Doctoral study programme: CIVIL ENGINEERING Branch of ...k134.fsv.cvut.cz/odk/cz/docs/Disertace/Disertace-Szabo.pdfpomůcky pro výpočet smykové i rotační tuhosti stěny podle

CZECH TECHNICAL UNIVERSITY IN PRAGUE

FACULTY OF CIVIL ENGINEERING

Doctoral study programme: CIVIL ENGINEERING

Branch of study: BUILDING AND STRUCTURAL ENGINEERING

Ing. Gábor Szabó

INTERACTION BETWEEN STEEL COLUMN AND CASSETTE WALL

Doctoral thesis for obtaining the Degree of “Doctor of Philosophy”,

abbreviated to “Ph.D.”

Supervisor: Doc. Ing. Tomáš Vraný, CSc.

Jun 2009, Prague

Gábor Szabó Interaction between steel column and cassette wall

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Abstract

Members with high slenderness are commonly used in steel structures. Those members’ load carrying capacities are limited due to global instability. One way to reduce this handicap is through lateral stabilization. Sheeting, which is commonly part of the structure and is primarily designed for exterior load only, could be included in the member global stability check. This may lead to a more efficient design of compression members.

In this thesis the positive effect of cassette wall cladding on the behaviour of structural members is investigated. This is commonly known as stressed skin design. Experimental investigation and numerical modelling were used to determine the favourable effect of the cladding made by cassette profiles. A parametric study was carried out to extend the experimentally obtained results.

The experimental work consisted of two parts. In the first part, the cassette wall torsional stiffness is determined. Altogether 17 specimens were tested with different sheeting thicknesses, fastener arrangements and connected flange properties. As a result, an equation was worked out for the calculation of the rotational stiffness of the cassette profile. This part of the thesis was used as the input parameter for following work.

Before the second part of the experimental investigation, the numerical model was prepared and the best arrangement of the model was worked out by ANSYS software package. The second type of experimental investigation included beam-columns full-scale tests and considered the load-carrying capacity and failure mode. The beam-columns were stabilized by cassette wall. Overall six specimens were prepared and tested. The beam-column cross section used was IPE300 in steel grade S355. The member's system lengths were 5330 mm and 5680 mm depending on the boundary condition. The loading was applied by end cantilevers which ensured combined bending-compression loading. The ratio between the bending moment and axial force was 1 m. Specimens were selected to include different sheeting stiffness, sheeting position and boundary condition. The results demonstrated that connected sheeting could fully stabilize the member against lateral-torsional buckling in cases when the sheeting is connected at compressed flange. In other case (connected at tensioned flange) torsional buckling failure occurred about imposed axis.

The above mentioned numerical model, which was used to predict the most suitable specimens, was updated, improved and calibrated by results from experiments. A parametric study was carried out to extend the experimentally obtained results with the help of numerical models. The parametric study was executed for hot rolled IPE and HEA profiles for different lengths and more cassette walls and bending moment distribution.

The main results of the thesis are wall stiffnesses which performed full or partial stabilization for specific member. These stiffnesses depend on wall properties and were calculated according to ECCS recommendation. Besides, the impact of rotational stiffness of sheeting was followed.


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Pro ocelové konstrukce se běžně používají pruty s vysokou štíhlostí. Únosnost takových prutů je často omezena globální ztrátou stability. Jedním ze způsobů omezení této nevýhody je příčné podepření. Plášť, který je součástí běžné konstrukce a je navržen primárně na přenos vnějšího zatížení, může být zahrnut do posouzení globální stability prutu. Takový postup umožňuje zvýšit efektivitu návrhu tlačených a ohýbaných štíhlých prutů.

Dizertační práce vyšetřuje kladný účinek kazetové stěny, připojené k ocelovému prutu. Využívá se plášťové působení stěny. Pro analýzu příznivého účinku se použilo experimentální vyšetřování a numerické modelování. Byla též provedena parametrická studie pro rozšíření získaných výsledků.

Experimentální část práce se skládala ze dvou částí. V první se určovala rotační tuhost přípoje kazetové stěny na sloup. Bylo provedeno 17 zkoušek s různou tlouštkou plechu kazety, uspořádáním šroubů a šířkou pásnice připojeného sloupu. Na základě zkoušek a numerického modelování byly odvozeny rovnice pro určení rotační tuhosti přípoje kazetového profilu k pásnici sloupu. Získané výsledky sloužily jako vstupní hodnoty pro další vyšetřování.

Druhou část experimentální práce předcházelo numerické modelování programem ANSYS pro zjištění nejvhodnějšího uspořádání zkoušky. Vyšetřoval se sloup skutečné velikosti namáhaný ohybem a tlakem, stabilizovaný připojenou kazetovou stěnou. Zjišťovala se jeho únosnost a způsob porušení. Bylo provedeno šest zkoušek. Byl použit profil IPE300 z oceli jakosti S355. Délka sloupů byla 5330 mm a 5680 mm v závislosti na okrajových podmínkách. Zatížení bylo aplikováno pomocí konzol pro dosažení kombinovaného namáhání tlakem a ohybem. Poměr osové síly k ohybovému momentu byl 1 m. Výsledky potvrdily, že v případě, kde je kazetová stěna připojená k tlačené pásnici, může plně stabilizovat prut proti ztrátě stability z roviny ohybu. V případě připojení k tažené pásnici dochází k ztrátě stability s vnucenou osou otáčení.

Numerický model použitý k návrhu experimentu byl vylepšen, zkalibrován podle výsledků experimentů a následně použit pro parametrickou studii. Parametrická studie byla provedena metodou GMNIA pro válcované profily řady IPE a HEA pro různé délky, jakosti oceli, tuhosti kazetové stěny a průběh ohybového momentu po délce prutu.

Z parametrické studie byly odvozeny potřebné tuhosti kazetové stěny pro úplnou nebo částečnou stabilizaci prutu v závislosti na výše uvedených vstupních parametrech. Dále byly vypracovány pomůcky pro výpočet smykové i rotační tuhosti stěny podle doporučení ECCS a vlastních výsledků. Byl též určen vliv rotační tuhosti přípoje stěny k prutu na jeho únosnost.


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Acknowledgements

This project was worked out in Steel and Timber Department at the Faculty of Civil Engineering in the Czech Technical University in Prague during 2004 – 2008. I am grateful for all expert help of mine supervisor Prof. Tomas Vrany.

I would like to acknowledge for the project financial support provided by the Czech Technical University (internal grant IG ČVUT CTU0502311 - 2005), the Ministry of Education, Youth and Sport of the Czech Republic (grant FRVŠ 1820 - 2006) and the support of the research project of the Czech Ministry of Education (grant no. 6840770003).

The experimental part of the project was conducted in the Experimental Centre of CTU. I am thankful to all the technicians who contributed to the work.

I would like to thank Ing. Vitezslav Hapl with whom I carried out the experimental part of the project, and for his advices during the work. Further thanks should also be given to all members of Steel and Timber Department for they reconciliation, extremely to colleagues from room D1064.

I am also grateful to Dr. Martin Heywood of The Steel Construction Institute (Ascot, UK) who has helped me with the language correction.

Finally, I will always be grateful to my wife Rose and my family for their support and encouragement throughout my study.


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Contents

Abstract ....................................................................................................................................................1

Acknowledgements ..................................................................................................................................3

Notation....................................................................................................................................................7

List of figures .........................................................................................................................................10

List of tables...........................................................................................................................................13

Chapter 1 Introduction ......................................................................................................................14

1.1. Background...........................................................................................................................14

1.2. Application of cassette wall..................................................................................................14

Chapter 2 Literature review ..............................................................................................................17

2.1. Stressed skin action...............................................................................................................17

2.1.1. Research overview ...........................................................................................................17

2.1.2. Principle of stressed skin action .......................................................................................17

2.1.3. Existing design procedures for cassette walls ..................................................................18

2.2. Members in bending and axial compression.........................................................................22

2.3. Interaction between sheeting and beam-columns .................................................................23

2.3.1. Interaction.........................................................................................................................23

2.3.2. Research overview ...........................................................................................................24

2.3.3. Idealization of stabilization effect ....................................................................................25

2.3.4. Existing design procedures...............................................................................................26

Chapter 3 Thesis objectives ..............................................................................................................33

Chapter 4 Experimental study...........................................................................................................34

4.1. Introduction ..........................................................................................................................34

4.2. Rotational stiffness ...............................................................................................................34

4.2.1. Experiments overview......................................................................................................35

4.2.2. Measured values ...............................................................................................................38

4.3. Full-scale tests of beam-column with cassette wall..............................................................41

4.3.1. Experiments overview......................................................................................................42

4.3.2. Imperfection .....................................................................................................................47

4.3.3. Measured values ...............................................................................................................50

4.3.4. Results of experiments .....................................................................................................53


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4.4. Additional tests..................................................................................................................... 55

4.4.1. Material properties ........................................................................................................... 55

4.4.2. Fasteners stiffness ............................................................................................................ 56

Chapter 5 Numerical modelling ....................................................................................................... 58

5.1. Introduction .......................................................................................................................... 58

5.2. Pre-modelling of specimens ................................................................................................. 58

5.2.1. Used elements, materials, boundary conditions and load ................................................ 58

5.2.2. Conclusions from pre-modelled specimens ..................................................................... 61

5.3. Experimentally tested specimen models .............................................................................. 61

5.3.1. Calibration ....................................................................................................................... 64

5.4. Parametric study................................................................................................................... 66

5.4.1. Parametric study assumptions.......................................................................................... 67

Chapter 6 Analysis of results .................................................................................................... 68

6.1. Rotational stiffness of cassette profile ................................................................................. 68

6.2. Behaviour of column supported by cassette wall ................................................................. 70

6.2.1. Experimentally obtained results....................................................................................... 71

6.2.2. Results from parametric study ......................................................................................... 71

Chapter 7 Conclusions...................................................................................................................... 91

References ............................................................................................................................................. 93

Appendix A – Tables of measured data................................................................................................. 96

Appendix B – Calculation example..................................................................................................... 103


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Notation

a stiffness factor derived from tests according to ECCS [kN/mm]

A cross section area

b1, b2 distance between screw and cassette profile edge / column flange edge

B whole length of the diaphragm B=ΣBu

Bo width of the narrow flange of a cassette

Bu width of the wide flange of a cassette

c total shear flexibility of a diaphragm [mm/kN]

ci,j component shear flexibilities for diaphragm [mm/kN]

cA rotational stiffness of the fasteners between sheeting and members [kNm/rad]

cM rotational stiffness of the sheeting profiles [kNm/rad]

cP rotational stiffness due to the distortion of the member [kNm/rad]

C rotational stiffness of a diaphragm [kNm/rad]

Cexp rotational stiffness of cassette profile determined experimentally

Ccalc calculated rotational stiffness of cassette profile

Cmy, Cmz equivalent uniform moment factors

Cyy, Cyz, etc. Factors

eL distance between fasteners in edge members

eNy ,eNz shift of the centroid of the effective area Aeff relative to the centre of gravity of the gross cross section

es distance between fasteners in adjacent cassettes

E modulus of elasticity

FL resistance of the fastener between cassette and edge member

Fp resistance of the fastener between cassette and framework

Fs resistance of the fastener between adjacent cassettes

fy steel yield strength

G shear modulus

h depth of the section


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iy, iz, ip gyration radius

I1 second moment of area of the wide flange of a cassette about the longitudinal axis of the cross section per metre [mm4/mm] , see Fig.7.

Iy second moment of area about the y-y axis

Iz second moment of area about the z-z axis

Iz,G second moment of area of the wide flange of a cassette about own centroid [mm4]

IT St. Venant torsional constant

Iω warping constant

Kυ factor for considering the type of analysis

Kq factor for considering the moment distribution and the type of restraint

L length of the diaphragm between columns, length of the column

M bending moment

Mcr elastic critical moment for lateral-torsional buckling

Mpl,k characteristic value of the plastic moment of the beam

My,Ed, Mz,Ed factored bending moment, y-y axis, z-z axis

MPl,y,, MPl,z member design plastic moment resistance about axis y-y, z-z

Ncr elastic critical force for the relevant buckling mode based on the gross cross sectional properties, critical flexural buckling load

NEd factored normal force

nf number of fasteners in the cassette web between cassette and framework

np number of columns per diaphragm

ns number of fasteners in the cassette web between adjacent cassettes

nsc number of fasteners between cassette web and edge member

nsh number of cassettes per diaphragm

Pmax shear resistance of diaphragm due to fasteners failure

P distance between fasteners cassette – framework [mm]

R member resistance

Rwithout_rot member resistance without elastic rotational support

Rwith_rot member resistance with elastic rotational support

S shear stiffness of diaphragm

S1 stiffness of the fasteners between the sheeting and the connected member

S2 stiffness of the cassette profile in own plane

S3 stiffness of the fasteners between the adjacent cassette members

Sact’ shear stiffness of diaphragm per unit length [kN/mm]

sp slip per sheet fastener shear flexibility [mm/kN]


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ss shear flexibility of the fastener in the cassette wall between adjacent cassettes [mm/kN]

ssc shear flexibility of the fastener between cassette and edge member [mm/kN]

t sheet core thickness excluding metallic and other coatings [mm]

Td minimal shear force in shear panel

Tv shear force in the diaphragm caused by the load in the serviceability limit state

TV shear flow in the ultimate limit state of fasteners

TV,L shear flow in the ultimate limit state of fasteners between cassette and edge member of wall

TV,Q shear flow in the ultimate limit state of fasteners between cassette and framework.

