Cidect 5bp 4-05 Part 2

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CIDECT Report : 5BP-4/05 November 2005

DEVELOPMENT OF A FULL CONSISTENT DESIGN APPROACH FOR

BOLTED AND WELDED JOINTS IN BUILDING FRAMES AND TRUSSES

BETWEEN STEEL MEMBERS MADE OF HOLLOW AND/OR OPEN

SECTIONS

-

APPLICATION OF THE COMPONENT METHOD

VOLUME 2 - PROGRESS OF THE SCIENTIFIC ACTIVITIES ON JOINT

COMPONENTS AND ASSEMBLY

Final report submitted to:

Comité International pour le Développement et l’Etude de la Construction Tubulaire

Authors:

J.P. Jaspart, C. Pietrapertosa

University of Liège, Liège, Belgium

K. Weynand, E. Busse, R. Klinkhammer

PSP Technologien GmbH, Aachen, Germany

coordinated by:

J.P. Grimault

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Foreword

The application of the component method for the characterisation of the mechanical properties of structural joints in tubular construction has been initiated into CIDECT few years ago, within the project 5BM. As an outcome of this first project, the possibility to extend to hollow joints this method initially developed for joints between open sections has been demonstrated and the advantage of this use has been pointed out.

Present project 5BP aims at developing further the concept, at indicating how the component method may be implemented in daily practice but also at identifying any lack of information which could limit the application. Finally developments were expected to be achieved so as to increase the scientific knowledge and progress in the preparation of appropriate answers to some of the still pending technical questions.

In the present report, the reader will find the outcome of the works performed within the 5BP project in the last two-and-a-half years in the form of two separate volumes, respectively entitled:

• Volume 1 : Practical guidelines

• Volume 2 : Progress of the scientific activities on joint components and assembly

Volume 1 gathers all the information available to the designer and helpful for the design of a wide range of structural steel joints connecting hollow and/or open sections. The use of this material requires anyway an experience which is not necessary widely shared at the moment and therefore simple design aids (called design sheets) more appropriate to daily practice have been prepared for some selected joint configurations. These ones are complemented by worked examples. Should these design sheets be appreciated, additional design sheets covering other joint configurations would have to be drafted by referring to the material made available in the first part of Volume 1.

Volume 2, on the other hand, reflects the progress of the scientific works achieved during the project. These ones contribute to a better understanding of the behaviour of CHS components and of their assembly. Further research activities which could not have been achieved in the 5BP project are required in this field so as to come to fully validated models. These works are planned to be achieved at PSP and at Liège University in the next months; they could be reported on at the occasion of the next ISTS Symposium to be held in Quebec in 2006.

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Part I Recent developments for the derivation of an

analytical formulation for CHS wall components

I.1 Introduction

In parallel with the work presented in the volume 1, some scientific developments have been performed in Liège in order to derive a new analytical formulation, based on physical aspects and plastic theory, for the resistance of CHS wall component. In the interim report BP-4/04, the first elements of this study have been presented. Since August 2004, this study has well progressed, some tools have been developed, a good understanding of the physical behaviour of the components has been obtained and some key steps have been crossed in view of the derivation of analytical formulation for component characterisation.

Hereunder the main elements of the interim reports are briefly reported and the more recent developments performed this year are presented. Further research steps have still to be performed. They are planned to be achieved in the next months at Liège University and at PSP; as this work has been initiated in the 5BP project, the two mentioned institutions will report in the next CIDECT meetings about the progress of these research works.

I.1.1 Summary of the interim report (5BP-4/04 – August 2004)

The first studies carried out on the CHS wall components have been presented in the second 5BP interim report [3]. The main conclusions of this report are summarised in this chapter. The new developments carried out this year are described in Chapter I.2.

I.1.1.1 Types of the plastic mechanisms

When CHS profiles are subjected to transverse compression and tension forces, plastic yield line mechanisms, membrane effects and possible instability effects develop. If second order effects are disregarded (membrane effects, instability effects, …), the resistance of the CHS section is a fully plastic one and the failure loads in compression and in tension are equal. The plastic mechanisms which form in the CHS section have been analysed through experimental tests and numerical simulations and, as a result, two types of plastic mechanisms may be identified (Figure 1):

global plastic mechanisms involving the whole section;

local plastic mechanisms involving a part of the whole section.

(a) One global mechanism (b) One local mechanism (c) Two local mechanisms Figure 1: Types of mechanisms

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I.1.1.2 Two contributions to the yield mechanisms

In the interim report, the form of the mechanisms has been studied. And it has been shown that the mechanisms may be divided into two different contributions (see Figures 2 and 3): a “ring model” mechanism (Npl(rm)) and two “external” mechanisms (Npl(em)).

A A

dm

Plane view Cut A - A :

Npl Npl B B p l p tm

Figure 2: Connection with a CHS chord and a rectangular brace

Figure 3: Two contributions for the plastic mechanism of the chord External mechanisms

Ring Model

Bem Br m Bem

Beff

Rectangular brace _{CHS chord}

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It has also been demonstrated that a good estimation of the plastic resistance Npl (tot) of the chord

may be derived by summing the resistance of the separate contributions:

Npl (tot) = Npl(rm) + 2*Npl(em). (1)

I.1.1.3 “Ring model” mechanism

An analytical formula for this part of the mechanism has been presented in the previous report. This formula has been validated by numerical tests. The plastic resistance of the “Ring model” contribution for a CHS loaded in transverse tension or compression may be determined by the following expression (Figure 4):

b ) t (d t B f 2 N 0 2 0 y0 pl(rm) = ₋ ₋ (2) with: d = diameter of the CHS b = width of the loading area B = length of the loading area

Figure 4: Application of the ring model theory to the component “CHS wall in tension or compression”

I.1.1.4 External mechanisms

The form of the external mechanisms observed in CHS in tension and compression is seen in Figure 4 in the case of a global mechanism. But an identical shape is observed in local mechanisms. Furthermore the yield line pattern shown in Figure 4 is quite similar to the one predicted by the so-called “Gomes model” for I or H column webs in transverse compression or tension (Figure 5); the main difference is obviously the nature of the surface where the yield lines develop:

- a shell in CHS profiles. - a plate in I or H column;

Gomes proposes an analytical expression to evaluate the plastic resistance of I or H column webs in transverse compression or tension (Formula 3 and Figure 6):

        + − − = L c 2 L b 1 L b 1 m 4 F_pl pl π π (3) B b d

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Yield lines in fan Rectangular area with longitudinal deformations

Yiled line along the loading area

Curved yield line continuing the « Ring Model » plastic

yield line

Figure 5: Scheme of an external mechanism

Figure 6: Schema of the Gomes mechanism for column webs

As said just before, in the CHS component considered in the present works, the mechanism forms on a curved surface (shell); as a consequence, the development of a traditional plastic approach is quite complex and therefore an indirect way to solve the problem had been suggested in the second interim report. It was consisting in:

