LICENTIATE T H E S I S

Luleå University of TechnologyDepartment of Civil and Environmental EngineeringDivision of Structural Engineering - Steel Structures

:|: -|: - -- ⁄ --

:

High Strength SteelLocal Buckling and Residual Stresses

Mattias Clarin

:

Universitetstryckeriet, Luleå

Mattias C

larin H

igh S

trength

Steel LIC

EN

TIA

TE

TH

ESIS

Licentiate Thesis 2004:54

High Strength Steel

- Local Buckling and Residual Stresses -

Mattias Clarin

Luleå University of Technology

Dept. of Civil and Environmental Engineering

Division of Structural Engineering - Steel Structures

Luleå, November 2004

Preface

I

Preface

Not long ago, I met a man I thought I knew fairly well, you know, one of these acquaintances

not in your inner circle, but still someone you know. This man works with steel and has done

so for a while. During our conversation he exclaimed: “It’s strange, you know about my past,

but do you know that working with steel has changed my life?”. I knew that this man had lost

everything he held valuable in his life, and he further explained to me that through doing an

effort concerning his work, doing these hard things threatening to break you, he found the way

back to his life and new valuable things to embrace. From this we may learn that the things we

are aiming for may bring other, more valuable, consequences. We know that by using steel we

can change the behaviour of a structure, but obviously it may have other effects too. I am not

sure if the change in this man’s life was material dependent, but nevertheless it is a nice thought:

That working with steel just may change your life, isn’t it?

Considering valuable, the support I have acquired in the task of steering my sailing ship to

the Licentiate island in the ocean of knowledge is invaluable. My supervisors Ove Lagerqvist

and Eva Hedman-Pètursson has contributed greatly to this thesis. Thank you for sharing of your

energy and technical expertise. You are the hull of my ship, protecting from the waves and

supporting me from shore to shore.

The personnel at TESTLAB has also contributed very much to this thesis. Especially Lars

Åström, Georg Danielsson, Hans-Olov Johansson and Claes Fahleson who has helped me with

the experimental work. The work you have helped me with is the rig and sails that have brought

the ship forward.

The people at the division, steel structures in particular, you are the deck of the ship. A solid

foundation to support all activities on board. Thanks!

Every ship of dignity has an orchestra bringing joy to the people on board. The orchestra on

this ship has been the members in “The Band of Brodders”. Arvid, Jimmy, Karin and Tobias,

may the KP live for ever and thank you for the music!

II

Another member in the band, as well as vice captain of the ship, that has helped me through

is Jonas Gozzi. Ready to help and support when needed, both at sea and in land. The journey

continues!

To the people waiting at the destination: family and friends. Now this is done and I promise

to improve!

That was it and all.

Luleå, 9th of November, 2004

Mattias Clarin

“And following our will and wind we may just go where no one's been

We'll ride the spiral to the end and may just go where no one's been

Spiral out. Keep going.”

/Maynard James Keenan

Abstract

III

Abstract

High strength steel provide designers with the possibility of creating more slender and

weight efficient structures than would be possible if using steels with lower strength. To be able

to do this, a structural designer needs updated and validated codes as aid in their work. This

thesis addresses the behaviour of high strength steel with respect to local buckling and residual

stresses. The thesis was aiming to determine if there exists any significant differences in the

resistance to local plate buckling of high strength steel (fy > 460 MPa) compared to steels with

lower strength. Furthermore, longitudinal residual stresses induced by welding were also

considered on a basis of material strength. Experimental work considering these two issues was

conducted concerning the three steel grades Domex 420, Weldox 700 and Weldox 1100.

The investigation concerning the local buckling resistance comprises experiments on 48

welded box section specimens made of the three grades. Nominal plate slenderness values were

altered between 0,7 and 1,5. Moreover, the experimental work was founded on plate theory with

respect to local buckling and a survey of other conducted comparable experiments. The results

from the tests and the literature survey were evaluated with respect to Eurocode 3. The gathered

test results from literature and experiments showed that no significant difference between the

local buckling resistance of different steel strengths could be concluded if compared to the

Winter function. However, the Winter function was concluded to overestimate the resistance for

more slender simply supported plates ( p > 0,9) with residual stresses (in as-welded condition).

