structural applications of ferritic stainless steels (safss) · cross-sections the study focuses on...

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.


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.


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.



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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).


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).


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.


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.


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



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



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



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


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


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


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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References [1] University of Oulu Report No. 41. Hyttinen, V. Design of cold-formed

stainless steel SHS beam-columns. Finland: University of Oulu, 1994.

[2] VTT Research Note 1619. Talja, A. & Salmi, P. Design of stainless steel RHS beams, columns and beam-columns. Espoo, Finland: VTT Technical Research Centre of Finland, 1995.

[3] Gardner, L. & Nethercot, D.A. Experiments on stainless steel hollow sections – Part 1: Material and cross-sectional behaviour. Journal of Constructional Steel Research 2004, 9, Vol. 60, No. 9, pp. 1291–1318. ISSN 0143-974X. doi: DOI: 10.1016/j.jcsr.2003.11.006.

[4] Manninen, T. SAFSS Work Package 1: Characterization of Stress–Strain Behavior. Tornio, Finland: Outokumpu Stainless Oy, 2012.

[5] Mirambell, E. & Real, E. On the calculation of deflections in structural stainless steel beams: an experimental and numerical investigation. Journal of Constructional Steel Research 2000, 4, Vol. 54, No. 1, pp. 109–133. ISSN 0143-974X. doi: DOI: 10.1016/S0143-974X(99)00051-6.

[6] VTT-R-06130-12. Talja, A. & Hradil, P. SAFSS Work Package 2: Report on model calibration tests. Espoo, Finland: VTT Technical Research Centre of Finland, 2012.

[7] Chauhan, M., Solin, J., Alhainen, J., Manninen, T. & Lönnqvist, C. Cyclic behavior and fatigue of stainless steels. Metallurgia Italiana 2012, September 2012, Vol. 2012, No. 9, pp. 13–18.

[8] WP31&32&33.3S.05. Talja, A. Test report on welded I and CHS beams, columns and beam-columns. Espoo, Finland: VTT Technical Research Centre of Finland, 1997.

[9] Theofanous, M. & Gardner, L. Testing and numerical modelling of lean duplex stainless steel hollow section columns. Engineering Structures 2009, 12, Vol. 31, No. 12, pp. 3047–3058. ISSN 0141-0296. doi: DOI: 10.1016/j.engstruct.2009.08.004.

[10] VTT-R-04651-12. Hradil, P., Talja, A., Real, E. & Mirambell, E. SAFSS Work Package 2: Review of available data. Espoo, Finland: VTT Technical Research Centre of Finland, 2012.

[11] VTT-R-04891-12. Hradil, P. & Talja, A. SAFSS Work package 2: Report on preliminary finite element study. Espoo, Finland: VTT Technical Research Centre of Finland, 2012.

[12] Hradil, P., Fülöp, L. & Talja, A. Global stability of thin-walled ferritic stainless steel members. In: Dubina, D. & Ungureanu, V. (eds.).Proceedings of the 6th International Conference on Thin-Walled Structures. Timisoara, Romania, 5-7 September 2011. Vol. 1. Mem Martins, Portugal: ECCS, 2011. Pp. 313. ISBN 978-92-9147-102-7.

64 (183)


63 (78)

[13] SCI-P276. Lawson, R.M., Chung, K.F. & Popo-Ola, S.O. Structural design to BS 5950-5:1998, Section Properties and Load Tables. Ascot, UK: Steel Construction Institute, 2002.

[14] Austenitic metric data sheet [Homepage of Stalatubes Oy], [Online]Available: http://www.stalatube.com/Global/Images/Documents/Stalatube_Austenitic_metric_EN.pdf [2012, .

[15] Ferritic data sheet [Homepage of Stalatubes Oy], [Online]Available: http://www.stalatube.com/Global/Images/Documents/Stalatube_ferritic_en.pdf [2012, .

[16] Lean duplex data sheet [Homepage of Stalatubes Oy], [Online]Available: http://www.stalatube.com/Global/Images/Documents/Stalatube_Lean_duplex_EN.pdf [2012, .