TV,S shear flow in the ultimate limit state of fasteners between adjacent cassettes

Vbuc shear resistance of diaphragm due to cassette profile failure

Weff,y,min, Weff,z,min minimum effective section modulus about y-y axis, z-z axis

α* factor for material non-linear behaviour

Β* factor for material non-linear behaviour

β1 fastener number factor between cassette and framework per sheet width

γM partial safety factor

λ slenderness of the member

μy, μz Factors

υ Poisson's ratio

χ reduction factor for the relevant buckling curve

χLT reduction factor for lateral-torsional buckling

χy, χz reduction factors due to flexural buckling, y-y axis, z-z axis

Ø rotational deflection [rad]

ΔMy, ΔMz moments due to the shift of the centroidal y-y, z-z axis


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List of figures

Fig.1. Cassette profile..................................................................................................................... 15

Fig.2. Possible cassette wall constructions, a) direct connection, b) non-direct connection of the covering panel........................................................................................................................................ 16

Fig.3. Longitudinal stiffeners in wide flange.................................................................................. 18

Fig.4. Cassette profile with geometrical properties ........................................................................ 19

Fig.5. Secondary structures connected on column A) bracing, B), C) covering systems............... 24

Fig.6. Idealization of interaction..................................................................................................... 25

Fig.7. Lindner’s model of independent stiffnesses......................................................................... 27

Fig.8. Ratio between stiffnesses S and C........................................................................................ 29

Fig.9. Assumed deflection of the element to stabilize with the resulting concentrated force at the supports ……………………………………………………………………………………………..30

Fig.10. Notation and sign definitions ............................................................................................... 32

Fig.11. Rotational stiffness about x-x axis. ...................................................................................... 34

Fig.12. Column flange replacement ................................................................................................. 35

Fig.13. Screws arrangement ............................................................................................................. 36

Fig.14. Used steel plates replacing column flange, dimensions, position of fasteners..................... 36

Fig.15. Used cassette profiles ........................................................................................................... 37

Fig.16. Draft of the experiments....................................................................................................... 37

Fig.17. The specimen, side-view, front-view ................................................................................... 38

Fig.18. Measured values................................................................................................................... 39

Fig.19. Deformed specimen.............................................................................................................. 39

Fig.20. Load deflection curves from experimental investigation, marked with respect of Tab. 3. .. 40

Fig.21. Specimen static scheme........................................................................................................ 42

Fig.22. Specimen V2 ........................................................................................................................ 42

Fig.23. Main frame joint; Set “V” .................................................................................................... 44

Fig.24. Main frame joint; Set “K” .................................................................................................... 44

Fig.25. Boundary conditions, specimens V and K ........................................................................... 45

Fig.26. Plan view – main frame and additional frame...................................................................... 45

Fig.27. Additional frame (with reference to Fig.26) ........................................................................ 46

Fig.28. Additional frame, specimen V3 with one sided wall ........................................................... 46


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Fig.29. The loading point with hydraulic jack and the support.........................................................47

Fig.30. Measured lateral imperfection of specimen V1....................................................................48



Fig.33. Measured lateral imperfection of specimen K1....................................................................49



Fig.36. Sensors arrangement, set V, top view...................................................................................50

Fig.37. Sensors arrangement, set V, side view .................................................................................51

Fig.38. Sensors arrangement, set K, top view...................................................................................52

Fig.39. Sensors arrangement, set K, side view .................................................................................52

Fig.40. Failure mode, V1 ..................................................................................................................53

Fig.41. Failure mode, K1 ..................................................................................................................53

Fig.42. Failure mode V2, K2 ............................................................................................................54

Fig.43. Failure mode V3 ...................................................................................................................54

Fig.44. Failure mode K3 ...................................................................................................................54

Fig.45. Load-deflection curves for all specimens, measured by gauge U3. .....................................55

Fig.46. Relative deflection between compressed and tensioned flanges. .........................................55

Fig.47. Fastener experiments arrangement .......................................................................................56

Fig.48. Force – displacement curves for specimens KK, one screw (both sheet thickness 0,75mm). ……………………………………………………………………………………………..57

Fig.49. Force – displacement curves for specimens KS, one screw (sheet thickness 0,75mm, steel plate thickness 10mm). ..........................................................................................................................57

Fig.50. Geometry of element SHELL181.........................................................................................59

Fig.51. Geometry of element COMBIN39, element force-deflection curve ....................................59

Fig.52. The model of the wall provided by spring elements.............................................................60

Fig.53. Specimen with load and boundary condition........................................................................61

Fig.54. Models boundary conditions K1, V1....................................................................................62

Fig.55. Beam-column material model (stress in MPa) .....................................................................62

Fig.56. Cantilever and additional frame material model...................................................................63

Fig.57. Elements BEAM188 as additional frame .............................................................................63

Fig.58. Comparison of load-deflection diagrams from model and experiment for specimens V1, K1. ……………………………………………………………………………………………...64

Fig.59. Comparison of load-deflection diagrams from model and experiment for specimens K2, V2. ……………………………………………………………………………………………...64

Fig.60. Comparison of load-deflection diagrams from model and experiment for specimens K3, V3. ……………………………………………………………………………………………...65


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Fig.61. Relative deflection of compressed and tensioned flange, comparison between model and experiment, specimens K1, V1.............................................................................................................. 65



Fig.64. Moment distribution............................................................................................................. 67

Fig.65. Decisive values, deformed specimen ................................................................................... 69

Fig.66. Linear approximation of stiffness for screw arrangement 2x2............................................. 69

Fig.67. Linear approximation of stiffness for screw arrangement 2x3............................................. 69

Fig.68. Numerical model of the connection loaded by positive bending moment, von Mises stress in MPa. ……………………………………………………………………………………………..70

Fig.69. Ratio between load carrying capacity for rotationally supported and non-supported members IPE – boundary condition “K”, supported at tensioned or compressed flange ...................... 71

Fig.70. Ratio between load carrying capacity for rotationally supported and non-supported members IPE – boundary condition “V”, supported at tensioned or compressed flange ...................... 72

Fig.71. Ratio between load carrying capacity for rotationally supported and non-supported members HEA – boundary condition “K”, supported at tensioned or compressed flange.................... 72

Fig.72. Ratio between load carrying capacity for rotationally supported and non-supported members HEA – boundary condition “V”, supported at tensioned or compressed flange.................... 72

Fig.73. Ratio between load carrying capacity for rotationally supported and non-supported members with length 6000 mm, impact of section torsional stiffness................................................... 73

Fig.74. Compressed flange lateral deflection for different wall properties; A three cases: without support, cassette wall support, full support, B two cases: cassette wall support, full support (same graph with larger scale) ......................................................................................................................... 74

Fig.75. Compressed flange lateral deflection for different wall stiffness, section IPE300 (t-thickness, ns-number of screws, cl-cassette profile length)................................................................... 75

Fig.76. Compressed flange lateral deflection for different steel grade, sections: IPE140, L=4 m; IPE300, L=8.4 m ................................................................................................................................... 76

Fig.77. Calculation tool for wall stiffness calculation...................................................................... 90


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List of tables

Tab. 1 Factor Kυ for considering the moment distribution and the type of restraint 28

Tab. 2 Factor Kυ for considering the moment distribution and type of restraint according to [25]

28

Tab. 3 Specimen overview and the experimentally obtained results 41

Tab. 4 System lengths 43

Tab. 5 List of specimens 43

Tab. 6 Summary of measured imperfections 50

Tab. 7 Steel properties 56

Tab. 8 Comparison table 65

Tab. 9 Required stiffness for V, section IPE – supported compressed flange 78

Tab. 10 Required stiffness for V, section IPE – supported tensioned flange 79

Tab. 11 Required stiffness for V, section IPE – supported compressed and tensioned flange

80

Tab. 12 Required stiffness for K, section IPE – supported compressed flange 81

Tab. 13 Required stiffness for K, section IPE – supported tensioned flange 82

Tab. 14 Required stiffness for K, section IPE – supported compressed and tensioned flange

83

Tab. 15 Required stiffness for V, section HEA – supported compressed flange 84

Tab. 16 Required stiffness for V, section HEA – supported tensioned flange 85

Tab. 17 Required stiffness for V, section HEA – supported compressed and tensioned flange

86

Tab. 18 Required stiffness for K, section HEA – supported compressed flange 87

Tab. 19 Required stiffness for K, section HEA – supported tensioned flange 88

Tab. 20 Required stiffness for K, section HEA – supported compressed and tensioned flange

89


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Chapter 1

Introduction

1.1. Background

Cassette walls are commonly used as cladding systems, which belong to the light weight facings. Nowadays these types are widely used for framed structures. Among the main advantages of this system is the simple assembly that arises from the low weight of the light gauge wall members. A wide range and high quality of those members increase the demand for the cassette walls.

Load-bearing frames provide support for cassette walls. Wall members are connected to the outer flange of the column. Cassette walls, which can provide load into own plane, contribute to the global stability of the building. The shear stiffness of the whole wall consisting of cassette profiles and trapezoidal panels depends on many variables. Support of column provided by cassette wall is generally assumed as a continuous lateral elastic support.

1.2. Application of cassette wall

One of the progressive cladding systems which are nowadays used for the steel framed structures is cassette wall. The main advantages of this system are [1]:

quick and simple installation,

simple details,

ensuring bracing without additional members,

stabilization of joined slender elements,

replacement of static function of girt with cassette profile,

high surface quality.

The cassette profile contains one wide, two narrow flanges and two web elements, see Fig.1. Particular elements of the cassette are commonly stiffened by longitudinal stiffeners because they are made from light gauge steel. The members have high slenderness ratio and it causes susceptibility to local buckling of the wall or flange, buckling due to shear forces or distortional buckling.


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Fig.1. Cassette profile

The cassette profiles are connected to the steel or concrete column flange face by screws or pins. Profiles are fitted to each other and the gaps between them are sealed with insulation strip. The connection between adjacent cassette profiles is ensured by self-tapping screws. The cassettes are filled with insulation panels due to increasing thermal properties of the wall. The system of insulated cassettes is closed with trapezoidal panels which are connected with screws. The trapezoidal panels may be connected directly to the narrow flange of the cassette wall or with help of distance profiles. These two connection modes of trapezoidal panel are illustrated on Fig.1. In the first type, either distance screws or insulation tape are used between cassette profile narrow flange and trapezoidal profile to improve the insulation capability of the wall. The thermal bridge at the cassette web may be reduced by an additional insulation layer between the cassette flange and trapezoidal panel. In the second type, (Fig.1 B) the additional profiles are added between the trapezoidal profile and cassette profile. This layout allows the trapezoidal profile to be fixed horizontally. Insulation material is used at the place of the contact of the steel members. The trapezoidal profile provides a covering function against the climate action and restrains the cassette profile section against the distortion.

1. cassette,

2. trapezoidal panel,

3. thermal insulation,

4. thermal insulation tape,

5. sealing tape between cassettes,

6. thread forming screws or pin connectors,

7. self-tapping screws,

8. thread forming screws with sealing washers,

9. framework,

10. thread forming screws.

1. cassette,

2. corrugated panel,

3. thermal insulation,

4. thermal insulation tape,

5. sealing tape between insulation,

6. distance profile,

7. distance profile

8. thread forming screws or pin connectors,

9. self-tapping screws,

10. thread forming screws with sealing washers,


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11. self tapping screws,

12. framework,

13. self adhesive tape.

Fig.2. Possible cassette wall constructions, a) direct connection, b) non-direct connection of the covering panel.

Beside using as cladding, the cassettes can be used as structural members. First idea of this was published in the 1960s by Baehre who used cassettes for modulated constructions. Davies has dealt with this problem and investigated the advantages of cassette wall for the low pitched buildings [1], [2], [3].


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Chapter 2

Literature review

2.1. Stressed skin action

2.1.1. Research overview

The investigation of the stressed skin action is in progress in Europe since the 1970s. The main participating countries have been Sweden, Germany and United Kingdom with authors Davies, Bryan, Baehre, Ladwein and others. The investigation primary has been focused on the diaphragm created by trapezoidal sheeting. Diaphragm from composite panels and cassettes was investigated additionally [1], [2], [3], [4], [5], [6], [7], [8]. Baehre's investigation has also included profiles from aluminium [9].

The result of the investigation is ECCS recommendation [11], which contains the state-of-art from the field of stressed skin action. The guideline includes design draft for diaphragm from trapezoidal sheeting and cassette walls for practical use. In addition it serves for the verification of stabilized beam and column by wall members. Basic informations for design with use of stressed skin action are included in present design codes [11], [12], [13] too.

The problem of stressed skin action was also investigated in Czech Republic. Strnad was concerned with light weight sheds [14]. In this context the interaction between frame and light gauge sheeting was investigated. The issue was solved also by Čepička in his dissertation thesis [15], [16]. Cassette wall was directly investigated by Rybín’s dissertation thesis [17]. The existing analytic model for the determining of the stiffness of cassette wall was improved. Non-linear behaviour of stiffeners was implemented into the existing linear diaphragm model of Ladwein. The primary model was developed for the composite members [9]. The similarity between composite panels and cassette wall was the basic idea for use Ladweins model for cassettes. The model of Rybín included the whole shear stiffness of the cassette wall into the calculation.

2.1.2. Principle of stressed skin action

Cassette wall consists of members. A diaphragm created in this manner is able to carry load in its own plane. This ability is called stressed skin action. In addition to cassette members, the diaphragm may also be created from structural roofing panels, tray members or other cladding members. If the diaphragm is properly connected to the frame it can increase the global stability resistance of the building.