The residual stress state present in three box sectioned specimens made of the three grades

was measured with the blind hole technique. Evaluation of the test results was made with

respect to the steel strength and complemented with test results collected from a literature

survey. The study showed that the tensile residual stresses induced by welding could not be

directly correlated to the material strength. Results from measurements on high strength steel

specimens showed that the longitudinal residual stresses was lower if made dimensionless with

respect to the strength of the steel.

IV

Notations & Symbols

V

Notations & Symbols

The notations and symbols used in this thesis are described below in alphabetical order, disregarding being roman or greek letters.

a - Weld size, numerical coefficient or length

A - Area or constant

A5 - Elongation measurement, 5 %

- Angle

b , bw - Plate width

beff - Effective width

B , C - Constant

L - Elongation

- Deformation

D - Flexural plate rigidity

- Strain or Material depentent parameter

r - Radial strain

- Tangential strain

E - Modulus of elasticity, Youngs modulus

fu - Ultimate strength

fue - Ultimate strength, electrode

fy - Yield strength

fye - Yield strength, electrode

VI

fyk - Characteristic yield strength

F - Force

Fc - Shrinkage force

h - Height

p - Plate slenderness

k - Weld factor

kcr - Buckling load coefficient

L - Plate length

m , n - Number of half waves over plate

Ncr - Critical load

n - Number of passes in weld

Nel - Buckling load

Nx , Ny - Normal forces per unit distance

Nxy - Shearing force per unit distance

q - Distributed variable load

Q - Heat input (circuit voltage x current)

R - Radius from drill centre

Ro - Drill radius

Rp0.2 - 0,2 % Proof stress

Rm - Ultimate resistance

- Stress

c , rc - Compressive residual stress

cr - Critical stress

r - Residual stress

’r - Initial radial stress

t,rs - Tensile residual stress

rs - Residual stress

Notations & Symbols

VII

´ - Initial tangential stress

u - Ultimate strength

x - Normal stress

t - Thickness

'r - Initial shear stress

v - Welding speed

w - Amplitude of plate deflection

w0 - Initial amplitude of plate deflection

x, y, z - Cartesian coordinates

X - Position

- Stress ratio

Throughout the thesis mean values are marked overlined, e.g. fy represents the mean yield strength.

VIII

Table of Contents

IX

Table of Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I

Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III

Notations & Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V

Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Disposition of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

Chapter 2: Plate Buckling - Theory . . . . . . . . . . . . . . . . . . . . 5

2.1 Bifurcation instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Plate theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.1 Elastic analysis / Calculation of critical load . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Simply supported plates under uniform compression. . . . . . . . . . . . . . . . 10 2.2.3 Initial plate imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.4 Geometric imperfections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.5 Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.3 Non linear theory / Post buckling behaviour . . . . . . . . . . . . . . . . 15 2.3.1 The von Kármán effective-width formula . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 The Winter function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Chapter 3: Plate Buckling - Survey of Literature . . . . . . . . . . 21

3.1 “Experimental Investigation of the Buckling of Plates withResidual Stresses” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.1.1 Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1.2 Test results and conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2 “Plate Slenderness Limits for High Strength Steel Sections” . . . . . 23 3.2.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2.2 Residual stress measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.2.3 Test results and conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

X

3.3 “Basic Compressive Strength of Steel Plates from Test Data” . . . . 26

3.4 “Local Buckling of Thin-Walled Columns”. . . . . . . . . . . . . . . . . 27 3.4.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5 “Welded Steel Plates in Compression” . . . . . . . . . . . . . . . . . . . . 28 3.5.1 Tests made by J.D. Harrison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5.2 Tests made by K.E. Moxham. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.6 “Buckling Tests on Rectangular Plates made of two Differenttypes of Weldox 1100 Steel” . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.6.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6.2 Test results and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.7 Discussion and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Chapter 4: Plate Buckling - Experimental Work . . . . . . . . . . . 35

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.2 Experimental investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3 Uniaxial tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.1 Specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3.2 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 4.3.3 Test results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.4 Buckling tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4.1 Specimens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 4.4.2 Test Setup. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.5 Test Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.6 Discussion and conclusions of test results . . . . . . . . . . . . . . . . . . . 45