[17] Burgan, B.A., Baddoo, N., Gardner, L., Way, J., Johansson, B., Olssen, A., Selen, E., Viherma, R., Kouhi, J., Talja, A., Lihavainen, V.M., Niemi, E., Ryan, I., Zhao, B., Stangenberg, H., Barteri, M., Budano, S. & Riscifuli, S. Development of the use of stainless steel in construction. Brussels: European Commission, 2000.

[18] Kuwamura, H. Local buckling of thin-walled stainless steel members. International Journal of Steel Structures 2003, Vol. 3, pp. 191–201.

[19] Gardner, L. & Saliba, N. Experimental study of lean duplex stainless steel. In: Dunai, L. (ed.). Eurosteel 2011. Budapest, Hungary, August 31 – September 2, 2011. Vol. C. 2011. Pp. 2241.

[20] Euro Inox and The Steel Construction Institute Design Manual For Structural Stainless Steel – Commentary. 3rd ed. Euro Inox, 2007.

[21] Young, B. & Liu, Y. Experimental investigation of cold-formed stainless steel RHS columns. Sixteenth International Specialty Conference on Cold-Fonned Steel Structures. Orlando, Florida USA, October 17-18, 2002. 2002. Pp. 398.

[22] Liu, Y. & Young, B. Buckling of stainless steel square hollow section compression members. Journal of Constructional Steel Research 2003, 2, Vol. 59, No. 2, pp. 165–177. ISSN 0143-974X. doi: DOI: 10.1016/S0143-974X(02)00031-7.

[23] Rasmussen, K.J.R. & Hancock, G.J. Stainless steel tubular columns tests and design. Tenth International Specialty Conference on Cold-formed Steel Structures. St. Louis, Missouri, U.S.A., October 23-24, 1990. 1990. Pp. 471.

[24] Gardner, L. & Nethercot, D.A. Experiments on stainless steel hollow sections – Part 2: Member behaviour of columns and beams. Journal of Constructional Steel Research 2004, 9, Vol. 60, No. 9, pp. 1319–1332. ISSN 0143-974X. doi: DOI: 10.1016/j.jcsr.2003.11.007.

65 (183)

http://www.stalatube.com/Global/Images/Documents/Stalatube_Austenitic_metric_EN.pdf

http://www.stalatube.com/Global/Images/Documents/Stalatube_Austenitic_metric_EN.pdf

http://www.stalatube.com/Global/Images/Documents/Stalatube_ferritic_en.pdf

http://www.stalatube.com/Global/Images/Documents/Stalatube_ferritic_en.pdf

http://www.stalatube.com/Global/Images/Documents/Stalatube_Lean_duplex_EN.pdf

http://www.stalatube.com/Global/Images/Documents/Stalatube_Lean_duplex_EN.pdf


64 (78)

[25] VTT Research Note 1864. Ala-Outinen, T. & Oksanen, T. Stainless steel compression members exposed to fire. Espoo, Finland: VTT Technical Research Centre of Finland, 1997.

[26] Gardner, L., Talja, A. & Baddoo, N.R. Structural design of high-strength austenitic stainless steel. Thin-Walled Structures 2006, 5, Vol. 44, No. 5, pp. 517–528. ISSN 0263-8231. doi: DOI: 10.1016/j.tws.2006.04.014.

[27] Young, B. & Lui, W. Behavior of Cold-Formed High Strength Stainless Steel Sections. Journal of Structural Engineering 2005, 11/01; 2012/10, Vol. 131, No. 11, pp. 1738–1745. ISSN 0733-9445. doi: 10.1061/(ASCE)0733-9445(2005)131:11(1738).

[28] Sarawit, A. CUTWP Thin-walled section properties. 2006.

[29] European Committee for Standardization Eurocode 3. Design of steel structures. Part 1-4: General rules. Supplementary rules for stainless steels. Brussels, Belgium: 2006.

