 0.961.10 0.98
1.03 0.911.03 0.911.03 0.921.05 0.93
1.00 0.891.00 0.881.01 0.891.02 0.90
0.96 0.850.97 0.860.97 0.860.99 0.88
0.92 0.810.92 0.820.92 0.820.93 0.82
0.87 0.770.88 0.780.89 0.790.90 0.79
0.84 0.750.84 0.740.85 0.750.86 0.76
1.24 1.101.29 1.151.38 1.231.50 1.34
1.23 1.091.27 1.131.35 1.191.43 1.26
1.21 1.071.25 1.101.30 1.151.35 1.19
1.26 1.091.30 1.121.34 1.151.37 1.18
1.26 1.091.30 1.121.34 1.161.37 1.18
1.23 1.061.25 1.081.26 1.091.27 1.09
1.19 1.051.19 1.061.20 1.061.19 1.05
1.19 1.06
6 3 8 3 7 3 9 3
5 3 5 3 6 3 8 3
1 3 1 3 2 3 3 3
9 3 8 4 9 3 0 3
5 4 6 4 6 4 8 4
1 4 2 4 2 4 2 4
7 4 8 4 9 4 9 4
5 4 4 4 5 4 6 4
0 2 or 1 5 2 or 1 3 2 or 1 4 2 or 1
9 2 or 1 3 2 or 1 9 2 or 1 6 2 or 1
7 2 or 1 0 2 or 1 5 2 or 1 9 2 or 1
9 2 or 1 2 2 or 1 5 2 or 1 8 2 or 1
9 2 or 1 2 2 or 1 6 2 or 1 8 2 or 1
6 2 or 1 8 2 or 1 9 2 or 1 9 2 or 1
5 2 or 1 6 2 or 1 6 2 or 1 5 2 or 1
6 2 or 1
58 (6
58
62)
138 (183)
S14CS14CS14C
S4C1S4C2S4C3S4C4
S6C1S6C2S6C3S6C4
S8C1S8C2S8C3S8C4
S13CS13CS13CS13C
S5C1S5C2S5C3S5C4
S12CS12CS12CS12C
S10CS10CS10CS10C
S7C1S7C2S7C3S7C4
S11CS11CS11CS11C
S9C1S9C2S9C3S9C4
S16CS16CS16CS16C
S17CS17CS17CS17C
S18CS18CS18CS18C
S19CS19CS19CS19C
S3M2S3M4
C2 10.8C3 10.8C4 10.8
1 1.622 1.623 1.624 1.62
1 2.662 2.663 2.664 2.66
1 3.102 3.103 3.104 3.10
C1 9.03C2 9.03C3 9.03C4 9.03
1 2.292 2.293 2.294 2.29
C1 8.16C2 8.16C3 8.16C4 8.16
C1 5.88C2 5.88C3 5.88C4 5.88
1 2.662 2.663 2.664 2.66
C1 7.28C2 7.28C3 7.28C4 7.28
1 5.172 5.173 5.174 5.17
C1 8.84C2 8.84C3 8.84C4 8.84
C1 10.5C2 10.5C2 10.5C4 10.5
C1 12.3C2 12.3C3 12.3C4 12.3
C1 14.4C2 14.4C3 14.4C4 14.4
2 1.344 1.34
89 9.64 89 9.64 89 9.64
2 1.44 2 1.44 2 1.44 2 1.44
6 2.36 6 2.36 6 2.36 6 2.36
0 2.74 0 2.74 0 2.74 0 2.74
3 7.99 3 7.99 3 7.99 3 7.99
9 2.02 9 2.02 9 2.02 9 2.02
6 7.22 6 7.22 6 7.22 6 7.22
8 5.20 8 5.20 8 5.20 8 5.20
6 2.35 6 2.35 6 2.35 6 2.35
8 6.45 8 6.45 8 6.45 8 6.45
7 4.57 7 4.57 7 4.57 7 4.57
4 7.83 4 7.83 4 7.83 4 7.83
4 9.34 4 9.34 4 9.34 4 9.34
9 10.98 9 10.98 9 10.98 9 10.98
40 12.76 40 12.76 40 12.76 40 12.76
4 1.19 4 1.19
2.82E‐05 2.82E‐05 2.82E‐05
5.14E‐05 5.14E‐05 5.14E‐05 5.14E‐05
4.35E‐05 4.35E‐05 4.35E‐05 4.35E‐05
4.04E‐05 4.04E‐05 4.04E‐05 4.04E‐05
2.83E‐05 2.83E‐05 2.83E‐05 2.83E‐05
4.35E‐05 4.35E‐05 4.35E‐05 4.35E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
3.14E‐05 3.14E‐05 3.14E‐05 3.14E‐05
4.04E‐05 4.04E‐05 4.04E‐05 4.04E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
3.14E‐05 3.14E‐05 3.14E‐05 3.14E‐05
2.57E‐05 2.57E‐05 2.57E‐05 2.57E‐05
2.35E‐05 2.35E‐05 2.35E‐05 2.35E‐05
2.17E‐05 2.17E‐05 2.17E‐05 2.17E‐05
2.01E‐05 2.01E‐05 2.01E‐05 2.01E‐05
7.01E‐05 7.01E‐05
11.56 11.64 11.61
1.66 1.66 1.66 1.63
2.73 2.73 2.72 2.68
3.16 3.15 3.15 3.07
9.18 9.21 9.23 8.95
2.27 2.27 2.26 2.21
8.14 8.12 8.06 7.90
5.85 5.83 5.78 5.65
2.60 2.61 2.58 2.52
6.94 6.94 6.89 6.74
4.85 4.83 4.78 4.67
8.11 8.27 7.99 7.88
9.22 9.20 9.16 9.01
10.58 10.55 10.45 10.27
11.89 11.87 11.83 11.60
1.48 1.54
4.123 14.345 14.813 1
3.0859 13.097 13.22 13.326 1
2.39 12.42 12.29 12.865 1
2.02 12.07 12.138 1
‐ 1
1.2439 11.519 11.7037 1
‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
>20 1>20 1
1.20 1.061.21 1.071.20 1.07
1.16 1.021.16 1.021.16 1.021.14 1.01
1.16 1.021.16 1.021.16 1.021.14 1.01
1.15 1.021.15 1.021.15 1.021.12 0.99
1.15 1.021.15 1.021.15 1.021.12 0.99
1.12 0.991.12 0.991.12 0.991.09 0.97
1.13 1.001.12 0.991.12 0.991.09 0.97
1.12 0.991.12 0.991.11 0.981.09 0.96
1.11 0.981.11 0.981.10 0.971.07 0.95
1.08 0.951.08 0.951.07 0.951.04 0.93
1.06 0.941.06 0.941.04 0.921.02 0.90
1.04 0.921.06 0.941.02 0.901.01 0.89
0.99 0.870.99 0.870.98 0.870.97 0.86
0.96 0.850.96 0.850.95 0.840.94 0.83
0.93 0.830.93 0.820.93 0.820.91 0.81
1.24 1.111.30 1.16
6 2 or 1 7 2 or 1 7 2 or 1
2 2 or 1 2 2 or 1 2 2 or 1 1 2 or 1
2 2 or 1 2 2 or 1 2 2 or 1 1 2 or 1
2 2 or 1 2 2 or 1 2 2 or 1 9 3
2 2 or 1 2 2 or 1 2 2 or 1 9 3
9 3 9 3 9 3 7 3
0 3 9 3 9 3 7 3
9 3 9 3 8 3 6 3
8 3 8 3 7 3 5 3
5 3 5 3 5 3 3 3
4 3 4 3 2 3 0 3
2 3 4 3 0 3 9 3
7 4 7 4 7 4 6 4
5 4 5 4 4 4 3 4
3 4 2 4 2 4 1 4
1 2 or 1 6 2 or 1
59 (6
59
62)
139 (183)
S3M6S3M8
S2M2S2M4S2M6S2M8
S1M2S1M4S1M6S1M8
R5MR5MR5MR5M
R4MR4MR4MR4M
R3MR3MR3MR3M
S15MS15MS15MS15M
S14MS14MS14MS14M
S4M2S4M4S4M6S4M8
S6M2S6M4S6M6S6M8
S8M2S8M4S8M6S8M8
S13MS13MS13MS13M
S5M2S5M4S5M6S5M8
S12MS12MS12MS12M
S10MS10MS10MS10M
S7M2S7M4S7M6
6 1.348 1.34
2 1.254 1.256 1.258 1.25
2 1.114 1.116 1.118 1.11
2 5.604 5.606 5.608 5.60
2 5.714 5.716 5.718 5.71
2 4.284 4.286 4.288 4.28
M2 10.7M4 10.7M6 10.7M8 10.7
M2 10.8M4 10.8M6 10.8M8 10.8
2 1.624 1.626 1.628 1.62
2 2.664 2.666 2.668 2.66
2 3.104 3.106 3.108 3.10
M2 9.03M4 9.03M6 9.03M8 9.03
2 2.294 2.296 2.298 2.29
M2 8.16M4 8.16M6 8.16M8 8.16
M2 5.88M4 5.88M6 5.88M8 5.88
2 2.664 2.666 2.66
4 1.19 4 1.19
5 1.10 5 1.10 5 1.10 5 1.10
1 0.98 1 0.98 1 0.98 1 0.98
0 4.81 0 4.81 0 4.81 0 4.81
1 4.91 1 4.91 1 4.91 1 4.91
8 3.68 8 3.68 8 3.68 8 3.68
76 9.51 76 9.51 76 9.51 76 9.51
89 9.64 89 9.64 89 9.64 89 9.64
2 1.44 2 1.44 2 1.44 2 1.44
6 2.36 6 2.36 6 2.36 6 2.36
0 2.74 0 2.74 0 2.74 0 2.74
3 7.99 3 7.99 3 7.99 3 7.99
9 2.02 9 2.02 9 2.02 9 2.02
6 7.22 6 7.22 6 7.22 6 7.22
8 5.20 8 5.20 8 5.20 8 5.20
6 2.35 6 2.35 6 2.35
7.01E‐05 7.01E‐05
7.07E‐05 7.07E‐05 7.07E‐05 7.07E‐05
7.07E‐05 7.07E‐05 7.07E‐05 7.07E‐05
3.64E‐05 3.64E‐05 3.64E‐05 3.64E‐05
3.63E‐05 3.63E‐05 3.63E‐05 3.63E‐05
3.63E‐05 3.63E‐05 3.63E‐05 3.63E‐05
2.83E‐05 2.83E‐05 2.83E‐05 2.83E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
5.14E‐05 5.14E‐05 5.14E‐05 5.14E‐05
4.35E‐05 4.35E‐05 4.35E‐05 4.35E‐05
4.04E‐05 4.04E‐05 4.04E‐05 4.04E‐05
2.83E‐05 2.83E‐05 2.83E‐05 2.83E‐05
4.35E‐05 4.35E‐05 4.35E‐05 4.35E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
3.14E‐05 3.14E‐05 3.14E‐05 3.14E‐05
4.04E‐05 4.04E‐05 4.04E‐05
1.69 1.99
1.36 1.42 1.55 1.77
1.19 1.24 1.33 1.50
6.11 6.33 6.74 7.51
6.11 6.46 6.89 7.68
4.56 4.66 4.88 5.27
11.33 11.54 11.89 12.44
11.55 11.65 12.17 12.74
1.66 1.68 1.73 1.79
2.73 2.76 2.82 2.91
3.15 3.16 3.22 3.29
9.14 9.22 9.42 9.59
2.26 2.26 2.28 2.30
8.02 8.13 8.03 8.14
5.70 5.73 5.80 5.81
2.53 2.55 2.56
>20 1>20 1
>20 1>20 1>20 1>20 1
18.652 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
>20 1>20 1>20 1>20 1
8.2724 19.845 111.526 1>20 1
3.34 13.856 14.5958 16.3625 1
4.002 14.613 16.082 18.719 1
3.37 13.6 14.49 16.01 1
2.59 12.73 13.41 14.38 1
2.36 12.204 12.56 14.025 1
1.465 11.9 1
2.454 13.63 1
‐ 1‐ 1‐ 1
1.511 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1
1.42 1.271.67 1.49
1.23 1.091.29 1.141.40 1.241.61 1.42
1.22 1.081.26 1.121.36 1.201.53 1.35
1.27 1.091.32 1.131.40 1.201.56 1.34
1.24 1.071.31 1.131.40 1.211.56 1.34
1.24 1.061.27 1.091.33 1.141.43 1.23
1.19 1.051.21 1.071.25 1.111.31 1.16
1.20 1.061.21 1.071.26 1.121.32 1.17
1.16 1.021.17 1.041.20 1.061.24 1.10
1.16 1.021.17 1.041.20 1.061.24 1.09
1.15 1.021.15 1.021.17 1.041.20 1.06
1.14 1.011.15 1.021.18 1.041.20 1.06
1.12 0.991.12 0.991.13 1.001.14 1.01
1.11 0.981.13 1.001.11 0.981.13 1.00
1.10 0.971.10 0.981.11 0.991.12 0.99
1.08 0.951.08 0.961.09 0.96
7 2 or 1 9 2 or 1
9 2 or 1 4 2 or 1 4 2 or 1 2 2 or 1
8 2 or 1 2 2 or 1 0 2 or 1 5 2 or 1
9 2 or 1 3 2 or 1 0 2 or 1 4 2 or 1
7 2 or 1 3 2 or 1 1 2 or 1 4 2 or 1
6 2 or 1 9 2 or 1 4 2 or 1 3 2 or 1
5 2 or 1 7 2 or 1 1 2 or 1 6 2 or 1
6 2 or 1 7 2 or 1 2 2 or 1 7 2 or 1
2 2 or 1 4 2 or 1 6 2 or 1 0 2 or 1
2 2 or 1 4 2 or 1 6 2 or 1 9 2 or 1
2 2 or 1 2 2 or 1 4 2 or 1 6 2 or 1
1 2 or 1 2 2 or 1 4 2 or 1 6 2 or 1
9 3 9 3 0 3 1 2 or 1
8 3 0 3 8 3 0 3
7 3 8 3 9 3 9 3
5 3 6 3 6 3
60 (6
60
62)
140 (183)
S7M8
S11MS11MS11MS11M
S9M2S9M4S9M6S9M8
S16MS16MS16MS16M
S17MS17MS17MS17M
S18MS18MS18MS18M
S19MS19MS19MS19M
8 2.66
M2 7.28M4 7.28M6 7.28M8 7.28
2 5.174 5.176 5.178 5.17
M2 8.84M4 8.84M6 8.84M8 8.84
M2 10.5M4 10.5M6 10.5M8 10.5
M2 12.3M4 12.3M6 12.3M8 12.3
M2 14.4M4 14.4M6 14.4M8 14.4
T
6 2.35
8 6.45 8 6.45 8 6.45 8 6.45
7 4.57 7 4.57 7 4.57 7 4.57
4 7.83 4 7.83 4 7.83 4 7.83
4 9.34 4 9.34 4 9.34 4 9.34
9 10.98 9 10.98 9 10.98 9 10.98
40 12.76 40 12.76 40 12.76 40 12.76
Table E.1 Param
4.04E‐05
2.82E‐05 2.82E‐05 2.82E‐05 2.82E‐05
3.14E‐05 3.14E‐05 3.14E‐05 3.14E‐05
2.57E‐05 2.57E‐05 2.57E‐05 2.57E‐05
2.35E‐05 2.35E‐05 2.35E‐05 2.35E‐05
2.17E‐05 2.17E‐05 2.17E‐05 2.17E‐05
2.01E‐05 2.01E‐05 2.01E‐05 2.01E‐05
metric study res
2.55
6.73 6.65 6.75 6.75
4.64 4.67 4.65 4.62
7.65 7.71 7.69 7.72
8.68 8.69 8.69 8.73
9.90 9.92 9.94 9.93
11.17 11.11 11.01 11.08
sults for hollow
‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 1‐ 1‐ 1‐ 1
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
‐ 0‐ 0‐ 0‐ 0
w sections. 4‐po
1.09 0.96
1.04 0.921.03 0.911.05 0.931.05 0.93
1.01 0.901.02 0.901.02 0.901.01 0.89
0.98 0.870.99 0.870.98 0.870.99 0.87
0.93 0.820.93 0.820.93 0.820.93 0.83
0.90 0.800.90 0.800.91 0.800.90 0.80
0.88 0.780.87 0.770.86 0.760.87 0.77
oint bending tes
6 3
2 3 1 3 3 3 3 3
0 3 0 3 0 3 9 3
7 4 7 4 7 4 7 4
2 4 2 4 2 4 3 4
0 4 0 4 0 4 0 4
8 4 7 4 6 4 7 4
st
61 (6
61
62)
141 (183)
62 (6
62
62)
142 (183)
Structural Applications of Ferritic Stainless Steels (SAFSS)
Work package 2
Recommendations: Web crippling
Departament d'Enginyeria de la Construcció,
Project
name:
Structural Applications of Ferritic Stainless Steels
Project's
short name:
SAFSS
Change log:
Version Date Status
(draft/proposal/updated/to be reviewed
/approved)
0.1 18.1.13 Final
Distribution: Project group
Structural Applications of Ferritic Stainless Steels (SAFSS)
Work package 2.4b. Parametric Study and
Recommendations: Web crippling
Marina Bock
Esther Real
Enrique Mirambell Departament d'Enginyeria de la Construcció,
Universitat Politècnica de Catalunya
Structural Applications of Ferritic Stainless Steels
(draft/proposal/updated/to be reviewed
/approved)
Author(s)
Marina Bock
Project group
1 (41)
1
Structural Applications of Ferritic Stainless Steels (SAFSS)
.4b. Parametric Study and
Remarks
Marina Bock et al.
143 (183)
EUROPEAN COMMISSION
The Research Fund for Coal and Steel
Title of Research Project:
Executive Committee: Contract: Commencement Date: Completion Date: Beneficiary: Research Location:
Project leader: Report authors:
EUROPEAN COMMISSION
Research Programme of The Research Fund for Coal and Steel-Steel RTD
Title of Research Project: Structural Application of Ferritic Stainless Steels (SAFSS)
Executive Committee: TGS8
RFSR-CT-2010-00026
Commencement Date: July 01, 201
June 30, 2013
Universitat Politècnica de Catalunya (UPC) Universitat Politècnica de CatalunyaC/ Jordi Girona, 31 08034-Barcelona España Esther Real
Bock, M., Real, E., Mirambell, E.