- proceed to the projection of the actual yield pattern on a plane surface perpendicular to the brace axis (see Figure 7);

- use the Gomes model to evaluate the plastic resistance Frd(plane) of the “projected yield

pattern”;

- derive a “projection” coefficient µ by which the Gomes plastic resistance should be multiplied to obtain an estimation of the actual plastic resistance Frd(shell) of the CHS

component:

b

c

L d

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Frd(shell) = µ . Frd(plane) with µ > 1 (4)

F

rd(shell)

F

rd(plane)

(a) Actual yield line (b) “Projected” yield line

Figure 7: Projection of a yield line

I.1.2 Objectives expressed in the second interim report

The main objective is to develop an analytical expression of the µ factor (Formula 4). In a first stage, different pure analytical approaches are followed. However, none of these approaches really enables to reach the objective. Therefore, a numerical parametric study is performed by means of the non-linear FEM software FINELG so as to progress in the derivation of an analytical expression for the factor µ.

I.1.3 Research strategy

The whole procedure followed is illustrated in Figure 8. This plan shows the part of the work that has been made since the last interim report.

I.1.4 Research steps

The research works carried out in the last year are presented in Sections I.2 and I.3:

- Direct analytical approaches: the aim is to derive a formulation of the µ factor through pure analytical investigations. This work is presented in Section I.2.

- Numerical simulations: the FEM approach is used to understand how the actual plastic mechanism forms on a curved surface and to find a correlation with the in-plane mechanisms. The numerical approach requires several steps:

validation of the FEM tool; • calibration of the model; • parametrical study;

• interpretation and analysis of the results; This activity is reported in Section I.3.

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Figure 8: Research strategy Local mechanism Two different mechanisms Experimental results two contributions Global mechanism Analytical model validated by numerical simulations Analysis of the plastic mechanisms Numerical investigations

External

mechanism

Ring model

similar

OK

Similar to Gomes plastic model Numerical investigation Parametrical study Analytical projection on curve surface CHS Tension – compression Plastic resistance Report 2005 Correlation with Gomes model Analytical formulation for plastic resistance

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I.2 Direct analytical approach

In order to derive the analytical formulation, assumptions are made:

- the plastic resistance on a curved surface can be calculated as on a plane surface, but with “projected” lengths for the yield lines L’=ρL with:

L’ = Lshell = length of the yield lines on the curve surface;

L = Lplate = length of the yield lines projected;

- the plastic resistance is proportional to the length of the yield lines of the plastic mechanism (Johanssen theory); therefore the ρ factor is equal to µ:

L ' L

µ= (5)

The equation to calculate the length of the projected yield line may be expressed in a very general case, as a function of the curvature of the curved surface. The only parameter to consider is R, the radius of curvature.

L and L’ are function of the 3 spatial coordinates: L = f(x,y,z)

L’ = f’(x,y,z)

The general equation for the line projected from a curved surface on a plane surface is (see Figure 9):     ⋅ = β β R0 ,sin2 x arcsin E cos R ' L (6) E […] = elliptical function

Figure 9: projection of yield line of curvature R

β

x0 x

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This general equation is rather complicated. The derivation of a single factor µ from this equation is not so easy.

But before trying to go further, it would be important to validate the simplifying assumptions made and therefore to check whether a direct analytical projection may provide an adequate response. So the approach has been applied to a very simple model for which the plastic mechanism is known. The model tested is an cantilever shell element and the corresponding projected plate subjected to a concentrated load applied at its extremity (Figure 10).

For this case, the problems of projection becomes much more simple. The yield line in the plate case is equal to the width of the plate: L = b

The projection of this yield line is L’ = 2αR, with R = radius of curvature and α = angle of the arc length.

In this particular situation, the factor µ is equal to:

b R 2 L ' L P P µ plane curve ₌ ₌ α = (7)

If half-a-CHS profile is considered for numerical application: α = 90° If b = diameter of the CHS is taken as equal to 200 mm Æ R =

90 sin 2 b = 100mm Æ µ = 0,5

(a) Actual yield line (b) Projected yield line Figure 10: Illustration of the example

By calculating the plastic resistance of the plane yield line Figure 10.b) and multiplying it by µ=0,5, an analytical expression of the actual resistance of the “shell” cantilever element (Figure 10.a) is obtained; it has been compared to the exact solution determined by numerical simulations (interim report [3]) and a poor agreement is obtained, so clearly demonstrating the weakness of the assumptions made.

R

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I.3 Numerical

study

The objective of the numerical study is to define the parameters that influence the plastic resistance of the CHS components and to find a correlation with the plate mechanisms. The value of the plastic resistances and the shape of the yield line patterns are analysed for different joint configurations.

The results of the simulations are compared to the analytical results of the Gomes approach for an “equivalent” plate and an expression of their ratio µ is expected to be derived.

I.3.1 Validation of the FEM tool

In Liège, the numerical study is performed with the full non-linear FEM software FINELG. In order to validate this FEM tool in the frame of the present research, a comparison has been made with experimental results. These results are presented in the part II of the present volume 2 (chapter II 4 - Figure 55). The results of the FEM simulation performed with FINELG for a specific test result (Y. Makino et al) are reported in Figure 11. These results show that the FINELG results are very close to the ABAQUS ones derived at PSP. On the basis of several such comparisons, FINELG can be considered as giving reliable results and can therefore be used for the numerical study.

0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 s [mm] P [kN] Test results

FEM ABAQUS results FEM Finelg results

Figure 11: Load displacement curves of X-joint XP1-T-1 under tension (Y. Makino et al.)

I.3.2 Definition of the numerical model for the study of the CHS component

A T-joint configuration has been chosen as numerical model to study the CHS component in tension or compression. This T-joint is composed of a tubular element and of a plate fixed perpendicularly to the tube.

The plate is submitted to an axial force (Figure 12). The nodes are blocked in the three directions at the extremities of the tube.

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Figure 12: FEM model of a plate to CHS joint I.3.2.1 FEM mesh

The model uses shell elements. Simulations have been computed with different meshes and the results have been compared. In Figure 14, it is seen that the adopted mesh gives same results then a more refined one.

I.3.2.2 Loading

The joint is subjected to a point load at the extremity of the plate. In order to avoid a local plasticity effects at the load introduction point, the edge of the plate has been reinforced by very stiff beam element. The material law used for the elements of the plate is a linear law. Therefore, only the face of the CHS is influenced by the loading.