Chapter 5: Residual Stresses - Theory . . . . . . . . . . . . . . . . . . 47

5.1 The origin of residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2 Residual stresses due to structural mismatch . . . . . . . . . . . . . . . . . 49

5.3 Residual stresses due to thermal or plastic strains . . . . . . . . . . . . . 49 5.3.1 Hot rolling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.3.2 Cold forming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5.3.3 Weld induced residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.4 Measurement methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.4.1 Destructive residual stress measurement methods. . . . . . . . . . . . . . . . . . . 55 5.4.2 Non-destructive residual stress measurement methods . . . . . . . . . . . . . . . 58

5.5 Effects of residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.6 How to reduce residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Chapter 6: Residual Stresses - Survey of Literature . . . . . . . . . 63

6.1 Modelling of residual stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Table of Contents

XI

6.1.1 Analytical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.2 Measurements of residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.3 Discussion and Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Chapter 7: Residual Stresses - Experimental Work . . . . . . . . . 71

7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

7.2 Experimental work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 7.2.1 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7.3 Test evaluation and test results . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.4 Discussion and conclusions of test results . . . . . . . . . . . . . . . . . . . 75

Chapter 8: Discussion and Conclusions . . . . . . . . . . . . . . . . . 77

8.1 Residual Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

8.2 Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

8.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

Chapter 9: References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

APPENDIX A: Plate Buckling - Experimental Work . . . . . . . . 87

APPENDIX B: Residual Stresses - Experimental Work . . . . . . 103

APPENDIX C: Residual Stresses - Survey of Literature . . . . . . 113

XII

Introduction

1

Chapter1:

Introduction

The world changes around you! Space travelling is privatized, researchers all around find

ways to cure diseases thought not possible to treat, even the very foundation beneath your feet

changes. Innovations, or maybe novelties, are also introduced in the field of materials.

Advanced fibre composites, cheramics or steels with strengths and quality only dreamt of 50

years ago are now available on the market for designers.

These new materials provides product designers working in areas ranging from floorball

sticks, fighter planes and bullet proof armour to vehicles, bridges and buildings, with new

possibilities to develop and construct better merchandises. Nevertheless, the outcome of a

designers new creation, has to be carefully investigated before constructed. A floorball stick

may be replaced, but regarding the bullet proof armour, one needs to be completely certain of

the capabilities and limitations of the new product. This is why researchers bend, pull and twist

new innovations in the purpose of establishing rules concerning the behaviour of the new

product or material. Does new calculation models have to be installed or may “old” be used

regarding the new issue? A malfunctioning product with a possibly lethal outcome (as the bullet

proof armour) is a structure, made to work with or around people. This thesis will hopefully be

a step towards providing the structural designers with some tools regarding an old material,

nevertheless under never ending development, which is named: Steel.

The tree of steel development has many branches; increased toughness, better weldability

and enhanced formability are examples. Another very thick branch is the one containing the

research and development work put into increasing the strength of the steel. Today, steels with

yield strengths of 1100 MPa and above are available on the market. Even though steel has been

used as a structural material over decades, most design models used today are based on

materials with essentially lower yield strengths. This fact once again raises the question as stated

above: Does new calculation models have to be installed or may “old” be used regarding the

new issue?

With this in mind the project LiftHigh - “Efficient Lifting Equipment with Extra High

Strength Steel” was initiated in 2002. The project, partially funded by RFCS - The Research

2

Fund for Coal and Steel, was launched with the purpose of investigating how high strength steel

can be used to produce more efficient lifting equipment. The analogy is simple even for the

layman: stronger material - higher capacity, in this case lifting capacity. Nevertheless, the

calculation rules still needs to be verified for the high strength steel, which in this thesis is

defines as steel with a yield strength > 460 MPa.

Today, one of the ruling design codes concerning plated steel structures in Europe, the

Eurocode 3, is only validated to comprise steels with strength up to 460 MPa.

1.1. Purpose

This thesis was focused on two aims. First, to investigate if the Winter function, in Eurocode

3 used for estimating the local buckling resistance, is adequate especially concerning plates

made of high strength steel. The two main questions to answer was:

• If plates made of steels with higher strength behaves differently than “ordinary”

steel grades, with respect to local buckling.