2 (41)
2
Steel RTD
Structural Application of Ferritic Stainless Steels (SAFSS)
Universitat Politècnica de Catalunya
tècnica de Catalunya
Bock, M., Real, E., Mirambell, E.
144 (183)
Contents 1. Experimental database ................................
1.1 Review of all available data
1.2 Cross sections ................................
1.3 Target ................................
2. Parametric study ................................
2.1 Cross-sections and test configuration
2.2 Materials ................................
2.3 Additional tests ................................
2.4 Parametric study recount
3. EN1993-1-3 formulations for web crippling strength and new proposal expression
3.1 EN1993-1-3 formulae ................................
3.2 New proposal expression
3.2.1 Material nonlinearities influence
3.2.2 Internal radius influence
3.2.3 Bearing length influence
4. Numerical results and comparison to EN1993
5. Validation of the new proposal with experimental results
6. References ................................
Annex A ................................................................
A.1 IOF tests in SHS and RHS ................................
A.2 IOF tests in hat sections ................................
A.3 EOF tests in SHS and RHS
A.4 EOF tests in hat sections ................................
................................................................................................
1.1 Review of all available data ................................................................................................
................................................................................................
................................................................................................................................
................................................................................................
sections and test configuration ................................................................
...........................................................................................................................
................................................................................................
ount ................................................................................................
3 formulations for web crippling strength and new proposal expression
................................................................................................
proposal expression ................................................................................................
3.2.1 Material nonlinearities influence ................................................................
3.2.2 Internal radius influence ............................................................................................
3.2.3 Bearing length influence ............................................................................................
Numerical results and comparison to EN1993-1-3 and new proposal ...............................
Validation of the new proposal with experimental results ................................
...........................................................................................................................
................................................................................................
................................................................................................
................................................................................................
................................................................................................
................................................................................................
3 (41)
3
.......................................... 4
................................. 4
...................................................... 8
................................ 18
................................................. 19
............................................... 19
........................... 21
................................................. 21
.................................. 25
3 formulations for web crippling strength and new proposal expression ......... 26
........................................ 26
.................................. 27
............................................... 27
............................ 28
............................ 28
............................... 29
................................................. 32
........................... 33
....................................... 34
....................................... 35
........................................ 36
...................................... 37
....................................... 39
145 (183)
1. Experimental dat
All available experimental data concerning stainless
presented through this section
1.1 Review of all available data
Figure 1.1 summarizes all experimental results found in the literature considering
cross sections and test configurations
Flange (EOF), Interior Two Flanges (ITF) and Exterior Two Flanges (ETF)
carried out in ten different cross sections: square hollow sections (SH
sections (RHS), Unstiffened trapezoidal
flange), I-sections, Lipped Channels, Unstiffened sheeting, flange stiffened sheeting and flange
(one stiffener in the flange) and web
Figure 1.1
The number of the different cross sections subjected to web crippling is plotted in Figure 1.2,
where no difference in test configuration has been considered. Finally, in Figure 1.3 the
different types of stainless steel that made up the different cross s
stainless steel types studied are Austenitic, High Strength Austenitic (HSAustenitic), Ferritic and
Duplex. Within each group different grades are considered. Since this project is focused on
database
ll available experimental data concerning stainless steel sections subjected to web crippling is
through this section.
Review of all available data
Figure 1.1 summarizes all experimental results found in the literature considering
test configurations. It was found Interior One Flange (IOF), Exterior One
Flange (EOF), Interior Two Flanges (ITF) and Exterior Two Flanges (ETF) experimental tests
in ten different cross sections: square hollow sections (SHS), rectangular hollow
trapezoidal, Hat sections, stiffened trapezoidal (one stiffener in the
sections, Lipped Channels, Unstiffened sheeting, flange stiffened sheeting and flange
(one stiffener in the flange) and web (2 stiffeners in the webs) stiffened sheeting.
Figure 1.1 Number of cross sections and test configuration
The number of the different cross sections subjected to web crippling is plotted in Figure 1.2,
where no difference in test configuration has been considered. Finally, in Figure 1.3 the
stainless steel that made up the different cross sections are presented.
stainless steel types studied are Austenitic, High Strength Austenitic (HSAustenitic), Ferritic and
Duplex. Within each group different grades are considered. Since this project is focused on
4 (41)
4
teel sections subjected to web crippling is
Figure 1.1 summarizes all experimental results found in the literature considering different
One Flange (IOF), Exterior One
experimental tests
S), rectangular hollow
(one stiffener in the
sections, Lipped Channels, Unstiffened sheeting, flange stiffened sheeting and flange
(2 stiffeners in the webs) stiffened sheeting.
The number of the different cross sections subjected to web crippling is plotted in Figure 1.2,
where no difference in test configuration has been considered. Finally, in Figure 1.3 the
ections are presented. The
stainless steel types studied are Austenitic, High Strength Austenitic (HSAustenitic), Ferritic and
Duplex. Within each group different grades are considered. Since this project is focused on
146 (183)
Ferritic grades, it is important to e
are the different found grades.
including the article where test were found
sections considering the stainless steel type as well as the test configuration
Figure 1.2 Different cross sections subjected to web crippling
Figure 1.3 Cross sections according to stainless steel type
Reference Test
configuration
Korvink and van
den Berg (1993)
IOF
IOF
Korvink et al.
(1995)
EOF
EOF
EOF
Talja and Salmi
(1995)
IOF
IOF
Ferritic grades, it is important to emphasize that 1.4016 (430), 1.4003 (3Cr12) and 1.450
grades. Table 1.1 summarizes all the available experimental data
test were found. Finally, Table 1.2 classifies the different cross
nsidering the stainless steel type as well as the test configuration.
Figure 1.2 Different cross sections subjected to web crippling
Figure 1.3 Cross sections according to stainless steel type
Section Number
of tests Grade
Lipped Channel 48 1.4016
Lipped Channel 50 1.4003
Lipped Channel 48 1.4016
Lipped Channel 49 1.4301
Lipped Channel 42 1.4003
SHS 2 1.4301
RHS 4 1.4301
5 (41)
5
mphasize that 1.4016 (430), 1.4003 (3Cr12) and 1.4509 (441)
experimental data,
Table 1.2 classifies the different cross
Material Type
430 Ferritic
3Cr12 Ferritic
430 Ferritic
304 Austhenitic
3Cr12 Ferritic
304 Austhenitic
304 Austhenitic
147 (183)
Reference Test
configuration
Talja (1997b)
ECSC (2000)
IOF
IOF
IOF
Sélen (2000)
ECSC (2000)
IOF
EOF
Zilli (2004)
ESCS (2004)
IOF
IOF
Talja (2004)
ESCS (2004)
IOF
IOF
IOF
IOF
IOF
IOF
IOF
IOF
Gardner et al.
(2006)
IOF
IOF
IOF
IOF
Zhou and Young
(2006a)
ETF
ETF
ITF
ITF
Zhou and Young
(2007a)
EOF
EOF
EOF
EOF
IOF
IOF
IOF
IOF
ETF
ETF
ETF
ETF
ITF
ITF
ITF
ITF
Talja and Hradil
(2011)
SAFSS Project
IOF
IOF
EOF
EOF
Section Number
of tests Grade
Unstiffened Sheeting 3 1.4301
SheetingFlangeStiffened 3 1.4301
Sheeting Flange (1) and Web
(2) Stiffened 3 1.4301
I-section 5 1.4301
I-section 4 1.4301
Unstiffened trapezoidal 3 1.4318 C700
Unstiffened trapezoidal 5 1.4318 C850
Unstiffened trapezoidal 1 1.4318 C700
Unstiffened trapezoidal 1 1.4318 C850
Unstiffened trapezoidal 1 1.4301 C850
HAT 2 1.4318 C700
HAT 2 1.4318 C850
HAT 2 1.4301 C850
Stiffened trapezoidal 3 1.4318 C700
Stiffened trapezoidal 3 1.4318 C850
SHS 1 1.4318 C700
RHS 2 1.4318 C700
SHS 1 1.4318 C850
RHS 2 1.4318 C850
SHS 8 1.4301
RHS 9 1.4301
SHS 8 1.4301
RHS 8 1.4301
SHS 4 1.4462
SHS 4
RHS 4 1.4462
RHS 2
SHS 4 1.4462
SHS 4
RHS 4 1.4462
RHS 2
SHS 4 1.4462
SHS 5
RHS 4 1.4462
RHS 2
SHS 4 1.4462
SHS 5
RHS 4 1.4462
RHS 2
SHS 1 1.4509
HAT 4 1.4509
SHS 1 1.4509
HAT 4 1.4509
Table 1.1 Review of experimental data
6 (41)
6
Material Type
304 Austhenitic
304 Austhenitic
304 Austhenitic
304 Austhenitic
304 Austhenitic
301LN Austhenitic
301LN Austhenitic
301LN Austhenitic
301LN Austhenitic
304 Austhenitic
301LN Austhenitic
301LN Austhenitic
304 Austhenitic
301LN Austhenitic
301LN Austhenitic
301LN Austhenitic
301LN Austhenitic
301LN Austhenitic
301LN Austhenitic
304 Austhenitic
304 Austhenitic
304 Austhenitic
304 Austhenitic
2250 Duplex
HSA
2250 Duplex
HSA
2250 Duplex
HSA
2250 Duplex
HSA
2250 Duplex
HSA
2250 Duplex
HSA
2250 Duplex
HSA
2250 Duplex
HSA
441 Ferritic
441 Ferritic
441 Ferritic
441 Ferritic
148 (183)
SHS
RHS
Unstiffened Trapezoidal
HAT
Stiffened Trapezoidal
I-section
Lipped Channel
Unstiffened Sheeting
Sheeting Flange Stiffened
Sheeting Flange (1) and Web
(2) Stiffened
IOF Totals
SHS
RHS
HAT
I-section
LippedChannel
EOF Totals
SHS
RHS
ITF Totals
SHS
RHS
ETF Totals
Web Crippling Total tests
Table 1.2 Available experimental data considering different cross sections, test
Austhenitic HSA Ferritic Duplex
4 4 1 4
8 2 0 4
Unstiffened Trapezoidal 11 0 0 0
6 0 4 0
6 0 0 0
5 0 0 0
0 0 98 0
3 0 0 0
Stiffened 3 0 0 0
Sheeting Flange (1) and Web 3 0 0 0
49 6 103 8
0 4 1 4
0 2 0 4
0 0 4 0
4 0 0 0
49 0 90 0
53 6 95 8
8 5 0 4
8 2 0 4
16 7 0 8
8 5 0 4
9 2 0 4
17 7 0 8
Web Crippling Total tests
Available experimental data considering different cross sections, test
configuration and material
7 (41)
7
Total
166
162
31
32
391
Available experimental data considering different cross sections, test
149 (183)
1.2 Cross sections
Once all data is presented, the study will be focused on SHS, RHS, HAT
as well as IOF and EOF tests.
Researchers usually present measured dimensions of cross sections in their experimental
studies. However, the presented values of
different criteria leading in a heterogeneous data base. In order to homogenize all
measurements in cross sections found in the literature, the parameters showed in Figure 1.4
will be considered.
RHS ans SHS sections
Figure 1.4 Nomenclature
Tables 1.3-1.13 gather all the available experimental data.Calculated values based on original data
Unspecified values
h
C
rm
hs
t
b
rm
ri
R
t
B
H
Once all data is presented, the study will be focused on SHS, RHS, HAT and trapezoidal
Researchers usually present measured dimensions of cross sections in their experimental
However, the presented values of the different researchers are measured following
different criteria leading in a heterogeneous data base. In order to homogenize all
sections found in the literature, the parameters showed in Figure 1.4
RHS ans SHS sections HAT sections
Unstiffened/ Stiffened Trapezoidal sections
Figure 1.4 Nomenclature of the different cross-sections
gather all the available experimental data. based on original data Not found values/not provided by the author
b
B
c
ɸ
Hr
ɸ
hr ri
bs
ls
Bs
b
h
ri
rm
R
B
C
ɸ h
8 (41)
8
and trapezoidal sections
Researchers usually present measured dimensions of cross sections in their experimental
the different researchers are measured following
different criteria leading in a heterogeneous data base. In order to homogenize all
sections found in the literature, the parameters showed in Figure 1.4
/not provided by the author
H
c
t
H
150 (183)
Paper Section
type Reference grade
Zhou and Young (2007a) SHS IOF40x40X2N50 HSDuplex
Zhou and Young (2007a) SHS IOF40x40X2N25 HSDuplex
Zhou and Young (2007a) SHS IOF50x50x1.5N50 HSDuplex
Zhou and Young (2007a) SHS IOF50x50x1.5N25 HSDuplex
Zhou and Young (2007a) SHS IOF150x150x3N150 HSA
Zhou and Young (2007a) SHS IOF150x150x3N75 HSA
Zhou and Young (2007a) SHS IOF150x150x6N150 HSA
Zhou and Young (2007a) SHS IOF150x150x6N75 HSA
Zhou and Young (2007a) RHS IOF140x80x3N75 HSDuplex
Zhou and Young (2007a) RHS IOF140x80x3N50 HSDuplex
Zhou and Young (2007a) RHS IOF160x80x3N75 HSDuplex
Zhou and Young (2007a) RHS IOF160x80x3N50 HSDuplex
Zhou and Young (2007a) RHS IOF200x110x4N100 HSA
Zhou and Young (2007a) RHS IOF200x110x4N50 HSA
Talja and Salmi (1995) SHS RHS -1 W-1 1.4301
Talja and Salmi (1995) SHS RHS -1 W-2 1.4301
Talja and Salmi (1995) RHS RHS -2 W-1 1.4301
Talja and Salmi (1995) RHS RHS -2 W-2 1.4301
Talja and Salmi (1995) RHS RHS -3 W-1 1.4301
Talja and Salmi (1995) RHS RHS -3 W-2 1.4301
Gardner et al. (2006) SHS RHS100x100x3-A 1.4318-
Gardner et al. (2006) RHS RHS120x80x3-A 1.4318-
Gardner et al. (2006) RHS RHS140x60x3-A 1.4318-
Gardner et al. (2006) SHS RHS100x100x3-C850 1.4318-
Gardner et al. (2006) RHS RHS120x80x3-C850 1.4318-
Gardner et al. (2006) RHS RHS140x60x3-C850 1.4318-
Talja and Hradil (2011) SHS SHS_IS 1.4509
Table 1.3 WC IOF SHS/RHS. Geometrical
grade Measured dimensions (mm) Mid-section dimensions (mm)
Span la H B t ri h b t rm
HSDuplex 370 50 40.4 40.20 1.94 2 38.46 38.26 1.94 2.97 3.94
HSDuplex 243 25 40 40.20 1.93 2 38.07 38.27 1.93 2.97 3.93