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The stressed skin design of a cassette wall may be solved in a similar way to a diaphragm composed of trapezoidal profiles. This idea has been proofed by Baehre and was based on the experimental investigation. During the experimental investigation the behaviour of empty and with insulation filled cassette members was established [4].

Similar way was used by Davies in his work [1] which was focused on the characterization of diaphragm created by cassette profiles. The main differences between the behaviour of cassettes and trapezoidal profiles used in diaphragm are as follows:

the distortion of the cross section caused by shear forces can be neglected in cassettes in consideration of the stiffness of the section. Therefore the deformation of the cassette wall is based on the deformation of the joints,

the load-carrying capacity is principally limited by local buckling of the wide flange against other modes of failure, common for the trapezoidal sheeting,

the edge members of the wall are often not present (horizontal members at the bottom and the top of the wall). Therefore the upper and lower cassette profile must be checked for the additional compression and tension forces.

The most important parts of the cassette wall for the stressed skin action are joints which have critical effect for the stiffness and for the load-carrying capacity of the wall. The basic possible modes of joint failure are as follows:

failure between adjacent profiles,

failure between cassette and frameworks (at least three fasteners should be arranged, [11]),

failure between cassette and edge members due to shear forces (if edge members are present).

Another mode of failure is local buckling of the wide flange.

The cassette wall shear flow carrying capability was investigated by Nyberg [18]. His work was focused on the determination of the stress distribution in cassettes. The analytical model was created. Based on the experimental investigation Nyberg pointed out that if joints are designed to the shear forces from tension field in the wall that the resistance of the wall is not limited by the buckling of the cassettes wide flange. The overcritical region exists in the form of shear-field through the whole cassette wall. The failing of the cassette wall is characterized by local buckling of the edge profiles, which are loaded by axial forces.

2.1.3. Existing design procedures for cassette walls

The basic recommendation in Europe which contains detailed procedures for design cassette walls acting as diaphragm is ECCS [11]. The document allows calculating with cassette walls as a diaphragm, which can ensure the global stiffness of the building and provide beam-columns stabilization with cassette walls. The calculation procedures for diaphragm from cassettes in [11] are mainly based on the Baehre research results, which are summarized in [4]. The results agree with published results of Davies works [2].

Fig.3. Longitudinal stiffeners in wide flange

ECCS recommendation [11] specifies the next conditions for the cassette design:


-19-

the wide flanges must be stiffened by longitudinal stiffeners, see Fig.3,

the distance between fasteners (es) in the adjacent webs is no more than 300 mm,

the distance between fasteners (a1) in narrow flange is no more than 1000 mm,

the fasteners in the webs must be as close as possible to wide flange (eu≤30 mm),

the other geometrical limits are defined as following: 30≤BO≤60 mm; 60≤H≤200 mm; 300≤Bu≤600 mm; 0.75≤t≤1.5 mm, Ia/bu≤10 mm4/mm, see Fig.4.

Fig.4. Cassette profile with geometrical properties

The shear resistance of a diaphragm created from cassette profiles is the lesser from values Pmax and Vbuc. Pmax (2.1) is the shear resistance of diaphragm due the fasteners failure and Vbuc (2.2) is the shear resistance of diaphragm due to cassette profile failure (buckling of the wide flange):

max 1s s pP n F F (2.1)

9412

8.43buc

u

ELV I t

B (2.2)

The cassette wall shear flexibility is equal to the sum of individual flexibilities of the diaphragm (2.3). The formula contains these sub flexibilities: shear flexibility of the diaphragm by shear deformation of the sheet c1,2 (2.4), shear flexibility of the diaphragm by the deformation of the fasteners between cassette and framework c2,1 (2.5), shear flexibility of the diaphragm by the deformation of the fasteners between adjacent cassettes c2,2 (2.6) and shear flexibility of the diaphragm by the deformation of the fasteners between cassettes and edge members c2,3 (2.7).

1,2 2,1 2,2 2,3c c c c c (2.3)

Equations for determines the individual flexibilities are followings:

1,2 2 1 /c B EtL (2.4)

22,1 2 /pc Bs p L (2.5)

2,2 12 1 / 2s p sh s p s sc s s n n s n s (2.6)

2,3 2 /sc scc s n (2.7)


-20-

Individual shear flexibility for screws should be determined experimentally. The safe values for screws can be also found in tables [11].

The difference of Baehre’s approach [4] in comparison with ECCS [11] is only in the formula for the shear flexibility of the fasteners between adjacent cassettes c2,2. The following published equation by Baehre could be used to obtain c2,2:

2,2 1 /s sh sc s n n (2.8)

The stiffness of the diaphragm according to ECCS [11] may be determined from the following simplified equation:

act actS S L (2.9)

In formula (2.9) Sact is the shear stiffness of the diaphragm which could be determined as a multiplication of the shear stiffness per unit length (2.10) and the total length of the diaphragm.

uact

s u

aLBS

e B B

(2.10)

The serviceability limit state requirement for diaphragm composed from cassettes is following:

375

act VS T

L

(2.11)

Factor ß1 in equation c2,2 (2.6) should be obtained from following formulas:

for uncountable value of nf:

3

1

2

i f

i

n

(2.12)

for countable value of nf:

1

2 1

i f

i

n

(2.13)

where i is from 1 to (nf -1)/2.

The following necessary conditions should be satisfied according to the ECCS [11] for the stressed skin diaphragms design:

the sheeting should first be designed for its primary purpose in bending according to EN 1993-1-3 [13] (either by calculation or by testing). It should then be checked that the maximum shear stress due to diaphragm action does not exceed 25% of the design yield (normal) stress.

it may be assumed in design that transverse load on a panel of sheeting will not affect its strength or flexibility as a shear diaphragm.

diaphragm forces in the roof or floor planes should be transmitted to the foundations by means of braced frames, stressed skin diaphragms, or other methods of sway resistance.

structural connections of adequate strength and stiffness should be used to transmit diaphragm forces to the main steel framework.


-21-

diaphragms should be provided with edge members. These members, and their connections, should be sufficient to carry the flange forces arising from diaphragm action.

Restrictions according the ECCS for the diaphragms are next:

diaphragms should not be used to resist permanent external loads (except for lateral support to beams and the dead load from light weight construction) but should be predominantly restricted to resisting

o loads applied through the cladding, such as wind loads and snow loads, and

o seismic forces and other similar (in magnitude and frequency) transient loads,

o crane forces,

o Note: the force induced in any fastener or group of fasteners by horizontal surge or braking effects from overhead cranes should not exceed 30% of the capacity of the fastenings.

stressed skin diaphragms should be treated as structural components and should not be removed without consideration of the effect on the stability of the building. Such consideration should not invalidate planned removal of areas of sheeting for maintenance purposes, provided the remaining areas are adequate as a diaphragm or temporary bracing is provided during maintenance.

the calculations, drawings and contract documents should draw attention to the fact that the building incorporates stressed skin diaphragms, subject to National rules.

openings totalling more than 3% of the area in each shear panel should not be permitted. Openings of less than this amount may be permitted without special calculation provided the total number of fasteners in each seam with openings is not less than that in a seam without openings.

stressed skin diaphragms should be designed predominantly for short-term imposed loads, unless long term phenomena such as creep are taken into account.

stressed skin buildings in which the frames have not been designed to carry the full unfactored load without collapse should be braced during erection. Buildings which utilize the roof or floors as stressed skin diaphragms should be erected so that the roof and floors are sheeted before the walls are cladded.

the structural effects of building modifications on stressed skin buildings should be checked. Changes in use or occupancy which might affect the original design assumptions should be noted in the contract documents and notified to the appropriate authority.

The shear stiffness of the diaphragm could be determined in accordance with [19] according to equation (2.10) if the following condition is valid for the second moment of area of wide flange about its major axis:

4

4, 7.75 10 u v

z G

B TI

t E

(2.14)

where TV = min (TV,Q, TV,L, TV,S):

, 0.8 1 /V Q f p uT n F B (2.15)

, /V L L LT F e (2.16)


-22-

,

1 1V S s

s

T Fe L

(2.17)

The value TV represents shear flow in the ultimate limit state of fasteners. Equations (2.15), (2.16) and (2.17) represent the individual possible failures of fasteners.

Davies, who is one of the dominant personalities in field of cladding structures, pointed out some weakness of the design procedures in [3]:

one of the basic assumption for the cassettes is that the wide flange need not be stiffened. In the context of cassette wall construction with wide flanges exposed externally this is architecturally undesirable. The design procedure for local shear buckling of the thin wide flange is equally applicable to both stiffened and unstiffened flanges.

the most worrying aspect is that Eurocode does not require any formal design check in the capacity of the fasteners.

2.2. Members in bending and axial compression

Members under axial compression and bending develop specific load-carrying behaviour in the different ranges of slenderness. At very low slenderness the cross-sectional resistance dominates, described by the well-known interaction formulae for elastic or plastic limit states:

, ,

, ,min , ,min

1/ / /

y Ed Ed Ny z Ed Ed NzEd

eff y M eff y y M eff z y M

M N e M N eN

A f W f W f

(2.18)

With increasing slenderness a second order effect appears, which is significantly influenced by both geometrical imperfection and residual stresses. In the high slenderness range, member buckling is dominated by elastic behaviour.

Depending on the emphasis given to the different ranges, different concepts of interaction formulae were proposed in the past:

the exponential form – stressing the plastic cross section behaviour,

linear-additive form – derived from linear-elastic buckling response.

The present approach of Eurocode [12] was based on the linear-additive form. In this method the effect of the axial force and the bending moments are linearly summed and the non-linear effects are accounted for by specific interaction factors. The preference for this concept results from its user-friendliness, since it allows the evaluation of the individual effects of the axial force and bending moments.

The code [12] includes two different formats of the interaction formulae called Method 1 [23] and Method 2 [24]. The main difference between them is the kind of presentation of the different structural effects, either by specific coefficients in Method 1 or by one compact interaction factor in Method 2. This makes Method 1 more adaptable to identifying and accounting for the structural effects, while Method 2 is mainly focused on the direct design of standard cases [25].


-23-

Design formula for Method 1

, ,*

,,mod , ,,mod , ,

,,

1

11

my y Ed mz z EdEd LTy

y pl Rd LT EdEdyz pl z Rdyy pl y Rd

cr zcr y

C M C MN k

N NNC MC M

NN

(2.19)

, ,*

,,mod , ,,mod , ,

,,

1

11

my y Ed mz z EdEd LTz

z pl Rd LT EdEdzz pl z Rdzy pl y Rd

cr zcr y

C M C MN k

N NNC MC M

NN

(2.20)

Design formula for Method 2

Buckling mode y-y:

, ,

, , , , ,

0,6 1my y Ed mz z EdEdy z

y pl Rd LT pl y Rd pl z Rd

C M C MNk k

N M M (2.21)

Buckling mode z-z:

, ,

, , , , ,

1y Ed mz z EdEdLT z

y pl Rd LT pl y Rd pl z Rd

M C MNk k

N M M (2.22)

In [12] the unified formulation of above mentioned methods is present (2.23), (2.24). The difference between both methods is handled by coefficients kyy, kzz, kyz, kzy. After substitution the according to chosen method the corresponding formula is achieved.

, , , ,

, ,

11 1

1y Ed y Ed z Ed z EdEdyy yz

y Rk LT y Rk z Rk

MM M

M M M MNk k

N M M

(2.23)

, , , ,

, ,

1 11

1y Ed y Ed z Ed z EdEdzy zz

z Rk LT y Rk z Rk

M MM

M M M MNk k

N M M

(2.24)

2.3. Interaction between sheeting and beam-columns

2.3.1. Interaction

Members of the secondary structure which are connected to the framework may have a significant beneficial effect on the behaviour of the primary frame members. In particular, in the right conditions, secondary members may either partially or fully stabilize the connected primary member against lateral deflection.

The secondary structure may be of several types:


-24-

bracing,

covering systems,

side rails, see Fig.5.

Fig.5. Secondary structures connected on column A) bracing, B), C) covering systems

Connected members could provide either continuous or discrete restraint with dependence on the connected member properties and the mode of connection. The discrete restraint is provided by bracings or secondary members with significant stiffness. The continuous restraint is ensured by covering members, connected directly on the framework. The continuous restraint is a group of discrete restraints in sufficiently small distances between each point.

The supported member may fail differently, depending on the mode of stabilization. Let us consider a member with high slenderness. Non-stabilized member under axial compression and bending moment fails by lateral torsional buckling. If the same member is fully stabilized in lateral direction the load carrying capacity is increasing and it fails by achieving the plastic resistance of cross section. Between those cases the case of the partial stabilization could be found, when the stabilization is not full stabilization but its effect is not negligible. The two extreme cases are included in present design standards [12].

2.3.2. Research overview

Issue of the member stabilization was and nowadays is still in focus of researchers. The beam under bending moment may fail by lateral torsional buckling. In case when other members of the structure are connected at loaded beam-column they may provide lateral and/or rotational restraint.

The problem of the interaction was investigated mainly in Germany by Lindner whose research was focused on the interaction between beams and trapezoidal decks [22], [26], [27]. The results of his research have pointed out the magnitude of the interaction and the possible application of results. The conclusions of this work are included in EN 1993-1-3 [13]. The same results were achieved by others like Heil [28] or Sochor [29]. The phenomenon of interaction from the point of view of mechanics was described by Trahair in [30].