I.3.2.3 Plastic model

In order to study the plastic resistance of the component, all the second order effects (membrane effects, instability, …) have to be disregarded. For this purpose, the steel material properties used in the model have been selected in such a way that no second order effect develops. The Young modulus has been taken equal to 2,1 1010 MPa. That doesn’t affect the maximum resistance. It only changes the initial stiffness and it prevents appearance of large displacements and therefore of second order effects.

As far as the plastic resistance is concerned, the numerical response should be the same in tension and compression. This is confirmed in Figure 13, where appearance of a horizontal plateau in all the four curves proves that the plastic resistance is reached.

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Tube: φ = 114,3mm ; t = 6,3mm Plate: Width = 76,1mm ; t = 5mm 0 20000 40000 60000 80000 100000 120000 140000 160000 180000 200000

0,00E+00 1,00E-04 2,00E-04 3,00E-04 4,00E-04 5,00E-04 6,00E-04 7,00E-04 8,00E-04 9,00E-04 1,00E-03

depx (mm)

P (

N

)

tension S235 compression S235 tension S355 compression S355

122131 183418

Figure 13: Plastic resistance of the CHS components I.3.2.4 Influence of the thickness of the plate

The thickness of the plate can not be taken into account in the numerical model as shell finite elements are used. Figure 14 shows that the thickness of the plate has no influence on the numerical plastic resistance. To take this parameter into account a model with solid elements should be built, what would lead to much heavier simulations.

In the Gomes analytical model (Formula 3), the thickness of the plate is explicitly taken into account. But in reality it will be shown in paragraph I.3.4 that this parameter has not a great influence on the value of the plastic resistance as long as realistic thickness values are considered. The numerical study can therefore be achieved without taking into account this parameter and a good estimation of the plastic resistance may be anyway expected.

For the numerical study, all the simulations are run with a plate thickness equal to 1mm.

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0 50000 100000 150000 200000 250000

0,00E+00 1,00E-03 2,00E-03 3,00E-03 4,00E-03 5,00E-03 6,00E-03 7,00E-03 8,00E-03 9,00E-03

depx (mm) P ( N ) t=1mm t=1mm (refined meshing) t = 10mm t = 5mm t = 0,1mm ~190000

Figure 14: Influence of the thickness of the plate on the plastic resistance in the shell FEM model

I.3.2.5 Influence of the length of the tube

A particular attention has to be paid to the length of the tube in the numerical model. Indeed, if the tube is too long, the failure occurs by a plastic mechanism involving three plastic hinges in the CHS profile (Figure 16) and the numerical resistance does not correspond to the studied phenomena. If the tube is too short, the yielding extends all olong the length of the CHS profile and the studied mechanism can not be isolated.

In fact, For each simulation, the failure mechanism has to correspond to a local mechanism close to the plate (Figure 15).

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As shown in Figure 16, for high values of the length, the beam mechanism appears; if the length decreases, the whole face of the tube is yielded. An intermediate value of the CHS length has therefore to be selected. 0 50000 100000 150000 200000 250000 0 0,005 0,01 0,015 0,02 0,025 dep x (mm) P ( N ) 300mm 600mm 1200mm 1800mm 3000mm

Figure 16: Influence of the length of the tube

I.3.3 Parametrical study

I.3.3.1 Objectives

The first objective of the parametrical study is to analyse the evolution of the plastic resistance according to the geometrical parameters of the joint configuration.

The main parameters influencing the plastic resistance are the following ones: t0 = thickness of the tube

d0 = diameter of the tube

b = width of the plate

The thickness of the plate, as it has been demonstrated on Figure 14, can not be taken in consideration through the numerical simulations. This parameter will therefore not be integrated in the study.

In Eurocode 3, use is often made to the two following values: 2γ = t0/d0

β = b/d

In fact, these two values involve the three main geometrical parameters listed here-above and will therefore be used as references in the parametrical study.

The second objective is to compare the numerical results to the Gomes formula and to derive an expression of the factor µ defined by Formula (3).

I.3.3.2 Description of the parametrical study

A set of 36 simulations has been performed. They are grouped into 4 series according to the thickness of the CHS profile:

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Set 1 Æ t0 = 8mm

Set 2 Æ t0 = 6,3mm

Set 3 Æ t0 = 10mm

Set 4 Æ t0 = 12mm

These thickness values are common ones.

For each set of simulations, the diameter of the tube varies from 76,1 to 1700mm: T3Æ d = 76,1mm T4Æ d = 114,3mm T5Æ d = 193,7mm T6Æ d = 244,5mm T7Æ d = 323,9mm T8Æ d = 508,0mm T9Æ d = 800,0mm T10Æ d = 1000mm T11Æ d = 1700mm

The diameters T4 to T8 are the usual diameters for CHS sections. Some simulations with diameters higher than the usual ones (T9, T10 and T11) have been performed in order to approach a limit study case (plate of infinite width). Figure 17 illustrates such a limit case where the yield mechanism is nearly located on a plane surface.

Figure 17: Model with high CHS diameter

The width of the plate is kept constant for all the simulations (b = 76,1mm).

The material law implemented in the model is a bilinear elastic-plastic one for the CHS elements, with fy0 = 355N/mm², and a linear elastic one for the plate elements.

I.3.3.3 Results of the parametric study

Figures 18 to 2& present the results of the FEM simulations (P and d are respectively the load applied to the transverse plate et the corresponding displacement at the CHS surface)

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Figure 18: P-d curves for models with t0 = 8mm

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Curves T3 and T4 correspond to beam mechanisms. The resulting plastic loads are therefore not relevant.

All these curves show that the plastic resistance increases when the diameter of the tube decreases. For limit cases with very high values of diameters, the plastic resistance does not decrease very much when the diameter increases further (from T10 to T11, D is multiplied by 1,7 but the plastic resistance does not decrease significantly). The plastic resistance seems to tend a limit constant value.

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Figure 22 presents the evolution of the plastic load obtained numerically versus the γ parameter. When γ → 0, Npl → ∝; this is logical as γ=0 corresponds to a CHS with an infinite thickness. For

high values of γ, the plastic resistance again tend to a limit value.

0 50000 100000 150000 200000 250000 300000 350000 400000 0 50 100 150 200 250 300 2γ0 Npl (N) t=8mm t=6,3 mm t=10 mm t=12 mm

Figure 22: Plastic resistance versus γ parameter

Figure 23 shows how the plastic load obtained by numerical simulations varies the β parameter. The evolution may be supposed to be linear.

y = 484159x + 197114 y = 379377x + 140751 y = 289710x + 93524 y = 200850x + 62822 0 50000 100000 150000 200000 250000 300000 350000 400000 450000 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 β Npl (N) t=8mm t=6,3 mm t=10 mm t=12 mm

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The numerical results also allow to visualise the yield mechanisms (Figure 24). For high diameters models, these numerically obtained mechanisms may be compared to results of plastic plate yield theories. Finally they should allow to better understand the correlations between “shell” and “plate” yield line patterns.