HSDuplex 402 50 50.2 50.10 1.54 1.5 48.66 48.56 1.54 2.27 3.04
HSDuplex 277 25 50.2 50.10 1.54 1.5 48.66 48.56 1.54 2.27 3.04
HSA 1205 150 150.7 150.60 2.80 4.8 147.90 147.80 2.80 6.20 7.60
HSA 826 75 150.7 150.50 2.79 4.8 147.91 147.71 2.79 6.20 7.59
HSA 1199 150 150.3 150.10 5.59 6 144.71 144.51 5.59 8.80 11.59
HSA 820 75 150.3 150.10 5.73 6 144.57 144.37 5.73 8.87 11.73
HSDuplex 794 75 140.3 80.30 3.08 6.5 137.22 77.22 3.08 8.04 9.58
HSDuplex 668 50 140.1 80.30 3.08 6.5 137.02 77.22 3.08 8.04 9.58
HSDuplex 854 75 160.5 80.90 2.88 6 157.62 78.02 2.88 7.44 8.88
HSDuplex 729 50 160.5 80.80 2.89 6 157.62 77.92 2.89 7.44 8.89
HSA 1103 100 198.2 109.00 4.01 8.5 194.19 104.99 4.01 10.50 12.51
HSA 850 50 202.6 104.10 3.98 8.5 198.62 100.12 3.98 10.49 12.48
1.4301 350 50 59.7 59.53 5.00 3.5 54.70 54.53 5.00 6.00 8.50
1.4301 400 100 59.52 59.35 5.00 3 54.52 54.35 5.00 5.50 8.00
1.4301 600 50 150.34 100.36 3.00 3 147.34 97.36 3.00 4.50 6.00
1.4301 650 100 150.22 100.31 3.00 2.5 147.22 97.31 3.00 4.00 5.50
1.4301 600 50 150.61 100.64 6.00 5.5 144.61 94.64 6.00 8.50 11.50
1.4301 650 100 149.58 100.05 6.00 5 143.58 94.05 6.00 8.00 11.00
-C700 800 50 99.9 100.20 3.06 2.5 96.84 97.14 3.06 4.03 5.56
-C700 800 50 120 79.70 3.08 4 116.92 76.62 3.08 5.54 7.08
-C700 799 50 140 60.50 3.10 4.5 136.90 57.40 3.10 6.05 7.60
-C850 797 50 100.5 100.00 3.05 3 97.45 96.95 3.05 4.52 6.05
-C850 799 50 120.2 80.40 3.08 4 117.12 77.32 3.08 5.54 7.08
-C850 800 50 139.7 60.20 3.04 4 136.66 57.16 3.04 5.52 7.04
1.4509 300 25 79.64 80.1 1.95 2.9 77.69 78.15 1.95 3.88 4.85
Table 1.3 WC IOF SHS/RHS. Geometrical properties and test results
9 (41)
9
Web Crippling test results
(kN or kNm)
Bending test
results (kNm)
R Pexp/web Pexp Mexp Mexp,b
3.94 30.30 60.60 4.85 3.45
3.93 27.90 55.80 3.04 3.45
3.04 21.70 43.40 3.82 3.48
3.04 19.20 38.40 2.42 3.48
7.60 59.30 118.60 31.28 31.68
7.59 51.40 102.80 19.30 31.68
11.59 228.90 457.80 120.06 108.60
11.73 207.00 414.00 77.11 108.60
9.58 51.40 102.80 18.48 33.97
9.58 49.00 98.00 15.14 33.97
8.88 52.50 105.00 20.45 39.36
8.89 49.10 98.20 16.67 39.36
12.51 98.60 197.20 49.45 80.15
12.48 82.30 164.60 32.92 80.15
8.50 96.00 192.00 14.40 15.03
8.00 89.00 178.00 13.40 14.37
6.00 39.10 78.20 10.80 26.25
5.50 47.00 94.00 12.90 26.25
11.50 118.00 236.00 32.50 70.37
11.00 149.50 299.00 41.10 70.37
5.56 53.55 107.10 20.08 23.30
7.08 54.15 108.30 20.31 29.80
7.60 53.75 107.50 20.13 34.60
6.05 59.60 119.20 22.26 26.70
7.08 59.10 118.20 22.13 33.70
7.04 63.35 126.70 23.76 39.00
4.85 21.96 43.91 3.02 17.67
151 (183)
Paper Section
type Reference grade
Zhou and Young (2007a) SHS IOF40x40X2N50 HSDuplex
Zhou and Young (2007a) SHS IOF40x40X2N25 HSDuplex
Zhou and Young (2007a) SHS IOF50x50x1.5N50 HSDuplex
Zhou and Young (2007a) SHS IOF50x50x1.5N25 HSDuplex
Zhou and Young (2007a) SHS IOF150x150x3N150 HSA
Zhou and Young (2007a) SHS IOF150x150x3N75 HSA
Zhou and Young (2007a) SHS IOF150x150x6N150 HSA
Zhou and Young (2007a) SHS IOF150x150x6N75 HSA
Zhou and Young (2007a) RHS IOF140x80x3N75 HSDuplex
Zhou and Young (2007a) RHS IOF140x80x3N50 HSDuplex
Zhou and Young (2007a) RHS IOF160x80x3N75 HSDuplex
Zhou and Young (2007a) RHS IOF160x80x3N50 HSDuplex
Zhou and Young (2007a) RHS IOF200x110x4N100 HSA
Zhou and Young (2007a) RHS IOF200x110x4N50 HSA
Talja and Salmi (1995) SHS RHS -1 W-1 1.4301
Talja and Salmi (1995) SHS RHS -1 W-2 1.4301
Talja and Salmi (1995) RHS RHS -2 W-1 1.4301
Talja and Salmi (1995) RHS RHS -2 W-2 1.4301
Talja and Salmi (1995) RHS RHS -3 W-1 1.4301
Talja and Salmi (1995) RHS RHS -3 W-2 1.4301
Gardner et al. (2006) SHS RHS100x100x3-A 1.4318-C700
Gardner et al. (2006) RHS RHS120x80x3-A 1.4318-C700
Gardner et al. (2006) RHS RHS140x60x3-A 1.4318-C700
Gardner et al. (2006) SHS RHS100x100x3-C850 1.4318-C850
Gardner et al. (2006) RHS RHS120x80x3-C850 1.4318-C850
Gardner et al. (2006) RHS RHS140x60x3-C850 1.4318-C850
Talja and Hradil (2011) SHS SHS_IS 1.4509
Material properties from tensile flat (σ in MPa)
Material properties
flat/stub column
E (GPa) σ0.01 σ0.2 σ1.0 σu n εf (%) m E (GPa) σ0.01
HSDuplex 216 164 707 827 29 220 230
plex 216 164 707 827 29 220 230
HSDuplex 200 182 622 770 37 216 200
HSDuplex 200 182 622 770 37 216 200
189 155 448 699 52 220 200
189 155 448 699 52 220 200
194 147 497 761 52 214 160
194 147 497 761 52 214 160
HSDuplex 212 199 486 736 47 220 200
HSDuplex 212 199 486 736 47 220 200
HSDuplex 208 167 536 766 40 200 210
HSDuplex 208 167 536 766 40 200 210
200 150 503 961 36 220 200
200 150 503 961 42.1 220 200
185 305.5 566 753 4.815 42.1 192 235
181 251.5 530 668.5 4.065 44.5 192 235
198.25 175.75 296 627 5.88 66.15 191 156
198.25 175.75 296 627 5.88 66.15 191 156
193 222 349.5 653.5 6.86 58.05 192 157
197.5 180 331.5 672 5.025 65.25 192 157
C700 195 280 481 806 5.55 42.5
C700 199.5 300 539 841 5.85 39.5
C700 196.5 312 555.5 847 5.65 38.5
C850 183.5 324 607.5 942.5 4.8 31.5
C850 190 339 658 970.5 4.6 30
C850 186 364 651 997 5.45 25.5
196 502 527 6.1 1.23 4.07
Table 1.4 WC IOF SHS/RHS. Material properties
10 (41)
10
Material properties fromcompression
flat/stub column(σ in MPa)
Mill certificates (σ in
MPa)
σ0.2 σ1.0 n σ0.2 σ1.0 σu εf (%)
747
747
652
652
547
547
678
678
513
513
569
569
622
622
569 776 3.39 284 335 604 52
569 776 3.39 284 335 604 52
310 4.8 287 348 620 54
310 4.8 287 348 620 54
385 481 3.33 300 340 612 52
385 481 3.33 273 318 579 50
352 389 753 50
352 389 753 50
352 389 753 50
616 677 929 35
616 677 929 35
542 588 960 31
355 377 478 46
152 (183)
Paper Section
type Reference
Zhou and Young (2007a) SHS EOF40x40X2N50
Zhou and Young (2007a) SHS EOF40x40X2N25
Zhou and Young (2007a) SHS EOF50x50x1.5N50
Zhou and Young (2007a) SHS EOF50x50x1.5N25
Zhou and Young (2007a) SHS EOF150x150x3N150
Zhou and Young (2007a) SHS EOF150x150x3N75
Zhou and Young (2007a) SHS EOF150x150x6N150
Zhou and Young (2007a) SHS EOF150x150x6N75
Zhou and Young (2007a) RHS EOF140x80x3N75
Zhou and Young (2007a) RHS EOF140x80x3N50
Zhou and Young (2007a) RHS EOF160x80x3N75
Zhou and Young (2007a) RHS EOF160x80x3N50
Zhou and Young (2007a) RHS EOF200x110x4N100
Zhou and Young (2007a) RHS EOF200x110x4N50
Talja and Hradil (2011) SHS SHS_ES
Table 1.5 WC EOF SHS/RHS. Geometrical
grade Measureddimensions (mm) Midsectiondimensions (mm)
Span e la H B t ri h b
HSDuplex 296 60.15 50 40.1 40.3 1.96 2 38.15 38.35 1.96
HSDuplex 247 60.15 25 40.1 40.3 1.93 2 38.17 38.37 1.93
HSDuplex 335 75.6 50 50.4 50.1 1.55 1.5 48.86 48.56 1.55
HSDuplex 254 75.45 25 50.3 50.1 1.54 1.5 48.76 48.56 1.54
HSA 1051 226.35 150 150.9 150.4 2.80 4.8 148.10 147.60 2.80
HSA 750 226.35 75 150.9 150.5 2.79 4.8 148.11 147.71 2.79
HSA 978 225.75 150 150.5 150.4 5.87 6 144.64 144.54 5.87
HSA 748 225.75 75 150.5 150.3 5.73 6 144.77 144.57 5.73
HSDuplex 719 210.75 75 140.5 80.4 3.08 6.5 137.42 77.32 3.08
HSDuplex 618 210.6 50 140.4 80.4 3.08 6.5 137.32 77.32 3.08
HSDuplex 779 241.35 75 160.9 80.7 2.89 6 158.01 77.81 2.89
HSDuplex 679 241.35 50 160.9 80.8 2.89 6 158.01 77.91 2.89
HSA 999 306.75 100 204.5 104.8 3.98 8.5 200.52 100.82 3.98
HSA 800 301.5 50 201 104.9 3.98 8.5 197.02 100.92 3.98
1.4509 350 75 25 80.04 80 1.97 2.9 78.07 78.03 1.97
Table 1.5 WC EOF SHS/RHS. Geometrical properties and test results
11 (41)
11
Midsectiondimensions (mm) Web Crippling test
results (kN)
t rm R Pexp/web Pexp
1.96 2.98 3.96 22.3 44.60
1.93 2.97 3.93 24.7 49.40
1.55 2.27 3.05 19.8 39.60
1.54 2.27 3.04 15.5 31.00
2.80 6.20 7.60 47.2 94.40
2.79 6.20 7.59 28.8 57.60
5.87 8.93 11.87 184.6 369.20
5.73 8.87 11.73 124.3 248.60
3.08 8.04 9.58 37.6 75.20
3.08 8.04 9.58 33.6 67.20
2.89 7.44 8.89 32.4 64.80
2.89 7.44 8.89 29.6 59.20
3.98 10.49 12.48 60.2 120.40
3.98 10.49 12.48 40.1 80.20
1.97 3.89 4.87 13.38 26.76
153 (183)
Paper Section
type Reference grade
Zhou and Young (2007a) SHS EOF40x40X2N50 HSDuplex
Zhou and Young (2007a) SHS EOF40x40X2N25 HSDuplex
Zhou and Young (2007a) SHS EOF50x50x1.5N50 HSDuplex
Zhou and Young (2007a) SHS EOF50x50x1.5N25 HSDuplex
Zhou and Young (2007a) SHS EOF150x150x3N150 HSA
Zhou and Young (2007a) SHS EOF150x150x3N75 HSA
Zhou and Young (2007a) SHS EOF150x150x6N150 HSA
Zhou and Young (2007a) SHS EOF150x150x6N75 HSA
Zhou and Young (2007a) RHS EOF140x80x3N75 HSDuplex
Zhou and Young (2007a) RHS EOF140x80x3N50 HSDuplex
Zhou and Young (2007a) RHS EOF160x80x3N75 HSDuplex
Zhou and Young (2007a) RHS EOF160x80x3N50 HSDuplex
Zhou and Young (2007a) RHS EOF200x110x4N100 HSA
Zhou and Young (2007a) RHS EOF200x110x4N50 HSA
Talja and Hradil (2011) SHS SHS_ES 1.4509
Material properties from tensile flat (σ in MPa)
Material properties
flat/stub column
E (GPa) σ0.01 σ0.2 σ1.0 σu n εf (%) m E (GPa) σ0.01
Duplex 216 164 707 827 29 220 230
Duplex 216 164 707 827 29 220 230
Duplex 200 182 622 770 37 216 200
Duplex 200 182 622 770 37 216 200
189 155 448 699 52 220 200
189 155 448 699 52 220 200
194 147 497 761 52 214 160
194 147 497 761 52 214 160
Duplex 212 199 486 736 47 220 200
Duplex 212 199 486 736 47 220 200
Duplex 208 167 536 766 40 200 210
Duplex 208 167 536 766 40 200 210
200 150 503 961 36 220 200
200 150 503 961 36 220 200
196 502 527 6.1 1.23 4.07
Table 1.6 WC EOF SHS/RHS. Material properties
12 (41)
12
Material properties fromcompression
flat/stub column(σ in MPa)
Mill certificates (σ in
MPa)
σ0.2 σ1.0 n σ0.2 σ1.0 σu εf (%)
747
747
652
652
547
547
678
678
513
513
569
569
622
622
355 377 478 46
154 (183)
Paper Section
type Reference grade
Span la
Talja et al.ECSC (2004) HAT H100-100x2 1.4318-C700 600 50
Talja et al.ECSC (2004) HAT H150-100x2 1.4318-C700 600 50
Talja et al.ECSC (2004) HAT H100-100x2 1.4318-C850 600 50
Talja et al.ECSC (2004) HAT H150-100x2 1.4318-C850 600 50
Talja et al.ECSC (2004) HAT H100-100x2 1.4301-C850 600 50
Talja et al.ECSC (2004) HAT H150-100x2 1.4301-C850 600 50
Talja and Hradil (2011) HAT TH_10_IS 1.4509 300 25
Talja and Hradil (2011) HAT TH_15_IS 1.4509 300 25
Talja and Hradil (2011) HAT TH_20_IS 1.4509 300 25
Talja and Hradil (2011) HAT TH_30_IS 1.4509 300 25
Table 1.7
Paper Sectiontype Reference grade
Talja et al. ECSC (2004) HAT H100-100x2 1.4318-C700
Talja et al. ECSC (2004) HAT H150-100x2 1.4318-C700
Talja et al. ECSC (2004) HAT H100-100x2 1.4318-C850
Talja et al. ECSC (2004) HAT H150-100x2 1.4318-C850
Talja et al. ECSC (2004) HAT H100-100x2 1.4301-C850
Talja et al. ECSC (2004) HAT H150-100x2 1.4301-C850
Talja and Hradil (2011) HAT TH_10_IS 1.4509
Talja and Hradil (2011) HAT TH_15_IS 1.4509
Talja and Hradil (2011) HAT TH_20_IS 1.4509
Talja and Hradil (2011) HAT TH_30_IS 1.4509
Measureddimensions (mm) Midsectiondimensions (mm)
H Hr B t C ɸ (°) ri h hr b
103.15 103.32 104 2.50 46.9 93.25 3 100.65 100.81 101.50 2.5
100.35 100.51 150 2.48 76.25 86.75 3 97.87 98.03 147.52 2.48
99.15 99.21 101 2.32 49.6 88 2.5 96.83 96.89 98.68 2.32
99.2 99.20 150 2.31 75.1 90 2.5 96.89 96.89 147.69 2.31
99.2 99.23 100 2.61 49.4 88.5 1.5 96.59 96.62 97.39 2.61
99.8 99.80 150 2.61 74.2 90.5 1.5 97.19 97.19 147.39 2.61
72.89 72.89 71.09 0.99 24.17 90 0.8 71.9 71.90 70.10 0.99
70.56 70.56 70.73 1.53 24.11 90 0.8 69.03 69.03 69.20 1.53
69.72 69.72 70.08 1.99 24.02 90 0.8 67.73 67.73 68.09 1.99
68.86 68.86 69.95 2.94 23.82 90 2 65.92 65.92 67.01 2.94
Table 1.7 WC IOF HAT sections. Geometrical properties and test results
Material properties from tensile flat (σ in MPa) Material properties
flat/stub column
E (GPa) σ0.01 σ0.2 σ1.0 σu n εf (%) m E (GPa) σ0.01
C700 207 228 331 825 8.1 44
C700 207 228 331 825 8.1 44
C850 195 262 523 951 4.3 30
C850 195 262 523 951 4.3 30
C850 190 309 686 854 3.8 29
C850 190 309 686 854 3.8 29
200 359 479 23.1 1.7 1.46
191 322 475 26.1 1.6 1.21
193 372 489 23 1.64 1.3
180 297 445 23.5 1.6 1.22
Table 1.8 WC IOF HAT sections. Material properties
13 (41)
13
Midsectiondimensions (mm) Web Crippling test
results (kN or kNm)
Bending
test results
(kNm)
t c rm Pexp/
web Pexp Mexp Mexp,b
2.50 45.65 4.25 24.75 49.50 6.81 11.69
2.48 75.01 4.24 25.01 50.01 6.88 12.71
2.32 48.44 3.66 31.20 62.40 8.58 13.80
2.31 73.95 3.66 31.02 62.04 8.53 15.10
2.61 48.10 2.81 44.34 88.67 12.19 18.90
2.61 72.90 2.81 45.67 91.34 12.56 20.80
0.99 23.68 1.65 5.00 10 0.69 3.41
1.53 23.35 1.9 10.37 20.73 1.43 6.71
1.99 23.03 2.4 17.42 34.84 2.40 10.97
2.94 22.35 4.25 27.51 55.01 3.78 14.06
Material properties from compression
flat/stub column(σ in MPa) Mill certificates (σ in MPa)
σ0.2 σ1.0 n σ0.2 σ1.0 σu εf (%)
352 390 800 47
352 390 800 47
604 662 951 32
604 662 951 32
759 867 882 35
759 867 882 35
381 395 477 59
338 359 470 49
396 415 490 46
322 501 37
155 (183)
Paper Section
type Reference grade
Span e
Talja and Hradil (2011) HAT TH_10_ES 1.4509 350 75
Talja and Hradil (2011) HAT TH_15_ES 1.4509 350 75
Talja and Hradil (2011) HAT TH_20_ES 1.4509 350 75
Talja and Hradil (2011) HAT TH_30_ES 1.4509 350 75
Table 1.9
Paper Sectiontype Reference grade
Talja and Hradil (2011) HAT TH_10_ES 1.4509
Talja and Hradil (2011) HAT TH_15_ES 1.4509
Talja and Hradil (2011) HAT TH_20_ES 1.4509
Talja and Hradil (2011) HAT TH_30_ES 1.4509
Measureddimensions (mm) Midsectiondimensions (mm)
la H Hr B t C ɸ (°) ri h hr b
25 72.85 72.85 71.05 0.99 24.15 90 0.8 71.86 71.86 70.06
25 70.47 70.47 70.84 1.53 24.03 90 0.8 68.94 68.94 69.31
25 69.65 69.65 70.52 1.99 23.98 90 0.8 67.66 67.66 68.53
25 68.86 68.86 69.39 2.94 23.74 90 2 65.92 65.92 66.45
Table 1.9 WC EOF HAT sections. Geometrical properties and test results
Material properties from tensile flat (σ in MPa) Material properties
flat/stub column
E (GPa) σ0.01 σ0.2 σ1.0 σu n εf (%) m E (GPa) σ0.01
200 359 479 23.1 1.7 1.46
191 322 475 26.1 1.6 1.21
193 372 489 23 1.64 1.3
180 297 445 23.5 1.6 1.22
Table 1.10 WC EOF HAT sections. Material properties
14 (41)
14
Midsectiondimensions (mm) Web Crippling test
results (kN)
t c rm Pexp/web Pexp
70.06 0.99 23.66 1.65 3.58 7.16
69.31 1.53 23.27 1.9 7.51 15.03
68.53 1.99 22.99 2.4 12.95 25.91
66.45 2.94 22.27 4.25 21.03 42.06
Material properties from compression
flat/stub column(σ in MPa) Mill certificates (σ in MPa)
σ0.2 σ1.0 n σ0.2 σ1.0 σu εf (%)
381 395 477 59
338 359 470 49
396 415 490 46
322 501 37
156 (183)
Paper Sectiontype Reference
ZilliECSC (2004) Unstiff. trapezoidal P30-45x9
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x9
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x9
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x8
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x8
Talja et al.ECSC (2004) Unstiff. trapezoidal H50-100x2
Talja et al.ECSC (2004) Unstiff. trapezoidal H50-100x2
Talja et al.ECSC (2004) Unstiff. trapezoidal H50-100x2
Talja et al.ECSC (2004) Stiff. trapezoidal P70-70-
Talja et al.ECSC (2004) Stiff. trapezoidal P90-70-
Talja et al.ECSC (2004) Stiff. trapezoidal P120-70-
Talja et al.ECSC (2004) Stiff. trapezoidal P70-70-
Talja et al.ECSC (2004) Stiff. trapezoidal P90-70-
Talja et al.ECSC (2004) Stiff. trapezoidal P120-70-
Reference grade Measureddimensions (mm)
Span la H Hr B t C
45x9 1.4318-C700 600 50
45x9 1.4318-C700 600 50
45x9 1.4318-C700 600 50
45x8 1.4318-C850 600 50
45x8 1.4318-C850 600 50
45x8 1.4318-C850 600 50
45x8 1.4318-C850 600 50
45x8 1.4318-C850 600 50
100x2 1.4318-C700 600 50 97.35 102.27 49 2.49 28
100x2 1.4318-C850 600 50 99.05 102.08 58 2.30 29.5
100x2 1.4301-C850 600 50 100 101.87 61 2.60 27.45
-Vx0.9 1.4318-C700 600 50 68.85 77.45 72.5 0.90 34.6
-Vx0.9 1.4318-C700 600 50 68.2 77.98 92.5 0.90 44.2