-25-

The interaction between various covering systems and beams was the theme of several dissertation thesis. The thesis of Petrusson was focused on the interaction between sandwich panels and steel column [31], [32]. The thesis was worked out in Luleå University of Technology. During the investigation three types of experiments were carried out:

determination of the rotational stiffness provided with sandwich panels, where the panels could act against the stabilized member rotational deflection (on Fig.6 labelled as C). The obtained rotational stiffness for one pair of panels with two screws was 1kNm/rad. The stiffness was linearly increasing according to the number of screws.

sandwich panel shear stiffness determination in own plane (on Fig.6 labelled as S).

full scale experiments with connected columns and sandwich panels. The experiments were focused on the determination of sandwich panel stabilization effect.

The used members were HEA120 and IPE200. Two modes of loading were used during the tests: i) axial compression, ii) compression and bending. The results of the experiments pointed out that HEA120 was fully stabilized by the panels under both modes of loadings and lateral torsional buckling was not appeared. The failure was caused by buckling. When IPE200 was tested the failure mode depended on the type of loading. For axial compression load the member failed by buckling. Under axial force and bending moment the lateral torsional buckling occurred. The conclusion of the work was that in common cases for the investigated members the sandwich panels provide sufficient elastic support and provide full lateral stabilization.

2.3.3. Idealization of stabilization effect

The interacting construction is commonly modelled as two individual springs connected on the place of fasteners, see Fig.6. The spring labelled as S represents the shear stiffness of the diaphragm in its own plane. The next one which is labelled as C signifies the rotational stiffness of the diaphragm. These two parameters are independent and depend on the properties of the diaphragm.

Fig.6. Idealization of interaction

Sign of beam-column load has significant effect to the intensity of interaction. When the stabilized member is under axial compressive load and bending moment, the compressed flange has a tendency for lateral movement. If the supporting members are connected at compressed flange then may come different behaviour depend on the value of shear stiffness S:

if shear stiffness S is sufficient for full stabilization of supported member then torsional deformation does not occur and the rotational stiffness does not activate.

if the shear stiffness is not enough for full stabilization and act only as a partial support then the torsional deformation appears and the rotational stiffness is activated and contributes on stabilization.


-26-

In this arrangement of elastic supports the stabilization may be full. In the other case when the supporting members are connected at tensioned flange the lateral-torsional buckling with imposed axis of rotation in tensioned flange occurs. In this case the stabilization effect is softer.

2.3.4. Existing design procedures

Design procedures for interacting sheeting can be found in Eurocodes [12], [13] in the German standard [33] and in ECCS recommendation [11]. These procedures were mainly developed by Lindner. The result of the investigation was published in [22] and [27], and became the parts of standards.

Lindner in his projects focused on the interaction between hot rolled I sections and trapezoidal panels but the results could be used for other types of structures. During his investigations the complex model was developed for trapezoidal panels.

2.3.4.1. Interaction calculating according to Lindner

The design procedures which were published by Lindner are based on the experimental investigation. The work was arisen from Fischer’s work [34] and from Lindners investigation. Sufficient stiffness S (Fig.6) for full stabilization of beam was published in [26]. Special evaluation was made out for IPE sections with a depth more than 200 mm.

The limiting shear stiffness for the full stabilization is following:

2 2

22 2

70

4T zS EI GI EI hL L h

. (2.25)

The same equation (2.25) may be found in codes [12] and [33].

Stiffness S for cassette profiles can be found out from experimental investigation, from the earlier project of Rybín [17] or from ECCS recommendation [11].

Even if the shear stiffness S does not reach the limiting value of (2.25), a remarkable positive effect on the ultimate lateral torsional buckling load is given in [25]. In such cases this effect can be taken into account by calculating the elastic lateral torsional buckling moment Mcr under the assumption of the given value for C (explained below) and S.

The next value which was investigated by Lindner is the rotational stiffness C (Fig.6) provided by connected sheeting. The rotational stiffness acts against the rotational movement of stabilized beam. The effect of stabilization is included at torsional stiffness of the member IT. The equation designed by Lindner is following:

2

*2T T

CL GI I

. (2.26)

Stiffness C presents the rotational stiffness whereby the sheeting acts on the member. This stiffness is defined as:

1 1 1 1

M A PC c c c

. (2.27)

The equation for obtaining the rotational stiffness is based on the idea that each component included is independent and could be defined separately. The individual stiffnesses are showed on Fig.7 and have following meanings:


-27-

cM – is rotational stiffness of the sheeting profiles (2.28),

cA – is stiffness of the fasteners between sheeting and members (2.29),

cP – is stiffness due to the distortion of the member (2.30).

Fig.7. Lindner’s model of independent stiffnesses

The rotational stiffness provided by sheeting cM could be obtained from the following equation:

M

EIc k

a , (2.28)

where: k – is the coefficient including the span of the sheeting. (4 for multi span, 2 for single or double span),

a – is the span of the sheeting.

The value of cϑA is commonly determined by experimental investigation. Equation (2.29) was presented in [26] by Lindner for the fasteners between trapezoidal sheeting and hot rolled sections and may be also found in [13].

2

100A A

bc c

(2.29)

For cold formed sections value Ac may be obtained according to the equation determined by Vraný

[35].

The equation (2.30) may be used for sections I and U [33]. Constant c1 depends on the shape of cross section (0.5 for I sections for random load; 0.5 for U sections for gravity load; 2 for U sections for uplift).

2

13 3

1

4 1P

w f

Ec

h bc

t t

(2.30)

Alternative equation included in code [12], to check the sufficient torsional stiffness provided by sheeting is following:


-28-

2

,pl k

z

MC K K

EI (2.31)

where Kυ is factor for considering the moment distribution, see Tab. 1, and K is equal to 1.00 for plastic analysis and equal to 0.35 for elastic analysis.

Tab. 1. Factor Kυ for considering the moment distribution and the type of restraint of compression flange

Tab. 2. Factor Kυ for considering the moment distribution and type of restraint according to [25]

In [25] another table could be found (Tab. 2), which contains detailed value for Kυ defined for each buckling curve and also for other moment distribution.


-29-

The hot rolled profiles with depth lesser than 200 mm are always sufficient supported against lateral torsional buckling. For sections with higher depth Lindner presents the limiting ratio for the trapezoidal panel shear stiffness S and rotational stiffness C whereby should be achieved for full stabilization of supported members, see Fig.8. The graph is operative for single span beams with end uniformly distributed loads and end moments.

Fig.8. Ratio between stiffnesses S and C

2.3.4.2. Interaction calculating according to Heil

The elastic support calculation according to Heil is based on the following idea. The point of application of the uniformly distributed load is in the same plane as the point of the connected secondary structure [28]. The stabilized member is sufficiently stabilized if equation (2.32) is valid.

2 22 2 2 2,

2 2 2 22 2

32 3 31 1

3 3 33pl y z

LT

M EI cS

h L h

, (2.32)

where rotational stiffness factor c is following:

2 2

2 t

z

EI GI Lc

EI

. (2.33)

In this equation the stiffness C of the sheeting against the rotational movement of connected member is not considered. The rotational stiffness factor c2 with respect of the sheeting rotational stiffness C could be obtained from equation (2.34).

2 2 4 2

2 /t

z

EI GI L L Cc

EI

(2.34)


-30-

We can consider that the member is fully stabilized against lateral torsional buckling if 0.4LT .

When this limit is substituted into (2.32) the obtained equation is following:

2

,

2 210.18 4.31 1 1 1.86pl y z

M EI cS

h L h

(2.35)

2.3.4.3. Stabilization of members according to recommendation ECCS

In ECCS [11] the possibility is given to use shear panels as stability bracing to prevent flexural, flexural torsional and lateral torsional buckling or combination of these behaviour. In this document the procedure is given for checking the stabilized state of columns and beams made from doubly symmetric I sections. The determination of the minimum strength and stiffness of the shear panel according to the recommendation ECCS was mentioned above, see section (2.1.3).

The formulae in [11] are based on a sinusoidal form of lateral deflection, which leads to a concentrated reaction force at the support (see Fig.9). The concentrated force can be regarded as an internal force in the diaphragm provided the fasteners between the sheeting and the element to stabilize can sustain this concentrated force on length of 1/8 of the span of the element. If these fasteners are unable to sustain this concentrated force, then that force should be introduced into the edge members via the fasteners between the diaphragm and the edge members.

Fig.9. Assumed deflection of the element to stabilize with the resulting concentrated force at the supports

If the unstiffened flange of the beam is in tension the beam is fully stiffened when the shear stiffness of the diaphragm S fulfils the following requirement:

2y

act y

f AS S (2.36)


-31-

Sact is the shear stiffness of the diaphragm and Sy is the required shear stiffness of a diaphragm for full stabilization. If the requirement for full stabilization is not fulfilled (Sact < Sy), the critical forces Mcr and Ncr are calculated from following formulae:

crM M (2.37)

crN N (2.38)

where ψ is the eigenvalue being the lowest value of ψ1 and ψ2. If both eigenvalues are negative, no stability problem exists for the given stress resultants M and N.

2

1 11,2

2 2 2

1

2 2 2z wp

k k hW W S

k k k i

(2.39)

where S’ is the minimum of Sact or Sy. Coefficients included in (2.39) should be obtained from following formulae:

1 2z wp

Shk N W W M

i

(2.40)

2 22 2

1

p

k N Mi

(2.41)

2

2z

z

EIW S

L

(2.42)

22

2 2

1

2w

w Tp

EC hW GI S

i L

(2.43)

2 2 2p y zi i i (2.44)

21

4w zC I h (2.45)

Cw is the warping constant for doubly symmetric I section. M is constant bending moment about y axis, N is constant centric normal force to be introduced with the actual sign, for definition see Fig.10.


-32-

Fig.10. Notation and sign definitions

The maximum shear force Td in a shear panel per member to be stabilized follows from next equation:

1

od

eT S

L

(2.46)

where eo is the initial lateral bow imperfection of the stiffened flange according to the Eurocode [12]. The maximum shear force Td shall be smaller than the design resistance of the fasteners Pmax as was mentioned above (2.1). Furthermore one of the following conditions shall be fulfilled:

the shear force Td shall be smaller than FpL/8p where Fp is the design strength per fastener between the sheeting and the stabilized element, p is the pitch of the fasteners between the sheeting and the stabilized element.

the fastenings of the sheeting to the edge elements shall be accounted for Td.


-33-

Chapter 3

Thesis objectives

The main objective of the PhD. thesis is to find out the effect of the sheeting from cassette profiles to the load carrying capacity of the connected slender beam-column.

The thesis was divided into experimental, numerical and theoretical parts.

The objects of the experimental part were focused on:

to determine the rotational stiffness of the cassette profile,

to determine the stabilization effect of the cassette wall to the load carrying capacity of hot-rolled beam-column.

The object of the numerical modelling is:

to make a numerical model of experimentally tested member,

to calibrate the numerical model according the experimentally obtained results,

to carry out parametric study so as to extend the results range.

The theoretical analysis is based on results of experimental and numerical work and the objectives are also the main ones of the thesis:

to derive formulae for determining the rotational stiffness of the cassette profiles,

to describe the behaviour of hot-rolled beam-column with connected cassette wall,

to work out the design tables for minimal cassette wall stiffness for full and partial stabilization of connected beam-column.


-34-

Chapter 4

Experimental study

4.1. Introduction

Experimental investigation belongs to the main part of the thesis. Experiments give the primary results data, which is the base of the investigation.

During the thesis altogether three types of experiments were carried out:

tests of rotational stiffness of the cassette profile,

full-scale tests of hot-rolled beam-columns with connected cassette wall,

additional tests (material properties, fasteners stiffness).

4.2. Rotational stiffness

The aim of these experiments were to determine the rotational stiffness of the connection between cassette profile and hot-rolled beam-column from I profile about its x-x axis, see Fig.11.

Fig.11. Rotational stiffness about x-x axis.


-35-

The experiments were carried out because useful data were not found for cassette profiles. A similar rotational stiffness value was worked out by Pétrusson for sandwich panels but these results couldn’t be used due to dissimilar behaviour between those two sheeting types [31].

The obtained values served as input parameter for following work. The experiments were focused on the rotational stiffness influenced by local behaviour of cassette in region of connection. From the statical points of view the investigated stiffness couldn’t be determined by calculation method available in standards or other literature. The experimental investigation was necessary due to the complex behaviour of profile in the area of local deformations.

The experiments were not made to derive a general equation for cassette profiles but as input parameters for following work. This was a reason why only specific specimen with similar properties was used.

Trapezoidal sheeting was neglected during the experiments because it did not influence the investigated stiffness.

4.2.1. Experiments overview

The specimen very simply represented the real situation of the connection between the column and cassette profile. The specimen was comprised of two cassette profile sections and a steel plate representing the column flange, see Fig.12. This simplified arrangement was chosen to ease the manipulation of the specimen. Besides, the steel plate fully satisfied the requirements of a flange because of its high stiffness. The cassette profiles were connected to the steel plate (further as flange) with screws.

Fig.12. Column flange replacement

As it could be seen in Fig.12 the length of the profiles was chosen as short because the experiment was focused on the local behaviour of connection area. The specimen was supported in a vertical position by special support, connected to laboratory column. The specimen was clamped by special steel plates and timber blocks in the middle of the cassette profile, see Fig.17. This configuration permitted the use of both ends of each profile for two different tests. Thread-cutting screws were used to connect the cassettes with flange plate. These screws require predrilling which was made with respect of manufacturer requirements. The screws with length of 19 mm and diameter 6,3 mm (EJOT/JZ-6.3x19-E16) were supplied by rubber chock.