Figure 24: Numerical yield patterns I.3.3.4 Comparison with Eurocode 3 formula

The numerical results have been compared to the current design formulae for CHS connections implemented in Part 1.8 of Eurocode 3 or in the design Guide book published by CIDECT [41]. The relevant formula is the following :

N* = f(β) . f(η) . f(n’) . fc,y . tc² (8)

with f(β) =

5.0 1 0.81

−

⋅

β

f(η) = 1 f(n’) = 1

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0 50000 100000 150000 200000 250000 300000 350000 400000 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 β Npl (N)

FEM t=8mm FEM t=6,3mm FEM t=10mm FEM t=12mm Annex K t=8mm Annex K t=6,3mm Annex K t=10mm Annex K t=12mm Figure 25: Comparison Eurocode 3 – numerical simulations

The “numerical” plastic resistances are quite close to the Eurocode and CIDECT recommendations. The design values are on the safe side except for low values of β (which is out of the field of the design recommendations).

I.3.4 Correlation with Gomes model

I.3.4.1 Application of the Gomes model to CHS components

The Gomes model has been developed to study the behaviour of minor axis joints between I or H profiles. Present research focuses on another component. Therefore, the parameters used by Gomes in his formulation have to be interpreted differently to be in agreement with the CHS problem.

The Gomes model for minor axis joint is:

4 ₂

1

pl

m

_b

_c

Npl

b

L

π



_

_



=



_

−

_

+



_









−

(9) mpl = 0,25 fy tw2

L = the width of the column web

b = the width of the beam flange (or plate) c is the thickness of the flange (or plate)

The aim is to apply the same formula for CHS connections but with a correction factor µ (Formula 3) taking into account the curvature of the CHS wall.

Therefore, if the Gomes model is applied to a CHS joint, the different parameters are defined as follow:

- mpl = 0,25 fy0 t02with t0 = thickness of the CHS

fy0 = yield limit of the CHS

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- L is the most complicated parameter to define. In the Gomes model, the parameter L is fixed by the geometrical layout of the joint (L = width of the column web). In the case of the CHS chord, an equivalent parameter is not so obvious to define. Indeed, the plastic mechanism is not limited by flanges, as for an I profile, and the length of the mechanism is, at first sight, unknown. Therefore, for the developments of the next paragraph, the Gomes model will be used with L equal to the length of the yield area defined by FEM simulations projected on a plane surface. This will allow to compare and understand the behaviour of the yield mechanism in comparison with the Gomes model. But to derive the final analytical formula, a fixed reference has to be chosen and L will be taken equal to the diameter of the CHS. Obviously, a corrective factor will have to be used.

- c is the thickness of the plate but as it is showed in Figure 14, this parameter can not be taken into account by the numerical simulations. Therefore, as a first approach, this parameter is neglected in the developments of the analytical formulation. The following example proves that the error made by neglecting this term is not important.

A case with a b/L and a very thick plate very high would be the most severe. For this example, L is taken as the diameter of the tube.

Diameter of the CHS: L = 100mm Width of the plate: b = 80mm Thickness of the plate: c = 12mm

L b 1− = 0,447 L c 2 π = 0,076

The second term L c 2

π can therefore be reasonably neglected in comparison with L b 1− .

I.3.4.2 Comparison numerical results and Gomes model

In Figures 27 and 28, the results of the numerical simulations have been compared to the Gomes model. As explained in the previous paragraph, the term

L c 2

π has been neglected.

Figure 26: Illustration of L parameter

L’

L = L’ projected on a plane surface

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For this comparison, the parameter L has been taken equal to the length of the yield mechanism obtained numerically, projected on a plane surface (Figure 26). The Gomes curves on Figures 27 and 28 are not pure analytical curves as they depend on a numerically determined parameter (L). The value of L obtained numerically has a physical meaning and this allows to draw interesting conclusions and see whether the application of the Gomes model for CHS walls has a sense. The analysis of the graphs shows that the shapes of the numerical curves and the shapes of the “Gomes“ curves are the same. That proves that the Gomes model is a reliable background from which the analytical formulation for the CHS wall component can be derived.

0 50000 100000 150000 200000 250000 300000 350000 400000 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 β Npl (N )l

Gomes t=8mm Gomes t=6,3mm Gomes t=10mm Gomes t=12mm FEM t=8mm FEM t=6,3mm FEM t=10mm FEM t=12mm Figure 27: Comparison Gomes model – numerical simulations versus β

The curves Npl(β) are almost linear, also for the Gomes model. The numerical plastic resistance is

always higher than the one obtained by Gomes, but the difference between the two values decreases for low values of β.

0 50000 100000 150000 200000 250000 300000 350000 400000 0 50 100 150 200 250 300 2γ0 Npl (N )

Gomes t=8mm Gomes t=6,3mm Gomes t=10mm Gomes t=12mm FEM t=8mm FEM t=6,3mm FEM t=10mm FEM t=12mm Figure 28: Comparison Gomes model – numerical simulations versus γ

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The graph Npl(γ) also shows that the plastic resistance tends to a limit value when γ increases. It

can therefore be supposed that, for an infinite diameter, a single value of the plastic resistance, not depending of any parameter, is reached.

In conclusion, the Gomes model can be considered as an adequate basis for the new analytical formulation. The correcting factor, which will allow to modify the Gomes model so as to get results close of the numerical resistances has now to be found.

Remark: Obviously for the final analytical formulation, the parameter L can not be equal to a value taken from numerical simulations. The formula relies on a known value of L. L could be taken as equal to the diameter of the CHS in a first stage.

I.3.4.3 Determination of the limit value

It would be interesting to define the limit of the plastic resistance in the extreme case where the diameter of the CHS section is equal to infinite.

If the diameter is equal to infinite, the CHS becomes an infinite plate.

The analytical solution may be found by referring to the Johanssen plastic theory (Figure 28): Ppl = mpl [2b 1/X + 2L 1/X + 2α + 2α + 4(L/2-b/2) 1/X] (10)

with X = (L/2 – b/2) tg (α/2)

To find the plastic resistance, the parameter α et L have to be optimised.

0

0 P

L

P

α

∂



₌

∂

 ∂



₌

∂



¨ (11)

The solution of this system of equations gives α = ±π/2 Æ X = ∞ Æ Ppl = 4πmpl

Figure 29: Plastic mechanism on an infinite plate

The limit of the plastic resistance when the D = ∞ equals 4πmpl.

In order to illustrate this limit value, the evolution of the plastic resistance with the diameter of the tube have been reported in Figure 30. In this case, the Gomes model has been used with L= diameter of the tube. The values of the resistance have been divided by the plastic moment (mpl).