-Vx0.9 1.4318-C700 600 50 64.85 74.15 122 0.90 62.8
-Vx0.8 1.4318-C850 600 50 67.75 78.23 71 0.82 34.6
-Vx0.8 1.4318-C850 600 50 68.15 78.30 91 0.82 45.5
-Vx0.8 1.4318-C850 600 50 69 79.47 120 0.82 58.2
Table 1.11 WC IOF Trapezoidal measured section dimensions
15 (41)
15
Measureddimensions (mm)
ɸ (°) ri bs ls ds
- - -
- - -
- - -
- - -
- - -
- - -
- - -
- - -
72.15 3 - - -
76 2.5 - - -
79 2 - - -
62.75 3 36.25 21.8 10.8
61 3 46.25 21 10.7
61 3 61 20.7 10.7
60 2.75 35.5 20.1 10.4
60.5 2.5 45.5 20.6 10.6
60.25 2.5 60 19.7 10.5
157 (183)
Paper Sectiontype Reference
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x9 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x9 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x9 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x8 1.4318
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x8 1.4318
Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4318
Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4318
Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4301
Talja et al. ECSC (2004) Stiff. trapezoidal P70-70-Vx0.9 1.4318
Talja et al. ECSC (2004) Stiff. trapezoidal P90-70-Vx0.9 1.4318
Talja et al. ECSC (2004) Stiff. trapezoidal P120-70-Vx0.9 1.4318
Talja et al. ECSC (2004) Stiff. trapezoidal P70-70-Vx0.8 1.4318
Talja et al. ECSC (2004) Stiff. trapezoidal P90-70-Vx0.8 1.4318
Talja et al. ECSC (2004) Stiff. trapezoidal P120-70-Vx0.8 1.4318
Table 1.12
grade Midsectiondimensions (mm)
h hr b t c rm bs ls
1.4318-C700
- -
1.4318-C700
- -
1.4318-C700
- -
1.4318-C850
- -
1.4318-C850
- -
1.4318-C850
- -
1.4318-C850
- -
1.4318-C850
- -
1.4318-C700 94.86 99.66 38.55 2.49 22.77 4.25 - -
1.4318-C850 96.75 99.71 48.69 2.30 24.84 3.65 - -
1.4301-C850 97.4 99.22 51.97 2.60 22.93 3.30 - -
1.4318-C700 67.955 76.44 65.57 0.90 31.14 3.45 32.79 21.80 10.80
1.4318-C700 67.303 76.95 85.68 0.90 40.79 3.45 42.84 21.00 10.70
1.4318-C700 63.955 73.12 115.19 0.90 59.39 3.45 57.59 20.70 10.70
1.4318-C850 66.93 77.28 64.82 0.82 31.51 3.16 32.41 20.10 10.40
1.4318-C850 67.334 77.36 85.23 0.82 42.61 2.91 42.61 20.60 10.60
1.4318-C850 68.185 78.54 114.24 0.82 55.32 2.91 57.12 19.70 10.50
Table 1.12 WC IOF Trapezoidal midsection dimensions and experimental results
16 (41)
16
Web Crippling test
results (kN or kNm) Bending test
results (kNm)
ds Pexp/web Pexp Mexp Mexp,b
- 2.38 4.76 0.65 0.73
- 2.56 5.12 0.70 0.87
- 2.16 4.31 0.59 0.87
- 2.95 5.89 0.81 0.82
- 2.92 5.83 0.80 0.82
- 2.41 4.81 0.66 0.82
- 3.06 6.11 0.84 0.95
- 2.65 5.29 0.73 0.95
- 21.88 43.75 6.02 9.46
- 29.21 58.42 8.03 11.90
- 42.60 85.20 11.72 17.10
10.80 4.02 8.04 1.11 2.13
10.70 3.84 7.67 1.05 2.35
10.70 3.67 7.33 1.01 2.15
10.40 4.72 9.44 1.30 2.24
10.60 4.56 9.12 1.25 2.37
10.50 4.26 8.52 1.17 2.12
158 (183)
Paper Sectiontype Reference grade
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x9 1.4318-C700
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x9 1.4318-C700
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x9 1.4318-C700
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8 1.4318-C850
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8 1.4318-C850
Zilli ECSC (2004) Unstiff. trapezoidal P30-45x8 1.4318-C850
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x8 1.4318-C850
Zilli ECSC (2004) Unstiff. trapezoidal P65-45x8 1.4318-C850
Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4318-C700
Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4318-C850
Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4301-C850
Talja et al. ECSC (2004) Stiff. trapezoidal P70-70-Vx0.9 1.4318-C700
Talja et al. ECSC (2004) Stiff. trapezoidal P90-70-Vx0.9 1.4318-C700
Talja et al. ECSC (2004) Stiff. trapezoidal P120-70-Vx0.9 1.4318-C700
Talja et al. ECSC (2004) Stiff. trapezoidal P70-70-Vx0.8 1.4318-C850
Talja et al. ECSC (2004) Stiff. trapezoidal P90-70-Vx0.8 1.4318-C850
Talja et al. ECSC (2004) Stiff. trapezoidal P120-70-Vx0.8 1.4318-C850
grade Material properties from tensile flat (σ in MPa)
Material properties
flat/stub column
E (GPa) σ0.01 σ0.2 σ1.0 σu n εf (%) m E (GPa) σ0.01
C700
C700
C700
C850
C850
C850
C850
C850
C700 207 228 331 825 8.1 44
C850 195 262 523 951 4.3 30
C850 190 309 686 854 3.8 29
C700 207 305 354 822 20.4 42
C700 207 305 354 822 20.4 42
C700 207 305 354 822 20.4 42
C850 203 359 641 972 5.2 27
C850 203 359 641 972 5.2 27
C850 203 359 641 972 5.2 27
Table 1.13 WC IOF Trapezoidal material properties
17 (41)
17
Material properties from compression
flat/stub column(σ in MPa) Mill certificates (σ in MPa)
0.01 σ0.2 σ1.0 n σ0.2 σ1.0 σu εf (%)
352 390 800 47
604 662 951 32
759 867 882 35
385 417 825 49
385 417 825 49
385 417 825 49
666 728 1007 34
666 728 1007 34
666 728 1007 34
159 (183)
1.3 Target
The study of web crippling
Stiffened elements will be excluded
multiple webs EN1993-1-3 formulation. IOF may require also four
into account interaction.
A preliminary study concluded that
influence on the web crippling resistance. However, in order to avoid the calculus of
inclusion of σ1.0 would be more suitable
parameter of stainless steel has no effects on the
(WC) phenomenon will focus on RHS/SHS and HAT
Stiffened elements will be excluded. IOF and EOF will be used to assess both single
ormulation. IOF may require also four-point bending test to
concluded that the material ultimate proof strength, σu
influence on the web crippling resistance. However, in order to avoid the calculus of
would be more suitable. On the other hand, it was found that the nonlinear
parameter of stainless steel has no effects on the web crippling resistance.
18 (41)
18
phenomenon will focus on RHS/SHS and HAT sections.
e used to assess both single and
point bending test to take
u, has a significant
influence on the web crippling resistance. However, in order to avoid the calculus of εu, the
On the other hand, it was found that the nonlinear
160 (183)
2. Parametric study
A wider parametric study to
properties and test setup on the web crippling resistance
two ways to predict web crippling resistance: 6.1.7.2 article
capacity in sections with a single web (channels, lipped channels, Z
6.1.7.3 article which is applicable to sections with more than one web
trays and hat sections). In both articles
which equation must be used
cumbersome since our load conditions might not r
identifiable. For this reason, EN1993
2.1 Cross-sections and test configuration
EC limitations (cross-sections)
Internal parts: hw/t<400
According to 6.1.7.2 article (unstiffened single webs):
According to 6.1.7.3 article (two or more unstiffened webs)
t (6.1.7.2) r<
0.5
1
1.5
2
2.5
3
4
Table 2
EC limitations for IOF/EOF conditions:
For two opposing loads (no symmetrical), c=0 (distance from support to a free end) will
studied. In article 6.1.7.3 the clear distance, c, from the bearing length for the support reaction
or local load to a free end must be at least 40mm.
EOF:
The following equations, according to EN1993
- 6.1.7.2 article: for two opposing local tra
e>1.5hw, then “support reaction” c=0 and S
- 6.1.7.3 article: Category 1 (EOF)
and Category 2 if e>1.5hw clear from the nearest support.
hw 1.5h
60
70
80
90
100
110
120
Table 2.2 Cross
Parametric study
parametric study to analyze the influence of cross section geometries, material
properties and test setup on the web crippling resistance is presented in this section.
to predict web crippling resistance: 6.1.7.2 article, which calculates
capacity in sections with a single web (channels, lipped channels, Z-profiles, I
6.1.7.3 article which is applicable to sections with more than one web (sheeting profiles, liner
In both articles load conditions and geometrical ratios
which equation must be used to calculate web crippling resistance. The procedure is quite
cumbersome since our load conditions might not resemble the available ones or are not easily
For this reason, EN1993-1-3 used equations are also specified herein.
and test configuration
sections):
(unstiffened single webs): hw/t<200; r/t<6; 45<ϕ<90
(two or more unstiffened webs): hw/t<200sin ϕ; r/t<10;
(6.1.7.2) r< (6.1.7.3) r< hw<
3 5 100
6 10 200
9 15 300
12 20 400 (slenderness limit)
15 25 500 (400)
18 30 600 (400)
24 40 800 (400)
2.1 Cross-section limitations specified in EN1993-1-3
EC limitations for IOF/EOF conditions:
For two opposing loads (no symmetrical), c=0 (distance from support to a free end) will
. In article 6.1.7.3 the clear distance, c, from the bearing length for the support reaction
or local load to a free end must be at least 40mm.
The following equations, according to EN1993-1-3 nomenclature must be considered:
: for two opposing local transverse forces closer together e<1.5h
then “support reaction” c=0 and Ss/t≤60 �6.15b and if Ss/t>60�6.15c
: Category 1 (EOF) if local load is applied with e≤1.5hw from the nearest s
clear from the nearest support.
1.5hw t Max Ss to apply 6.15d (IOF) or
6.15b (EOF)
90 0.5 30
105 1 60
120 1.5 90
135 2 120
150 2.5 150
160 3 180
180 4 240
oss-section/test setup limitations specified in EN1993-1-3
19 (41)
19
of cross section geometries, material
is presented in this section. There are
calculates the load carrying
profiles, I-sections), and
(sheeting profiles, liner
and geometrical ratios determine
to calculate web crippling resistance. The procedure is quite
esemble the available ones or are not easily
3 used equations are also specified herein.
<90
; r/t<10; 45<ϕ<90
For two opposing loads (no symmetrical), c=0 (distance from support to a free end) will only be
. In article 6.1.7.3 the clear distance, c, from the bearing length for the support reaction
3 nomenclature must be considered:
<1.5hw � 6.15f. If
6.15c
from the nearest support
Max Ss to apply 6.15d (IOF) or
161 (183)
IOF:
For a single local load or support reaction only symmetrical configuration will be studied.
following equations must be considered:
- 6.1.7.2: c (distance from a free end)>1.5hw
- 6.1.7.2: c (distance from a free end)>1.5hw and S
- 6.1.7.3: Category 2 (IOF) reaction at internal support
- 6.1.7.3: Category 2 (IOF) local load applied
free end.
Cross-sections and test configuration for parametric study:
It is proposed to study cross sections and test configurations specified in table
2.1. Tables 2.4 and 2.5 specify the equations to determine web crippling resistance.
bxh; bxhxc
rm
t
L
Ltot
Ssa/Ssb (IOF)
SsL (IOF) Crippling load
c (distance from end to plate) (IOF)
Ssa (EOF) Crippling load
Ssb/SsL (EOF)
e
e+Ss (c=0)
1.5hw
Max Ss to apply 6.15b(EOF), 6.15d(IOF)
Table 2.3 Cross sections and test setup of the parametric study
Applicable equations to predict web crippling resistance according to EN1993
IOF Ss=25
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.4 Equations to determine web crippling resistance in cross sections. IOF test and 25mm of bearing
EOF Ss=25
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.5 Equations to determine web crippling resistance in cross
IOF
ssa L
F
(a)
For a single local load or support reaction only symmetrical configuration will be studied.
following equations must be considered:
6.1.7.2: c (distance from a free end)>1.5hw and Ss/t≤60 � 6.15d (all available exp. Data)
6.1.7.2: c (distance from a free end)>1.5hw and Ss/t>60 � 6.15e
Category 2 (IOF) reaction at internal support
(IOF) local load applied/reaction at end support with c>1.5h
sections and test configuration for parametric study:
It is proposed to study cross sections and test configurations specified in table
.5 specify the equations to determine web crippling resistance.
SHS (S1) RHS (S2) HAT (S3) HAT (S4)
70x70 60x120 60x60x20 120x120x50
3 3 3 3
2; 4 2; 4 1; 2 1;
500 500 500 500
550 550 550 550
50 50 50 50
25 25 25 25
(distance from end to plate) (IOF) 262.5 262.5 262.5 262.5
25 25 25 25
50 50 50 50
125 125 125 125
150 150 150 150
105 180 90 180
(IOF) 120; 240 120; 240 60; 120 60;
.3 Cross sections and test setup of the parametric study
Applicable equations to predict web crippling resistance according to EN1993
6.1.7.2 6.1.7.3
c>1.5hw and Ss/t≤60 � 6.15d c>1.5h
c>1.5hw and Ss/t≤60 � 6.15d c>1.5h
c>1.5hw and Ss/t≤60 � 6.15d c>1.5h
c>1.5hw and Ss/t≤60 � 6.15d c>1.5h
c>1.5hw and Ss/t≤60 � 6.15d c>1.5h
Equations to determine web crippling resistance in cross sections. IOF test and 25mm of bearing
length
6.1.7.2 6.1.7.3
e>1.5hw and Ss/t≤60 � 6.15b e>1.5hw
e<1.5hw�6.15f e≤1.5hw
e>1.5hw and Ss/t≤60 � 6.15b e>1.5hw
e<1.5hw�6.15f e≤1.5hw
e>1.5hw and Ss/t≤60 � 6.15b e>1.5hw
Equations to determine web crippling resistance in cross sections. EOF test and 25mm of bearing length
Figure 2.1 Tests setup variables
EOF
ssb
ssL
ssa ssb
ssL F
(b)
L
e
20 (41)
20
For a single local load or support reaction only symmetrical configuration will be studied. The
(all available exp. Data)
1.5hw clear from a
It is proposed to study cross sections and test configurations specified in table 2.3 and figure
.5 specify the equations to determine web crippling resistance.
HAT (S4) HAT (S5)
120x120x50 60x80x25
3 3
; 2 1; 2
500 500
550 550
50 50
25 25
262.5 262.5
25 25
50 50
125 125
150 150
180 120
120 60; 120
Applicable equations to predict web crippling resistance according to EN1993-1-3:
6.1.7.3
c>1.5hw Category 2
c>1.5hw Category 2
c>1.5hw Category 2
c>1.5hw Category 2
1.5hw Category 2
Equations to determine web crippling resistance in cross sections. IOF test and 25mm of bearing
6.1.7.3
� Category 2
� Category 1
� Category 2
� Category 1
� Category 2
sections. EOF test and 25mm of bearing length
162 (183)
2.2 Materials
It is proposed to study 3 nonlinear factors and four hard
Nonlinear factor Group
A
B
C
E0 σ0.2
A1 200 250
B1 200 250
C1 200 250
(A1*) 200 250
(B1*) 200 250
(C1*) 200 250
A2 200 250
B2 200 250
C2 200 250
(A2*) 200 250
(B2*) 200 250
(C2*) 200 250
It was found in the preliminary study that the non
web crippling resistance. For that reason, this parametric study is going to be focused in
hardening rate variations. Four materials will be studied:
Total of numerical simulations
materials=120 numerical simulations
2.3 Additional tests
The internal radius and bearing length parameters have an important role in the WC
formulation and additional test will be carried out to study this effect more accurately.
Internal radius
SHS
bxh; bxhxc 70x70
rm 4; 5
t 2; 4
L 500
Ltot 550
Ssa/Ssb (IOF) 50
SsL (IOF) 25
Ssa (EOF) 25
Ssb/SsL (EOF) 50
e 150
2 more radii per section in 2 materials
2x5x2x3x2=120
The internal radius influence in I
It is proposed to study 3 nonlinear factors and four hardening rates.
n
5
10
20
Hardening rate
Group
1
(1*)
2
(2*)
σ1.0 σu εu n
256 275 0.4 5
256 275 0.4 10
256 275 0.4 20
262.2 300 0.4 5
262.2 300 0.4 10
262.2 300 0.4 20
275 350 0.4 5
275 350 0.4 10
275 350 0.4 20
300 450 0.4 5
300 450 0.4 10
300 450 0.4 20
Table 2.6 Material models
It was found in the preliminary study that the non-linear factor does not have influence in the
web crippling resistance. For that reason, this parametric study is going to be focused in
our materials will be studied: B1, (B1*), B2, (B2*)
of numerical simulations: 5 sections x 2thickness x 3 tests (IOF,EOF, 4-point bending)
numerical simulations
The internal radius and bearing length parameters have an important role in the WC
formulation and additional test will be carried out to study this effect more accurately.