The screw arrangement was one of the altered parameters. Their positions depended on another altered dimension, the width of the column flange. Used screw arrangements and plate widths were as follows:

Number of screws in connection, see Fig.13:

2x2,


-36-

2x3.

Fig.13. Screws arrangement

Width of the flange (thickness 8 mm), see Fig.14:

300 mm,

250 mm,

150 mm.

Fig.14. Used steel plates replacing column flange, dimensions, position of fasteners

Screw arrangement with respect of the flange centriod, see Fig.14:

symmetrically to the flange axis [a], (for plate width 150 mm),

symmetrically to the flange axis – near axis [b], (for plate width 250 mm and 300 mm),

symmetrically to the flange axis – near edge [c], (for plate width 250 mm and 300 mm),

un-symmetrically to the flange axis [d], (only for plate width 250 mm and 300 mm, used non symmetrical fasteners arrangement about flange axis).

The last variable, which had significant effect and was followed in experiments, was the cassette profile. Two types of cassette profile were used with two different thicknesses; see Fig.15, [37]:


-37-

Cassette profiles:

K 120B/600, thickness 0.75 mm,

K 120B/600, thickness 0.88 mm,

K 130F/600, thickness 0.75 mm.

The nominal yield strength of the light gauge steel used for cassettes was 320 MPa.

Fig.15. Used cassette profiles

Fig.16. Draft of the experiments


-38-

Altogether 17 specimens were made from combinations of above listed parameters. The list of the specimens is presented in Tab. 3. (Arrangement of the screws which is in the table labelled by letters is noted in “Screw arrangement” capitulation above in squared bracket). The specimens were assembled by hand. The distance between the cassette profiles was 10 mm. Screws were tightened by torque wrench. The assembly was carried out horizontally and lifted up onto the laboratory column. The loading was applied by weights. A cantilever, which was welded to flange, served for the application of load. A loading platform was hung from the end of the cantilever where the weights were put. The gauge was clamped on the cassette. The deflection of the cantilever was measured by manual deflectometer. The measuring equipment precision was 0.05 mm.

Fig.17. The specimen, side-view, front-view

4.2.2. Measured values

The goal of the experiments was the rotational stiffness determination provided by cassette profiles. In order to determine the required bending moment and rotational deflection following data was recorded:

a1, a2,b1, b2 – screw positions,

m – gauge distance from flange,

n – distance of load application point,

p – measured displacement, see Fig.18.


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Fig.18. Measured values

It should be noted that distances a1, a2 do not influence the behaviour of specimens while b1, b2 are relevant and thus they are listed in Tab. 3, see Fig.18, Fig.19. Distances b1, b2 act as force arm in contact between the screw and the compressed point of cassette wall either the cassette profile end or the steel plate end. During the rotational movement the cassette profile acts against this movement. The local deformation of the profile shows the acting points where the forces arise. The stiffness magnitude depends on force arm.

Fig.19. Deformed specimen

The stiffness depends on two values: bending moment and rotation. These demanded values could be calculated form two measurands:

deflection of the cantilever,

load.

The bending moment was calculated from load and force arm according to Fig.18.


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M Fn (4.1)

and the rotation was determined from the cantilever movement and gauge position

arctanp

m

. (4.2)

Following figure shows the values as rotational deflection and applied moment.

Fig.20. Load deflection curves from experimental investigation, marked with respect of Tab. 3.

The rotational stiffness is defined as:

/M Nm

C cassette widthrad

(4.3)

where stiffness C is used as secant stiffness for 0.05 rad of rotation.

The obtained stiffnesses C and other data are summarized in the following Tab. 3.


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Tab. 3. Specimen overview and the experimentally obtained results

4.3. Full-scale tests of beam-column with cassette wall

The main goal of the project is to determine the stabilization effect of cassette wall to the load carrying capacity of the beam column. The effect of the sheeting would have been determined directly from numerical model but experimental study was necessary to prove the correctness of the model. These facts lead to provide full scale experiments of beam-column stabilized by cassette wall.

This test arrangement was chosen so that lateral torsional buckling would be governing for the load capacity. According to the theoretical assumption the connected sheeting should obstructed this failure mode.

The stabilization effect depends on several parameters. Let’s see which these are and how could influence the results:

Position of the connected sheeting with respect of the member flanges has significant influence to the stabilization effect. Cassette profile connected to the tensioned flange allows free lateral movement of compressed flange but partially prevents the cross-section against torsional deformation. The column resistance is less increased in this arrangement. In the other case when the wall is connected at the compressed flange the effect of the wall is stronger. The wall provides lateral restraint of the compressed flange. During the experiments both cases were tested.

Shear stiffness of the cassette wall in its own plane depends on cassette profile properties and amount of screws between adjacent cassettes. The stiffness of the wall commonly is not a weak point of the construction. Defined maximum pitch of 300 mm according to [11] presents sufficient intensity. The length of used cassette profiles was smaller as in normal case. Therefore higher density of screws between adjacent cassettes was chosen. The screw density was constant during the investigation.

Number of connection between the flange and the cassette profile influenced both lateral and rotational stiffness of the connection. Connection with two fasteners was chosen for all specimens.

Static scheme and the boundary conditions play an important part in the beam-column behaviour. These conditions were chosen so that the lateral torsional buckling occurred.


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Cantilever was used to achieve combined (M+N) internal forces in the member. Two types of the beam-column boundary condition were chosen with different out of plane behaviour.

The specimen comprises more members than only beam-column, cantilevers, cassette profiles and corrugated sheeting. An additional frame was made which supported cassette profiles in the desired position. These necessary additional members affected the behaviour of whole specimen and could increase the load carrying capacity of the beam-column. This effect was taken into account during the numerical modelling and analysing of results.

4.3.1. Experiments overview

The specimens were designed as a frame because combined bending and axial loading was required, see Fig.21. The ratio between bending moment and axial force equal to 1 m was chosen. This combined load was necessary to achieve the desirable lateral-torsional failure.

Fig.21. Specimen static scheme

Fig.22. Specimen V2

The parts of the specimen were as follows:

beam-column,

two cantilevers,

cassette profiles covered by trapezoidal panels,


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frame supported cassette profiles.

Altogether six specimens were produced, each of them with different properties. The variables were:

boundary conditions. Two types of boundary conditions were used. One was the typical frame corner joint with partial warping and out-of-plane bending restraint which provided a significant prevention against beam-column distortional deflection (V), see Fig.23. The second one was a fork connection allowed free warping of beam-column end sections and free out-of-plane rotation (K), see Fig.24. The connection consisted from tension contact represented by pin and from compression contact, which was made by cubes where one of them was modified to sphere. Rotation about x-x axis was restrained for both types. In plane static scheme for both types of specimens was the same. For both types of specimen different cantilevers and beam-column were produced. The system length of the beam-column and cantilever for each type is noted in Tab. 4.

amount and position of cassette profiles. The cassette profiles were put on the specimen in three different arrangements:

o double-sided cassette arrangement on compressed flange of beam-column,

o double-sided cassette arrangement on tensioned flange of beam-column,

o one side cassette arrangement on compressed flange of beam-column.

The following Tab. 5 contains all specimens with boundary conditions and cassette arrangements.

Tab. 4. System lengths

Tab. 5. List of specimens

The specimens were produced in – DT výhybkarna a mostarna, Prostějov - and built up in CTU Experimental centre. During the experiments the same cantilevers were used for all specimens, only the tested beam column was replaced. For the beam-column section IPE300 and for the cantilevers HEA320 were used. Steel grade 355 MPa was used. The joints are shown in Fig.23 and Fig.24. The specimens were symmetrical about vertical plane.


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Fig.23. Main frame joint; Set “V”

Fig.24. Main frame joint; Set “K”


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Fig.25. Boundary conditions, specimens V and K

The columns and the joints were dimensioned to the expected load. Tensioned flange of the beam-column in joint area in set K was strengthened due to the high concentration of stress close to the joint, see Fig.23, Fig.24 and Fig.25.

The wall had to be kept in plane perpendicular to the main frame. An additional frame was prepared to serve as a support for cassette profiles and trapezoidal panels. The structure was made from four U160 profiles and twelve L60x6 angles. Two U160 beams ensured the support for the cassette profiles and the rest members created the whole support structure, see Fig.26, Fig.27. The additional frame was connected on the cantilevers. The cassette profiles were laid or clamped with U160 beam with respect of the position of the wall which may be on compressed or on tensioned flange of the beam-column. The connections between the cassette profiles and U160 beam were made by slotted holes.

Fig.26. Plan view – main frame and additional frame

The same additional frame was used for all specimens. The frame was designed so that could be used for both situations: profiles connected to compressed and to tensioned flange.


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Fig.27. Additional frame (with reference to Fig.26)

Fig.28. Additional frame, specimen V3 with one sided wall

The cassette wall was made by following members:

cassette profiles (delivered by Kovove profily s.r.o., type B K145/600, 0.75mm, S320 GD),

trapezoidal panels (delivered by Kovove profily s.r.o., type TR 35/207, 0.75mm, S320 GD),


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screws:

o cassette/beam-column flange – thread-cutting screws (EJOT/JZ-6.3x19-E16),

o adjacent cassettes – self-tapping screws (EJOT/ JT2-3H-5.5 x19-V16),

o cassette/trapezoidal panel – self-tapping screws (EJOT/ JT2-3H-5.5 x19-V16).

Loading was applied by hydraulic jack. The acting point was on one of the cantilevers in 1 m distance from centroid of beam-column. The loading was controlled by displacement. As first step 30% load of theoretical load carrying capacity was carried out due to screws haul before main loading was applied. The tests were conducted until collapse.

Fig.29. The loading point with hydraulic jack and the support

During the experiments three types of sensors were used:

potentiometer sensor,

inductive sensor,

strain gauge.

The position of the sensors and measured data are included in following chapters.

4.3.2. Imperfection

Global imperfection of beam-column has considerable influence to the buckling behaviour of the member. This was the reason why the imperfection of the beam-column was examined.

The Czech standard CSN 73 2611 [38] (adequate to EN 1090-2) specifies the maximum allowable production imperfection. To follow the specimen behaviour the imperfection in minor axis orientation was important. According to the standard the members are sorted to three classes A, B and C. Each class has got different limit:

A) 0,0015L, max. 15 mm,

B) 0,002L, max. 20mm,

C) 0,003L, max. 30mm.


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The initial imperfection was measured. Measuring was carried out by level instruments for each beam-column, see Fig.30 to Fig.35.

Fig.30. Measured lateral imperfection of specimen V1




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Fig.33. Measured lateral imperfection of specimen K1



The summary of the measured imperfections is in Tab. 6. The results lead to conclusions that the members fulfil limits for members initial imperfections.


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Tab. 6. Summary of measured imperfections

4.3.3. Measured values

Altogether 21 sensors were used for specimens in set V and 23 for specimens in set K. The monitored values are shown in figures Fig.36, Fig.37, Fig.38 and Fig.39.

The measured values may be sorted to three groups:

horizontal and vertical absolute deflection (towards the laboratory floor),

relative lateral movement between adjacent cassettes,

strains at midspan of beam-column.

Fig.36. Sensors arrangement, set V, top view


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Fig.37. Sensors arrangement, set V, side view

The arrangements of the sensors basically were the same for all specimens. Only the strain gauges were set in different place. Absolute and relative deflections for both sets (K, V) were measured in the following location:

U1 – lateral deflection of beam-column top flange,

U2 – lateral deflection of beam-column bottom flange,

U3 – vertical deflection of the beam-column in the midspan,

U4, U5, U6 – lateral deformation of first three cassette profiles counted from cantilever,

U7, U8 – lateral deflection of cantilevers, measured in the crossing of beam-column and cantilevers centrelines,

U9 – longitudinal deformation of cantilevers in position of hydraulic jack; this value was used for loading handles,

R1, R2, R3 – lateral relative movement between cassettes and beam-column top flange.


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Fig.38. Sensors arrangement, set K, top view

Fig.39. Sensors arrangement, set K, side view

The strain gauges were set in different position on the beam-column for each set of specimens.

Strain gauges location for set V:

T1, T2 – top flange, both edges, midspan,

T3, T4 – bottom flange, both edges, midspan,

T5, T6 – top flange, both edges, 370 mm from end plate of beam-column from bearing side,

T7, T8 – bottom flange, both edges, 370 mm from end plate of beam-column from bearing side.

Strain gauges location for set K:

T1, T2 – top flange, both edges, midspan,


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T3, T4 – bottom flange, both edges, midspan,

T5 – top flange, 640 mm from cantilever centreline from bearing side,

T6 – bottom flange, 640 mm from cantilever centreline from bearing side,

T7, T8, T9, T10 – web of the beam-column, midspan, vertically arranged in one line.

4.3.4. Results of experiments

The experimental investigation led towards the following failure modes defined with maximal achieved load:

V1, K1 – lateral torsional buckling about imposed axis, see Fig.40, Fig.41. Cassette wall connected at tensioned flange could not prevent beam-column torsion. Cassette profiles failed locally in place of cassette-flange screws.

Fig.40. Failure mode, V1

Fig.41. Failure mode, K1

V2, K2 – plastic moment resistance of beam-column reached. Cassette wall fully stabilized the beam column with in plane stiffness, no relevant lateral movements at collapse, see Fig.42.


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Fig.42. Failure mode V2, K2

V3, K3 – lateral torsional buckling. One sided cassette wall with decreased plane stiffness buckled in connection with beam-column lateral movement, see Fig.43, Fig.44. Cassette profiles failed by two ways, locally and globally.

