Buckling of T-section beam-columns in aluminium with or without transverse welds

0 0.2 0.4 0.6 0.8 1 1.2 1.4

-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2

L=500 mm L=1020 mm L=1020 mm L=1540 mm L=1540 mm

c

Sd z xz

N A f

η

χ ω η

çç ÷÷

Totally 47 beams

c

y Sd

LT xLT y Rd

M M

γ

χ ω

ç ÷ Flange in compression

Web in compression

Buckling of T-Section Beam- Columns in Aluminium with or without Transverse Welds

Stefan Edlund

TRITA-BKN. Bulletin 54, 2000 ISSN 1103-4270

ISRN KTH/BKN/B--54--SE

Buckling of T -Section Beam-Columns in Aluminium with or without Transverse Welds

Stefan Edlund

Department of Structural Engineering Royal Institute of Technology S-100 44 Stockholm, Sweden

TRITA-BKN. Bulletin 54, 2000 ISSN 1103-4270

ISRN KTH/BKN/B--54--SE

Doctoral Thesis

©Stefan Edlund 2000

Abstract

This thesis deals with buckling of T-section beam-columns in aluminium with or without transverse welds. Totally 26 unwelded and 39 transversely welded T-section beam-columns were tested. Five of the welded beams were clamped. All unwelded and the rest of the welded beams were simply supported for bending. The welding affects the load-carrying capacity of the beam-columns, because it introduces a heat-affected zone with reduced strength. All beam- columns had the same theoretical cross-section dimensions. The thickness of the flange and the web was 6 mm. The depth and the width were 60 mm. The theoretical beam lengths were 500, 1020 and 1540 mm, respectively. Tensile tests of both the parent and the heat-affected material were made in order to determine the material properties.

Comparisons were made between the buckling tests and three codes, the European aluminium code Eurocode 9, the British aluminium code BS 8118 and the Swedish steel code BSK. Some interpretations of the codes had to be made, be cause the codes are not totally clear when applied on T-sections. Most problems are related to the fact that the section modulus is not the same for the two edges. In the interaction formulas, only the edge in compression was

considered when the bending moment capacity was calculated. The chosen interpretation of the codes was often very conservative when compared with the buckling tests.

The general-purpose finite element program Abaqus was used to develop numerical models of the tested beam-columns. Shell elements were used. The models were calibrated with the results from the buckling tests. The stress-strain curves used in the finite element calculations were obtained from the tensile tests. The results of the finite element calculations were

satisfactory. The numerical models could predict the load carrying capacity accurate enough. A similar deformed shape of the tested and calculated beam-columns was also obtained.

Different modifications of Eurocode 9 were analysed in order to improve the results. O ne modification was that the ultimate strength of the heat-affected zone was used instead of the yield strength of the parent material when the buckling reduction factors of a welded section were calculated. The calculation of the bending moment capacity in the interaction formulas was also modified. The plastic section modulus was used to calculate the bending moment capacity when the tip of the web was in tension. When the bending moment acted in the opposite direction, the calculation of the bending moment capacity was based on a modified classification of the web element. The investigation in this thesis indicates that Eurocode 9 is too severe in the classification of the cross-section. The way the bending moment capacity is calculated for unsymmetric cross-sections in the interaction formulas needs to be further analysed. Tensile failure at the tip of the web was also discussed. This thesis shows that the codes need to be improved when it concerns unsymmetric cross-sections. Some information how Eurocode 9 can be improved is given.

Keywords: Buckling, buckling tests, Eurocode 9, aluminium beam-columns, beam-columns,

T-sections, finite element analysis, transverse welds, codes, unsymmetric cross-sections.

Preface

The research presented in this doctoral thesis was carried out at the Department of Structural Engineering at the Royal Institute of Technology in Stockholm.

Especially I would like to thank:

My supervisor Prof. Torsten Höglund for his guidance, help and for being a discussion partne r, assoc. Prof. Costin Pacoste for reading the manuscript and giving valuable comments, SkanAluminium and SAPA for the financial support, SAPA for delivering the aluminium profiles free of charge and the laboratory personnel, Mr. Stefan Trillkott, Mr. Claes Kullberg, Mr. Olle Läth and Mr. Daniel Hissing, for performing the tests.

Stockholm, February 2000

Stefan Edlund

Notations

A Gross cross-section area A ef Effective cross-section area E Modulus of elasticity G Shear modulus

I ef . x Effective second moment of area, major axis I x Second moment of area, major axis

I y Second moment of area, minor axis K v Saint-Venant torsion constant K w Warping constant

M Bending moment M cr Critical bending moment

M RSx Bending moment capacity according to BS 8118 M Rxd Bending moment capacity according to BSK M y Rd _. Bending moment capacity according to Eurocode 9 N Axial force, centric or eccentric

N cr Critical axial force

ef x c

W . . Effective section modulus of the edge in compression, major axis

ef x t

W . . Effective section modulus of the edge in tension, major axis

el x c

W _{. .} Elastic section modulus of the edge in compression, major axis

el x t

W _{. .} Elastic section modulus of the edge in tension, major axis W el. y Elastic section modulus, minor axis

W pl x . Plastic section modulus, major axis W _{pl. y} Plastic section modulus, minor axis b Width of flange

b f Width of flange element b w Depth of web element e Load eccentricity

0 2 ,

f Yield strength of parent material f u Ultimate strength of parent material f haz Ultimate strength of heat-affected material h Cross-section depth

k 1y Unsymmetry factor used in Eurocode 9 L

l, Beam length l c Buckling length

r Radius between flange and web t f Flange thickness

t w Web thickness

t y Cross-section constant

w mid Midspan deflection

y _{ef . gc} Location of centre of gravity for an effective cross-section y gc Location of centre of gravity

y pl Location of plastic neutral axis

y s Distance between centre of gravity and shear centre z haz Location of transverse weld