RHS HAT HAT
60x120 60x60x20 120x120x50
4; 5 4; 5 5; 6
2; 4 1; 2 1; 2
500 500 500
550 550 550
50 50 50
25 25 25
25 25 25
50 50 50
150 150 150
Table 2.7 Additional internal radiuses
in 2 materials in the three test configurations and 2 thicknesses
e internal radius influence in IOF Hat 120x120x50 is not going to be studied:
21 (41)
21
σ1.0/σ0.2
1.025
(1.05)
1.1
(1.20)
m σu /σ0.2
3 1.1
3 1.1
3 1.1
3 1.2
3 1.2
3 1.2
3 1.4
3 1.4
3 1.4
3 1.8
3 1.8
3 1.8
linear factor does not have influence in the
web crippling resistance. For that reason, this parametric study is going to be focused in
point bending) x 4
The internal radius and bearing length parameters have an important role in the WC
formulation and additional test will be carried out to study this effect more accurately.
HAT
120x120x50 60x80x25
4; 5
1; 2
500
550
50
25
25
50
150
and 2 thicknesses more:
is not going to be studied: (-16)
163 (183)
Bearing length
SsL
Ssa
IOF: 3 more bearing lengths in
EOF: 6 more bearing lengths in 1SHS and 2 HAT for 2 materials
Variation in IOF:
According to EN1993-1-3 there are some geometrical ratios that must be considered in order
to identify the load case to obtain the web crippling
articles. Variations in the bearing length might imply variations in the
different formula or different parameters
equations are the same as EN1993
Article 6.1.7.2
For a single local load or support reaction and a cross
section with unstiffened flanges (c>1.5h
end)
Figure 2.2 Equations in EN1993
rm
t
L
Ltot
Ssa/Ssb (IOF)
SsL (IOF) Crippling load
c (distance from end to plate) (IOF)
1.5hw
Max Ss to apply 6.15d (if Ss is greater than the value
6.15.e must be used instead)
Table 4.
IOF Ss=50
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.9 Equations to determine web crippling resistance in cross sections. IOF test and 50mm of bearing length
IOF EOF
50;75;100 75;100
- 40;50;75;100
Table 2.8 Additional bearing lengths
IOF: 3 more bearing lengths in 1SHS and 2 HAT for 2 materials and 2 thicknesses
EOF: 6 more bearing lengths in 1SHS and 2 HAT for 2 materials and 2 thicknesses
3 there are some geometrical ratios that must be considered in order
to identify the load case to obtain the web crippling resistance in both 6.1.7.2 and 6.1.7.3
. Variations in the bearing length might imply variations in the load case and then, a
or different parameters must be used as shown below. The names of the
equations are the same as EN1993-1-3.
Article 6.1.7.3→Always eq 6.18
For a single local load or support reaction and a cross
section with unstiffened flanges (c>1.5hw clear from a free
Category 2: Reaction at internal support
Category 2: local load applied with c>1.5h
a free end
Category 2→la=10mm (6.19b) or la=Ss (6.19c)
The value of la will always be considered as Ss
if Ss/t≤60→6.15d)
if Ss/t>60→6.15e)
Equations in EN1993-1-3 to predict web crippling resistance in IOF test
SHS RHS HAT
70x70 60x120 60x60x20
3 3 3
2; 4 2; 4 1; 2
500 500 500
550 550 550
50 50 50
50; 75; 100
c (distance from end to plate) (IOF) 250; 237.5; 225
105 180 90
(if Ss is greater than the value 120; 240 120; 240 60; 120
Table 4.8 New limits in the additional IOF tests
6.1.7.2
c>1.5hw and Ss/t≤60 � 6.15d c>1.5hw Category 2
c>1.5hw and Ss/t≤60 � 6.15d c>1.5hw Category 2
c>1.5hw and Ss/t≤60 � 6.15d c>1.5hw Category 2
c>1.5hw and Ss/t≤60 � 6.15d c>1.5hw Category 2
c>1.5hw and Ss/t≤60 � 6.15d c>1.5hw Category 2
determine web crippling resistance in cross sections. IOF test and 50mm of bearing length
22 (41)
22
and 2 thicknesses: 3x3x2x2=36
and 2 thicknesses 6x3x2x2=72
3 there are some geometrical ratios that must be considered in order
in both 6.1.7.2 and 6.1.7.3
load case and then, a
The names of the
Category 2: Reaction at internal support
Category 2: local load applied with c>1.5hw clear from
la=10mm (6.19b) or la=Ss (6.19c)
The value of la will always be considered as Ss
3 to predict web crippling resistance in IOF test
HAT HAT
120x120x50 60x80x25
3 3
1; 2 1; 2
500 500
550 550
50 50
180 120
60; 120 60; 120
6.1.7.3
Category 2
Category 2
Category 2
Category 2
Category 2
determine web crippling resistance in cross sections. IOF test and 50mm of bearing length
164 (183)
IOF Ss=75;100
SHS 70x70 c>1.5hw
RHS 60x120 c>1.5hw
HAT 60x60x20 c>1.5hw
HAT 120x120x50 c>1.5hw
HAT 60x80x25 c>1.5hw
Table 2.10 Equations to determine web crippling resistance in cross sections. IOF test and 75 and 100mm of bearing
Variation in EOF (Ssa crippling load
According to EN1993-1-3 there are some geometrical ratios that must be considered in order
to identify the load case to obtain the web crippling
articles. Variations in the bearing length might imply variations in the load case and then, a
different formula must be used as shown below.
Article 6.1.7.2
Figure 2.3 Equations in
rm
t
L
Ltot
Ssa (EOF) Crippling load
Ssb/SsL (EOF)
e
e+Ss (EOF) (c=0)
1.5hw
Max Ss to apply 6.15b (if grater→ 6.15c)
Table 2.11
6.1.7.2
w and Ss/t≤60 � 6.15d
w and Ss/t≤60 � 6.15d
w and Ss/t(=1)>60 � 6.15e; Ss/t(=2)≤60 � 6.15d
w and Ss/t(=1)>60 � 6.15e Ss/t(=2)≤60 � 6.15d
w and Ss/t(=1)>60 � 6.15e Ss/t(=2)≤60 � 6.15d
Equations to determine web crippling resistance in cross sections. IOF test and 75 and 100mm of bearing
length
crippling load)
3 there are some geometrical ratios that must be considered in order
e load case to obtain the web crippling resistance in both 6.1.7.2 and 6.1.7.3
articles. Variations in the bearing length might imply variations in the load case and then, a
different formula must be used as shown below.
Article 6.1.7.2 Article 6.1.7.3→Always eq 6.18
For a single local load or
support reaction and a
cross section with
unstiffened flanges (c=0
and e>1.5hw):
if Ss/t≤60→6.15b)
if Ss/t>60→6.15c)
Category 1: local load applied with e
from the nearest support
Category 1→la=10mm (always)
For two opposing local
transverse forces closer
together than 1.5hw
(e≤1.5hw).
If c=0→6.15f
Category 2: local load applied with e>1.5h
from the nearest support
Category 2→la=10mm (6.19b) or l
Equations in EN1993-1-3 to predict web crippling resistance in EOF test
SHS RHS HAT HAT
70x70 60x120 60x60x20 120x120x50
3 3 3 3
2; 4 2; 4 1; 2 1;
500 500 500 500
550 550 550 550
40; 50; 75; 100
50 50 50 50
110; 100; 75; 50
150; 150; 150; 150
105 180 90 180
6.15c) 120;240 120;240 60;120 60;
11 New limits in the additional EOF tests. Ssa variation
23 (41)
23
6.1.7.3
c>1.5hw Category 2
c>1.5hw Category 2
c>1.5hw Category 2
c>1.5hw Category 2
c>1.5hw Category 2
Equations to determine web crippling resistance in cross sections. IOF test and 75 and 100mm of bearing
3 there are some geometrical ratios that must be considered in order
resistance in both 6.1.7.2 and 6.1.7.3
articles. Variations in the bearing length might imply variations in the load case and then, a
Always eq 6.18
Category 1: local load applied with e≤1.5hw clear
=10mm (always)
Category 2: local load applied with e>1.5hw clear
=10mm (6.19b) or la=Ss (6.19c)
3 to predict web crippling resistance in EOF test
HAT HAT
120x120x50 60x80x25
3 3
; 2 1; 2
500 500
550 550
50 50
180 120
;120 60;120
165 (183)
EOF Ssa=40
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.12 Equations to determine web crippling resistance in cross sections. EOF test and 40 mm of bearing length
EOF Ssa=50
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.13 Equations to determine web crippling resistance
EOF Ssa=75;100
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.14 Equations to determine web crippling resistance in cross sections. EOF test and 75 and 100 mm of
Variation in EOF (SsL length of applying
rm
t
L
Ltot
Ssa (EOF) Crippling load
Ssb
SsL (EOF)
e
c (e+Ss) (EOF)
1.5hw
Max Ss to apply 6.15b, 6.15d
Table 2.1
EOF SsL=75,100
SHS 70x70
RHS 60x120
HAT 60x60x20
HAT 120x120x50
HAT 60x80x25
Table 2.16 Equations to determine web crippling resistance in cross sections. EOF test and 75 and 100 mm of
6.1.7.2 6.1.7.3
e<1.5hw�6.15f e>1.5hw
e<1.5hw�6.15f e≤1.5hw
e>1.5hw and Ssa/t≤60 � 6.15b e>1.5hw
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
Equations to determine web crippling resistance in cross sections. EOF test and 40 mm of bearing length
(Ssa)
6.1.7.2 6.1.7.3
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
e>1.5hw and Ssa/t≤60 � 6.15b e>1.5hw
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
Equations to determine web crippling resistance in cross sections. EOF test and 50 mm of bearing length
(Ssa)
6.1.7.2 6.1.7.3
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
e<1.5hw�6.15f e≤1.5hw
Equations to determine web crippling resistance in cross sections. EOF test and 75 and 100 mm of
bearing length (Ssa)
length of applying load)
SHS RHS HAT HAT
70x70 60x120 60x60x20 120x120x50
3 3 3
2; 4 2; 4 1; 2 1
500 500 500 500
550 550 550 550
25 25 25
50 50 50
75; 100
112.5; 100
150 150 150 150
105 180 90 180
Max Ss to apply 6.15b, 6.15d 120; 240 120; 240 60; 120 60
15 New limits in the additional EOF tests. SsL variation
6.1.7.2 6.1.7.3
e>1.5hw and Ss/t≤60 � 6.15b e>1.5hw;c=0
e<1.5hw�6.15f e≤1.5hw
e>1.5hw and Ss/t≤60 � 6.15b e>1.5hw;c=0
e<1.5hw�6.15f e≤1.5hw
e>1.5hw and Ss/t≤60 � 6.15b e>1.5hw;c=0
Equations to determine web crippling resistance in cross sections. EOF test and 75 and 100 mm of
bearing length (SsL)
24 (41)
24
6.1.7.3
� Category 2
� Category 1
� Category 2
� Category 1
� Category 1
Equations to determine web crippling resistance in cross sections. EOF test and 40 mm of bearing length
6.1.7.3
� Category 1
� Category 1
� Category 2
� Category 1
� Category 1
in cross sections. EOF test and 50 mm of bearing length
6.1.7.3
� Category 1
� Category 1
� Category 1
� Category 1
� Category 1
Equations to determine web crippling resistance in cross sections. EOF test and 75 and 100 mm of
HAT HAT
120x120x50 60x80x25
3 3
1; 2 1; 2
500 500
550 550
25 25
50 50
150 150
180 120
60; 120 60; 120
6.1.7.3
;c=0 � Category 1
� Category 1
;c=0 � Category 1
� Category 1
;c=0 � Category 1
Equations to determine web crippling resistance in cross sections. EOF test and 75 and 100 mm of
166 (183)
2.4 Parametric study recount
Base
5 sections
2 thicknesses
3 test configurations
4 materials
Total: 5x2x3x4=120
Study of the internal radius
2 more radiuses in each section
2 materials
3 test configurations
2 thicknesses
Total: 2x5x2x3x2=120-16=104
IOF bearing length study
3 bearing lengths
3 sections
2 materials
2 thicknesses
Total: 3x3x2x2=36
EOF bearing length study:
4 bearing lengths (support)
2 applied load lengths
3 sections
2 materials
2 thicknesses
Total: 6x3x2x2=72
Total of totals
Total: 120+104+36+72=332
The results of this parametric study are gathered in Annex
recount
in each section
16=104
2 numerical simulations
The results of this parametric study are gathered in Annex A.
25 (41)
25
167 (183)
3. EN1993-1-3 formulations for web crippling strength and
new proposal expression
3.1 EN1993-1-3 formulae
The current equations to predict web crippling resistance are
EN1993-1-3§6.1.7.3), 3.2 (6.15d from EN1993
3§6.1.7.2), 3.4 (interaction equation). ��,�� � �� ��� .� �1 �Category 1 (EOF): �� � 10��Category 2 (IOF):
-�� � 0.2 �� � ��
-�� � 0.3 �� � 10��
-0.2 � �� � 0.3: interpolate linearly between the values of
With:
In which !"�,# and !"�, are the absolute values of the transverse shear forces on each side of
the local load or support reaction, and
And α worths:
Category 1
SHS/RHS
α 0.075
Table 3.1 Current nondimensional coefficient
��,�� � �� $%$&$' (14.7 � +
��,�� � �� $%$&$' (14.7 � +
Where $% � 0.7 , 0$& � 1.22$' � 1.06$ �
�./012 � R45 � 1.25#78,9: , ;<=>&?�@A0BC � �D� E��,�� , 4FG,���HIJWhere:
Rw,Rd is the predicted resistance by EN1993
resistance from IOF test.
Mc,Rd is the numerical (MBD,num
lIOF is the span in IOF test.
3 formulations for web crippling strength and
expression
3 formulae
The current equations to predict web crippling resistance are 3.1 (this is equation 6.18 from
.2 (6.15d from EN1993-1-3§6.1.7.2), 3.3 (6.15e from EN1993
.4 (interaction equation).
0.1�KL ⁄ N �0.5 , �0.02�� ⁄ N O2.4 , OP 90⁄ RR��
: interpolate linearly between the values of ��
�� � !"�,# � !"�, !"�,# , !"�, are the absolute values of the transverse shear forces on each side of
the local load or support reaction, and !"�,# � !"�, . Ss is the length of stiff bearing.
Category 1 Category 2
Hat section SHS/RHS
0.057 0.15
Table 3.1 Current nondimensional coefficient α
+S/U&V.' W (1 , 0.007 XYU W Z[\]^#
+S/U&V.' W (0.75 , 0.011 XYU W Z[\]^#
0.3OP 90⁄ R 22 � 0.22$ � 0.06 K ⁄ � � ./228
but $' �1.0
with � . in N/mm2
<=>?`,9:
��HIJ a
predicted resistance by EN1993-1-3 or the numerical (RWC,num
BD,num) bending moment resistance from 4-point bending test.
26 (41)
26
3 formulations for web crippling strength and
.1 (this is equation 6.18 from
.3 (6.15e from EN1993-1-
R R ]^#b
3.1
are the absolute values of the transverse shear forces on each side of
Ss is the length of stiff bearing.
Category 2
Hat section
0.115
3.2
3.3
3.4
WC,num) web crippling
point bending test.
168 (183)
3.2 New proposal expression
Based on the preliminary study results, the new following expression is proposed to predict
web crippling strength:
��,�� � �� ��� .� �c �#�Where
la must be taken from:
Category 1 (EOF):
Category 2 (IOF):
Three mainly changes have been proposed (further details are explained in the following
sections):
• The internal radius is considered differently.
• The term that takes into account the bearing length, l
1-3§6.1.7.3 considered an invariable bearing length equal to 10mm when
(the most common state)
length must be used instead.
• A new term has been added to consider possible material nonlinearities.
In addition, three nondimensional coefficients (β,
better adjustment of the different parameters.
new proposal formulation were adjusted considering numerical results from both preliminary
FEM study and parametric study. It is important to mention that some EOF tests from the
parametric study were Category 2 and consequently not
Category 1 specimens. The obtained results are presented in Table 1.
Category 1 (EOF)
SHS/RHS
α 0.07
β 2.14
δ 0.22
ξ 2200
Table 3.2 Nondimensional
Since the preliminary study concluded that the nonlinear parameter has no influence on the
web crippling strength, this new proposal expression is applicable
3.2.1 Material nonlinearities influence
The material influence in the web crippling resistance is considered by means of the material
proof strength (σ0.2) because EN1993
steel, stainless steel has rounded stress
crippling strength calculation. The effect of the nonlinear parameter ‘n’ in the ultimate web
crippling strength, which was assessed by comparing N1, N2 and N3 specim
preliminary FEM study was found to be negligible. Then, the inclusion of that parameter in the
web crippling formulation was ruled out. On the other hand, numerical results from N2 and F1
3.2 New proposal expression
Based on the preliminary study results, the new following expression is proposed to predict
#. � Nd e� K �0.5 , �0.01�� ⁄ N O2.4 , OP 90⁄ RRf$ � gK ⁄
Category 1 (EOF): �� � 0.01��
Category 2 (IOF): �� � 2.2�� Three mainly changes have been proposed (further details are explained in the following
The internal radius is considered differently.
term that takes into account the bearing length, la, has changed. Current
6.1.7.3 considered an invariable bearing length equal to 10mm when
(the most common state) and the new proposal recommends that the real bearing
ed instead.
A new term has been added to consider possible material nonlinearities.
addition, three nondimensional coefficients (β, δ and ξ) have also been added to allow a
better adjustment of the different parameters. The four nondimensional coefficients from the
new proposal formulation were adjusted considering numerical results from both preliminary
FEM study and parametric study. It is important to mention that some EOF tests from the
parametric study were Category 2 and consequently not considered in the adjustment of
Category 1 specimens. The obtained results are presented in Table 1.