• If, by using a reference grade in the experimental work (Domex 420), the whole

Winter function concept, established mainly trough tests on cold formed profiles,

can be improved in general terms.

Residual stresses induced by welding is also of great interest, since these may limit the

resistance of a welded member. The second aim of the investigation was to evaluate:

• If a correlation between residual stresses induced by welding can be put in

correlation with the strength of the steel.

1.2. Limitations

This thesis is limited to comprise experimental work of three different steel grades; the hot-

rolled Domex 420, quenched and tempered Weldox 700 and quenched Weldox 1100.

Furthermore, the measurements of residual stresses was limited to the longitudinal direction

(along the welds) and the stress state post-welding.

The evaluation of the experiments and the literature survey is only made with respect to

Eurocode 3 and the evaluation of the residual stresses is limited to consider tensile stresses only.

1.3. Method

An experimental investigation comprising welded specimens of the three different steel

grades was chosen to evaluate the local buckling behaviour of the high strength steel. The

Domex 420 grade was used as a reference enclosed in and validated for Eurocode 3. Uniaxial

tests of welded box specimens were done to investigate the local buckling behaviour of simply

Introduction

3

supported plates in as-welded condition. Moreover, a comprehensive survey of the literature

was done to support the test results.

The longitudinal residual stresses was chosen to be measured in as-welded condition with the

blind hole method. Three different steel grades were considered in the experimental work and

the specimens were of the same type as used for the local buckling tests. The steel grades

Weldox 700 and Weldox 1100 were chosen to represent the high strength steel and Domex 420

as a steel with “ordinary” strength. With measurements within this strength range,

complemented with evaluated results from a literature survey, an eventual correlation between

material strength and tensile residual stresses could be determined.

1.4. Disposition of the Thesis

In chapter 2 the theory behind the plate buckling phenomena is reviewed. Structural stability

with focus on local buckling is regarded. The establishment of equations describing local

buckling of simply supported plates are presented. Furthermore “the effective width approach”,

nowadays widely spread as a theoretical interpretation of the phenomena, is introduced along

with the Winter function used in the Eurocode 3 of today.

Chapter 3 comprises a survey of previously conducted experimental work concerning local

buckling of plates. Test results concerning range of steel grades from “ordinary” grades with

yield strength of approx. 250 MPa to 1100 MPa high strength grades, are presented and re-

evaluated.

The experimental work conducted at LTU with respect to local buckling is presented in

chapter 4. The test method, used equipment and the measurement of mechanical properties of

the three grades are enclosed, as well as the results from the buckling tests.

How residual stresses are formed in steel and some possible consequences of these are

presented in chapter 5. Different available measurement techniques, as well as how to avoid or

reduce residual stresses is also presented.

In chapter 6 the results of a literature survey concerning measurements of residual stresses

in welded members is presented. The chapter was focused on as-welded members and some

models of prediction are also described. Moreover, the results from 47 individual measurements

of a multitude of steel grades are also presented in this chapter.

Measurements of residual stresses with the blind hole method may be studied in chapter 7.

The results from the experimental work regarding three box shaped specimens are presented

and evaluated. Furthermore, the equipment used for the experiments are described.

4

The acquired test data concerning local buckling and residual stresses are discussed and

concluded in chapter 8. All re-evaluated test data gathered from the two different literature

surveys are put together with the test data acquired from experiments at LTU.

Chapter 9 contains the references used herein.

In Appendix A all of the test data concerning the buckling tests are enclosed. Furthermore,

the measuring equipment concerning these tests are described more thoroughly.

Appendix B comprises the evaluation model used for the data from the residual stress

measurements. Moreover, the relevant test data from these experiments is presented.

In Appendix C data sheets containing the 47 specimens used along with the experimental

work conducted with respect to residual stresses. These are extracts from the test data acquired

from the literature survey.