Fig.43. Failure mode V3

Fig.44. Failure mode K3


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Tables including all the measured values are presented in Appendix A. Fig.45 shows the load-deflection (measured by gauge U3 see Fig.37 and Fig.39) curves for both types of specimens for each combination of wall arrangements.

Fig.45. Load-deflection curves for all specimens, measured by gauge U3.

The failure mode could be followed by relative deflection of flanges. Fig.46 shows the relative lateral movement of flanges (the difference of deflections U1 and U2). The failure of specimens K2 and V2 was caused by reaching the plastic cross-section capacity. In specimens K1, K3, V1 and V3 lateral-torsional buckling occurred.

Fig.46. Relative deflection between compressed and tensioned flanges.

4.4. Additional tests

In this section two types of tests are noted. The first type was focused on determination of the used material properties of beam-column. The second one was about the stiffness of the screw connections.

4.4.1. Material properties

The standard tests were focused on the determination of beam-column material properties. Altogether three tests were carried out from the beam-column material. For the specimen production parts from tensioned flange and parts of the web close to the tensioned flange were used. The position of used material with respect of the whole length was at 1/6 of span from the beginning of the member. The specimens were taken from three members. Following table contains the obtained steel properties.


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Tab. 7. Steel properties

4.4.2. Fasteners stiffness

Two types of tests on the fasteners stiffness were made. First of them was the test of fasteners between the cassette profile and column flange (marked as KS), the second one was the test of fasteners between the adjacent cassettes (marked as KK), see Fig.47. Altogether six tests were carried out, three for each type. The obtained stiffnesses were used for numerical model.

The specimens were prepared from the same material and screw types as were used for full-scale tests. The specimens contained two screws, see Fig.47. The obtained force-deflection graphs, which were recalculated for one screw, are presented in Fig.48 and Fig.49.

Fig.47. Fastener experiments arrangement


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Fig.48. Force – displacement curves for specimens KK, one screw (both sheet thickness 0,75mm).

Fig.49. Force – displacement curves for specimens KS, one screw (sheet thickness 0,75mm, steel plate thickness 10mm).


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Chapter 5

Numerical modelling

5.1. Introduction

Numerical modelling comprises two parts. At first during the experiments preparation, the models of beam-column with cassette wall were developed. The models served to test and tune the specimens. Secondarily the real specimens were modelled. They confirmed the experimentally obtained results. The numerical model was used for the parametric study additionally. The numerical modelling was carried out by ANSYS 11.0 software package.

5.2. Pre-modelling of specimens

The numerical modelling was first used for predicting the results of experiments and basically facilitated the experiments design. The goal was to find out the profile of sufficient slenderness to illustrate the effect of connected sheeting stiffness.

The model contains from following main parts:

beam-column,

cantilevers,

sheeting.

The cantilevers served for the loading and for generation of combined loading on beam-column. The sheeting was connected at either compressed or tensioned flange of beam-column. The connections between the cantilevers and the beam-column were made according to mentioned details marked as V and K.

5.2.1. Used elements, materials, boundary conditions and load

Shell element SHELL181 was used to model the sections (flanges and web). The element is suitable for analysing thin to moderately-thick shell structures. It is a 4-node element with six degrees of freedom at each node. SHELL181 is well-suited for linear, large rotation, and/or large strain nonlinear


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applications. The element is defined by four nodes (I, J, K, L) in rectangular position. The length to width ratio may be up to 3. The geometry definition of the element is presented on Fig.50.

Fig.50. Geometry of element SHELL181

The beam-column was modelled with half sinusoidal imperfection. The amplitude of the imperfection was worked out from EN 1993-1-1 [12]. The imperfection amplitude in direction of minor axis was L/250.

Furthermore nonlinear spring elements COMBIN39 were used for modelling the connected sheeting. This element is unidirectional element with nonlinear generalized force-deflection capability. The element has longitudinal or torsional capability in 1-D, 2-D, or 3-D applications. The longitudinal option is a tension-compression element with up to three degrees of freedom at each node: translations in the nodal x, y, and z directions. The torsional option is a purely rotational element with three degrees of freedom at each node: rotations about the nodal x, y, and z axes. The element is defined by two nodes (I, J) optimally in the same node. The force-deflection curve is defined by pair values of force and deflection, see Fig.51.

Fig.51. Geometry of element COMBIN39, element force-deflection curve

During the pre-modelling of specimens the cassette wall was modelled by spring elements. Each part of the wall, cassette profiles and screws were modelled by springs which were reciprocally connected. The whole cassette wall with all connectors comprised four types of spring elements which presented the following parts of the wall:

screws between cassette profile and column flange, S1,

screws between adjacent cassette profiles, S2,

two parts of cassette profiles due to proper wall model, S3, S4; see Fig.52.


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Fig.52. The model of the wall provided by spring elements

The stiffnesses of wall and fasteners were worked out from ECCS [11] and from previous project of Rybín [17].

Nonlinear spring elements were used for defining the rotational capability of sheeting, which was obtained from rotational stiffness experiments. The springs which presented the rotational stiffness C were placed continuously along the whole length of beam-column.

The connections between cantilevers and beam-column were made by contact elements. One of the simplest contact elements available in ANSYS package CONTAC52 was used. This element represents two surfaces which may maintain or break the physical contact and may slide relative to each other. The element is capable of supporting only compression in the direction normal to the surfaces and shear in the tangential direction. The element has three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element is defined by two nodes (I, J) placed each at other part of structure which may be connected. Two stiffnesses (normal stiffness and sticking stiffness) and initial gap or interference had to be defined.

Loading was applied at cantilevers. Arc-Length nonlinear solver with large displacement was used.

Bilinear (elasto-plastic) material model was used. Different steel grades were used for beam-column and for cantilevers. For beam-columns material model with yield strength 355 MPa was used and for cantilevers fy = 235 MPa. These values fulfilled nominal material properties used in experiments.


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Fig.53. Specimen with load and boundary condition

5.2.2. Conclusions from pre-modelled specimens

The pre-modelling pointed out the following summary:

The section geometry and the length of the beam-column governed the slenderness of the member which determined the type of failure. During the numerical modelling such kind of section was searched which slenderness allows for lateral-torsional failure. The aim was to prove the sheeting impact to the member failure. Section IPE300 was chosen against HEA due to higher slenderness about weak axis.

The following ratios between bending moment M and axial force N were checked: 0.5 m, 1 m and 2 m. For the experimental investigation the ratio 1 m was chosen when the influence of bending moment was significant.

The boundary condition of the primary examined beam-column was rigid connection “V” with cantilevers. This option prevents the distortion of beam-column end cross section. It was decided to prepare the specimens with fork boundary conditions as well. The specimen type “K” was designed based on this idea.

The results suggested that a cassette wall could be sufficient for full stabilization of the beam column. Therefore, specimens with both side walls and one side wall were designed for testing.

5.3. Experimentally tested specimen models

As mentioned in the previous section, the experimental investigation was preceded by numerical modelling. These numerical models were used as the basis for a modified model that was developed after the experimental investigation. The main modifications are listed below:


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Boundary conditions of beam column. Finally two types of beam column were tested, see Chapter 4. For both of them the adequate models were created, see Fig.54.

Fig.54. Models boundary conditions K1, V1

The yield strength and the ultimate strength were calculated as a mean value from standard tests, see 4.4.1, Tab. 7, and used for the modeling. For material properties of other parts (cantilevers, pin), the nominal values delivered by manufacturer were used. Different material models were used for beam-columns and for the other structures. For beam-columns multilinear with kinematic hardening, for cantilevers and other parts bilinear material (elasto-plastic) model were used, see Fig.55, Fig.56.

Fig.55. Beam-column material model (stress in MPa)


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Fig.56. Cantilever and additional frame material model

The cassette wall was modelled with a system of spring elements, Fig.52. Each segment of the wall was used separately as a spring, and connected with adjacent elements according to the mentioned system. The force deflection relations of screws were taken from experiments, see chapter 4.4.2. The wall stiffness was calculated according to ECCS [11]. The whole system gives sufficient results as proved by Hapl [36].

An additional structure was used to support the cassette wall on the specimens. A frame providing the wall support was modelled using beams. Their presence in the model was necessary because during the experimental investigation their effect on the load carrying capacity was detected. The numerical model allowed their elimination from final results. The frame was made from BEAM188 3-D linear finite strain beam, see Fig.57.

Fig.57. Elements BEAM188 as additional frame


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The boundary conditions of whole specimens were changed. The additional frame worked as lateral support in plane of cassette wall. Therefore the lateral supports were removed.

Beam-column imperfection was used e0,y= L/300, e0,z=L/250, according to standard [12].

5.3.1. Calibration

The updated model was calibrated according to the experimentally obtained results. Three main parameters were followed during the calibration:

load-carrying capacity defined as maximally achieved loading in both cases; experiments and numerical model,

stiffness,

failure mode.

For comparison of stiffness the force-deflection curves at midspan were used, see Fig.58, Fig.59, Fig.60.

Fig.58. Comparison of load-deflection diagrams from model and experiment for specimens V1, K1.

Fig.59. Comparison of load-deflection diagrams from model and experiment for specimens K2, V2.


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Fig.60. Comparison of load-deflection diagrams from model and experiment for specimens K3, V3.

Following Tab. 8 table contains comparison of load-carrying capacity of models and specimens.

Tab. 8. Comparison table of load carrying capacity obtained from numerical model and experiments.

The mean value of numerically and experimentally obtained load carrying capacity is 0.956 and the standard deviation is 0.027.

The lateral movement of the beam-column flanges was followed when the failure mode was studied, namely if lateral-torsional bending occurred or not. Following graphs show the difference of deflections between compressed and tensioned flange lateral movement (U2-U1, see Fig.37, Fig.39) obtained from experiments and from numerical models, see Fig.61, Fig.62, Fig.63.

Fig.61. Relative deflection of compressed and tensioned flange, comparison between model and experiment, specimens K1, V1.


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The graphs show that tested specimens V2, K2 were fully stabilized by cassette profiles. In other cases the lateral movement of the flanges was significant.

5.4. Parametric study

During the experimental investigation six specimens were tested. From these results general conclusions could not be made. Therefore, a parametrical study was executed to expand the result set.

The parametric study was carried out on the calibrated models. The data expansion covered the length of the specimens, the profile types, numbers of screws between adjacent cassettes, thickness of cassette profiles and the bending moment distribution. The altered parameters were as follows:

sections: series of IPE and HEA sections (IPE80 - IPE600, HEA140 - HEA700),

length: 6, 8, 12, 15m,

number of screws between adjacent profiles: from 1 up to 30,

cassette thickness: 0.75, 1.5mm,

bending moment distribution: a) constant, b) triangular, c) bi-triangular, see Fig.64.


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Fig.64. Moment distribution

The ratio between the maximum bending moment and the axial force was always 1m (M/N=1m).

The stiffness of the cassette wall could be also influenced by the cassette profile length which was not introduced. It was found that it did not affect the results during the parametric study therefore it was not used as parameter.

The study embraced the full- and not-supported members’ load-carrying capacity calculation as well. Those values were used for definition of the greatness of the stabilization effect.

The parametric study was also used to determine the influence of the rotational restraint stiffness provided by cassette profile. Therefore specimens were solved with and without rotational stiffness.

Total amount of calculated cases: 8400.

5.4.1. Parametric study assumptions

The parametric study was carried out based on the following assumptions:

Ideal elastic-plastic material models of S235 and S355 were used.

Shear stiffness of the wall was not influenced by global buckling of wide flange of cassette profile.

Imperfection according to EN 1993-1-1 [12] was used as e0,y= L/300, e0,z=L/250.


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Chapter 6

Analysis of results

The project leads to several results that could be sorted into two main parts; the rotational stiffness provided by cassette profiles and the effect of the sheeting to the load carrying capacity of connected hot-rolled beam-column member. The first part was based on the experimental investigation followed by the theoretical analysis (see Chapter 6.1 bellow). The investigation on the sheeting restraint presented the main part of the work and contained experiments, numerical modeling and parametric study.

6.1. Rotational stiffness of cassette profile

This part of the project was focused on the determination of the rotational stiffness provided by cassette profiles. These results were necessary for the modelling of the main specimens and were therefore used as input parameters during the work.

Experimentally obtained results which lead to the rotational stiffness C of the connection are summarised in Tab. 3, see Chapter 4.2.2.

The results were divided into two groups (connection with 2x2 and 2x3 screws, respectively). The parameters on which the stiffness C depends were the thickness t and the distances b1 and b2. As illustrated on deformed connection in Fig.65, the stiffness C depends on distances of screws between column–cassette profile compression contacts. Distances b1 and b2 were relevant for given sign of torsion moment while distances a1 and a2 did not influence the connection behaviour.


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Fig.65. Decisive values, deformed specimen

In this case the total rotational stiffness is equal to the summation of individual stiffnesses of cassette profile on both sides of the column. The relation of stiffness on specified input parameters was searched in form of equation C / t

n, depending on function (kb1 + b2). Therefore two constants (n, k) were proposed and derived. Suitable approximation was found in linear form as shown in Fig.66, Fig.67.

Fig.66. Linear approximation of stiffness for screw arrangement 2x2

Fig.67. Linear approximation of stiffness for screw arrangement 2x3


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The coefficient k was determined by FE model, see Fig.68. The different behaviour of positive and negative bending moment of the cassette profile and its effect on the whole stiffness was followed by the model. The constant n was selected to minimize the scatter of results.