ε max Maximum strain ε min Minimum strain

Abbreviations

EC9 Eurocode 9

haz Heat-affected zone

lap Load application point

Contents

Abstract Preface Notations Abbreviations

1 Introduction . . . 1

1.1 Aim and scope . . . 1

1.2 Previous work . . . 2

2 Buckling tests . . . 9

2.1 Introduction . . . 9

2.2 Tensile tests . . . 13

2.3 Results . . . 19

3 Comparisons between tests and different codes . . . 25

3.1 Introduction . . . 25

3.2 Buckling according to Eurocode 9 . . . 33

3.2.1 Cross -section classification . . . 33

3.2.2 Effective cross-section . . . 35

3.2.3 Flexural buckling . . . 37

3.2.4 Lateral-torsional buckling . . . 39

3.3 Buckling according to BS8118 . . . 42

3.3.1 Cross -section classification . . . 42

3.3.2 Effective cross-section . . . 44

3.3.3 Flexural buckling (major axis buckling) . . . 46

3.3.4 Lateral-torsional buckling (minor axis buckling) . . . 47

3.4 Buckling according to BSK . . . 48

3.4.1 Cross -section classification . . . 48

3.4.2 Effective cross-section . . . 50

3.4.3 Flexural buckling . . . 51

3.4.4 Lateral-torsional buckling . . . 53

3.5 Critical loads according to the theory of elastic beam-columns . . . 54

3.6 Comparisons between buckling reduction factors . . . 57

3.7 Results . . . 58

4 Finite element calculation . . . 69

4.1 Introduction . . . 69

4.2 Material model . . . 69

4. 3 Finite element model . . . 75

4.4 Results and conclusions . . . 82

5 Further analysis of Eurocode 9 . . . 89

5.1 Buckling and tensile failure . . . 89

5.2 Section check . . . 100

5.3 Suggestions for improvements . . . 105

6 Conclusions, comments and further research . . . 121

7 References . . . 123

Appendix A. Photos of the test equipment . . . 129

Appendix B. Load-deflection curves of the tested beam-columns . . . 131

Appendix C. Example of Abaqus input files . . . 149

List of Bulletins . . . 155

1. Introduction 1.1 Aim and scope

Load carrying constructions in aluminium are increasingly used in offshore and transportation industry. The main reasons are the extrusion technique, corrosion resistance and the lightness of the material. Examples of constructions in the offshore industry are helicopter decks, telescoping bridges, stair towers, cable ladders, accommodation modules and other parts exposed to the marine environment. In the shipping industry aluminium constructions are used in hulls for high-speed ferries and other vessels, topside parts of ships and large gas storage tanks. The car industry is using aluminium constructions in the space-frame concept and energy absorbing components. Aluminium constructions are used in train coaches.

Furthermore, the use of aluminium constructions in the aircraft industry has a long history.

Lot of research has been made on bi-symmetric I-sections, whereas unsymmetric cross- sections are not so widely studied. Most steel and aluminium codes are mainly written for bi- symmetric I-sections and rectangular hollow sections and are just partly adjusted to fit other cross-sections. The use of the extrusion technique makes unsymmetric cross-sections in aluminium more common than in steel. It is therefore especially important that aluminium codes can handle unsymmetric cross-sections. Extruded aluminium profiles can be adjusted to fit many different purposes and therefore they often end up unsymmetric. These are some reasons for studying buckling of aluminium beam-columns with unsymmetric cross-sections.

The T-section is one of the most monosymmetric sections to be found. To choose a totally unsymmetric cross-section would likely have been a too large step.

Most of the aluminium beam-columns in this thesis are transversely welded. When aluminium is welded there will be a heat-affected zone with reduced strength. This will affect the load carrying capacity of the beam-columns. When structural steel is welded there will normally not be a zone with reduced strength. For hig h strength steel, such a reduced strength zone may however occur, but the strength is not so drastically reduced as for aluminium. The width of the heat-affected zone is much smaller in steel than in aluminium due to the difference in heat transfer. The he at-affected zone makes buckling of aluminium beam-columns more

complicated than steel beam-columns. The loss of strength in the heat-affected zone is a disadvantage for aluminium in comparison to steel. The effect of the loss of strength can to some extent be reduced by making a “smart” construction. The extrusion technique is a usefully tool for this. Suitable cross-sections can be made and welds can be located where they do less harm. Modern welding techniques such as friction stir welding cause less reduction of the strength in the heat-affected zone but is difficult to use for transverse welding.

The content of this thesis is not only applicable on T-sections in aluminium. Parts of it are also applicable to other unsymmetric cross-sections, like monosymmetric I-sections. This type of cross-sections are perhaps more common than T -sections. A T-section can be seen as an extreme case of a monosymmetric I-section. All monosymmetric cross-sections have that in common that the section modulus for the two edges is not the same. How this should be treated is not clearly explained in the codes of today. At least not for the codes analysed in this thesis.

Even though aluminium and steel are two different materials and have different qualities, the

way of calculating aluminium and steel constructions have similarities. Parts of this thesis

could therefore also be applicable on steel constructions. Hopefully this thesis can contribute to

make the future codes better, especially aluminium codes but perhaps also steel codes.

The use of beam-columns with monosymmetric I-sections is discussed in Hernelind et al. [25].

When the compressive axial load is eccentric, a monosymmetric cross-section can be more material effective than a symmetric one. One practical example where eccentric loads exist is a beam-column with loads from a roof and an overhead crane. Even a T -section can be more material effective than a bi-symmetric I-section under certain loading conditions. When considering that the usage of a building can be changed in the future, it can however be preferable to choose a not too unsymmetric cross-section.

The objectives of this thesis are:

1. Perform a literature search to find out was has been done. A literature search increases the knowledge of the topic being considered and avoids duplicate work.

2. Perform buckling tests as reference material when evaluating different calculation methods.

It is also important that they are documented so accurate that other future researchers can make use of them. Buckling tests are important when evaluating different design formulas.

The tests should preferable be unique.

3. Evaluate different codes and compare the results from the buckling tests with the results from the codes. Eurocode 9 is one of the most important codes.

4. Develop a numerical model and see if this model can predict the load carrying capacity of the beam-columns accurate enough. The model should not only be able to predict the capacity, it is also important that it describes the physical behaviour of the tested beam- columns. Otherwise it can be more difficult to claim that it can predict the capacity for other not tested beam-columns. The goal of the development of the model is to have a tool that numerically can simulate a buckling test. It is time consuming to learn the chosen computer program, develop the numerical model and to calibrate the model with physical tests. To come up with realistic results the computer program has to be advanced and these programs tend to be non-user-friendly. The user must have knowledge about the theory used in the program. However, when the numerical model has been developed, it is fast and easy to use the model for extensive numerical simulations. Parametric studies and perhaps also shape optimisation can be performed.

5. Make suggestions for improved design of aluminium beam-columns with unsymmetric cross-sections with or without transverse welds.

1.2 Previous work

Below is a list of short descriptions of previous work related to the work presented in this

thesis. The search of literature was focused on buckling of aluminium columns or beam-

columns, with or without transverse welds. The references are chronologically ordered. The

undated report by Gilson and Cescotto [23] was inserted where it was believed to be produced.

Hill and Clark [26] made buckling tests on extruded I-section beam-columns. Four different lengths and load eccentricities were used. Totally 33 beam-columns were tested and they failed by flexural-torsional buckling. Comparisons with some theories were made. One conclusion was that an earlier proposed design formula gave unconservative results. The work by Hill and Clark was comment on in an appended discussion.