[30] Gardner, L. & Ashraf, M. Structural design for non-linear metallic materials. Engineering Structures 2006, 5, Vol. 28, No. 6, pp. 926–934. ISSN 0141-0296. doi: DOI: 10.1016/j.engstruct.2005.11.001.

[31] Gardner, L. & Cruise, R.B. Modeling of Residual Stresses in Structural Stainless Steel Sections. Journal of Structural Engineering 2009, 01, Vol. 135, No. 1, pp. 42–53. ISSN 07339445. doi: 10.1061/(ASCE)0733-9445(2009)135:1(42).

[32] Cruise, R.B. & Gardner, L. Strength enhancements induced during cold forming of stainless steel sections. Journal of Constructional Steel Research 2008, 11, Vol. 64, No. 11, pp. 1310–1316. ISSN 0143-974X. doi: DOI: 10.1016/j.jcsr.2008.04.014.

[33] Abdella, K. An explicit stress formulation for stainless steel applicable in tension and compression. Journal of Constructional Steel Research 2007, 3, Vol. 63, No. 3, pp. 326–331. ISSN 0143-974X. doi: DOI: 10.1016/j.jcsr.2006.06.001.

[34] Rossi, B., Degée, H. & Pascon, F. Enhanced mechanical properties after cold process of fabrication of non-linear metallic profiles. Thin-Walled Structures 2009, 12, Vol. 47, No. 12, pp. 1575–1589. ISSN 0263-8231. doi: DOI: 10.1016/j.tws.2009.05.004.

[35] Zhang, L. & Tong, G.S. Lateral buckling of web-tapered I-beams: A new theory. Journal of Constructional Steel Research 2008, 12, Vol. 64, No. 12, pp. 1379–1393. ISSN 0143-974X. doi: DOI: 10.1016/j.jcsr.2008.01.014.

[36] Report No. 22. European Convention for Constructional Steelwork Manual on Stability of Steel Structures, Second edition. ECCS Committee 8 - Stability, 1976.

66 (183)


65 (78)

[37] Riks, E. An incremental approach to the solution of snapping and buckling problems. International Journal of Solids and Structures 1979, Vol. 15, pp. 529–551.

[38] Hradil, P., Fülöp, L. & Talja, A. Virtual testing of cold-formed structural members. Rakenteiden Mekaniikka (Journal of Structural Mechanics) 2011, Vol. 44, No. 3, pp. 206–217. ISSN 0783-6104.

[39] The SciPy community SciPy Reference Guide. 2011. ISBN Release 0.10.0 dev. http://docs.scipy.org/doc/scipy/scipy-ref.pdf.

[40] Ayrton, W.E. & Perry, J. On struts. The Engineer 1886, Vol. 62, pp. 464–465.

[41] Talja, A. SAFSS Work Package 2: Report on model calibration tests. Espoo, Finland: VTT Technical Research Centre of Finland, 2011.

[42] ABAQUS User Manual (version 6.11). Pawtucket, RI, USA: Hibbitt, Karlsson & Sorensen Inc., 2011.

67 (183)

http://docs.scipy.org/doc/scipy/scipy-ref.pdf


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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

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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

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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)


71 (78)


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


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)


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


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


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)


73 (78)


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


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


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)


74 (78)


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)


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)).


77 (183)


76 (78)


Figure C4. Proposed curve for welded open sections major axis flexural buckling (α = 0.49, λ0 = 0.2).

78 (183)


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)


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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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





Austeniti

AustenitiAustenitiAusteniti

Duplex HSA

Duplex HSA

07 Super dup

N AustenitiN Austeniti

01 Lean dupl01 Lean dupl


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

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

meter, the gher slendern

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

‐ri. It is wortdes even mo

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.

.1 1.2 1.3

=100 SerSerG&T

ase, the ele

‐ri) which waare worth

rial.

therefore a

dures to evaected to un

eduction factorsDistinction betw

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


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



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

and Spangemde 3, Part 1.