Fig.68. Numerical model of the connection loaded by positive bending moment, von Mises stress in MPa.

Two equations were derived, one for connection with 2x2 screws (6.2) and the other one for 2x3 screws (6.3).

1 2/ nC t kb b (6.1)

2.31 2(0.0554 0.0198 0.45)C b b t (6.2)

2.61 2(0.0757 0.0445 0.68)C b b t (6.3)

The mean value of ratio of experimentally and calculated (according to eq. (6.2) and (6.3)) acquired torsional stiffness Cexp/ Ccalc is 0.992 for 2x2 screws, the standard deviation is 0.158. For screw arrangement 2x3 the mean value is 1.004 and the standard deviation is 0.083.

6.2. Behaviour of column supported by cassette wall

The second part of the project was focused on determination of the effect of the sheeting on the load carrying capacity of the column and the understanding of the interaction between them. An experimental investigation and numerical model were used to achieve the results.


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6.2.1. Experimentally obtained results

Altogether six specimens were experimentally tested. These specimens gave results which may be used directly. Section IPE300 (S355 and lower), length from 5680 mm, boundary condition either ”V” or “K”, with connected both sided cassette wall thickness of 0.75mm and length 1200mm, at least two screws between each profile and column flange and two screws between adjacent cassettes, loaded by constant bending moment and axial force in ratio M/N=1m is fully supported in case that the cassette is connected to compressed flange. The sheeting connected to tensioned flange leads to lateral-torsional buckling failure with imposed axis of rotation.

6.2.2. Results from parametric study

Results from parametric study are sorted to three units:

impact of rotational stiffness to stabilization effect,

connected beam-columns flange behaviour,

lateral support stabilization effect on the load carrying capacity of the supported members.

6.2.2.1. Impact of rotational support

The cassette wall provides two independent supports to the connected member: lateral restraint and rotational restraint. The effect of the support was investigated. Two cases were compared: wall connected to the compression flange and wall connected to the tension flange. The effect of the rotational stiffness is significant only when the wall is connected to the tension flange. In the other case, when the compression flange is laterally restrained, rotational movement about the longitudinal axis did not occur and the rotational stiffness was not activated. This example is valid for most cases when the cassette wall connected at the compression flange is able to restrain the member against rotational movement.

The following figures show the effect of the rotational stiffness to the stabilization effect. Load carrying capacity was determined with and without rotational restraint (lateral restraint was always applied). The study was conducted for IPE and HEA sections with S235 and S355 materials. Two types of wall were used, one by sheeting thickness 0.75mm and the other for 1.5mm. Constant moment distribution with length from 2010 mm up to 15000 mm was used. The boundary conditions are “K” or “V”.

Fig.69. Ratio between load carrying capacity for rotationally supported and non-supported members IPE – boundary condition “K”, supported at tensioned or compressed flange


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Fig.70. Ratio between load carrying capacity for rotationally supported and non-supported members IPE – boundary condition “V”, supported at tensioned or compressed flange

Fig.71. Ratio between load carrying capacity for rotationally supported and non-supported members HEA – boundary condition “K”, supported at tensioned or compressed flange

Fig.72. Ratio between load carrying capacity for rotationally supported and non-supported members HEA – boundary condition “V”, supported at tensioned or compressed flange

Figures Fig.69 - Fig.72 present value between load carrying capacity of members with and without rotational support according to following equation:

_

_

with rot

without rot

R

R. (6.4)

The rotational stiffness influence for supported compressed flange is neglectible, especially for boundary conditions “V”. When the cassette wall is connected at tensioned flange the rotational


-73-

stiffness may grant by 133% - “K” and 77% - “V” members load carrying capacity for section IPE and 71% - “K” and 38% - “V”for section type HEA.

The impact of the rotational stiffness depends on the section properties as it is shown on Fig.73. Sections with greater torsional stiffness are able to act against rotation easier. This behaviour is reflected on the rotational stiffness impact.

Fig.73. Ratio between load carrying capacity for rotationally supported and non-supported members with length 6000 mm, impact of section torsional stiffness

6.2.2.2. Connected beam-columns flange behaviour

Distribution of deformation and internal forces along the member length is influenced by connected cassette wall. The cassette wall presented the diaphragm with complex behaviour. The wall includes relatively weak and stiff elements as the fasteners between adjacent cassette profiles and the cassette profiles respectively. This feature of cassette wall leads to additional local bending of the connected members about their weak axis and is studied in this section.

The following graph shows the different behaviour of the compressed flange for three types of lateral support, see Fig.74:

Wall: elastic lateral restraint is presented by cassette wall (thickness 0.75 mm, 6 screws/adjacent cassettes, 2 screws between cassette and flange, cassette length 3000 mm),

Full: lateral support provides full restraint,

Without: member without lateral restraint.

The investigated member properties IPE300, boundary conditions V, constant bending moment distribution, L=9000 mm, cassette wall connected at compressed flange. Fig.74 A shows compressed flange behaviour for all three cases “Full”, “Wall”, “Without”. Flange lateral deflection without any restraint is smooth with maximum amplitude 138 mm. Fully supported flange graph shows that points in place of support do not move laterally. In case three, cassette “Wall” provides (1.42 mm) nearly same support as “Full” (from amplitude) which leads to the fact that the wall support must be significant, see Fig.74 B. The lateral deflection comparison of all cases shows that “Wall” stabilize up to 99% against lateral movement if boundary values “Full” is equal to 100% and “Without” is assigned to 0%.


-74-

Fig.74. Compressed flange lateral deflection for different wall properties; A three cases: without support, cassette wall support, full support, B two cases: cassette wall support, full support (same graph with larger scale)

The cassette wall stiffness has a significant impact on the global deformation of the loaded member. The local lateral deformation amplitude (the difference of minimum and maximum deformation within the width of one cassette) is not influenced by cassette stiffness as shown in Fig.75. This result leads to the conclusion that the additional local bending from the sheeting connection does not depend on cross section properties and cassette wall stiffness.


-75-

Fig.75. Compressed flange lateral deflection for different wall stiffness, section IPE300 (t-thickness, ns-number of screws, cl-cassette profile length)

Fig.76 compares two identical members with same sheeting but different steel grade. The graphs prove that lateral movement of compressed flange is mainly influenced by cross-section properties and the steel grade not by the sheeting stiffness.


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Fig.76. Compressed flange lateral deflection for different steel grade, sections: IPE140, L=4 m; IPE300, L=8.4 m

6.2.2.3. Lateral support-stabilization effect

The last presented results are wall stiffnesses required for full (98% of load carrying capacity of laterally restrained member) or partial (80%) member stabilization by connected cassette wall. The results were worked out from parametric study.

Definition of full stabilization: supported column flange is restrained against lateral movement. The expression “stabilized” does not mean the same for the two investigated cases; sheeting connected at compressed flange and sheeting connected at tensioned flange. In the case when the compressed flange is restrained, “stabilized” really means that the member is globally stabilized against out-of-plane buckling. In the other case, “stabilization” means lateral-torsional buckling about imposed axis.

Above mentioned cases could be presented with following formulae:

Fully stabilized beam-column resistance is equal to member loading capacity under combined load (M+N) with ratio 1m and lower:

1 1

,

,

0.98 1.0y EdEdyy

y y LT pl y y

M M

MNk

f A W f

(6.5)

1 1

,

,

0.98 1.0y EdEdzy

z y LT pl y y

M M

MNk

f A W f

(6.6)


-77-

when LT, z = 1; for cassette wall connected at compressed flange. For cassette wall connected at tensioned flange the lateral-torsional buckling about imposed axis should be considered.

Partially stabilized beam-column resistance is equal to 0.8x member loading capacity under combined load (M+N) with ratio 1m and lower. The definition of reduction factors are same as for full stabilization:

1 1

,

,

0.8y EdEdyy

y y LT pl y y

M M

MNk

f A W f

(6.7)

1 1

,

,

0.8y EdEdzy

z y LT pl y y

M M

MNk

f A W f

(6.8)

Result tables are divided into six parts per section type according to boundary conditions and beam-column moment distribution. In each table are results for stabilized compressed and stabilized tensioned flange. The required wall stiffnesses are presented for full and for partial member stabilization as defined at the beginning of this paragraph. Steel grade S235 and S355 are also included in the results.

Values of wall stiffnesses for each wall arrangement were worked out by ECCS recommendation [25], see eq. (2.3). The considered minimum wall stiffness was defined as follows:

cassette profile sheeting thickness 0.75 mm

two screws per cassette-column flange contact

screws number between adjacent cassette: IPE, HEA140-180: 3 pcs.; 200-300: 5 pcs.; 330-600: 6 pcs.

The cassette profile length was also different, but as this does not influence the result, it was not presented. The screws at the flange were placed at the quarter of flange width from both sides. The maximum considered web stiffness was calculated with a cassette sheeting thickness of 1.5 mm. In the following result tables one stiffness value is given for several types of profiles because the minimum considered wall stiffness was sufficient for several members.

The numerical models were calculated according to GMNIA (Geometrically and Materially Nonlinear Analysis of the Imperfect Structure) analysis. The rotational stiffness of the connection between cassette profiles and column flange was applied during calculation. For members without values given in the following tables, the wall stiffness from used range did not satisfy the stabilization condition. For the stabilization higher wall stiffness is required, which could be achieved for example with higher number of screws between adjacent cassettes.


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Tab. 9. Required stiffness for V, section IPE – supported compressed flange


-79-

Tab. 10. Required stiffness for V, section IPE – supported tensioned flange


-80-

Tab. 11. Required stiffness for V, section IPE – supported compressed and tensioned flange


-81-

Tab. 12. Required stiffness for K, section IPE – supported compressed flange


-82-

Tab. 13. Required stiffness for K, section IPE – supported tensioned flange


-83-

Tab. 14. Required stiffness for K, section IPE – supported compressed and tensioned flange


-84-

Tab. 15. Required stiffness for V, section HEA – supported compressed flange


-85-

Tab. 16. Required stiffness for V, section HEA – supported tensioned flange


-86-

Tab. 17. Required stiffness for V, section HEA – supported compressed and tensioned flange


-87-

Tab. 18. Required stiffness for K, section HEA – supported compressed flange


-88-

Tab. 19. Required stiffness for K, section HEA – supported tensioned flange


-89-

Tab. 20. Required stiffness for K, section HEA – supported compressed and tensioned flange

The tables pointed out following conclusions:

Boundary condition “V” prevents higher resistance against section deplanation as “K”, which leads to member stabilization with lower cassette wall stiffness S.

Member with lower steel grade (S235 in this case) needs equal or lower wall stiffness for stabilization. This behaviour could be explain:

y yLT

cr

W f

M (6.9)

235 355S Scr crM M (6.10)

235 355 235 355S S S SLT LT LT LT (6.11)

wallLT

full

R

R (6.12)

The tables could be used for design. The sheeting is primarily designed for bending due to the exterior loads. When the stabilization effect is also considered the sheeting is subjected to combined actions. The project did not focus on this interaction but it is known that such combination is not usually governing for the steel cold-formed sheeting.


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Fig.77. Calculation tool for wall stiffness calculation

During the project a calculation tool was developed (Fig.77) to determine the wall stiffness according to ECCS recommendation [11]. The tool is available on website of Department of Steel and Timber Structures: http://www.ocel-drevo.fsv.cvut.cz.


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Chapter 7

Conclusions

The rotational stiffness of the connection between cassette profile and hot-rolled beam-column was determined according to experimental study (Chapter 4.2). Altogether 17 specimens were tested (Tab. 3). Different cassette profile thickness, connected column flange width and screw arrangement was investigated. Obtained results were used as input data for main experiments (Chapter 4.3). Formulae were derived for rotational stiffness calculation of connection for different screw arrangements, (Eq. (6.1).

A numerical model was developed and was used to prepare full scale experiments of beam-column connected with cassette wall (Chapter 5.2). The software package ANSYS was used. The modelling was focused to find the most suitable hot-rolled section for experimental investigation. The connected cassette walls were modelled by spring elements, beam-column by shells. The stiffness of the cassette wall was calculated according to ECCS [11]. During the numerical modelling the effect of the cassette wall position and their stiffness were followed. The full scale experiments were prepared with respect of obtained results.

Full scale tests were carried out to determine the effect of the cassette wall to beam-column load-carrying capacity (Chapter 4.3). Profile IPE300 with steel grade S355 was used. Two types of specimens were used with different boundary conditions; rigid frame support, fork support. Altogether 6 specimens were made; 3 for both boundary condition arrangements. The system lengths of the specimens were 5330 mm and 5680 mm according to boundary conditions. Three types of cassette wall arrangements were analysed: connected at compressed flange, connected at tensioned flange and half sided wall at compressed flange. To achieve combined load in member cantilevers were used for the load application. The ratio between bending moment and axial force was 1m. The load was applied until specimen failure. Tests pointed out that cassette wall could fully stabilize the connected beam-column (Chapter 4.3.4).

The numerical model was calibrated (Chapter 5.3.1) according to experimentally obtained results. Necessary changes were made to adjust the model according to specimens. A parametric study was carried out (Chapter 5.4) for sections IPE and HEA with following altered parameters: section type, beam-column length, number of screws between adjacent profiles, cassette thickness, bending moment distribution. Load carrying capacity and failure mode were observed. Altogether 8400 models for section type IPE and HEA were calculated.