In Clark [14] buckling tests on eccentrically compressed aluminium beam-columns were made . The cross-sections were rectangular, solid or hollow. Totally 36 buckling tests were made. The alloy was AA6061-T6. The failure was plane plastic buckling. Comparisons were made with various design formulas. One conclusion was that an existing design formula used for lateral buckling also could be used for the tested beam-columns.

Hill et al. [27] discussed the design of aluminium beam-columns. Different interaction formulas were used. Comparisons were made with earlier buckling tests. The results of 12 eccentrically compressed aluminium beam-columns with circular tube cross-sections were presented. Some proposals were made. Only flexural buckling was considered. In an appended discussion the work was comment on.

A theoretical study of how the shape of the stress-strain curve affects the load carrying capacity of compressed aluminium columns is given in Baehre [2]. Local and flexural-torsional buckling are not considered.

Höglund [31] described a method to design beam-columns with respect to flexural buckling.

The way Eurocode 9 treats the effect of transverse welds has its origin in this design method.

In Bernard et al. [5] buckling of unwelded axially compressed aluminium columns with I- or O-sections were considered. Compression and tensile tests of the material were made. The residual stresses of the extruded profiles were measured. Normally the residual stresses were lower than 30 MPa, but a few peaks of 50 MPa were found. Totally 66 columns were tested. A computer program was used to calculate buckling curves, i.e. the buckling reduction factor as function of the slenderness parameter. The program could only consider in-plane buckling.

Imperfections were considered. Ramberg-Osgood material model was used based on the material data from the compression tests. The buckling tests were used to check the buckling curves. This work was used by the ECCS committee 16, described by Frey and Mazzolani [21].

Klöppel and Bärsch [35] produced tables with buckling reduction factors for axially

compressed aluminium columns. The tables were produced with help of a German code for

steel structures and the results from an extensive test series with compressed aluminium

columns. Only flexural buckling and extruded unwelded columns were considered. Among

other things, the effect of imperfections, undesired load eccentricity, the shape of the cross-

sections and different material properties were studied. The test series was likely the same as

the flexural buckling tests presented in Klöppel and Bärsch [36].

Klöppel and Bärsch [36] presented results of a test series with 120 unwelded aluminium columns with I-, T- or tubular cross-sections. Only flexural buckling was considered for these columns. Three different alloys, three different slenderness values and some undesired load eccentricity was used. The results of a test series with 39 columns with channel sections were also presented. The axial load was applied at the centre of gravity and the column-ends were free to warp. The columns with low slenderness failed by local buckling whereas the other columns failed by flexural-torsional buckling. Also some tests with beams failing by lateral- torsional buckling was made as well as some buckling tests on shell cylinders. The results of the tests were compared with a new version of the German aluminium code DIN 4113 and good agreement was obtained.

Frey and Mazzolani [21] presented the results of ECCS (European Convention for

Constructional Steelwork) committee 16, “Aluminium Alloy Structures”. The main task for this committee was to establish buckling curves for axially loaded, unwelded and extruded aluminium columns. The effect of initial curvature, variation of wall thickness of hollow cross- sections and different material properties of the different alloys were considered.

Valtinat and Müller [56] used a computer program for beam-columns to calculate the buckling load of longitudinally or transversely welded aluminium columns, centrically or eccentrically loaded. The alloy was AA6082-T6. Only bi-symmetrical I-sections were considered. By a parametric study the upper and lower bound of the influence of the welds on the strength of the columns was investigated. A design method for longitudinally welded columns was proposed.

Gilson and Cescotto [23] made flexural buckling tests on extruded unwelded aluminium columns with T-sections. Tensile and stub column tests were made to determine the material properties. The dimensions of the cross-section and the imperfections were measured. Totally 14 buckling tests were made. The capacities from the tests were compared with the capacities from ECCS recommendations and some computer program. Good agreement was obtained between the capacities from the tests and the computer program. ECCS recommendations were conservative.

Kitipornchai and Wang [34] made a theoretical study on lateral buckling of T-beams under moment gradient. An energy approach and Fourier series were used. Two assumptions were made: the material was linear elastic and the cross-section was rigid. Beam theory was used.

One conclusion was that a design formula used in some codes was unsafe to use. One of these codes was Eurocode 3, the European steel code.

Valtinat and Dangelmaier [57] dealt with buckling of unwelded and welded axially loaded aluminium columns mainly with I-, circular or square tube cross-sections. The results from interaction formulas of a German code and a German dissertation were compared with the results of an earlier theoretical study and with some previously made buckling tests. Some of the buckling tests were made on columns with hollow cross-sections with transverse welds.

One of the results was that the position of the transverse welds only had a minor influence on

the load-carrying capacity of the columns. The German dissertation gave in general better

results than the German code.

In Baehre and Riman [3] buckling tests on extruded aluminium columns with rectangular hollow cross-sections and transverse welds were made. Totally 123 columns were tested. A computer program was also used to calculate the load carrying capacity of aluminium columns.

A reduction factor was proposed to be inserted in the interaction formulas of the draft aluminium code DIN 4113. The reduction factor takes into account the position of the transverse weld. A new interaction formula was also proposed.

Bulson and Nethercot [11] gave some aspects on the draft version of BS 8118 regarding the design of aluminium columns, beams and beam-columns.

Nethercot [44] presented aspects on the design of aluminium columns in the draft version of BS 8118. The interaction formulas of the draft code were presented and the results of them were compared with many buckling tests found in the literature.

Hong [28] presented buckling design curves for aluminium columns failing by flexural buckling. Local and flexural-torsional buckling were not considered. The type of alloy, symmetry of the cross-section and welding condition affected the shape of buckling curves.

The buckling curves were the results of a study at Cambridge during 1979-1983 and were recommended to the revisionary committee of the British aluminium code CP118. Likely these curves were at least partly adopted in BS 8118.

Bradford [8] developed a finite element method that incorporated plate behaviour for

modelling the lateral-distortional buckling of elastic T-beams. The theory does not assume that the cross-section is rigid. The method was verified with other theoretical methods. When the beam was subjected to equal end moments such that the tip of the web was in tension, lateral- distortional and lateral-torsional buckling gave similar result. Under the same loading

condition but when the tip of the web was in compression, lateral-distortional buckling gave a lower moment capacity than lateral-torsional buckling. For a beam with length-to-height ratio of 15, the buckling moment was 36% lower. Lateral-torsional buckling assumes that the cross- section is rigid.