In such a way, all the curves calculated with the Gomes model do not depend on the thickness X

b α

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anymore. Therefore one single reference curve represents the Gomes model. The value 4 4 pl m mpl

π

= has also been reported on the graph and it can be observed that all the values of Npl/mpl (numerical and “analytical”) tends to the value 4π.

0 5 10 15 20 25 30 35 40 45 100 300 500 700 900 1100 1300 1500 1700 1900 Diameter of the CHS (mm) Npl /m pl

Gomes reference FEM t=8mm FEM t=6,3mm FEM t=10mm FEM t=12 mm 4pi

Figure 30: Limit value of plastic resistance

I.3.5 First conclusions of the parametrical study

This parametrical study allows to understand the general behaviour of the component and to establish the link with the analytical model of Gomes for plane surfaces. This study proves that the Gomes model can be used as a reliable basis for the development of the analytical formulation. The numerical results show also that the limit in the field of high diameters for CHS is the same than the limit of the Gomes model.

I.4 Conclusions – further developments

The developments for the derivation of an analytical formulation are still in progress. A set of interesting elements has been presented in this report. The objective of the present research works (which were not part of the 5BP project) is not yet reached and several steps are still required: - To finalise the analytical formulation for the CHS wall, the right parameter taking the curvature

aspects into account should be derived. This key parameter applied in the Gomes model would lead to an analytical formulation for the CHS wall.

- This formula would give the plastic resistance value for the local mechanism. For complete RHS to CHS joints, this plastic resistance should be combined to the “Ring Model” contribution. - This model will have to be further worked out for braces in compression. In this case, a

reduction factor has to be applied to take into account a loss of resistance due to local instability phenomena.

- At this level, the formula will be then directly applicable to I-profile to CHS joints and RHS to CHS joints. As a last step, the formula will have to be modified so as to allow to cover CHS to CHS joints; in this case, the brace cross-section is not composed of plane walls and this parameter is likely to affect the plastic resistance of the CHS chord.

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Part II Recent developments for the verification of

component and assembly models

II.1 Introduction

Volume 1 presents a full consistent approach for the design of joints between open and/or hollow sections. This approach is based on the component method, i.e. for each individual component the main properties (stiffness, resistance) should be determined and in a second step these properties will be assembled to obtain the joint resistance and stiffness respectively. For quite a number of components detailed rules for the determination of the component properties are given. As these rules are taken from existing standards or other technical publications the validity of the rules has already been proved. However, if rules for new components will be developed, it is necessary to validate such new models at the level of the component and at the level of the joint.

Part I of the present Volume 2 presents the progress of the scientific works achieved during the project with respect to the behaviour of CHS components. Other components have been studied in other CIDECT research projects as for example 5BH [54], 5BS [55], 8D/E [56], 8G [57].

In order to be able to validate such mechanical models at the joint level, i.e. the use of a new component in any joint configuration, a more general tool would be required to validate the mechanical model with test results.

This Part II of Volume 2 presents the progress achieved during this project with respect to the development of such a tool.

In order to validate the mechanical models both test results from literature and numerical simulations can be used. To compare the joint characteristics with test results, a database on test results has been created. This work is briefly presented in section II.2. Several test results were added since the second interims report [3].

Finally a study with FE simulations can be performed in order to validate those configurations where no experimental tests are available. With the aim to cover a large number of different joint configurations, a specific software tool has been developed. With this tool FE models of hollow section joints with different dimensions of the members and different material laws can be generated in a very flexible way. Section II.3 contains more information concerning this FE model generator.

In a next step various FE models have to be calibrated against experimental tests, to ensure the accuracy of the numerical models (see section II.4). In this step the test results of the database can be used.

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II.2

Database on test results

In the literature quite a number of test results can be found. However, in most cases the description of the individual data of such experiments is not complete. In order to validate design models with experimental tests, it is required that the following data are available:

• layout of the test arrangement

• loading and support conditions

• measured geometrical and material data

• measured load-displacement curves • description of the failure mode

For the present research project, literature containing documentations on test results have be reviewed. Tests which are sufficiently complete documented have been collected and a database on test results was created. In order to prepare an more automatic handling of these data, some software tools have been developed to create a visual representation of the joint configuration of the tests on one side and to generate a preliminary FE model from the basic data on the other side. An overview of the tests collected is given in the following tables. In total 320 tests have been introduced in the database. Of course, not all test are fully in line with the scope of the project, but it is hoped that the consideration of those tests may also be helpful for the validation of the models in development.

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Table 1: Joint configurations of experimental test from reference [33]: Joint Column Beam(s) Tests F-∆-diagram Loading

2

✓

Compression

EHS EHS

4

✓

Tension

Σ = 6

5 - Compression 8 - Tension 10 - Bending 6 - Compression + bending CHS CHS 12

✓

Tension + bending Σ = 41

CHS CHS 5

✓

Compression

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Joint Column Beam(s) Tests F-∆-diagram Loading

CHS CHS 3

✓

Compression

Σ = 12

5 1x Compression CHS flat steel (horizontal) 4 1x Tension 14 - Compression CHS flat steel (horizontal) 6 - Tension 12 - Compression 21 - Tension CHS flat steel (vertical) 6 2 x Bending 8 - Compression 8 - Tension CHS flat steel (vertical) 9 - Bending

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Joint Column Beam(s) Tests F-∆-diagram Loading 4 - Compression CHS cross 3 - Tension CHS cross 2 - Compression 6 - Compression 3 - Tension CHS I-profile 7 2 x Bending CHS I-profile 2 - Compression CHS RHS 3 - Compression CHS RHS 1 - Compression Σ = 124

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Table 5: Joint configurations of experimental test from reference [38], [39]: Joint Column Beam(s) Tests F-∆-diagram Loading

CHS flat steel 8

✓

Combinations of compression and tension 2

✓

Compression CHS double flat steel 1

✓

Tension CHS I-profile 8 (4 with floor)

✓

Bending RHS flat steel 8

✓

Different combinations of compression and tension 2

✓

Compression

RHS _{flat steel}double

1

✓

Tension RHS I-profile 8 (4 with floor) 4 x Bending Σ = 38

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86 15 x Bending

RHS RHS

13 - _compressionBending +

Σ = 99

II.3

FE model generator for hollow section joints

In order to prepare a parametrical study a flexible tool to generate various FE models of hollow section joints had to be developed. For the FE-simulation the program system ABAQUS was chosen. This FEM simulation software is suitable because of the interface of the interactive version, which allows to generate FE models with an integrated program language called Python. 8 different types of T-joint configurations with hollow section members were considered, because of their typical, often used basic components. Examples of the chosen configurations are given in Figure 31.