Category 1 (EOF) Category 2 (IOF)
Hat section SHS/RHS Hat section
0.085 0.13 0.14
1.65 0.59 0.81
0.13 0.14 0.065
2275 2700 2000
Nondimensional coefficient values for the new proposal expression
Since the preliminary study concluded that the nonlinear parameter has no influence on the
web crippling strength, this new proposal expression is applicable to any stainless steel
Material nonlinearities influence
The material influence in the web crippling resistance is considered by means of the material
) because EN1993-1-3 is only applicable to carbon steel. Unlike carbon
stainless steel has rounded stress-strain behaviour which might be considered in the web
crippling strength calculation. The effect of the nonlinear parameter ‘n’ in the ultimate web
crippling strength, which was assessed by comparing N1, N2 and N3 specimen results from the
preliminary FEM study was found to be negligible. Then, the inclusion of that parameter in the
web crippling formulation was ruled out. On the other hand, numerical results from N2 and F1
27 (41)
27
Based on the preliminary study results, the new following expression is proposed to predict
R R ]^#f
3.5
Three mainly changes have been proposed (further details are explained in the following
, has changed. Current EN1993-
6.1.7.3 considered an invariable bearing length equal to 10mm when �� � 0.3
and the new proposal recommends that the real bearing
A new term has been added to consider possible material nonlinearities.
δ and ξ) have also been added to allow a
coefficients from the
new proposal formulation were adjusted considering numerical results from both preliminary
FEM study and parametric study. It is important to mention that some EOF tests from the
considered in the adjustment of
Hat section
0.14
0.81
0.065
2000
coefficient values for the new proposal expression
Since the preliminary study concluded that the nonlinear parameter has no influence on the
to any stainless steel
The material influence in the web crippling resistance is considered by means of the material
3 is only applicable to carbon steel. Unlike carbon
strain behaviour which might be considered in the web
crippling strength calculation. The effect of the nonlinear parameter ‘n’ in the ultimate web
en results from the
preliminary FEM study was found to be negligible. Then, the inclusion of that parameter in the
web crippling formulation was ruled out. On the other hand, numerical results from N2 and F1
169 (183)
materials, which behaviour is exactly the same b
suggest including the ultimate stress, σ
too. In addition, it was noticed that thicker sections were more sensitive to that parameter and
therefore, the thickness influence should also be considered. It is important to point out that if
the σu parameter is included, the value of ε
not always possible, the stress at 1.0% strain, σ
3.2.2 Internal radius influence
Although the internal radius is considered in the web crippling resistance, the EN1993
formulation is more conservative for small radius. The numerical simulations results showed
that the ultimate web crippling strength follow
Moreover, it was noticed that the web crippling resistance decreases for increasing radius,
which was taken into account in the new proposal formulation.
3.2.3 Bearing length influence
The numerical results from the preliminary FEM study concluded that the bearing length in the
IOF test (category 2) is properly considered and therefore the new proposal only rewrites the
value of la. On the other hand, in the EOF test (category 1) the value of l
rewritten to keep consistency with category 2.
materials, which behaviour is exactly the same before σ0.2 but differs beyond that stress,
suggest including the ultimate stress, σu, since the numerical ultimate load increases when σ
too. In addition, it was noticed that thicker sections were more sensitive to that parameter and
ess influence should also be considered. It is important to point out that if
parameter is included, the value of εu must be known. To avoid that calculus, which is
not always possible, the stress at 1.0% strain, σ1.0, was included instead.
nternal radius influence
Although the internal radius is considered in the web crippling resistance, the EN1993
formulation is more conservative for small radius. The numerical simulations results showed
that the ultimate web crippling strength follows an internal radii square root function.
Moreover, it was noticed that the web crippling resistance decreases for increasing radius,
which was taken into account in the new proposal formulation.
Bearing length influence
the preliminary FEM study concluded that the bearing length in the
IOF test (category 2) is properly considered and therefore the new proposal only rewrites the
. On the other hand, in the EOF test (category 1) the value of la
rewritten to keep consistency with category 2.
28 (41)
28
but differs beyond that stress,
, since the numerical ultimate load increases when σu
too. In addition, it was noticed that thicker sections were more sensitive to that parameter and
ess influence should also be considered. It is important to point out that if
must be known. To avoid that calculus, which is
Although the internal radius is considered in the web crippling resistance, the EN1993-1-3
formulation is more conservative for small radius. The numerical simulations results showed
s an internal radii square root function.
Moreover, it was noticed that the web crippling resistance decreases for increasing radius,
the preliminary FEM study concluded that the bearing length in the
IOF test (category 2) is properly considered and therefore the new proposal only rewrites the
was changed and
170 (183)
4. Numerical results and c
proposal
This section presents a graphical comparison from the preliminary FEM study and the
parametric study with the studied analyt
3§6.1.7.3 and the new proposal. Figures 4.1 and 4.2 plot the R
load/analytical web crippling strength considering interaction with bending moment) ratio for
hollow sections and hat sections subjected to IOF, respectively. On the other hand, Figures 4.3
and 4.4 displays the Ru,num/R
ratio for category 1 hollow sections and hat sections undergoing EOF. The comparison
been assessed statistically comparing mean values and standard deviations of all considered
formulations. The numerical results are presented in Annex A.
The main conclusions from Fig
• Both EN1993-1-3§6.1.7.3
dispersion. However, there are less hat specimens than hollow ones with a ratio below
the unity.
• Results from the new proposal are more accurate providing safe values and decreasing
the standard deviation of current design provisions.
Figure 4.1 Comparison of the FE results with analytical formulations in SHS/RHS undergoing IOF load
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Ru
,nu
m/R
WC
-BD
6.1.7.3 (EN1993-1-3)
Numerical results and comparison to EN1993-1-3
This section presents a graphical comparison from the preliminary FEM study and the
parametric study with the studied analytical formulations: EN1993-1-3§6.1.7.2, EN1993
3§6.1.7.3 and the new proposal. Figures 4.1 and 4.2 plot the Ru,num/RWC-BD (numerical ultimate
load/analytical web crippling strength considering interaction with bending moment) ratio for
hat sections subjected to IOF, respectively. On the other hand, Figures 4.3
/Rw,Rd (numerical ultimate load/analytical web crippling strength)
ratio for category 1 hollow sections and hat sections undergoing EOF. The comparison
been assessed statistically comparing mean values and standard deviations of all considered
The numerical results are presented in Annex A.
The main conclusions from Figures 4.1 and 4.2 (IOF) are:
3§6.1.7.3 and 6.1.7.2 provide results under the unity with considerably
dispersion. However, there are less hat specimens than hollow ones with a ratio below
Results from the new proposal are more accurate providing safe values and decreasing
d deviation of current design provisions.
Comparison of the FE results with analytical formulations in SHS/RHS undergoing IOF load
6.1.7.3 (EN1993-1-3) 6.1.7.2 (EN1993-1-3) Proposal
Mean
6.1.7.3 1.06 6.1.7.2 1.00 Proposal 1.11
29 (41)
29
3 and new
This section presents a graphical comparison from the preliminary FEM study and the
3§6.1.7.2, EN1993-1-
(numerical ultimate
load/analytical web crippling strength considering interaction with bending moment) ratio for
hat sections subjected to IOF, respectively. On the other hand, Figures 4.3
(numerical ultimate load/analytical web crippling strength)
ratio for category 1 hollow sections and hat sections undergoing EOF. The comparison has
been assessed statistically comparing mean values and standard deviations of all considered
and 6.1.7.2 provide results under the unity with considerably
dispersion. However, there are less hat specimens than hollow ones with a ratio below
Results from the new proposal are more accurate providing safe values and decreasing
Comparison of the FE results with analytical formulations in SHS/RHS undergoing IOF load
Standard Deviation
0.137 0.136 0.073
171 (183)
Figure 4.2 Comparison of the FE results with analytical formulations in hat sections undergoing IOF load
The most relevant conclusions from Fig
• Despite EN1993-1-3§6.1.7.3 recommends taking 10mm as the bearing length, both
Fig.9 and Fig.10 demonstrate that it is more suitable consider real plate length which
produces crippling (s
results.
• In general, EN1993-1
than current EN1993-
• The new proposal predicts the best adjustment
and a reasonably dispersion.
• In Figure 4.3 there are some ultimate loads unsatisfactory predicted with R
ratios upward 2.0 in every formulation considered and in some cases this value
reaches more than 3.
• A similar situation is plotted in Fig
improves these imprecise results and relocates the specimens in lower ratios providing
the most precise results. This is very satisfactory since it means that the proposed
changes allow a better prediction of web crippling strength in hat sections subjected to
EOF.
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
Ru
,nu
m/R
WC
-BD
6.1.7.3 (EN1993-1-3)
Comparison of the FE results with analytical formulations in hat sections undergoing IOF load
The most relevant conclusions from Figures 4.3 and 4.4 (EOF) are:
3§6.1.7.3 recommends taking 10mm as the bearing length, both
Fig.9 and Fig.10 demonstrate that it is more suitable consider real plate length which
produces crippling (ss). This assumption provides less conservative and less scattered
1-3§6.1.7.2 presents quite dispersed results but less conservative
-1-3§6.1.7.3 formulation.
The new proposal predicts the best adjustment providing the least conservative results
and a reasonably dispersion.
there are some ultimate loads unsatisfactory predicted with R
ratios upward 2.0 in every formulation considered and in some cases this value
reaches more than 3.0. Despite this, the new proposal gives the most suitable ratios.
A similar situation is plotted in Figure 4.4. However, it seems that the new formulation
improves these imprecise results and relocates the specimens in lower ratios providing
se results. This is very satisfactory since it means that the proposed
changes allow a better prediction of web crippling strength in hat sections subjected to
6.1.7.3 (EN1993-1-3) 6.1.7.2 (EN1993-1-3) Proposal
Mean
6.1.7.3 1.146.1.7.2 0.92Proposal 1.11
30 (41)
30
Comparison of the FE results with analytical formulations in hat sections undergoing IOF load
3§6.1.7.3 recommends taking 10mm as the bearing length, both
Fig.9 and Fig.10 demonstrate that it is more suitable consider real plate length which
This assumption provides less conservative and less scattered
3§6.1.7.2 presents quite dispersed results but less conservative
providing the least conservative results
there are some ultimate loads unsatisfactory predicted with Ru,num/Rw,Rd
ratios upward 2.0 in every formulation considered and in some cases this value
0. Despite this, the new proposal gives the most suitable ratios.
. However, it seems that the new formulation
improves these imprecise results and relocates the specimens in lower ratios providing
se results. This is very satisfactory since it means that the proposed
changes allow a better prediction of web crippling strength in hat sections subjected to
Mean Standard Deviation
1.14 0.117 0.92 0.098 1.11 0.074
172 (183)
Figure 4.3 Comparison of the FE results with analytical formulations in SHS/RHS undergoi
Figure 4.4 Comparison of the FE results with analytical formulations in hat sections undergoing EOF load
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Ru
,nu
m/R
w,R
d
6.1.7.3 (EN1993-1-3); la=10mm
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Ru
,nu
m/R
w,R
d
6.1.7.3 (EN1993-1-3); la=10mm
Comparison of the FE results with analytical formulations in SHS/RHS undergoi
Comparison of the FE results with analytical formulations in hat sections undergoing EOF load
6.1.7.3 (EN1993-1-3); la=10mm 6.1.7.3 (EN1993-1-3); la=ss 6.1.7.2 (EN1993-1-3)
6.1.7.3 (EN1993-1-3); la=10mm 6.1.7.3 (EN1993-1-3); la=ss 6.1.7.2 8EN1993-1-3)
Mean
6.1.7.3; la=10mm 2.02 6.1.7.3; la=ss 1.60 6.1.7.2 1.74 Proposal 1.39
Mean
6.1.7.3; la=10mm 1.76 6.1.7.3; la=ss 1.36 6.1.7.2 1.46 Proposal 1.23
31 (41)
31
Comparison of the FE results with analytical formulations in SHS/RHS undergoing EOF load
Comparison of the FE results with analytical formulations in hat sections undergoing EOF load
6.1.7.2 (EN1993-1-3) Proposal
6.1.7.2 8EN1993-1-3) Proposal
Standard Deviation
0.336 0.281 0.470 0.303
Standard Deviation
0.332 0.183 0.308 0.247
173 (183)
5. Validation of the new proposal with experimental results
The new proposal formulation presented in Eq.
validated herein by comparing with all the available experimental resul
5.1 - 5.4). These data gather documentation from
(2006), Zhou and Young (2007a) and Talja and Hradil (2011).
quite conservative and how the new proposal provides a better adjustment. The comparison with
experimental results is approximately in line with those conducted in the param
Figure 5.1 Comparison of experimental results with analytical formulations in SHS/RHS undergoing IOF
Figure 5.2 Comparison of experimental results with analytical formulations in hat sections undergoing
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Ru
,ex
p/R
WC
-BD
6.1.7.3 (EN1993-1-3)
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Ru
,exp/R
WC
-BD
6.1.7.3 (EN1993-1-3)
lidation of the new proposal with experimental results
The new proposal formulation presented in Eq. 3.5 with nondimensional coefficients from Table
validated herein by comparing with all the available experimental results found in the literature (Figures
). These data gather documentation from Talja and Salmi (1995), Talja (2004), Gardner et al.
d Young (2007a) and Talja and Hradil (2011). These figures show that EN1993
quite conservative and how the new proposal provides a better adjustment. The comparison with
experimental results is approximately in line with those conducted in the parametric study section.
Comparison of experimental results with analytical formulations in SHS/RHS undergoing IOF
load
Comparison of experimental results with analytical formulations in hat sections undergoing
IOF load
6.1.7.3 (EN1993-1-3) 6.1.7.2 (EN1993-1-3) Proposal
6.1.7.3 (EN1993-1-3) 6.1.7.2 (EN1993-1-3) Proposal
Mean
6.1.7.3 1.56 6.1.7.2 1.47 Proposal 1.50
Mean
6.1.7.3 1.586.1.7.2 1.27Proposal 1.19
32 (41)
32
lidation of the new proposal with experimental results
coefficients from Table 3.2 is
ts found in the literature (Figures
Talja and Salmi (1995), Talja (2004), Gardner et al.
These figures show that EN1993-1-3 is
quite conservative and how the new proposal provides a better adjustment. The comparison with
etric study section.
Comparison of experimental results with analytical formulations in SHS/RHS undergoing IOF
Comparison of experimental results with analytical formulations in hat sections undergoing
Standard Deviation
0.274 0.304 0.275
Mean Standard Deviation
1.58 0.081 1.27 0.107 1.19 0.092
174 (183)
Figure 5.3 Comparison of experimental results with analytical formulations in SHS/RHS undergoing EOF
Figure 5.4 Comparison of experimental results with analytical formulations in hat sections undergoing
6. References
Zhou and Young (2006a)
Zhou,B. and Young, F. (2006)
Journal of Structural Engineering
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Ru
,ex
p/R
w,R
d
6.1.7.3 (EN1993-1-3); la=10mm
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Ru
,exp/R
w,R
d
6.1.7.3 (EN1993-1-3); la=10mm
Comparison of experimental results with analytical formulations in SHS/RHS undergoing EOF
load
Figure 5.4 Comparison of experimental results with analytical formulations in hat sections undergoing
EOF load
). Cold-formed stainless steel sections subjected to web crippling.
Journal of Structural Engineering (2006), ASCE. Vol. 132(1), 134-44.
6.1.7.3 (EN1993-1-3); la=10mm 6.1.7.3 (EN1993-1-3); la=ss 6.1.7.2 (EN1993-1-3)
6.1.7.3 (EN1993-1-3); la=10mm 6.1.7.3 (EN1993-1-3); la=ss 6.1.7.2 (EN1993-1-3)
Mean
6.1.7.3; la=10mm 2.59 6.1.7.3; la=ss 1.72 6.1.7.2 2.46 Proposal 1.40
Mean
6.1.7.3; la=10mm 2.576.1.7.3; la=ss 2.086.1.7.2 1.61Proposal 1.33
33 (41)
33
Comparison of experimental results with analytical formulations in SHS/RHS undergoing EOF
Figure 5.4 Comparison of experimental results with analytical formulations in hat sections undergoing
formed stainless steel sections subjected to web crippling.
6.1.7.2 (EN1993-1-3) Proposal
6.1.7.2 (EN1993-1-3) Proposal
Standard Deviation
0.648 0.390 0.808 0.461
Mean Standard Deviation
2.57 0.069 2.08 0.046 1.61 0.177 1.33 0.184
175 (183)
Zhou and Young (2007a)
Zhou, B. and Young, F. (2007
subjected to web crippling. Journal
377.
Korvink et al. (1995)
Korvink, S. A., van den Berg, G.J. and van der Merwe, P. (1995).
cold-formed beams. Journal of Constructional Steel Research
Korvink and van den Berg (1993)
Korvink, S. A. and van den Berg, G.J. (1993).
Beams. SSRC Annual Technical Session. April 1993.
Talja (1997b)
Talja, A. (1997). Test report on
Development of the use of atainless steel in construction.
Talja and Salmi (1995)
Talja, A. and Salmi, P. (1995).
VTT Research Notes 1619. Espoo, Finland: VTT Technical Research Centre of Finland, 1995.
Gardner et al. (2006)
Gardner, L., Talja, A. and Baddoo, N.R. (2006), Structural design of
stainless steel. Thin-Walled Structures (2006). Vol. 44(5), 517
Gardner and Nethercot (2004)
Gardner, L. and Nethercot, D.A.
Components: A Consistent Approach. Journal o
Vol. 130(10), 1586-1601.
Sélen (2000)
Sélen, E. (2000). Work Package 3.5
Development of the use of stainless st
Talja (2004)
Talja, A. (2004). Test results of RHS, tophat and sheeting profiles.
(2004): Structural design of austenitic cold worked stainless steel
Talja and Hradil (2011).
Talja, A. and Hradil, P. (2011).
Applications of Ferritic Stainless Steel (SAFSS) Project. VTT Technical Research Centre of
Finland.
Zilli (2004)
Zilli, G. (2004). WP3: Cold formed profiles and sheeting
Centro Sviluppo Materiali, 2003
austenitic cold worked stainless steel
Annex A
Numerical results of the 332 simulations conducted are presented in this section and
compared with the new proposal, EN1993
sections, there are some geometrical and configuration ratios that must be previousl
Zhou, B. and Young, F. (2007). Cold-formed high-strength stainless steel tubular sections
Journal of structural Engineering (2007), ASCE.
Korvink, S. A., van den Berg, G.J. and van der Merwe, P. (1995). Web crippling of stainless steel
formed beams. Journal of Constructional Steel Research (1995). Vol. 34(2
d van den Berg (1993)
Korvink, S. A. and van den Berg, G.J. (1993). Web Crippling of Stainless Steel Cold
Technical Session. April 1993.
Test report on sheeting. Final test report. Report to the ECSC
Development of the use of atainless steel in construction.