Höglund [32] compared results from buckling tests found in the literature with different interaction formulas, among others a proposal by Mazzolani and a proposal based on the Swedish steel code BSK [7]. The results from 220 buckling tests were used. The tested beam- columns were all unwelded and centrically or eccentrically compressed. The shape of the cross-sections varied. The literature, where the tests were found, is included in the reference list of this thesis.

Benson [4] tested 19 hollow square, thin-walled aluminium extruded beam-columns. The test specimens were eccentrically compressed. The alloy was AA6063-T6. The test results were used to evaluate the design methods in the Swedish Regulation for Light Gauge Structures, the ISO working draft ISO/TC 167/SC 3 N122E and a modified version of the Swedish steel code BSK.

Höglund [33] presented interaction formulas for flexural and lateral-torsional buckling of I-

beam-columns. The formulas are used in the Swedish steel code, BSK. Comparisons were

made with tests on steel and aluminium beam-columns reported in the literature. The

agreement was found to be excellent, especially for the aluminium tests.

Hong [29] used a computer program to simulate flexural buckling of transversely welded aluminium columns with solid rectangular cross-sections. Local and flexural-torsional buckling were not considered. Ramberg-Osgood material model was used. Transverse welding was simulated by depositing weld material on the four faces of the tubular section. The alloy was AA6061. To verify the results of the computer simulations buckling tests on aluminium columns with square tubular cross-sections were made. Especially the effect of the transverse weld’s position on the load carrying capacity was studied. Different buckling curves were drawn. One finding was that a sine curve was suitable to be used to describe the load carrying capacity of a column as function of the transverse weld’s position, similar to the calculations in Eurocode 9 and the modified Swedish steel code BSK. Only pin -ended columns were considered.

The paper by Nethercot [45] deals with buckling of aluminium columns, beams and beam- columns with transverse welds. Numerical results from the two computer programs INSTAF and BIAXIAL were compared with a draft version of BS 8118. The two computer programs are described in Lai and Nethercot [37]. One result was that it is only somewhat conservative to design a transversely welded aluminium column as if the whole column consisted of heat- affected material, irrespective of the transverse weld’s position.

Buckling curves for aluminium columns, beams, plates and shear webs were discussed in Marsh [41]. The effect of welds was also discussed.

Lai and Nethercot [37] used two finite element computer programs to analyse welded and unwelded aluminium structural members. The first program, INSTAF, was used for in-plane analysis. It could consider geometric and material nonlinearity, the effect of residual stresses and strain hardening of the material. The results of the program were compared with some earlier made buckling tests and showed good agreement. The second program, BIAXIAL, was used to analyse the 3D-behaviour of beam-column elements. This program could consider the effect of twisting, warping, residual stresses and initial curvature. Both programs could

consider the effect of longitudinal and transverse welds. A piecewise form of Ramberg-Osgood material model was used in both programs. Five unwelded and 22 welded beams were tested in 4-point bending tests to check parts of the programs. All tested beams had a rectangular cross- section, which expected the beams to fail in pure bending. Plates of different lengths were welded to the two flanges to create the heat-affected material. Tensile tests were made both on parent and heat-affected material. The beams were tested up to a reasonable high deflection but not up to failure. INSTAF was generally conservative with a maximum difference of 10%

between the tested and calculated load. The two programs were used to make parametric

studies on transversely welded beams and columns, with bi-symmetrical I-sections. The

columns were pin-ended and subjected to axial load only. The beams were simply supported

with a point load at midspan. Also some other structures were calculated. The parametric study

showed that it is unsafe to neglect the softening effect of welds at the ends of columns. It also

showed that the load carrying capacity of columns were lowered most when the welds were

located at mid-height. The capacity was almost equal as if the whole column was made of heat-

affected material.

The two computer programs INSTAF and BIAXIAL described above were used in Lai and Nethercot [38] to calculate various types of axially loaded aluminium columns. The purpose was to check the column design curves of a draft version of BS 8118. All cross-sections were

“compact” for which no local buckling occurred. Imperfections were considered. The cross- sections were I- or T-shaped. The columns were unwelded, transversely welded or longitudinal welded. The strength of most types of columns was safely predicted by the method of the draft code. However, some improvements of the draft code were presented, especially for

transversely welded columns when the welds were located at the column ends.

Sanne et al. [49] describe buckling tests of unwelded aluminium columns with I-sections. A few beam-columns were tested with a centric load, but for most beam-columns the

compressive load was applied eccentrically. The maximum eccentricity was 5 times the depth of the cross-section. Also tests with unequal load eccentricity at the two ends of the beam- column were made. Totally 40 beam-columns were tested. The alloy was AA6351. The material properties were determined by tensile tests. The load carrying capacity from the tests were compared with the capacities from the Swedish steel code BSK, the ECCS

recommendations and the Norwegian aluminium code NS 3471. BSK gave the best results.

In Sanne [50] 24 extruded aluminium beam-columns with I-sections were tested. The beam- columns were welded with one transverse weld at different sections along the beam-column.

The load was applied with an eccentricity such that major axis bending and axial compression occurred. Some beam-columns were loaded centrically. The alloy was AA 6351-T6. The results were compared with a modified version of the Swedish steel code, BSK. The modifications made it possible to take into account the weakening effect of the weld. The comparisons showed that it was possible to use the modified BSK under the condition that the ultimate strength of the heat-affected zone was used as design strength. Using the yield strength will give very conservative results.

The book by Sharp [52] deals with design of aluminium structures. Much of the research presented in the book was conducted at Alcoa Laboratories (Aluminium Company of America) during the last 30-40 years. Among other things, the design of columns, beams and beam- columns were discussed.

Hellgren [24] presented the results of two test series with totally 28 extruded beam-columns with I-sections. The alloy was AA 6351-T6. The beam-columns were welded with one transverse weld at different sections along the beam-column. The compressive load was applied with an eccentricity in one or two directions. For some beam-columns the load was applied centrically. The results from the tests were compared with BS 8118 and a draft version of Eurocode 9. The draft Eurocode 9 was less conservative than BS 8118.

Corona and Ellison [15] made an experimental and theoretical study of T-beams under pure bending. The investigation was focused on the case when the tip of the web was in

compression. The tested beams were hot rolled and made of steel. They had length-to-height ratios ranging from 10 to 20. Tensile and compression tests were made to determine the material properties. Some theory was developed to calculate the moment-curvature response.

The theory was only briefly described, but the stress-strain curve was trilinear. The theory showed good agreement with the tests.

The work by Edlund [17,18,20] is included in this thesis.

Bradford [9] studied lateral-distortional buckling of elastic T-section cantilevers. The study was pure theoretical where the finite element method described in Bradford [8] was used. The case when the tip of the web was in compression was studied. Lateral-distortional buckling generally gave a lower buckling load than lateral-torsional buckling.