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For the 8 given joint configurations all geometrical properties, as length of the column, height and width of the beam, thickness of profiles, thickness of the welds, etc., can be modified. If an examination of the influence of 1 parameter is required, all the other parameters can be fixed, while the parameter of interest is varied in a given increment. The tool generates all the joints with the different geometrical properties and the simulation to get stress-displacement curves can be started.

The material behaviour of the column and the beam in the simulation can be described by a bi-linear or a tri-bi-linear stress-strain curve (see Figure 32). The properties of the material have to be provided.

Figure 32: Bi- and tri-linear stress-strain curves

Due to the fact that buckling problems were expected in some joint configurations under load, the simulations were controlled by displacement. For these purposes the displacements/rotations of the end of the beam can be set in three individual directions or a combination of them (see Figure 33).

Figure 33: Directions, in which displacements can be applied

The dimensions of the shell elements can be adapted very easily.

The tool can generate for example a RHS-RHS T-joint configuration, where the width of the column RHS-profile is varied from 160 to 200 mm in the increment of 20 mm as demonstrated in Figure 34, while all the other geometrical parameters are fixed. The shell dimensions are kept constant, and the mesh is adjusted automatically. In Figure 35 the height of the beam is varied from 120 to 180 mm in 30 mm steps.

So it is easy to perform systematical parameter studies taking into account the typical parameter characterising hollow section joints (β, γ, τ, etc.).

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Figure 34: Varying the width of the column/chord

Figure 35: Varying the height of the beam/brace

The simulations run with physical and geometrical non-linear algorithms. The chosen element types and dimensions are specified in II.4.

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II.4

Calibration of the FE models

To be sure to get reliable results in the FE simulations and to ensure realistic results of the simulations, which are used to replace real test results, the numerical models have to be calibrated. For this purpose the influence of the shell type, element size, solver algorithm etc. on the simulation results have to be examined, and the results of the numerical simulations have to be compared with test results. It is the aim, to create robust FE models, that reproduce the load-displacement curves of real test results as exact as possible.

The first test results that were used to calibrate the FE model are based on the work of the university of Karlsruhe (see [40]; Table 6). In this study T-joints with RHS columns and RHS beams were tested. The specimen were fixed at the ends of the column and the loads were applied at the end of the beams. The displacements were measured at the point, where loads were applied, in direction of the loads. A principal sketch of the experimental setup is given in Figure 36.

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The test M21, that was reproduced by FE modelling, has the following geometrical properties:

P

460 [mm] 13 00

Figure 37: Geometrical properties of specimen M21

The dimensions of the RHS-profiles, according to the notations given in Figure 36, are: Table 7: Geometrical properties of specimen M21

Joint member h [mm] b [mm] t [mm]

Column 140 140 8,8 Beam 100 100 4,0 The material properties are:

Table 8: Material properties of specimen M21 Joint member fy [N/mm²] fu [N/mm²] εf [-]

Column 335,7 528,9 0,2885

Beam 424,6 527,1 0,33375

where: fy is the yield strength

fu is the ultimate strength

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As the strain when the material reaches the ultimate tensile strength fu is not given, as an

approximation different material laws for the beam and for the column are used, see Figure 38 and Figure 39. An initial stiffness of E=210000 N/mm² is assumed.

0 100 200 300 400 500 600 0 0,05 0,1 0,15 0,2 0,25 0,3 strain [-] str ess [N /mm²] Curve 1 Curve 2 Curve 3 Curve 4

Figure 38: Different approximations of the material law for the column of model M21

0 100 200 300 400 500 600 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 strain [-] stress [N/mm²] Curve 5 Curve 6 Curve 7 Curve 8

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8 node shell elements (S8R-elements in the ABAQUS-library) and 4 node shell elements (S4R- elements in the ABAQUS-library) with reduced integration were tested. The side length was varied between 8 and 4 mm.

By taking thicker shell elements with the width of 0,8a 2 , the welds are considered.

All displacements and loads are plane-symmetric. That means, that modelling only one half of the joint should lead to correct results, if the required boundary conditions are set.

As an example one model with an approximate shell element length of 8 mm is given in Figure 40.

Figure 40: FE model of test specimen M21

In Table 9 the main parameters for the different FE models of test M21 are summarized and the changes are marked. The σ-ε curves are in accordance with those given in see Figure 38 and Figure 39.

Table 9: Main parameters of the FE model M21 Model name Element type Approximate size _{length [mm]} σ-ε curve

column σ-ε curve beam

Further modifications

FEM 21-5 S8R 8 Curve 1 Curve 5 -

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The comparison of the test results and the results of the numerical simulations of M21 is given in Figure 41, where P is the applied load, see Figure 37, and s is the deformation at the point of load introduction. 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 30 35 40 s [mm] P [ k N] Test results FEM M21-5 FEM M21-6 FEM M21-7 FEM M21-8 FEM M21-9 FEM M21-10 FEM M21-11

Figure 41: Comparison test results – FE simulations for specimen M21

The S8R element is an 8 node element, considering thick shell theory. The element S4R is used for thin shells. To avoid shear locking effects, S4R uses reduced integration when determining the stiffness matrix. The S4R results seem to fit better, and the refinement of the mesh has no significant influence on the load displacement curve. The system seems to be convergent.

With σ-ε curve 1 and 5 in the first models stiffness after yielding seems to be underestimated. To raise the gradient of the stress strain curve after yielding, and to describe the material behaviour more realistic, ε at the level of the ultimate stress was reduced, and a zero stiffness after reaching fu was assumed (see Figure 38, Figure 39). With this modifications the joint model produces

sufficient results (see FEM 21-10). The initial stiffness and the behaviour of the joint in the non elastic range is close to the test result.

For FEM 21-11 the σ-ε curves were modified in a way, that the stiffness of the material after yielding is 1/50 of the initial E-modulus. This assumption overestimates the stiffness of the whole joint.

To check the results and to increase the knowledge about robust joint modelling, different other joints tested by the university of Karlsruhe [40] were modelled.

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The measured properties of test specimen M10 are given in Table 10 and Table 11. Table 10: Geometrical properties of specimen M10

Column 100 100 6,3 Beam 80 80 3,6

Column 242,5 353,1 0,3725

Beam 298,5 392,9 0,3706

εf is the plastic strain at tensile failure

As there is again no exact information about the stress-strain curve, different material laws for the beam and for the column are tested, see Figure 42 and Figure 43.

0 50 100 150 200 250 300 350 400 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 strain [-] stress [N/mm²] Curve 1 Curve 2

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0 50 100 150 200 250 300 350 400 450 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 strain [-] stress [N /m m ²] Curve 3 Curve 4

Figure 43: Different approximations of the material law for the beam of model M10

The main parameters of model M10and their variation are summarized in Table 12.