(1995). Design of stainless steel RHS beams, columns and beam
VTT Research Notes 1619. Espoo, Finland: VTT Technical Research Centre of Finland, 1995.
Gardner, L., Talja, A. and Baddoo, N.R. (2006), Structural design of high-strength austenitic
Walled Structures (2006). Vol. 44(5), 517-528.
Gardner and Nethercot (2004)
Nethercot, D.A. (2004) Numerical Modeling of Stainless Steel Structural
A Consistent Approach. Journal of Structural Engineering 2004, October 2004,
Work Package 3.5- Final Report. Report to the ECSC
Development of the use of stainless steel in construction.
Test results of RHS, tophat and sheeting profiles. Report to the ECSC
Structural design of austenitic cold worked stainless steel.
Talja, A. and Hradil, P. (2011). Work package 2: Model calibration tests – Test report. Structural
Applications of Ferritic Stainless Steel (SAFSS) Project. VTT Technical Research Centre of
WP3: Cold formed profiles and sheeting - Test results on unstiffened profiles
Materiali, 2003. Report to the ECSC Project (2004): Structural design of
austenitic cold worked stainless steel.
Numerical results of the 332 simulations conducted are presented in this section and
compared with the new proposal, EN1993-1-3§6.1.7.3 and 6.1.7.2. According to these two
sections, there are some geometrical and configuration ratios that must be previousl
34 (41)
34
strength stainless steel tubular sections
Vol. 133(3), 368-
ng of stainless steel
(2-3), 225-248.
Web Crippling of Stainless Steel Cold-Formed
Report to the ECSC Project (2000):
Design of stainless steel RHS beams, columns and beam-columns.
VTT Research Notes 1619. Espoo, Finland: VTT Technical Research Centre of Finland, 1995.
strength austenitic
s Steel Structural
f Structural Engineering 2004, October 2004,
Report to the ECSC Project (2000):
Report to the ECSC Project
Test report. Structural
Applications of Ferritic Stainless Steel (SAFSS) Project. VTT Technical Research Centre of
Test results on unstiffened profiles.
Structural design of
Numerical results of the 332 simulations conducted are presented in this section and
3§6.1.7.3 and 6.1.7.2. According to these two
sections, there are some geometrical and configuration ratios that must be previously
176 (183)
considered in order to identify the properly equation to apply. The following sections present
tables with results where different equations and situations have been considered. Again, all
partial safety factors have been set to unity to enable a direct
labeled to easily identify load condition, material, section and thickness as well as internal
radius and bearing length values of additional simulations. For example, the labels
IOFB2*S615, EOFB2*S62100 and EOFB2*S621002 def
• The first three letters define the loading condition, where IOF refers to interior one
flange test and EOF to exterior one flange test.
• The notation B2* indicates the material type.
• The following letter and first number,
• The following number indicates the thickness in mm, which worths 1mm in the first
specimen and 2mm in the second one.
• Additional numbers are added when the internal radius or the bearing length is being
varied. For example, 5 (from IOFB2*S615) means that the internal radius has been changed to
5mm) and 100 (from EOFB2*S62100) means that the support length that produces crippling
(ssa) is 100mm. The number two is added (EOFB2*S621002) when the previously number
refers to the plate length that applies the load (s
A.1 IOF tests in SHS and RHS
Numerical results from SHS and RHS undergoing IOF test are presented in Table A.1 where
Ru,num is the numerical web crippling resistance, M
resistance, RWC-BD is the web crippling strength considering interaction with bending moment
and Rw,Rd is the analytical web crippling resistance.
Specimen
Numerical tests
Ru,num
(kN)
IOF B1S52 16.94
IOF B1S62 18.91
IOF B1*S52 17.22
IOF B1*S524 15.5
IOF B1*S525 14.65
IOF B1*S5250 20.24
IOF B1*S5275 21.74
IOF B1*S52100 25.29
IOF B1*S62 19.34
IOF B1*S624 18.57
IOF B1*S625 17.33
IOF B2S52 17.73
IOF B2S62 20.16
IOF B2*S52 18.53
IOF B2*S524 16.96
IOF B2*S525 16.64
IOF B2*S5250 21.31
IOF B2*S5275 22.61
IOF B2*S52100 25.78
IOF B2*S62 21.82
IOF B2*S624 20.24
IOF B2*S625 20.3
IOF B1S54 53.81
IOF B1S64 65.58
considered in order to identify the properly equation to apply. The following sections present
tables with results where different equations and situations have been considered. Again, all
partial safety factors have been set to unity to enable a direct comparison. All specimens were
labeled to easily identify load condition, material, section and thickness as well as internal
radius and bearing length values of additional simulations. For example, the labels
IOFB2*S615, EOFB2*S62100 and EOFB2*S621002 define the following specimens:
The first three letters define the loading condition, where IOF refers to interior one
flange test and EOF to exterior one flange test.
The notation B2* indicates the material type.
The following letter and first number, S6, defines the section.
The following number indicates the thickness in mm, which worths 1mm in the first
specimen and 2mm in the second one.
Additional numbers are added when the internal radius or the bearing length is being
(from IOFB2*S615) means that the internal radius has been changed to
5mm) and 100 (from EOFB2*S62100) means that the support length that produces crippling
(ssa) is 100mm. The number two is added (EOFB2*S621002) when the previously number
te length that applies the load (ssL) in EOF test.
A.1 IOF tests in SHS and RHS
Numerical results from SHS and RHS undergoing IOF test are presented in Table A.1 where
is the numerical web crippling resistance, MBD,num is the numerical bending mom
is the web crippling strength considering interaction with bending moment
is the analytical web crippling resistance.
Numerical tests 6.1.7.3 6.1.7.2 New proposal
u,num
MBD,num
(kNm)
Rw,Rd
(kN)
RWC-BD
(kN)
Rw,Rd
(kN)
RWC-BD
(kN)
R
(kN)
16.94 3.717 25.32 17.092 28.89 18.318 20.842
18.91 7.402 25.32 22.168 27.85 23.678 20.842
17.22 3.757 25.32 17.176 28.89 18.414 20.947
3.720 24.77 16.898 28.00 18.034 19.819
14.65 3.695 24.29 16.666 27.11 17.675 19.367
20.24 3.757 30.76 19.002 31.22 19.141 25.389
21.74 3.757 35.04 20.222 33.54 19.814 28.797
25.29 3.757 38.73 21.153 35.87 20.441 31.671
19.34 7.458 25.99 22.632 27.85 23.735 20.947
18.57 7.382 25.60 22.324 26.99 23.155 19.819
17.33 7.327 25.27 22.073 26.13 22.591 19.367
17.73 3.800 26.52 17.705 28.89 18.518 21.158
20.16 7.557 26.70 23.150 27.85 23.834 21.158
18.53 3.887 26.88 18.021 28.89 18.721 21.548
16.96 3.863 26.48 17.826 28.00 18.364 20.581
16.64 3.810 26.14 17.590 27.11 17.934 20.302
21.31 3.887 33.12 20.046 31.22 19.473 26.118
22.61 3.887 37.73 21.308 33.54 20.170 29.624
25.78 3.887 41.72 22.269 35.87 20.819 32.579
21.82 7.723 28.01 24.088 27.85 23.997 21.548
20.24 7.650 27.59 23.771 26.99 23.413 20.581
7.627 27.24 23.541 26.13 22.868 20.302
53.81 7.923 101.61 48.795 117.25 51.430 87.989
65.58 15.747 102.32 70.576 115.19 75.212 87.989
35 (41)
35
considered in order to identify the properly equation to apply. The following sections present
tables with results where different equations and situations have been considered. Again, all
All specimens were
labeled to easily identify load condition, material, section and thickness as well as internal
radius and bearing length values of additional simulations. For example, the labels
ine the following specimens:
The first three letters define the loading condition, where IOF refers to interior one
The following number indicates the thickness in mm, which worths 1mm in the first
Additional numbers are added when the internal radius or the bearing length is being
(from IOFB2*S615) means that the internal radius has been changed to
5mm) and 100 (from EOFB2*S62100) means that the support length that produces crippling
(ssa) is 100mm. The number two is added (EOFB2*S621002) when the previously number
Numerical results from SHS and RHS undergoing IOF test are presented in Table A.1 where
is the numerical bending moment
is the web crippling strength considering interaction with bending moment
New proposal
Rw,Rd
(kN)
RWC-BD
(kN)
20.842 15.317
20.842 19.270
20.947 15.430
19.819 14.871
19.367 14.626
25.389 17.203
28.797 18.382
31.671 19.276
20.947 19.380
19.819 18.549
19.367 18.196
21.158 15.594
21.158 19.591
21.548 15.910
20.581 15.443
20.302 15.232
26.118 17.743
29.624 18.963
32.579 19.887
21.548 19.971
20.581 19.252
20.302 19.041
87.989 46.055
87.989 64.756
177 (183)
IOF B1*S54 54.85
IOF B1*S544 51.79
IOF B1*S545 48.94
IOF B1*S5450 60.83
IOF B1*S5475 62.71
IOF B1*S54100 67.07
IOF B1*S64 67.4
IOF B1*S644 63.13
IOF B1*S645 60.25
IOF B2S54 56.81
IOF B2S64 70.84
IOF B2*S54 60.44
IOF B2*S544 57.13
IOF B2*S545 54.12
IOF B2*S5450 65.43
IOF B2*S5475 67.35
IOF B2*S54100 72.89
IOF B2*S64 76.84
IOF B2*S644 68.43
IOF B2*S645 66.55
Table A.1. Numerical results, EN1993
A.2 IOF tests in hat sections
Table A.2 presents numerical results from hat sections subjected to IOF where the same
nomenclature of Table A.1 has been used.
Specimen
Numerical tests
Ru,num
(kN)
IOF B1S71 4.2
IOF B1S81 5.47
IOF B1S91 4.58
IOF B1*S71 4.25
IOF B1*S714 3.93
IOF B1*S715 3.69
IOF B1*S7150 4.87
IOF B1*S7175 5.34
IOF B1*S71100 6.34
IOF B1*S81 5.59
IOF B1*S91 4.69
IOF B1*S914 4.31
IOF B1*S915 4.28
IOF B1*S9150 5.33
IOF B1*S9175 5.86
IOF B1*S91100 7.01
IOF B2S71 4.38
IOF B2S81 5.87
IOF B2S91 4.88
IOF B2*S71 4.65
IOF B2*S714 4.25
IOF B2*S715 4.11
IOF B2*S7150 5.09
54.85 8.143 103.04 49.890 117.25 52.348 88.210
51.79 8.057 102.24 49.414 117.25 51.988 79.848
48.94 7.993 101.60 49.058 115.49 51.447 74.648
60.83 8.143 123.28 53.278 122.16 53.111 103.769
62.71 8.143 138.10 55.331 127.08 53.835 115.707
67.07 8.143 150.91 56.880 131.99 54.523 125.772
16.227 107.47 73.492 115.19 76.289 88.210
63.13 16.085 106.64 72.893 115.19 75.975 79.848
60.25 15.932 105.99 72.334 113.46 75.031 74.648
56.81 8.562 109.77 52.721 117.25 54.045 88.652
70.84 17.093 110.55 76.413 115.19 78.152 88.652
60.44 9.367 111.34 55.986 117.25 57.146 89.466
57.13 9.317 110.49 55.636 117.25 56.959 81.367
54.12 9.232 109.82 55.196 115.49 56.309 76.429
65.43 9.367 133.25 59.953 122.16 58.056 105.246
67.35 9.367 149.29 62.364 127.08 58.923 117.355
72.89 9.367 163.16 64.188 131.99 59.748 127.563
76.84 18.902 116.20 82.134 115.19 81.727 89.466
68.43 18.723 115.32 81.444 115.19 81.392 81.367
66.55 18.545 114.62 80.828 113.46 80.364 76.429
Table A.1. Numerical results, EN1993-1-3 and new proposal predicted resistance for SHS/RHS
to IOF loading
A.2 IOF tests in hat sections
Table A.2 presents numerical results from hat sections subjected to IOF where the same
nomenclature of Table A.1 has been used.
Numerical tests 6.1.7.3 6.1.7.2 New proposal
u,num
(kN)
MBD,num
(kNm)
Rw,Rd
(kN)
RWC-BD
(kN)
Rw,Rd
(kN)
RWC-BD
(kN)
Rw,Rd
(kN)
1.002 5.52 4.085 7.76 4.927 6.199
5.47 2.588 5.52 5.447 7.06 6.580 6.199
4.58 1.448 5.52 4.673 7.52 5.702 6.199
4.25 1.012 5.52 4.102 7.76 4.951 6.248
3.93 0.993 5.34 3.992 7.76 4.906 6.192
3.69 0.980 5.18 3.900 7.76 4.874 6.338
4.87 1.012 6.86 4.640 8.91 5.302 7.793
5.34 1.012 7.89 4.992 10.40 5.688 8.980
6.34 1.012 8.75 5.256 12.21 6.084 9.979
5.59 2.560 5.52 5.434 7.06 6.562 6.248
4.69 1.473 5.52 4.698 7.52 5.740 6.248
4.31 1.443 5.34 4.564 7.52 5.694 6.192
4.28 1.477 5.18 4.503 7.52 5.745 6.338
5.33 1.473 6.86 5.419 8.64 6.234 7.793
5.86 1.473 7.89 5.906 10.08 6.793 8.980
7.01 1.473 8.75 6.278 11.85 7.385 9.979
4.38 1.023 5.52 4.121 7.76 4.978 6.347
5.87 2.582 5.52 5.444 7.06 6.576 6.347
4.88 1.483 5.52 4.709 7.52 5.755 6.347
4.65 1.033 5.52 4.137 7.76 5.002 6.532
4.25 1.025 5.34 4.042 7.76 4.982 6.570
4.11 1.018 5.18 3.959 7.76 4.967 6.825
5.09 1.033 6.86 4.685 8.91 5.360 8.148
36 (41)
36
88.210 46.840
79.848 44.581
74.648 43.053
103.769 50.026
115.707 52.100
125.772 53.646
88.210 65.651
79.848 61.591
74.648 58.845
88.652 48.300
88.652 67.230
89.466 50.973
81.367 48.625
76.429 46.949
105.246 54.712
117.355 57.165
127.563 59.005
89.466 70.262
81.367 65.907
76.429 63.053
3 and new proposal predicted resistance for SHS/RHS subjected
Table A.2 presents numerical results from hat sections subjected to IOF where the same
New proposal
w,Rd
(kN)
RWC-BD
(kN)
6.199 4.369
6.199 5.963
6.199 5.048
6.248 4.407
6.192 4.350
6.338 4.381
7.793 4.963
8.980 5.321
9.979 5.586
6.248 5.984
6.248 5.104
6.192 5.038
6.338 5.156
7.793 5.864
8.980 6.371
9.979 6.755
6.347 4.469
6.347 6.069
6.347 5.169
6.532 4.561
6.570 4.559
6.825 4.642
8.148 5.129
178 (183)
Specimen
Numerical tests
Ru,num
(kN)
IOF B2*S7175 5.52
IOF B2*S71100 6.39
IOF B2*S81 6.28
IOF B2*S91 5.23
IOF B2*S914 4.84
IOF B2*S915 4.83
IOF B2*S9150 5.62
IOF B2*S9175 6.06
IOF B2*S91100 7.12
IOF B1S72 14.66
IOF B1S82 19.89
IOF B1S92 16.58
IOF B1*S72 14.91
IOF B1*S724 13.41
IOF B1*S725 12.47
IOF B1*S7250 16.52
IOF B1*S7275 17.54
IOF B1*S72100 19.36
IOF B1*S82 20.32
IOF B1*S92 16.9
IOF B1*S924 14.93
IOF B1*S925 13.77
IOF B1*S9250 19.42
IOF B1*S9275 21.22
IOF B1*S92100 25.24
IOF B2S72 15.35
IOF B2S82 21.13
IOF B2S92 17.44
IOF B2*S72 15.96
IOF B2*S724 14.45
IOF B2*S725 13.41
IOF B2*S7250 17.25
IOF B2*S7275 18.28
IOF B2*S72100 20.32
IOF B2*S82 22.9
IOF B2*S92 18.36
IOF B2*S924 16.43
IOF B2*S925 15.94
IOF B2*S9250 20.54
IOF B2*S9275 22.14
IOF B2*S92100 25.63
Table A.2. Numerical results, EN1993
A.3 EOF tests in SHS and RHS
Results from SHS and RHS undergoing EOF test are shown in Table 20 where numerical
ultimate loads (Ru,num), category (Cat.) and predicted resistances (
section EN1993-1-3§6.1.7.3 specifies that the l
Numerical tests 6.1.7.3 6.1.7.2 New proposal
u,num
(kN)
MBD,num
(kNm)
Rw,Rd
(kN)
RWC-BD
(kN)
Rw,Rd
(kN)
RWC-BD
(kN)
Rw,Rd
(kN)
5.52 1.033 7.89 5.045 10.40 5.756 9.388
6.39 1.033 8.75 5.314 12.21 6.162 10.433
6.28 2.593 5.52 5.449 7.06 6.584 6.532
5.23 1.497 5.52 4.722 7.52 5.775 6.532
4.84 1.487 5.34 4.607 7.52 5.760 6.570
4.83 1.493 5.18 4.518 7.52 5.770 6.825
5.62 1.497 6.86 5.450 8.64 6.275 8.148
6.06 1.497 7.89 5.943 10.08 6.843 9.388
7.12 1.497 8.75 6.320 11.85 7.443 10.433
14.66 2.492 19.41 12.292 30.00 14.971 23.724
19.89 7.383 19.41 18.261 28.71 24.151 23.724
16.58 4.007 19.41 15.111 29.57 19.227 23.724
14.91 2.538 19.41 12.405 30.00 15.138 23.818
13.41 2.485 18.99 12.141 30.00 14.947 22.066
12.47 2.492 18.62 12.034 30.00 14.971 21.114
16.52 2.538 23.43 13.598 32.42 15.607 28.868
17.54 2.538 26.51 14.374 34.83 16.035 32.743
19.36 2.538 29.11 14.953 37.25 16.427 36.010
20.32 7.423 19.41 18.285 28.71 24.194 23.818
16.9 4.053 19.41 15.177 29.57 19.334 23.818
14.93 4.023 18.99 14.929 29.57 19.266 22.066
13.77 3.987 18.62 14.696 29.57 19.181 21.114
19.42 4.053 23.43 17.002 31.95 20.118 28.868
21.22 4.053 26.51 18.233 34.33 20.845 32.743
25.24 4.053 29.11 19.176 36.71 21.523 36.010
15.35 2.605 19.41 12.562 30.00 15.373 24.006
21.13 7.592 19.41 18.386 28.71 24.370 24.006
17.44 4.142 19.41 15.299 29.57 19.533 24.006
15.96 2.697 19.41 12.771 30.00 15.687 24.353
14.45 2.668 18.99 12.562 30.00 15.591 22.730
13.41 2.680 18.62 12.457 30.00 15.631 21.910
17.25 2.697 23.43 14.039 32.42 16.192 29.517
18.28 2.697 26.51 14.869 34.83 16.653 33.479
20.32 2.697 29.11 15.489 37.25 17.076 36.820
22.9 7.767 19.41 18.487 28.71 24.548 24.353
18.36 4.295 19.41 15.504 29.57 19.867 24.353
16.43 4.272 18.99 15.259 29.57 19.817 22.730
15.94 4.270 18.62 15.064 29.57 19.814 21.910
20.54 4.295 23.43 17.413 31.95 20.696 29.517
22.14 4.295 26.51 18.707 34.33 21.466 33.479
25.63 4.295 29.11 19.700 36.71 22.186 36.820
Table A.2. Numerical results, EN1993-1-3 and new proposal predicted resistance for hat sections
subjected to IOF loading
A.3 EOF tests in SHS and RHS
Results from SHS and RHS undergoing EOF test are shown in Table 20 where numerical
), category (Cat.) and predicted resistances (Rw,Rd) are presented. Since
3§6.1.7.3 specifies that the la value of specimens with category 1 should be
37 (41)
37
New proposal
w,Rd
(kN)
RWC-BD
(kN)
9.388 5.495
10.433 5.765
6.532 6.210
6.532 5.283
6.570 5.290
6.825 5.430
8.148 6.060
9.388 6.577
10.433 6.969
23.724 13.540
23.724 21.157
23.724 17.042
23.818 13.702
22.066 13.073
21.114 12.817
28.868 14.901
32.743 15.667
36.010 16.231
23.818 21.250
23.818 17.165
22.066 16.364
21.114 15.880
28.868 19.090
32.743 20.365
36.010 21.328
24.006 13.945
24.006 21.507
24.006 17.400
24.353 14.299
22.730 13.760
21.910 13.545
29.517 15.580
33.479 16.399
36.820 17.004
24.353 21.870
24.353 17.815
22.730 17.063
21.910 16.686
29.517 19.847
33.479 21.196
36.820 22.217
proposal predicted resistance for hat sections
Results from SHS and RHS undergoing EOF test are shown in Table 20 where numerical
) are presented. Since
value of specimens with category 1 should be
179 (183)
taken as 10mm, it has been decided asses two values for that parameter: the real bearing
length ss and the proposed value of 10mm
Specimen Ru,num
(kN)
EOF B1S52 15.503
EOF B1S52 17.265
EOF B1*S52 15.968
EOF B1*S524 14.888
EOF B1*S525 13.793
EOF B1*S5240 17.715
EOF B1*S5250 18.615
EOF B1*S5275 19.215
EOF B1*S52100 19.350
EOF B1*S52752 16.688
EOF B1*S521002 17.363
EOF B1*S62 17.745
EOF B1*S624 15.900
EOF B1*S625 14.310
EOF B2S52 16.815
EOF B2S62 18.623
EOF B2*S52 18.308
EOF B2*S524 16.920
EOF B2*S525 15.600
EOF B2*S5240 19.785
EOF B2*S5250 20.790
EOF B2*S5275 22.020
EOF B2*S52100 22.268
EOF B2*S52752 19.088
EOF B2*S521002 20.070
EOF B2*S62 20.160
EOF B2*S624 18.030
EOF B2*S625 16.155
EOF B1S54 48.090
EOF B1S64 53.580
EOF B1*S54 49.860
EOF B1*S544 47.783
EOF B1*S545 44.715
EOF B1*S5440 53.108
EOF B1*S5450 57.353
EOF B1*S5475 60.998
EOF B1*S54100 63.120
EOF B1*S54752 52.845
EOF B1*S541002 56.288
EOF B1*S64 55.358
EOF B1*S644 52.020
EOF B1*S645 48.773
EOF B2S54 53.348
EOF B2S64 58.635
EOF B2*S54 60.075
EOF B2*S544 56.325
EOF B2*S545 52.838
EOF B2*S5440 62.903
EOF B2*S5450 65.235
taken as 10mm, it has been decided asses two values for that parameter: the real bearing
and the proposed value of 10mm.