Langhelle [39] studied aluminium structures exposed to fire. Eight buckling tests were made at room temperature. The aluminium columns in these tests had rectangular hollow cross-sections and were centrically compressed. The alloy was AA6082 and the temper was T4 or T6. Two columns were transversely welded at mid-height. The wall thickness was 5 or 7 mm. Global buckling occurred before local buckling for the columns with 7 mm wall thickness. For the columns with 5 mm wall thickness, global and local buckling occurred simultaneously. Besides the 8 tests at room temperature, 23 buckling tests were made at elevated temperature.

Comparisons were made with Abaqus, another nonlinear finite element program and with three different codes, Eurocode 9, BS 8118 and the Norwegian aluminium code NS 3471.

The paper by Rasmussen and Rondal [47] is dealing with column curves for extruded

aluminium columns failing by flexural buckling. A column curve is the same as the previously

used expression “buckling curve”.

2 Buckling tests

2.1 Introduction

Buckling tests were performed. The tested beams were divided in two test series. The first series consisted of 26 unwelded beams, which were tested in 1996. The second series was larger, 39 welded beams tested in 1997 and 1998. All unwelded beams and 34 of the welded beams were simply supported for bending. The remaining five of the welded beams had clamped ends. Most welded beams were transversely welded either at the quarterspan or at the midspan, but for some beams two or three transverse welds were used. A transverse weld is perpendicular to the longitudinal axis of the beam. The lengths of the beams were 500, 1020 and 1540 mm, respectively. The theoretical cross-section dimensions were the same for all beams. The dimensions are shown in figure 2.1. The six load application points I-VI are also shown in the figure. The notation a in figure 2.1 is equal to the distance between the centre of gravity and the shear centre.

60

60 6

6 6

SC

GC a

a

a a I II III IV V VI

a

Figure 2.1. Theoretical cross-section dimensions in mm and load application points.

The beams were cut from profiles of five meters in length. All profiles were delivered free of charge from SAPA (Skandinaviska Aluminium Profiler AB) in Vetlanda. The alloy and temper for the welded beams were AA6082-T6. In order to get a sufficient large difference in strength between the parent and the heat-affected material it was necessary to use temper T6. The profiles from 1996 were taken from stocks so the alloy and temper were unknown, but probably the material was AA6082-T6 as for the profiles from 1997 and 1998. However, this was of no real importance since the material properties were determined by tensile tests.

Figure 2.2 shows a sketch of the test equipment when the beam was simply supported for

bending. In appendix A two photos of the test equipment are also presented. The compression

force was applied by a hydraulic jack. With some time interval the load was increased by a

suitable load step. Most beams were tested by using a time interval of two minutes during the

whole test process. When quite many beams had been tested it was found out that it was

necessary to speed up the test process. This was done by increasing the load instantaneously up

to about 75% of the theoretical load carrying capacity and then use a two minutes interval. The

theoretical load carrying capacity was calculated according to the Swedish steel code BSK [7],

see section 3.4. The load step used in connection with the two minutes interval was chosen

with help of the theoretical load carrying capacity. After each load step the distance between

the supports was fixed so the deflection in the direction of the applied load was constant during the whole load step. One reason for this was to avoid difficulties that otherwise would have occurred in conjunction with possible leaks in the hydraulic system. The measuring data was used to determine the failure load and to draw load-deflection diagrams. The reason for the time interval was that the transverse deflection of the beam should be stabilised. The value of the applied load changed somewhat during the two minutes interval due to the fixed

deformation in the direction of the applied load. This can be seen in the load-deflection curves in appendix B.

2 HEA 800

mp3

Aluminium beam

jack load cell

mp4 mp6

mp2 mp5

mp1

mp9 mp0

mp8 mp7

steel plate steel plate

steel ball

steel ball

mp = measuring point

Figure 2.2. The test equipment seen from the side and from above, simply supported case.

Three measurements of the deflection at the midspan were made. This made it possible to see if the beam twisted during the test. In 1996 and 1997, the beams were tested such that the force of gravity acted parallel with the web. During the testing in 1998 the force of gravity acted along the flange. The reason for this was that different persons from the laboratory personnel made the tests and also that there was a year between the different test series so details were likely forgotten by the laboratory personnel.

The measurements are illustrated in figure 2.3. The deflection was also measured at the supports. By this way it was possible to compensate the midspan deflection from the possible movements of the steel ball at the supports when the applied load was increased.

It was important to know if the deflection was parallel with the flange or the web. Any other information about the direction of the deflections was not considered as important. This means for instance that all measured deflection values could have been multiplied with –1 in a load- deflection diagram in appendix B, if this was considered to give a more “beautiful” diagram.

All deflections were measured with rotational potentiometers.

1996, 1997

1998

Figure 2.3. Measurement of the deflection.

Figure 2.4 shows the steel plate used to transfer the load into the beam. Only the most important dimensions are shown in the figure. To prevent the beam from sliding at the supports, seven eight mm screws with sharpened tips were used in each steel plate together with a 20 mm deep milled groove. Two of the screws are shown in the figure. The hinge at the supports was accomplished by a 14 mm steel ball. The friction was reduced by a sheet of teflon.

Figure 2.4. Steel plate used to transfer the load into the beam, dimensions in mm.

Five of the welded beams had clamped ends, which were obtained by removing the steel balls and the teflon sheets so the load was applied directly to the steel plates at the beam-ends. The load was applied at the centre of gravity of the T-section for the clamped beams. A steel ring was screwed to the back of the steel plates in order to fix the beam. The steel rings also prevented to some extent the beam from rotating at the supports. This adjustment of the supports was believed to give an accurate enough approximation of clamped ends. This fact was also confirmed to a certain extent by a visual inspection of the supports. When the load carrying capacities according to the different codes were calculated, the possible non-perfect clamped ends were considered by testing different buckling lengths.

For all beams, the cross-section dimensions were measured with a slide-calliper and the beam length with a ruler. The results of the measurements are shown in table 2.7 and 2.8. In these tables, some data about the test series can also be found.

The welds were obtained by introducing weld material on the surface around the beams. If the beams had been jointed with traditional butt welds, the initial curvature of the beams would have probably been larger. It was also more convenient to introduce the heat-affected material in this way. The initial curvature of aluminium profiles is very low, because immediately after the extrusion the profiles are stretched. The heating during the welding could have induced some initial curvature, but visually no curvature was seen.

According to Mazzolani [42], the initial curvature of an extruded aluminium profile is about l 2000 (displacement at midspan), where l is the length of the profile. For the tested beams, the midspan deflection will then be 0,25-0,77 mm. In the codes the initial curvature is considered in the buckling formulas. For the Abaqus calculated beams, the initial curvature can be seen as included in the imperfections. It was decided that the initial curvature of both the unwelded and the welded beams were not necessary to measure.