. J. (1995). Tal Steel Rese

.A. Structur1.4 and tes

sign.

of steel stru

ign of steelCEN.

tructural staerial College

tructural staEngineering‐

erritic StainlSCE. In Press

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

h of Stainles. Vol 34, 131

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

62)

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

ner and Theoner, L. and Tless steel el.

ner et al. (20ner, L., Wangn of steel s11(5), 855‐87

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

006) a, A. and Bahin‐Walled St

hercot (2004Nethercot, Dss‐ sectional

hercot (2004Nethercot, Dour of colum2.

ba (2011) Saliba, N. (20Hungary.

ofanous (200Teofanous, Mements. Jou

011) ng, F. and Lietructures. In75.

) 003). Local 191–201.

003) g, B. (2003)l of Construc

Hancock (199R. and Hancmns. Journa

Hancock (199R. and Hancms. Journal o

tinuous Streuildings. Vol.

addoo, N.R. tructures (20

4a) .A. (2004a). behaviour. J

4b) .A. (2004b). mns and bea

011). Experim

08) M. (2008). Durnal of Cons

ew, A. (2011nternational

buckling of t

). Buckling octional Steel

93a) ock, G.J. (19l of Structura

93b) ock, G.J. (19of Structural

ength Metho161(3), 127‐

(2006), Stru006). Vol. 44

ExperimentsJournal of St

Experimentsms. Journal

mental stud

Discrete and structional S

). Influence Journal of S

thin‐walled

of stainless sResearch (20

993a). Desigal Engineerin

993b). DesigEngineering

od. Proceedi‐133.

uctural desig4(5), 517‐528

s on stainlestructural Stee

s on stainlessof Structura

y of lean du

continuous tSteel Resear

of strain harStructural St

stainless ste

steel square003). Vol. 59

gn of cold‐fong (1993), AS

gn of cold‐fo(1993), ASC

ngs of the I

gn of high‐st.

s steel hollowel Research (

s steel hollowal Steel Rese

plex stainles

treatment orch (2008). V

rdening on ttability and

eel members

e hollow sec9(2), 165‐177

ormed stainSCE. Vol. 119

ormed stainE. Vol. 119(8

Institution o

trength aust

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.

62)

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

fanous and Gfanous, M. less steel ho

fanous and Gfanous, M. less steel be

and Young (, F. and YouWalled Struc

g and Liu (20g, B. and Lmns. Journal

g and Lui (20g, B. and Luictural Engine

0) (2000). Receeel Research

ell (2005) rambell, E. (. Vol. 27,146

dmann (1995Feldmann, M1.1. Backgro

99) WP3.5S.02. Cf stainless stconstruction

00) WP6.5S.02

the use of at

1995) mi, P. (1995). tes 1619. Esp

Gardner (200and Gardnellow section

Gardner (201and Gardneams. Journa

(2005) ung, B (2005ctures (2005

003) Liu, Y. (200 of Structura

005) , W. (2005). ering (2005)

ent researchh (2000). Vol

2005). Flexu65‐1475.

5) M. The b/t‐raound Docume

Classificationeel. Report tn.

. Ferritic sttainless steel

Design of stpoo, Finland

09) er, L. (2009columns. En

10) r, L. (2010).l of Construc

). Tests of c5). Vol. 43(9),

03). Experimal Engineerin

Behaviour o), ASCE. Vol.

h on stainlel.54(1), 75‐88

ural behavio

atios controlent 5.09 for

n of stainlessto the ECSC P

tainless steel in construct

tainless steel: VTT Techni

9). Testing angineering St

. Experimentctional Steel

cold‐formed , pp. 1325‐13

mental Invesng (2003). Vo

of cold‐form131(11), 173

ess steel tu8

our of stainl

ling the applchapter 5 of

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

to the ECSC

, 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


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


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


Work package 2.4b. Parametric Study and

Recommendations: Web crippling

Marina Bock

Esther Real

Enrique Mirambell Departament d'Enginyeria de la Construcció,


Structural Applications of Ferritic Stainless Steels

(draft/proposal/updated/to be reviewed

/approved)

Author(s)

Marina Bock

Project group

1 (41)

1


.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)


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



stainless steel that made up the different cross sections are presented.