The load displacement curves and the comparison to the test result are given in Figure 44.

column

σ-ε curve beam

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0 2 4 6 8 10 12 14 16 18 20 0 10 20 30 40 50 60 s [mm] P [ kN] Test results FEM M10-1 FEM M10-2 FEM M10-3

The results of this comparison confirm the previous conclusion, that element type S8R is not adequate for such simulations. The simulation of FEM 10-1, where S8R is used, is aborted after 30 mm displacement. The simulation FEM 10-3 with the reduced ε 'at the level of ultimate strength

(1/4 of the value in FEM 10-1 and FEM 10-2) fits very well. The initial stiffness and the load displacement curve after yielding is very close to the test result.

The calibration is repeated with test M78, taken from [40].

The measured properties of test specimen M78 are given in Table 13 and Table 14. Table 13: Geometrical properties of specimen M78

Column 180 180 14,2 Beam 100 100 6,3

Column 227,7 380,1 0,324

Beam 242,5 353,1 0,3725

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In this model a stress-strain curve with a reduced ε at the ultimate strength level (∼1/4 of εf) is used

directly, because of the results of the former tests.

The used curves for the column and for the beam are given in Figure 45 and Figure 46.

0 50 100 150 200 250 300 350 400 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 strain [-] st ress [ N /mm² ] Curve 1

Figure 45: Material law for the column of model M78

0 50 100 150 200 250 300 350 400 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 strain [-] st ress [ N /mm² ] Curve 2

Figure 46: Material law for the beam of model M78

The main parameters of model M78and their variation are summarized in Table 15.

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column

σ-ε curve beam

FEM 78-4 S4R 5 Curve 1 Curve 2

The whole joint was modelled (not only one half with axis symmetric boundary conditions) 0 10 20 30 40 50 60 0 5 10 15 20 25 30 35 40 s [mm] P [k N] Test results FEM M78-1 FEM M78-2 FEM M78-3 FEM M78-4

The results of this simulation confirm again, that S4R elements work well, even if the walls of the RHS profiles are thick (14,2 mm). The mesh refinement has no significant influence and the boundary conditions are set correctly, so that the results of the model, where only one plane symmetric part is modelled to increase the efficiency of the simulation, lead to correct results (see Figure 48 and Figure 49).

Considering all the simulations of the test one arrives at the conclusion that using the ABAOQUS 4-node elements S4R with a material behaviour close to the stress strain curve of the real material leads to sufficient results.

With this knowledge further test results are rechecked by using S4R elements when generating the models with the tool described in section II.3.

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Figure 48: Test specimen FEM 78-2 under load

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The next test, that are reproduced by FE simulation are part of the work presented by Y. Makino, Y. Kurobane, J.C. Paul, Y. Orita and K. Hiraishi in 1991 (see [37] and Table 4).

In this tests X- and T-joints were examined under normal- and bending loads of the beam. The column was always a CHS-profile with different geometrical properties, while the profile types of the beams were diversified.

The joint that was reproduced by FE modelling was a X-joint with horizontal gusset plates under tension and compression. The geometrical properties of the joints are given in Figure 50 and Figure 51.

Figure 50: Dimensions of test specimen XP-1-C-1

Figure 51: Dimensions of test specimen XP-1-T-1

For this test specimen there is no information about the measured material properties available. Because of this lack of information a bi-linear stress strain curve with a theoretical value of 488 N/mm² for fy is used for the simulation of test XP-1-C-1 and XP-1-T-1. This value is obtained from

an expression given in [37].

Loads and displacements of the specimen are double symmetric, so that only a quarter of the structure had to be generated. The mesh for the simulation of test XP-1-C-1 is given in Figure 52.

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Figure 52: Mesh of test specimen FEM XP1-Compression

The load displacement curve of the specimen under compression is given in Figure 53.

0 50 100 150 200 250 300 350 400 450 0 5 10 15 20 25 30 s [mm] P [kN] Test results FEM XP1-Compression

Figure 53: Load displacement curves of X-joint XP1-C-1 under compression (FEM and test results)

With regard to the ultimate resistance the FE model doesn't fit exact with the test results. But as said above, there is poor information about the material behaviour. The buckling of the CHS profile, can be identified in the FE simulation. The deformed specimen is given in Figure 54.

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Figure 54: FEM XP1-C-1 under compression loads

The results of the same joint configuration under tension loads are given in Figure 55.

0 100 200 300 400 500 600 700 800 0 5 10 15 20 25 s [mm] P [ k N] Test results FEM XP1-Tension

Figure 55: Load displacement curves of X-joint XP1-T-1 under tension (FEM and test results)

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After analysing all FE simulations carefully, the results lead to the conclusion, that real test results can be reproduced by FE modelling in a sufficient way. If there is enough information about the material behaviour and the test setup, the load displacement curves derived from numerical simulations are nearly identical with those ones measured at real tests.

Effects like buckling and yielding can be simulated, and the computation runs reliable, if the ABAQUS shell elements S4R are used. In its final version the FE model generator uses for all required joint configurations shell elements S4R. The size length has to be specified adequate.

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References

[1] K. WEYNAND, J.P. JASPART

“Application of the component method to joints between hollow and open sections” CIDECT research project 5BM; Aachen, Liège, 2002.

[2] J.P. JASPART, K. WEYNAND, R. KLINKHAMMER

“Development of a full consistent design approach for bolted and welded joints in building frames and trusses between steel members made of hollow and/or open sections - Application of the component method”

CIDECT research project, First interim report 5BP-6/03, Aachen, Liège, 2003. [3] J.P. JASPART, K. WEYNAND, R. KLINKHAMMER

“Development of a full consistent design approach for bolted and welded joints in building frames and trusses between steel members made of hollow and/or open sections - Application of the component method”

CIDECT research project, Second interim report 5BP-4/04, Aachen, Liège, 2004. [4] P. ANSOURIAN

“Rigid-frame connections to concrete-filled tubular steel columns” CRIF report, MT 86, Belgium, January 1974.

[5] COST C1 European Research Action on “Control of the semi-rigid behaviour of civil engineering structural connections”, 1991, 1999.

Belgian contribution, Fourth semestrial report, Period 16.03.94 to 15.09.94, University of Liège, Department MSM.

[6] D. VANDEGANS

“Liaison entre poutres métalliques et colonnes en profils creux remplis de béton, basée sur la technique du goujonnage (goujons filetés)”

CRIF report, MT 193, Belgium, October 1995. [7] X. NAVEAU, R. MAQUOI, J. RONDAL

“Assemblages de charpente métallique basés sur la technique du goujonnage” CRIF report, MT 152, Belgium, May 1983.