Residual stresses are very small in extruded profiles. The quenching, which is a part of the heat-treatment of temper T6, induce some residual stresses, but according to Mazzolani [42]

they are very small (less than 20 MPa) and have negligible effect on the load carrying capacity.

However, residual stresses in welded profiles are not small. All welded beams in this thesis were transversely welded. Residual stresses of transverse welds have less influence on the load carrying capacity than longitudinal welds because they are local and they are mostly directed perpendicular to the longitudinal axis of the beam. Residual stresses are mostly directed parallel with the welds. The effect of the residual stresses is at least partly included in the heat- affected material model based on the tensile tests. For the reasons given above, it was decided that the residual stresses were not necessary to measure. If the welds were longitudinal, residual stresses had to be considered.

The weld itself was not studied but rather the affect of the heat-affected zone adjacent to the

weld. MIG-welding was used for all welds, both the beams and the tensile tests.

2.2 Tensile tests

The strength of the material was determined by tensile tests. All tensile tests were made for the material in the direction of the extrusion. According to Hopperstad [30] and Moen [43] the material is anisotropic, so the direction of measurement is of importance. From each profile a tensile test for the parent material was made. The reason for this was to determine the

characteristics of the different materials as thoroughly as possible. Even if two profiles were made of the same alloy and temper, the material properties still could vary to a certain extent.

The different alloying elements are allowed to vary in a quite wide range for a certain alloy.

This means that two alloys with the same designation can have different material properties.

When welded beams were cut from a profile, a tensile test for the heat-affected material was also made. The test specimens were tested in a Material Test System, MTS 311.21s, according to the Swedish standard. The heat-affected material for the welded tensile tests was obtained by introducing weld material on the surface of profile parts. The test specimens were then cut from the web of these parts. Two initial tensile tests were made, one where a traditional butt weld was used and one where the weld material was introduced on the surface. The failure for the jointed tensile test was brittle and the failure load was very low. The non-jointed tensile test behaved in a better way. For the welded tensile tests and beams, there were mainly two reasons for introducing weld material on the surface instead of using traditional butt welds: the result of the two initial tensile tests and that it was more convenient. The beams and corresponding tensile test must be welded as similar as possible.

When the load carrying capacity according to different codes was calculated, only the yield strength f _0.2 of the parent material and the ultimate strength f _haz of the heat-affected material were needed. The ultimate strength f _haz was evaluated as the maximum stress that occurred.

When more complicated calculation methods are used, like the finite element calculations in chapter 4, the whole stress-strain curve is needed.

During a buckling test it is the compression strength rather than the tensile strength that is most decisive for the load carrying capacity of the beam. However, it is difficult to perform good compression tests, and therefore the compression strength was approximated with the tensile strength. The most important reason for this fact is connected to difficulties in avoiding buckling of the specimen. For this reason the test specimens must be very short. This will in turn make the strain measurements more difficult. Moreover, the prevented lateral contraction at the supports will have a larger influence when the length of the specimens is short. For these reasons the compression strength was taken equal to the tensile strength.

However, a brittle tensile test is a bad approximation of the compression strength. From the buckling tests of the welded beams it was possible to see that the load carrying capacity of the beams was not determined by the strength of the weld itself. For one beam where the bending induced compression in the flange and tension in the web, a crack appeared in the weld.

However, this was most certainly a secondary failure caused by large displacements. The other welds were uncracked. For these reasons it was desirable that the failure of the welded tensile tests should be ductile and occur at the heat-affected zone beside the weld.

In this section, nominal stresses and strains are shown. It means that the stresses were

calculated as measured force divided by original cross-section area and the strains as measured

elongation divided by original length. The elongation was measured over a distance of 50 mm.

This distance was the same as the original length. There exists other ways of calculating stresses and strains. In chapter 4, “true” or Cauchy stresses and log-strains are used and explained.

The beams tested during 1996 were all unwelded. These beams were cut from six profiles.

From each of these profiles a tensile test was made. The values of the yield strength and the modulus of elasticity from these tensile tests are shown in table 2.1. These values were evaluated graphically from the printouts of the testing machine.

Table 2.1. f 0,2 and E for the unwelded tensile tests from 1996.

Tensile test 1 2 3 4 5 6

f _0,2 [MPa] 323 268 326 324 320 313

E [GPa] 68,8 71,0 70,3 65,0 70,7 70,7

The yield strength for tensile test 2 was much lower than the rest so all profiles may not have been made of the same alloy. As already mentioned, it was however likely that the material was AA6082-T6. The modulus of elasticity should be close to 70 GPa. For tensile test number 4 the modulus of elasticity differed quite much from 70 GPa. It is difficult to give a reasonable explanation for this. The reason was likely not slip in the measuring device. The stress-strain curve would then have similar shape as the curve for the understiff behaviour in figure 2.5, but this was not the case. The slope of the stress-strain curve was constant in the elastic region, which can be seen in figure 4.2. All stress-strain curves from 1996 were left unmodified, because no detectable errors occurred during the testing.

The tensile tests from 1997 were denoted A-G and AW-GW, where A-G were unwelded and AW-GW were welded. Corresponding notations from 1998 were 1-4 and 1W-4W. The

profiles, from which the tensile tests and the beams were cut, were denoted in the same way as the parent material. Profile F was excluded. In table 2.2 the results from the first series of tensile tests from 1997 and the tensile tests from 1998 are shown.

The failure for the welded tensile tests CW, DW and EW in table 2.2 occurred at the weld. For the other welded tensile tests in table 2.2, the failure occurred beside the weld in the heat- affected zone. In table 2.2, the failure strain at maximum load is shown for the welded tensile tests. The failures which occurred at the heat-affected zone were significant more ductile than the failures which occurred in the weld.

The welded tensile test CW had significant lower ultimate strength than the other tensile tests.

One explanation is that less weld material was used for tensile test CW than for the other

welded tensile tests. There could also be welding defects like enclosed pores. Studying the

welded zone thoroughly made it possible to observe that the penetration of the weld material

was deeper for the specimens were failure occurred at the weld, as opposed to the cases when

the failure occurred at the heat-affected zone. The reason why the failure did not occur more

often at the weld was that the welds were overfilled in most cases, which in turn enlarged the

cross-section area.

The materials which correspond to the tensile tests 1, 1W, 3W, 4 and 4W were slightly modified due to under- or overstiff behaviour at the start of the stress-strain curve, see figure 2.5.

0 50 100 150 200 250 300 350

Strain [-]

Understiff behaviour Overstiff behaviour

Figure 2.5. Under- and overstiff behaviour at the start of the stress-strain curve.