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.



ections are presented. The



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





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





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


However, the presented values of the different researchers are measured following


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


the different researchers are measured following


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 IOF50x50x1.5N50 HSDuplex


Zhou and Young (2007a) SHS IOF150x150x3N150 HSA




Zhou and Young (2007a) RHS IOF140x80x3N75 HSDuplex




Zhou and Young (2007a) RHS IOF200x110x4N100 HSA


Talja and Salmi (1995) SHS RHS -1 W-1 1.4301


Talja and Salmi (1995) RHS RHS -2 W-1 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






















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) RHS EOF140x80x3N75






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


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) RHS EOF140x80x3N75 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


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


Span la

Talja et al.ECSC (2004) HAT H100-100x2 1.4318-C700 600 50






Talja and Hradil (2011) HAT TH_10_IS 1.4509 300 25




Table 1.7

Paper Sectiontype Reference grade

Talja et al. ECSC (2004) HAT H100-100x2 1.4318-C700






Talja and Hradil (2011) HAT TH_10_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


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


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


Span e

Talja and Hradil (2011) HAT TH_10_ES 1.4509 350 75




Table 1.9


Talja and Hradil (2011) HAT TH_10_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


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


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



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







Talja et al.ECSC (2004) Unstiff. trapezoidal H50-100x2



Talja et al.ECSC (2004) Stiff. trapezoidal P70-70-






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








Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4318



Talja et al. ECSC (2004) Stiff. trapezoidal P70-70-Vx0.9 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)


Zilli ECSC (2004) Unstiff. trapezoidal P30-45x9 1.4318-C700








Talja et al. ECSC (2004) Unstiff. trapezoidal H50-100x2 1.4318-C700



Talja et al. ECSC (2004) Stiff. trapezoidal P70-70-Vx0.9 1.4318-C700






grade Material properties from tensile flat (σ in MPa)

Material properties

flat/stub column


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



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


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



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


point bending) x 4



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





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


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


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)


e load case to obtain the web crippling resistance in both 6.1.7.2 and 6.1.7.3


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


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


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


resistance in both 6.1.7.2 and 6.1.7.3


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


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


(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


bearing length (SsL)

24 (41)

24

6.1.7.3

� Category 2

� Category 1

� Category 2

� Category 1

� Category 1


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


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


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)


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



#. � 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



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


web crippling strength, this new proposal expression is applicable to any stainless steel

Material nonlinearities influence


) 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, which was assessed by comparing N1, N2 and N3 specimen results from the



27 (41)

27


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



considered in the adjustment of

Hat section

0.14

0.81

0.065

2000

coefficient values for the new proposal expression


to any stainless steel


3 is only applicable to carbon steel. Unlike carbon

strain behaviour which might be considered in the web


en results from the



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


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


that the ultimate web crippling strength follows an internal radii square root function.


which was taken into account in the new proposal formulation.

Bearing length influence

the preliminary FEM study concluded that the bearing length in 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


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


s an internal radii square root function.


the preliminary FEM study concluded that the bearing length in 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


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


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


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


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


3§6.1.7.2, EN1993-1-

(numerical ultimate


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


and 6.1.7.2 provide results under the unity with considerably


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


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


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


se results. This is very satisfactory since it means that the proposed


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


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


0. Despite this, the new proposal gives the most suitable ratios.

. However, it seems that the new formulation


se results. This is very satisfactory since it means that the proposed


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


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


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


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


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


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


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


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


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


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


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


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.


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.


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


Test results on unstiffened profiles.

Structural design of


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



partial safety factors have been set to unity to enable a direct comparison. All specimens were



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



te length that applies the load (ssL) in EOF test.

A.1 IOF tests in SHS and RHS


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



All specimens were



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




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


nomenclature of Table A.1 has been used.


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


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


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


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



), 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


) 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


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


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


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


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)