u,num
(kN)
6.1.7.3 6.1.7.2
Cat. Rw,Rd (kN)
(la=10)
Rw,Rd (kN)
(la=ss)
Rw,Rd (kN)
15.503 2 20.66 25.32 11.39
17.265 1 10.33 12.66 11.53
15.968 2 20.66 25.32 11.39
14.888 2 20.22 24.77 10.47
13.793 2 19.82 24.29 9.55
17.715 2 20.66 28.67 12.15
18.615 1 10.33 15.28 13.69
19.215 1 10.33 17.29 15.06
19.350 1 10.33 18.99 16.42
16.688 2 20.66 25.32 11.39
17.363 1 10.33 12.66 12.32
17.745 1 10.33 12.66 11.53
15.900 1 10.11 12.38 10.60
14.310 1 9.91 12.14 9.66
16.815 2 20.66 25.32 11.39
18.623 1 10.33 12.66 11.53
18.308 2 20.66 25.32 11.39
16.920 2 20.22 24.77 10.47
15.600 2 19.82 24.29 9.55
19.785 2 20.66 28.67 12.15
20.790 1 10.33 15.28 13.69
22.020 1 10.33 17.29 15.06
22.268 1 10.33 18.99 16.42
19.088 2 20.66 25.32 11.39
20.070 1 10.33 12.66 12.32
20.160 1 10.33 12.66 11.53
18.030 1 10.11 12.38 10.60
16.155 1 9.91 12.14 9.66
48.090 2 76.27 89.97 47.63
53.580 1 38.14 44.98 50.95
49.860 2 76.27 89.97 47.63
47.783 2 75.15 88.65 47.63
44.715 2 74.17 87.49 45.84
53.108 2 20.66 28.67 12.15
57.353 1 38.14 52.70 55.65
60.998 1 38.14 58.63 58.74
63.120 1 38.14 63.62 61.83
52.845 2 76.27 89.97 47.63
56.288 1 38.14 44.98 52.56
55.358 1 38.14 44.98 50.95
52.020 1 37.58 44.32 50.95
48.773 1 37.08 43.74 49.04
53.348 2 76.27 89.97 47.63
58.635 1 38.14 44.98 50.95
60.075 2 76.27 89.97 47.63
56.325 2 75.15 88.65 47.63
52.838 2 74.17 87.49 45.84
62.903 2 20.66 28.67 12.44
65.235 1 38.14 52.70 55.65
38 (41)
38
taken as 10mm, it has been decided asses two values for that parameter: the real bearing
New proposal
Rw,Rd (kN)
12.115
12.115
12.211
11.882
11.941
12.425
12.545
12.802
13.018
12.211
12.211
12.211
11.882
11.941
12.405
12.405
12.766
12.608
12.859
12.990
13.116
13.383
13.609
12.766
12.766
12.766
12.608
12.859
56.655
56.655
56.879
52.214
49.503
12.425
58.001
58.862
59.587
56.879
56.879
56.879
52.214
49.503
57.328
57.328
58.157
53.784
51.371
58.891
59.304
180 (183)
Specimen Ru,num
(kN)
EOF B2*S5475 70.980
EOF B2*S54100 74.378
EOF B2*S54752 64.433
EOF B2*S541002 70.328
EOF B2*S64 64.800
EOF B2*S644 61.163
EOF B2*S645 57.300
Table A.3.Numerical results, EN1993
A.4 EOF tests in hat sections
Finally, Table A.4 presents the results from the parametric study in hat sections subjected to
EOF. Again, it has been assessed two values
RHS undergoing EOF.
Specimen Ru,num
EOF B1S71 3.338
EOF B1S81 3.203
EOF B1S91 3.248
EOF B1*S71 3.375
EOF B1*S714 2.933
EOF B1*S715 2.625
EOF B1*S7140 4.313
EOF B1*S7150 4.913
EOF B1*S7175 5.850
EOF B1*S71100 6.000
EOF B1*S71752 3.435
EOF B1*S711002 3.818
EOF B1*S81 3.240
EOF B1*S814 2.940
EOF B1*S815 2.723
EOF B1*S91 3.285
EOF B1*S914 2.858
EOF B1*S915 2.543
EOF B1*S9140 4.095
EOF B1*S9150 4.598
EOF B1*S9175 5.820
EOF B1*S91100 6.090
EOF B1*S91752 3.375
EOF B1*S911002 3.788
EOF B2S71 3.450
EOF B2S81 3.315
EOF B2S91 3.353
EOF B2*S71 3.615
EOF B2*S714 3.143
EOF B2*S715 2.888
EOF B2*S7140 4.448
u,num
(kN)
6.1.7.3 6.1.7.2
Cat. Rw,Rd (kN)
(la=10)
Rw,Rd (kN)
(la=ss)
Rw,Rd (kN)
70.980 1 38.14 58.63 58.74
74.378 1 38.14 63.62 61.83
64.433 2 76.27 89.97 47.63
70.328 1 38.14 44.98 52.56
64.800 1 38.14 44.98 50.95
61.163 1 37.58 44.32 50.95
57.300 1 37.08 43.74 49.04
EN1993-1-3 and new proposal predicted resistance for SHS/RHS subjected
to EOF loading
A.4 EOF tests in hat sections
Finally, Table A.4 presents the results from the parametric study in hat sections subjected to
EOF. Again, it has been assessed two values for the la value as it was performed for SHS and
6.1.7.3 6.1.7.2
u,num (kN) Cat.
Rw,Rd
(kN)
(la=10)
Rw,Rd (kN)
(la=ss) Rw,Rd (kN)
3.338 2 4.33 5.52 2.31
3.203 1 2.15 2.74 2.03
3.248 2 4.33 5.52 2.25
3.375 2 4.33 5.52 2.31
2.933 2 4.19 5.34 1.82
2.625 2 4.07 5.18 1.65
4.313 2 4.33 6.38 2.59
4.913 2 4.33 6.86 2.78
5.850 1 2.15 3.91 3.39
6.000 1 2.15 4.34 3.88
3.435 2 4.33 5.52 2.31
3.818 2 4.33 5.52 2.31
3.240 1 2.15 2.74 2.03
2.940 1 2.08 2.65 1.59
2.723 1 2.02 2.57 1.45
3.285 2 4.33 5.52 2.25
2.858 2 4.19 5.34 1.77
2.543 2 4.07 5.18 1.61
4.095 1 2.15 3.16 2.57
4.598 1 2.15 3.40 2.75
5.820 1 2.15 3.91 3.21
6.090 1 2.15 4.34 3.67
3.375 1 2.15 2.74 2.29
3.788 1 2.15 2.74 2.29
3.450 2 4.33 5.52 2.31
3.315 1 2.15 2.74 2.03
3.353 2 4.33 5.52 2.25
3.615 2 4.33 5.52 2.31
3.143 2 4.19 5.34 1.82
2.888 2 4.07 5.18 1.65
4.448 2 4.33 6.38 2.59
39 (41)
39
New proposal
Rw,Rd (kN)
60.184
60.926
58.157
58.157
58.157
53.784
51.371
3 and new proposal predicted resistance for SHS/RHS subjected
Finally, Table A.4 presents the results from the parametric study in hat sections subjected to
value as it was performed for SHS and
New proposal
Rw,Rd (kN)
Ssa
2.529
2.529
2.529
2.553
2.548
2.627
2.614
2.649
2.723
2.785
2.553
2.553
2.553
2.548
2.627
2.553
2.548
2.627
2.614
2.649
2.723
2.785
2.553
2.553
2.601
2.601
2.601
2.691
2.733
2.868
2.755
181 (183)
Specimen Ru,num
EOF B2*S7150 5.033
EOF B2*S7175 6.270
EOF B2*S71100 6.443
EOF B2*S71752 3.750
EOF B2*S711002 4.163
EOF B2*S81 3.420
EOF B2*S814 3.135
EOF B2*S815 2.933
EOF B2*S91 3.503
EOF B2*S914 3.068
EOF B2*S915 2.820
EOF B2*S9140 4.208
EOF B2*S9150 4.688
EOF B2*S9175 5.880
EOF B2*S91100 6.578
EOF B2*S91752 3.653
EOF B2*S911002 4.110
EOF B1S72 12.780
EOF B1S82 12.203
EOF B1S92 12.525
EOF B1*S72 13.028
EOF B1*S724 11.453
EOF B1*S725 10.328
EOF B1*S7240 16.868
EOF B1*S7250 17.925
EOF B1*S7275 19.425
EOF B1*S72100 20.858
EOF B1*S72752 12.968
EOF B1*S721002 13.425
EOF B1*S82 12.420
EOF B1*S824 11.115
EOF B1*S825 10.065
EOF B1*S92 12.743
EOF B1*S924 11.213
EOF B1*S925 10.140
EOF B1*S9240 16.350
EOF B1*S9250 18.668
EOF B1*S9275 21.203
EOF B1*S92100 21.795
EOF B1*S92752 12.908
EOF B1*S921002 13.890
EOF B2S72 13.470
EOF B2S82 12.795
EOF B2S92 13.155
EOF B2*S72 14.213
EOF B2*S724 12.540
EOF B2*S725 11.340
EOF B2*S7240 18.285
EOF B2*S7250 20.115
EOF B2*S7275 21.443
EOF B2*S72100 22.875
6.1.7.3 6.1.7.2
u,num (kN) Cat.
Rw,Rd
(kN)
(la=10)
Rw,Rd (kN)
(la=ss) Rw,Rd (kN)
5.033 2 4.33 6.86 2.78
6.270 1 2.15 3.91 3.39
6.443 1 2.15 4.34 3.88
3.750 2 4.33 5.52 2.31
4.163 2 4.33 5.52 2.31
3.420 1 2.15 2.74 2.03
3.135 1 2.08 2.65 1.59
2.933 1 2.02 2.57 1.45
3.503 2 4.33 5.52 2.25
3.068 2 4.19 5.34 1.77
2.820 2 4.07 5.18 1.61
4.208 1 2.15 3.16 2.57
4.688 1 2.15 3.40 2.75
5.880 1 2.15 3.91 3.21
6.578 1 2.15 4.34 3.67
3.653 1 2.15 2.74 2.29
4.110 1 2.15 2.74 2.29
12.780 2 15.84 19.41 11.47
12.203 1 7.85 9.62 11.53
12.525 2 15.84 19.41 11.32
13.028 2 15.84 19.41 11.47
11.453 2 15.50 18.99 10.54
10.328 2 15.20 18.62 9.61
16.868 2 15.84 21.98 12.24
17.925 2 15.84 23.43 12.75
19.425 1 7.85 13.14 15.25
20.858 1 7.85 14.43 16.63
12.968 2 15.84 19.41 11.47
13.425 2 15.84 19.41 11.47
12.420 1 7.85 9.62 11.53
11.115 1 7.68 9.41 10.60
10.065 1 7.53 9.23 9.66
12.743 2 15.84 19.41 11.32
11.213 2 15.50 18.99 10.40
10.140 2 15.20 18.62 9.48
16.350 1 7.85 10.89 12.97
18.668 1 7.85 11.61 13.51
21.203 1 7.85 13.14 14.86
21.795 1 7.85 14.43 16.21
12.908 1 7.85 9.62 12.16
13.890 1 7.85 9.62 12.16
13.470 2 15.84 19.41 11.47
12.795 1 7.85 9.62 11.53
13.155 2 15.84 19.41 11.32
14.213 2 15.84 19.41 11.47
12.540 2 15.50 18.99 10.54
11.340 2 15.20 18.62 9.61
18.285 2 15.84 21.98 12.24
20.115 2 15.84 23.43 12.75
21.443 1 7.85 13.14 15.25
22.875 1 7.85 14.43 16.63
40 (41)
40
New proposal
Rw,Rd (kN)
Ssa
2.792
2.870
2.935
2.691
2.691
2.691
2.733
2.868
2.691
2.733
2.868
2.755
2.792
2.870
2.935
2.691
2.691
11.307
11.307
11.307
11.359
10.562
10.142
11.558
11.670
11.909
12.110
11.359
11.359
11.359
10.562
10.142
11.359
10.562
10.142
11.558
11.670
11.909
12.110
11.359
11.359
11.465
11.465
11.465
11.662
10.938
10.596
11.866
11.981
12.225
12.432
182 (183)
Specimen Ru,num
EOF B2*S72752 14.220
EOF B2*S721002 15.263
EOF B2*S82 13.410
EOF B2*S824 12.203
EOF B2*S825 10.950
EOF B2*S92 13.830
EOF B2*S924 12.225
EOF B2*S925 10.808
EOF B2*S9240 17.325
EOF B2*S9250 19.590
EOF B2*S9275 23.340
EOF B2*S92100 24.068
EOF B2*S92752 14.093
EOF B2*S921002 15.390
Table A.4.Numerical results, EN1993
6.1.7.3 6.1.7.2
u,num (kN) Cat.
Rw,Rd
(kN)
(la=10)
Rw,Rd (kN)
(la=ss) Rw,Rd (kN)
14.220 2 15.84 19.41 11.47
15.263 2 15.84 19.41 11.47
13.410 1 7.85 9.62 11.53
12.203 1 7.68 9.41 10.60
10.950 1 7.53 9.23 9.66
13.830 2 15.84 19.41 11.32
12.225 2 15.50 18.99 10.40
10.808 2 15.20 18.62 9.48
17.325 1 7.85 10.89 12.97
19.590 1 7.85 11.61 13.51
23.340 1 7.85 13.14 14.86
24.068 1 7.85 14.43 16.21
14.093 1 7.85 9.62 12.16
15.390 1 7.85 9.62 12.16
Table A.4.Numerical results, EN1993-1-3 and new proposal predicted resistance for hat sections
subjected to EOF loading
41 (41)
41
New proposal
Rw,Rd (kN)
Ssa
11.662
11.662
11.662
10.938
10.596
11.662
10.938
10.596
11.866
11.981
12.225
12.432
11.662
11.662
3 and new proposal predicted resistance for hat sections
183 (183)