The understiff behaviour was most likely due to slip in the test equipment. The overstiff behaviour was more difficult to explain. A modification was performed such that the start of the stress-strain curve was straightened and the whole curve was moved parallel with the strain-axis so the curve started at zero stress and strain. The values that are shown in table 2.2 are the values that were obtained after the modification due to under- or overstiff behaviour.

Table 2.2. Tensile tests from 1997 (first series) and 1998.

Tensile Unwelded tensile test Welded tensile test

Test f _0,2 [ MPa ] E [GPa] f _haz [ MPa ] E [GPa] Failure strain, A ₅₀ [ % ]

A, AW 296 71,1 227 76,6 4,96

B, BW 293 71,1 213 71,7 4,50

C, CW 298 71,4 68 57,1 0,452

D, DW − − 167 71,0 2,04

E, EW − − 183 70,0 2,72

G, GW 276 70,5 205 76,3 4,79

1, 1W 312 70,7 188 90,9 7,42

2, 2W 307 71,4 189 65,6 7,40

3, 3W 283 69,8 183 99,4 7,36

4, 4W 321 69,8 191 76,2 7,42

From the longest beams tested during 1997, pieces were sawn out and used as tensile tests after

the beams were tested. These tensile tests are shown in table 2.3. The failure for tensile test

CW in table 2.3 occurred at the weld while the failure for tensile tests DW and EW occurred at

the heat-affected zone.

Table 2.3. Second series of tensile tests from 1997.

Tensile Unwelded tensile test Welded tensile test

Test f _0,2 [MPa] E [GPa] f _haz [MPa] E [GPa] Failure strain, A ₅₀ [%]

C, CW 293 74,0 137 73,3 1,74

D, DW 284 71,2 179 79,0 6,73

E, EW 311 70,5 183 74,1 6,55

From table 2.2 and 2.3 it is clear that the values for the welded tensile tests were uncertain and highly dependent on how the welding was performed. Another question was if the beams and corresponding tensile test were welded in the same way. Even a small difference in, for instance, the depth of penetration seemed to affect the strength to a very high degree. The welds of the tensile tests from 1998 seemed to have more even quality, at least when considering the values of f _haz and the failure strain, but the wide scatter of the modulus of elasticity was undesired. For the welded tensile tests from 1997, the start of the stress-strain curve was non-linear, which made the evaluation of the modulus of elasticity rather arbitrary.

This non-linearity was not present for the welded stress-strain curves from 1998. An example of a non-linear start of a stress-strain curve is given in figure 2.6.

The value of f _0,2 was possible to determine more accurate. The value of f _0,2 for material C in table 2.2 and 2.3 does not differ much. The yield strength in table 2.1 is for all profiles except one, not so widely scattered, but the material was unknown so not too many conclusions can be drawn.

0 20 40 60 80 100 120

0.0000 0.0004 0.0008 0.0012 0.0016 0.0020 0.0024 Nominal strain [-]

Figure 2.6. The start of the stress-strain curve for material BW.

It is evident that there were more uncertainties with the welded tensile tests than the unwelded.

There were several possible causes for that. One cause was that the section area was much

enlarged in areas where the weld material was located. It was likely that the elongation only

occurred for the parts where the section area was not enlarged. The result would be too low

strain values, which means that the modulus of elasticity would be enlarged. Another cause

could be residual stresses due to welding. The failures did not occur perpendicular to the

longitudinal axis of the test specimens. This indicates that the strength was not uniformly

distributed over the width of the specimens. The residual stresses due to welding could also be one explanation why the start of some welded stress-strain curves was non-linear.

A third cause could be eccentricity of the test specimens. The load was applied through two holes, see figure 2.7. If the holes were not located centric along the centre line of the test specimens there would be an additional moment to the axial force. How much the eccentricity affected the strain values depended on which side of the specimens the strains were measured.

No information was given on the location of measurement points for the strains. The effect of the eccentricity was thus uncertain. Problems with this kind of eccentricity can also be present for unwelded tensile tests. It is likely that the different causes sometimes interacted and

sometimes counteracted each other. This could be an explanation why the modulus of elasticity differed so much, but it is doubtful if this explanation is good enough, because it was not possible to see any significant difference in size and extension of the weld material. It would have been more realistic if the values were not so widely scattered.

20 mm

Figure 2.7. Test specimen for the tensile tests.

The value of f _haz is not affected by any strain problems, since it is evaluated as the maximum stress value. The calculation according to different codes in chapter 3 only uses f _haz and is accordingly not affected by any strain problems. This is not the case for the finite element calculations in chapter 4. In this calculation the whole stress-strain curve is used. It appeared necessary in this context to correct at least some stress-strain curves due to unrealistic values of the modulus of elasticity. The uncertainties discussed above were present for all welded tensile tests and therefore it was decided that all stress-strain curves of the heat-affected material should be modified. The modification was performed such that all strain values for the heat- affected materials were multiplied with a factor so a modulus of elasticity close to 71 GPa was obtained. Before this modification could be made, it was necessary to decide which tensile tests that should represent the different heat-affected materials. For most materials there was only one choice. For material CW there were no satisfactory choices. Material A and C were almost identical, see figure 4.3. For this reason material CW was set equal to material AW. Both materials DW and EW were taken from table 2.3, probably because of the lower strain values in table 2.2. The value of f _haz for material DW in table 2.2 is also quite low. When the different heat-affected materials had been selected, the strains were multiplied with the factors that are given in table 2.4.

Table 2.4 Strain multiplication factors.

Material AW BW DW EW GW 1W 2W 3W 4W

Factor 1,08 1,00 1,27 1,04 1,07 1,29 0,918 1,40 1,08

Some comments about material C must also be made. For this material there were two

reasonable tensile tests. The yield strength f _0,2 for material C was set equal to the mean value

from table 2.2 and 2.3. In the finite element calculations in chapter 4, the stress-strain curve for

material C was taken from table 2.3. When considering the value of the modulus of elasticity probably it would have been better to choose the other tensile test, but this was not done.

The strength values for the chosen and sometimes modified materials from 1997 and 1998 are summarised in table 2.5. These values were used when the load carrying capacities according to different codes were calculated.

Table 2.5. Final nominal strength values for the materials from 1997 and 1998.

Profile A B C D E G 1 2 3 4

f 0,2 [Mpa] 296 293 296 284 311 276 312 307 283 321

f _haz [ MPa ] 227 213 227 179 183 205 188 189 183 191 In section 4.2, the stress-strain curves for all tensile tests are shown. These curves are the material models used in the Abaqus calculations. They are shown after the modifications due to under- or overstiff behaviour at the start of the stress-strain curves and unrealistic values of the modulus of elasticity. The curves for the heat-affected materials are also modified at large strain values. Only the “true” stress and log-strain versions of the curves are shown. It was decided that these curves were more important to show than the nominal stress-strain curves, because they were used in the Abaqus calculations.