Plate Buckling - Theory

5

Chapter 2:

Plate Buckling - Theory

The words “stable” or “instable” are used by people in various contexts. Almost everyone

have a relation or thought concerning the two words describing the state of something. The

terms are used in the wide range from psychology and politics to nuclear and chemical

applications. The term “stable” is often connected to something positive and rigid when

“instable” is closely linked to the possibility of an abrupt loss of something. One of the most

known and used context of the two words, which almost all people have a relation to, is when

used in medical surroundings; a stable or instable health state.

The interest in stability / instability is also a central concern regarding mechanical systems,

e.g. structural or civil engineering, see Figure 2.1. In this field the stability or instability of a

structure is often confined to regard the elastic part of the phenomena. However, as will be

shown later herein, a structural engineer may also have to consider the inelastic state of stability

/ instability. As an example of structural instability one can consider the columns in a building

made with a steel frame. These columns have not only to withstand the vertical loads of the dead

weight and e.g. snow, but also lateral loads caused by the wind. This well known instability

phenomenon is usually referred to as column or flexural buckling.

Figure 2.1: Maybe an up-coming example of global structural instability?

6

The buckling may be of global nature, as described above, but may also be of localized

(local) type. Buckling of local sort are regional located buckling, e.g. a flange of a beam or at a

certain level of a silo, see Figure 2.2. Local buckling occur due to compressive stresses and may

in a further perspective cause global buckling because of the loss of resistance of the cross

section in question.

Figure 2.2: Different examples of local buckling. Local buckling in a silo,

Farshad (1994) (left) and box shaped profile (right).

A structure or a member in an equilibrium state under e.g. compressive load may become

unstable and the structure acquires a new equilibrium state or a new trend of behaviour. When

considering classical buckling theory the critical stress level is situated where the equilibrium

of the load - deformation path diverge. This point is called the bifurcation point or bifurcation

load. Usually two more types of elastic instabilities are distinguished. These are limit

equilibrium instability (snap-through buckling) and dynamic or flutter instability, Farshad

(1994).

2.1. Bifurcation instability

Considering the load - displacement behaviour of a column or a plate subjected to

compressive stresses, a load level lower than the bifurcation point corresponds to a state where

eventual buckles are of elastic type. Hence, the secondary path in Figure 2.3 represents the post

buckling stadium.

Plate Buckling - Theory

7

Figure 2.3: Schematic description of the bifurcation of equilibrium.

The bifurcation load or critical load has under the years been thoroughly investigated. As

mentioned above, the critical load is determined with respect to elastic analysis and have been

examined theoretically by many different researchers, e.g. Timoshenko and Gere (1963).

2.2. Plate theory

A thin plate is, by definition, a two-dimensional flexural element of which the thickness is

much smaller than its other two dimensions. A plane passing through the middle of the plate is

called the middle plane.

Thin plate elements are used in various structures; they may be elements in a complex

structure or may themselves constitute the major part of a structure. Examples of plate elements

are walls of containers, silos, and reservoirs, flat roofs, flat elements of vehicles and aircrafts,

and sheet piles. Examples of plates in civil engineering applications are the flanges and the web

of a beam. Plate elements may be homogeneous and isotropic or they may be stiffened and / or

have a composite construction.

Depending on the mode of application, a plate can be subjected to various lateral as well as

in-plane forces. Under certain circumstances, applied in-plane loading may cause buckling

which can be global or in some cases, have a localized nature; delamination buckling of

composite plates or buckling of a web in a steel beam are examples of local buckling. For thin

plates, buckling is a phenomenon which may influence the load-bearing capacity of plate

elements. Therefor, this must be taken into consideration in the design of plate elements.

Loa

d

Deformation

Bifurcation point

Critical load

Secondary path

Primary path

8

2.2.1. Elastic analysis / Calculation of critical load

The theory behind the behaviour of a thin plate under compressive forces is usually divided

into two parts; firstly the calculation of the critical load and secondly the determination of the

ultimate load level. The critical load level is by definition the point were the structure, or

member, in question loose its stability.