The parametric study pointed out the following conclusions:

o The effect of rotational connection between cassette wall and flange was examined. The rotational stiffness influence for supported compressed flange is negligible,


-92-

especially for boundary conditions “V”. When the cassette wall is connected at tensioned flange the rotational stiffness may grant by 133 - “K” and 77% - “V” members load carrying capacity for section IPE and 71% - “K” and 38% - “V”for section type HEA (Chapter 6.2.2.1).

o The supported flange behaviour observation pointed out that the lateral deflection amplitude between full supported and supported by cassette wall was 1%. Cassette wall stiffness has a significant impact on the global deformation of the loaded member. The local lateral deformation amplitude (the difference of minimum and maximum deformation within the width of one cassette) is not influenced by cassette stiffness (Chapter 6.2.2.2).

o Design tables with required wall stiffness to ensure the full stabilization of beam-column were made for different cassette wall stiffnesses, compressed and tensioned flange connection, bending moment distribution, sections and lengths (Chapter 6.2.2.3). Two types of sections were studied: IPE and HEA. Calculation tool was made for cassette wall stiffness calculation, Fig.77. With help of the tables the positive effect of cassette wall could be used for design.


-93-

References

[1] Davies J.M.: Light gauge steel cassette wall construction, Nordic steel construction conference 98, p. 427-440, 1998.

[2] Davies J.M., Fragos A.S.: The local shear buckling of thin-walled cassette infilled by rigid insulation – 1.Tests, – 2. Finite element analysis, Eurosteel Coimbra 2002, p. 669-688, Akadémiai kiadó, Budapest, 2002.

[3] Davies J.M.: Light gauge steel cassette wall construction – theory and practice, Journal of Constructional Steel Research 62, p. 1077 – 1086, 2006.

[4] Baehre R.: Zur Schubfeldwirk und -bemessung von Kassettenkonstruktionen, Stahlbau 56, Heft 7, p. 197-202, 1987.

[5] Baehre R., Ladwein T.: Diaphragm action of sandwich panels, Journal of Constructional Steel Research 31, p. 305-316, Elsevier Science Limited, 1994.

[6] Baehre R., Holz R., Voß R.P.: Befestung von Trapezprofiltalfeln auf Stahlkassettenprofil- Stahlbau 57, Heft 10, s. 309-311, 1988.

[7] Kisin S.: The realistic effect of stressed skin design of typical industrial hall structure, Proceedings of the Conference Eurosteel 99, ČVUT v Praze, p. 243-246, 1999.

[8] Davies J.M., Omadibi I.A.: An ultimate limit state theory for stressed skin design, Proceedings of the Third International Conference on Structural Engineering, Mechanics and Computation, s. 87-92, Cape Town, South Africa, 2007

[9] Ladwein T.: Zur Schubfeldwirkung von Sandwichelementen, Stahlbau 62, Heft 11, p. 342-346, Heft 12, s. 361-363, 1993.

[10] Baehre R.: Zur Schubfeldwirkung von Aluminiumtrapezprofilen, Stahlbau 62, Heft 3, p. 81-87, 1993.

[11] European convention for construction steelwork: European recommendations for the application of metal sheeting acting as a diaphragm. ECCS Technical Committee 7, Technical working group 7.5, Publication 88, 1995.

[12] Eurocode 3: Design of steel structures – Part 1-1: General rules and rules for buildings, European Committee for Standardization, Brussels, 2005.

[13] Eurocode 3: Design of steel structures – Part 1-3: General rules -Supplementary rules for cold- formed members and sheeting, European Committee for Standardization, Brussels, 2005.

[14] Strnad M.: Spolupůsobení plášťů u lehkých ocelových hal, Stavební informační středisko, Praha, 1975.

[15] Čepička D.: Smykové spolupůsobení plášťů z tenkostěnných profilů, dizertační práce, FSv, ČVUT v Praze, 2003.

[16] Čepička D., Macháček J., May I.M.: Shear diaphragms in purlin roofs, Eurosteel Coimbra 2002, p. 235-242, Akadémiai kiadó, Budapest, 2002.


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[17] Rybín J.: Plášťové působení tenkostěnných kazet, dizertační práce, FSv, ČVUT v Praze, 2001.

[18] Nyberg G.: Diaphragm action of assembled C-shaped panles, Swedish council for buildings research, Document D9, 1976.

[19] DASt-Richtlinie 016: Bemessung und konstruktive Gestaltung von Tragwerken aus dünnwandigen kaltgeformten Bauteilen, 2. Überarbeitet Auflage, Stahlbau-Verlagssgesellschaft, 1992.

[20] The Steel Construction Institute: Steel designers' manual, Sixth Edition, Blackwell Science, 2003.

[21] The Steel Construction Institute: Design of Single-Span Steel Portal Frames to BS 5950- 1:2000, The Steel Construction Institute, 2004.

[22] Lindner J., Gregull T.: Torsional restraint coefficients of profiled sheeting, IABSE colloquium, p. 161-168, Stockholm, 1986.

[23] Boissonnade N., Jaspart J.P., Muzzeau J.P., Villette M.: New interaction formulae for beam-columns in Eurocode 3: The French Belgian approach, Journal of Constructional Steel Research 60, p. 421-431, 2004.

[24] Greiner R., Lindner J.: Interaction formulae for members subjected to bending and axial compression in EUROCODE 3 – the Method 2 approach, Journal of Constructional Steel Research 62, p. 757-770, 2006.

[25] European convention for construction steelwork: Rules for Member Stability in EN 1993-1-1, Background documentation and design guidelines, ECCS Technical Committee 8 – Stability, Publication 119, 2006.

[26] Lindner J.: Stabilisierung von Trägern durch Trapezbleche, Stahlbau 56, Heft 1, s. 9-15, 1987.

[27] Lindner J.: Stabilisierung von Biegeträgern durch Drehbettung – eine Klarstellung, Stahlbau 56, Heft 12, s. 365-373, 1987.

[28] Heil W.: Stabilisierung von biegedrillknickgefährdeten Trägern durch Trapezblechscheiben, Stahlbau 63, Heft 6, s. 169-178, 1994.

[29] Sochor R.: Únosnost vazníc a paždíků stabilizovaných proti klopení účinkem plášťů, Pozemní stavby 3, s. 124-131, Praha, 1976.

[30] Trahair N.S.: Flexural torsional buckling of structures, E&FN Spon, London, 1993.

[31] Pétursson E.H.: Column buckling with restraint from wall elements, Nordic steel construction conference 98, Volume 1, p. 157-166, Bergen,1998.

[32] Pétrusson E.H: Column buckling with restraint from sandwich wall elements, 9th Nordic steel construction conference, p. 291-298, Helsinki, 2001

[33] DIN 18 800:1990 Stahlbauten, Teil 1-4.

[34] Fischer M.: Zum Kipp-Problem von kontinuierlich seitlich gestützten I-Trägern, Stahlbau 45, Heft 4, p. 120-124, 1976.

[35] Vraný T.: Rotační podepření tenkostěnné ocelové vaznice krytinou, Inaugural dissertation, CTU Prague, 2002.

[36] Hapl V., Vraný T.: Vliv spolupůsobící konstrukce a konstrukčního detailu na únosnost ohýbaného prvku, Teoretické a konštrukčné problémy oceľových a drevených konštrukcií - Ľahké oceľové konštrukcie, s. 111-116, Mojmírovce, 2005.

[37] www.kovprof.cz


-95-

[38] ČSN 73 2611:1978 Dimension and shape deviations of steel structures

[39] Release 10.0 documentation for ANSYS, ANSYS Inc., 2005


-96-

Appendix A – Tables of measured data

Data from experimentally measured data:

V1, V2, V3, K1, K2, K3


-97-

Specimen V1


-98-

Specimen V2


-99-

Specimen V3


-100-

Specimen K1


-101-

Specimen K2


-102-

Specimen K3


-103-

Appendix B – Calculation example

Following example show how to use the tables for design.

Check following member. IPE 450 with length 9 m, S355. Connected cassette profiles at compressed flange, width 600 mm, S320, length 3 m, thickness 0,75 mm, fasteners between adjacent cassettes at step 600 mm. Fasteners flexibility: for adjacent cassettes 0.3 mm/kN, for connection between cassette and column flange 0.35 mm/kN. Distances between screws at column flange 500 mm. Edge members are not present at wall. Member is under combined axial and bending load with ratio ≤ 1 m, triangular moment distribution. The member boundary conditions are “K”.

Wall stiffness calculation according to ECCS recommendation:

nsh = 9000/600 = 15, (number of cassette profiles in wall)

Bu =600 mm, (width of cassette profile)

t = 0.75 mm, (cassette profile thickness)

L = 3000 mm, (cassette profile length)

sp = 0.35 mm/kN, (fasteners flexibility for screws between cassette profile and column flange)

ss = 0.3 mm/kN, (fasteners flexibility for screws between adjacent cassette profiles)

p = 500 mm, (distance between screws at column flange)

ns = 10, (number of screws between adjacent cassette profiles)

The wall flexibility calculation according to (2.3)

1,2 2,1 2,2c c c c

1,2 2 1 /c B EtL

22,1 2 /pc Bs p L

2,2 1 /s sh sc s n n

After substitution:

1,2 2 600 15 1 0.3 /(210 0.75 3000) 0.0495 /c mm kN

22,1 2 600 15 0.35 500 / 3000 0.35 /c mm kN

2,2 0.3 15 1 /10 0.42 /c mm kN

0.0495 0.35 0.42 0.82 /c mm kN

Stiffness is the reverse value of flexibility:


-104-

1/ 0.82 1.22 /S kN mm

This value can also be obtained with help of the calculation tool shown in Fig.77.

According to design tables the required wall stiffness for boundary conditions “K”, wall connected at compressed flange, triangular bending moment distribution, member length 9000 mm, S355, for full stabilization: 0.52 kN/mm, see Tab. 12.

0.52 /reqS kN mm reqS S

The cassette wall provides full stabilization against lateral torsional buckling for member.

Member check under combined axial force and bending moment, full stabilized, cassette wall connected at compressed flange:

Check the member resistance under combined axial force and bending moment, supported compressed flange, full stabilization (IPE450, S355, L=9m):

0.52 /reqS kN mm , see Tab. 12

1.22 /S kN mm - wall properties see above calculated example

reqS S - cassette wall stiffness condition for full stabilization passed

MEd = 450 kNm

NEd = 450 kN

iy = 184.8mm

Lcr,y = 9000 mm

Wpl,y=1702.103 mm3

9000 10.64

184.8 76.06y

0.874y (buckling curve a)

355 9882 3508yf A kN

1.00myC for 1.00

3

31

450.101 0.2 1.00 1 0.64 0.2 1.07

/ 0.874 3508.10 /1Ed

yy my yy Rk M

Nk C

N

3

31

450.101 0.8 1.00 1 0.8 1.12

/ 0.874 3508.10 /1Ed

yy myy Rk M

Nk C

N

1.07yyk

1 1

,

,

1y EdEdyy

y y LT pl y y

M M

MNk

f A W f

bending moment distribution


-105-

Due to full stabilization the reduction factor 1.0LT

3 6

3 3

450.10 450.101.07 0.94

0.874 3508.10 /1 1.0 1702.10 355 /1

0.94 1

Satisfactory

Member check under combined axial force and bending moment, full stabilized, cassette wall connected at tensioned flange:

Check the member under combined axial force and bending moment, supported tensioned flange, full stabilization (IPE450, S355, L=9m).

0.52 /reqS kN mm , see Tab. 13

1.22 /S kN mm - wall properties see above calculated example

reqS S - cassette wall stiffness condition for full stabilization passed

C = 1.98 kNm/m/rad - connection rotational stiffness calculated by calculation tool Fig.77

MEd = 200 kNm

NEd = 200 kN

iy = 184.8mm

iz = 41.2mm

Lcr,y = 9000 mm

A = 9882 mm2

Wpl,y=1702.103 mm3

Iw = 791.109 mm6

It = 668.7.103 mm4

9000 10.64

184.8 76.06y

0.874y (buckling curve a)

For critical elastic moment calculation LTBeam software was used with following boundary conditions: continuous lateral restraint at tensioned flange – fixed, contionuous rotational restraint C = 1.98 kNm/m/rad, see draft.

Mcr = 214 kNm

6

1702000 3551.68

214.10y y

LTcr

W f

M

0.284LT (buckling curve b)

bending moment distribution


-106-

355.9882 3508yf A kN

1.00myC for 1.00

3

31

450.101 0.2 1.00 1 0.64 0.2 1.07

/ 0.874 3508.10 /1Ed

yy my yy Rk M

Nk C

N

3

31

450.101 0.8 1.00 1 0.8 1.12

/ 0.874 3508.10 /1Ed

yy myy Rk M

Nk C

N

1.07yyk

1 1

,

,

1y EdEdyy

y y LT pl y y

M M

MNk

f A W f

3 6

3 3

200.10 200.101.07 1.31

0.874 3508.10 /1 0.284 1702.10 355 /1

Not satisfactory.

, 2 2

1 wcr T t

o T

EIN GI

i l

2 2 2 2 2 2 2 2 2 2184.8 41.2 225 0 86473.48o y z o oi i i y z mm

294.1oi mm

6 96

, 2 2

1 210.10 791.1081.10 668700 700.7

294.1 9000cr TN kN

,

9882 3552.24

700700y

Tcr T

Af

N

0.176T (buckling curve b)

0.6 0.6 1.07 0.64zy yyk k

355 9882 3508yf A kN

1 1

,

,

1y EdEdzy

T y LT pl y y

M M

MNk

f A W f

3 6

3 3

200.10 200.100.64 1.07

0.176 3508.10 /1 0.284 1702.10 355 /1

Not satisfactory.

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