[8] F.C.T. GOMES

“Etat-limite ultime de la résistance de l’âme d’une colonne dans un assemblage semi-rigide d’axe faible”

Université de Liège, MSM Department, Internal report N° 203, Belgium, August 1990. [9] Y.W. KIM

“The behaviour of beam-to-column web connections with flush end plates”

Ph. D. Thesis, University of Warwick, Department of Engineering, U.K., July 1988. [10] J.E. FRANCE

“Bolted connections between open section beams and box columns”

Ph. D. Thesis, University of Sheffield, Department of Civil and Structural Engineering, U.K., January 1997.

[11] JASPART, J.P.

"Recent advances in the field of steel joints – Column bases and further configurations for beam-to-column joints and beam splices"

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[12] R. MAQUOI, B. CHABROLIN

“Frame design including joint behaviour”

ECSC Report 18563, Office for Official Publications of the European Communities, Luxembourg, 1998.

[13] BSCA and SCI

“Joints in Steel Construction – Moment Connections”

Publication 207/95,The Steel Construction Institute, Ascot, U.K, 1995. [14] L.F.C. NEVES, F.C.T. GOMES

“Semi-rigid behaviour of beam-to-column minor axis joints”

Proceedings of the IABSE Colloquium on Semi-Rigid Structural Connections, Istanbul, Turkey, September 25-27, 1996, pp. 207-216.

[15] L.F.C. NEVES

“Nos semi-rigidos em estruturas metalicas. Avaliaçao da rigidez em configuraçoes de eixo fiaco”

Master Thesis, University of Coimbra, 1996. [16] FINELG Non-linear Finite Element Programme

Department MSM, University of Liège, Belgium [17] J.P. JASPART

“Etude de la semi-rigidité des assemblages poutre-colonne et de son influence sur la résistance et la stabilité des ossatures en acier”

PH.D. Thesis, Department MSM, University of Liège, Belgium, 1991. [18] D. VANDEGANS

“Use of threaded studs in joints between I-beams and RHS columns”

Proceedings of the IABSE Colloquium on Semi-Rigid Structural Connections, Istanbul, Turkey, September 25-27, 1996, pp. 53-62.

[19] N. FERTE

“Étude du comportement d’assemblages d’axe faible en construction métallique - Comparaison d’approches théorique et expérimentale”

Diploma work form C/U/S/T Clermont-Frerrand – Work carried out at the Department MSM, University of Liège, Belgium, 2001.

[20] K. WEYNAND, J.-P. JASPART et al “CoP - The Connection Program”

PC software for the calculation of joints in steel building frames, Aachen, Liège, 1997-2001. [21] CEN

prEN 1993 “Eurocode 3 Design of Steel Structures”, Brussels, 2003. [22] CEN

prEN 1993-1-8: 2003

“Eurocode 3: Design of steel structures – Part 1.8: Design of joints” Brussels, 05 May 2003.

[23] CEN EN 1994-1-1

“EN 1994 Design of composite steel and concrete structures – Part 1.1: General rules and rules for buildings”

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[24] R. PUTHLI

“Hohlprofilkonstruktionen aus Stahl“

Werner Verlag, 1998 – ISBN 38-04129-75-7. [25] F. GRIMM

“Konstruieren mit Walzprofilen“

Verlag Ernst und Sohn, 2003 – ISBN 3-433-02840-0. [26] F. GRIMM

“Konstruieren mit Hohlprofilen“

Verlag Ernst und Sohn, 2003 – ISBN 3-433-02833-8. [27] L.F.C. NEVES, F.C.T. GOMES

“Semi-rigid behaviour of beam-to-column minor axis joints”

September 1996 – Proceedings of the LABSE Colloquium, Istanbul, Turkey, p. 207 – 216. [28] C. BRASSIER

“Caractérisation du comportement en rotation d’assemblages soudés de construction métallique en poutre en I et poteau tubulaire de forme circulaire – Développement d’une méthode analytique ”

June 2003 – Diploma work, Department M&S, University of Liège – CUST Clermont-Ferrand. [29] J. MARRA

“Assemblage dans les poutres en treillis tubulaire de section elliptique” June 2003 – Diploma work, Department M&S, University of Liège. [30] C. PIETRAPERTOSA

“Etude du comportement des assemblages soudés de poutres en treillis constitués de profilés métalliques tubulaires de forme elliptique”

June 2002 – Diploma work, Department M&S, University of Liège. [31] J. WARDENIER

“Hollow section joints”

1982 – Delft University Press, Delft (The Netherlands). [32] J. WARDENIER

“Hollow section in structural applications”

CIDECT – Bouwen met Staal, 2002 – ISBN 90-72830-39-3. [33] ”Experimental test – EHS joints”, Internal report, Univ. Liège 2003. [34] S. WILLIBALD, J.A. PACKER, R. S. PUTHLI

”Bolted connections for RHS tension members” University of Toronto

Draft Final Report, CIDECT Project: 8D / 8E, Report 8D / 8E – 8/02. [35] Y. KUROBANE, Y. MAKINO, K. OGAWA, T. MARUYAMA

”Capacity of EHS-joints under combined OPB and axial loads and its interactions with frame behaviour”

Kumamoto University, Japan

Tubular Structures, 4th_{International Symposium, Delft 1991.}

[36] J.C. PAUL, T. UENO, Y. MAKINO, Y. KUROBANE ”The ultimate behaviour of circular multiplanar TT-joints” Kumamoto University, Faculty of Engineering, Japan

Cidect 5bp 4-05 Part 2

DEVELOPMENT OF A FULL CONSISTENT DESIGN APPROACH FOR

BOLTED AND WELDED JOINTS IN BUILDING FRAMES AND TRUSSES

BETWEEN STEEL MEMBERS MADE OF HOLLOW AND/OR OPEN

SECTIONS

-

APPLICATION OF THE COMPONENT METHOD

VOLUME 2 - PROGRESS OF THE SCIENTIFIC ACTIVITIES ON JOINT

COMPONENTS AND ASSEMBLY

TABLE OF CONTENTS

Foreword

Part I Recent developments for the derivation of an

analytical formulation for CHS wall components

I.1 Introduction

I.1.1 Summary of the interim report (5BP-4/04 – August 2004)

F

F

I.1.2 Objectives expressed in the second interim report

I.1.3 Research strategy

I.1.4 Research steps

External

mechanism

Ring model

OK

I.2 Direct analytical approach

I.3 Numerical

study

I.3.1 Validation of the FEM tool

I.3.2 Definition of the numerical model for the study of the CHS component

I.3.3 Parametrical study

5.0

1 0.81

−

⋅

β

I.3.4 Correlation with Gomes model

4

2

1

1

m

b

c

Npl

b

L

L

L

π

π









=







−



+













−

L’

0

0

P

L

P

α

∂



=

∂

 ∂

₂

_b

_c

_

_

_

_

_

_

₌

₌