To estimate the reasonableness of the strength values from the tensile tests, comparisons were made with values from the literature. The values are given in table 2.6 and are valid for the extruded alloy AA6082, temper T6, thickness 6 mm and MIG-welding.

Table 2.6. Strength values from some literature.

Literature f _0,2 [ MPa ] f _haz [ MPa ] f _u [ MPa ]

Eurocode 9 [12] 260 202 * 310

BS 8118 [10] 255 128 ** 275

SAPA’s handbook [51] 260 310

BKR 99 [6] 245 180 290

“Goda råd…..” [ 54 ] 190 290

TALAT [ 40 ] 270

* f _haz = ρ _haz ⋅ f _u = 0 65 310 , ⋅ = 202 MPa

** f _haz = k _z ⋅ f _{0 2 ,} = 0 5 255 , ⋅ = 128 MPa

Eurocode 9, BS 8118, SAPA’s handbook and BKR 99 give the same type of values and they can be considered as minimum guaranteed values. For the other literature no additional information about the values was found. BKR 99 does not distinguish between different welding techniques, so the value of f _haz does not require MIG-welding.

It was not found in BS8118 that it is allowed to use f _u when the strength of the heat-affected

material is calculated, like it is in Eurocode 9 and BSK, and therefore the strength of the heat-

affected material was set equal to k f _{z 0 2 ,} . In section 5.5.2 of Eurocode 9 it is clearly stated that

f _0,2 and f _u should be multiplied with the same reduction factor ρ haz . Such a clear statement was

not found in BS 8118, but it was assumed that k _z should be used in the same way. Both Eurocode 9 and BS 8118 say that f _0,2 is lowered more than f _u when the material is welded. It can therefore be questioned that both f _0,2 and f _u are lowered with the same reduction factor, but probably this should be seen as an acceptable approximation which has been adopted. Perhaps it would have been better to give values of the yield and ultimate strength of the heat-affected material instead of a reduction factor?

A few conclusions can be drawn when the values in table 2.5 and 2.6 are compared. The lowest value of f _haz is given by BS 8118. Eurocode 9 gives a higher value of f _haz than quite many of the tensile tests.

2.3 Results

In table 2.7 and 2.8 there are some data and measured results of the tested beams. From the two major series three minor test series were selected. These latter series were tested in connection with a course for the ungraduate students of the last year. There was a desire that the

numeration of the three minor series should be continuous, which is the reason for the numeration in table 2.7 and 2.8. Among other things, the measurements showed that the thickness t for all beams was a bit larger ( 6 03 , mm ≤ ≤ t 6 20 , mm ) than the theoretical (6 mm).

The notations b, h, t _w and t _f in the tables are explained in figure 3.5.

In table 2.8 the desired weld locations are shown. As can be seen, for some beams two or three transverse welds were used. When the beams were simply supported for bending, a weld location of 0 or l _c was not possible. This location corresponded to the centre of the steel ball. It was not possible to locate the welds closer to the centre of the steel ball than about 65 mm. The buckling length and the beam length were denoted l _c and l, respectively. z _haz is the distance between the point of contra flexure of the buckling curve and the most critical weld. No value of z _haz is given for the clamped beams since several buckling lengths were tested and for each buckling length a new value of z _haz was obtained. Both l _c and z _haz are further explained in section 3.1. The beam length l is equal to the distance between the two groove bottoms of the steel plates at the beam-ends.

One horizontal and one vertical load-deflection diagram is shown for each beam in appendix B.

For all eccentrically loaded beams which were simply supported for bending, the load- deflection curves according to the first and second order beam theory were inserted in one of the two diagrams. The beam theory formulas are shown below. The buckling length l _c is equal to the distance between the steel balls at the supports.

mid

w e l c

EI N

,1 2

= 8 , first order analysis

mid

E

w e N

, ₂ cos P

2

1 2 1

= é ç ÷ −

ë ê

ê ú

ú π

E

x c

P E I

2 l

2

= π 2

, second order analysis

From the diagrams in appendix B it can be seen that the load-deflection curves for the second order analysis coincide fairly well with the corresponding measured curves when the load level is reasonable low.

Somewhat generalized, the course of events for the tests can be described as follows. The load- deflection diagrams in appendix B give additional information.

Load application point I-II: During the test the beam bent in the direction of the web. The deflection parallel with the flange was generally small, except at failure when this deflection became very large.

Load application point IV-VI: During the test the beam bent in the direction of the web. The deflection parallel with the flange was mostly small. At failure there was a local buckle in the web.

Load application point III: The deflection parallel with the web was small. The deflection parallel with the flange was also small, except at failure when this deflection became very large.

When the marks from the seven screws were studied at one of the two ends of PB-39 in table 2.8, it was possible to see that slip had occurred. The slip mark from all screws had the same shape. The most reasonable explanation for this was that the beam was not properly knocked into the bottom of the groove when the testing started. In the beginning when the load was applied, the beam sank uniformly into the bottom of the groove. The result was probably that PB-39 obtained too low load carrying capacity. This can also be seen when the failure load for PB-39 is compared with the failure load for PB-37. It is reasonable to believe that these two beams should have closer failure loads (67,4 kN and 51,3 kN). For the reasons given above PB- 39 was not part of the evaluation of the test results.

The slip for PB-22 in table 2.7 was more easily seen. In this case the screws and the groove could not withstand the moment caused by the applied load and therefore a rotation of the steel plates occurred.

The load-deflection curves for the welded column PB-23 in table 2.8 are shown in appendix B.

The deflection parallel with the web, i.e. the stiff direction, is large while the deflection parallel

with the flange, i.e. the weak direction, is small. This situation seems not realistic and it does

not occur for the other centrically compressed columns. When the test specimen for PB-23 was

studied it was observed that local buckling had occurred at the tip of the web. Furthermore, it

was observed that the penetration of the weld material in the flange was not so deep, which

could mean that the heat-affected zone was small in the flange. In the web the penetration was

larger and the softer web therefore buckled for the centric load. The deformation of the test

specimen agreed with the information obtained from the load-deflection diagrams in appendix

B. This buckling test indicates that it can be more unfavourable when just a part of the cross-

section is welded than if the whole cross-section is welded. Due to these observations, the

tested load carrying capacity for PB-23 could be too low. The welded column PB-23 is used in

the further evaluation in this thesis, but it is given special comments.