Analytical calculation of the bifurcation or critical load on the basis of the classical theory of

elasticity may be done either through solving the differential plate equation or via the energy

method. The differential equation describing the buckling of a plate loaded in its plane was

established by Saint-Venant in 1870, Dubas and Gehri (1986), and states

(2.1)

where the flexural rigidity of the plate is given by

(2.2)

This plate equation was derived under the assumptions that the material is behaving in a

ideally elasto-plastic way, the plate is without initial imperfections such as initial curvature or

residual stresses. Furthermore, the plate deformations are assumed to be small. Under these

assumptions the plate shows no lateral deformations until the critical stress level is reached. At

this point, the deflection can either be negative or positive regarding the coordinate system of

the plate, Figure 2.4.

Figure 2.4: System bifurcation in point A. The plate buckles in either a positive or

negative direction, w.

The plate equation may be convenient to use when a rigorous solution of (2.1) is possible.

When the plate in question is for example reinforced with stiffeners, the problem gets more

x4

4w

24w

x2

y2

----------------y

4

4w

+ +1D---- q Nx

x2

2w

– Nyy

2

2w

– 2Nxy

2w

x y-----------+=

DEt

3

12 12

–-------------------------=

w

cr

A

Plate Buckling - Theory

9

advanced. These more advanced applications led to the development of other models, better

describing the actual behaviour of plates.

The solution to this problem was delivered by Bryan in 1891 through the establishment of an

energy based approach. The approach of this method is to study the plate energy in the

bifurcation point, where the plate cease to be in its assumed perfectly flat state and instead

follow its secondary equilibrium path (see Figure 2.3) in a laterally deformed state. The energy

based solution is built on the classical correlation between the internal energy of bending and

the external work done by the forces acting in the middle plane of the plate. The expression for

describing the strain energy stored in the deformed plate is

(2.3)

Furthermore the equation describing the work conducted by the externally applied forces is

(2.4)

The equations (2.3) and (2.4) are only valid for small deformations, which is assumed to be

the case up to the bifurcation point. With Figure 2.3 in mind, the comparison between the

internal energy and external work gives, according to Timoshenko and Gere (1963), the

following information concerning the stability of the plate in question at the bifurcation point:

• If U > T, the flat form of equilibrium of the plate is stable (primary path)

• If U < T, the plate is unstable and buckling occurs (secondary path)

However, the critical load amplitude may be found by setting

(2.5)

which can be solved under the condition that the change in energy potential must have a

minimum value for a stable equilibrium. This may be used for the derivation of a differential

equation form of the equilibrium. Another way to solve the problem is to apply an expression

for the lateral deformation of the plate.

U12---D

2w

x2

---------2w

y2

---------+

2

2 1 –2w

x2

---------2w

y2

---------2w

x y-----------

2

–– x ydd=

T12--- Nx

x2

2w

Nyy

2

2w

2Nxy

2w

x y-----------+ + x ydd–=

T U U T– 0= =

10

2.2.2. Simply supported plates under uniform compression

Figure 2.5: Simply supported plate under uniform compressive load. Dubas and

Gehri (1986).

If considering a plate subjected to evenly distributed forces along two of the edges, according

to Figure 2.5, the determination of the critical load level of the plate in question is dramatically

simplified. Since the only load applied on the plate, in the form of a uniform distributed

compressive force, acting along the edges x = a and x = -a, the rest of the external applied loads

according to equation (2.1) equals zero:

(2.6)

The edge constraints of the plate leads to the following boundary conditions:

Along the edges x = a and x = -a

(2.7)

and along the edges y = 0 and y = b

(2.8)

q Ny Nxy 0= = =

wx

2

2w

0= =

wy

2

2w

0= =

Plate Buckling - Theory

11

The boundary conditions implies that the deformed shape of the simply supported plate may

be described by a double trigonometric Fourier series on the form

(2.9)

By substituting the proposed solution according to equation (2.9) into (2.3) and (2.4) under

the above described conditions in (2.6), (2.7) and (2.8), and by using the relation between the

external work done by the applied load and the strain energy according to equation (2.5), the

following relation may be evolved:

(2.10)

To satisfy the equation (2.10) for all positions on the plate, i.e. all values of x and y, the

following relation has to be true:

(2.11)

or in another form

. (2.12)

The combination of the two integer parameters now have to be chosen in such a way that the

applied load, Nx, reach a minimum value, i.e. the sought critical load value, Ncr. It can be shown

that the lowest critical load is reached when the plate buckles in a shape such that one half sinus

wave is formed over the width of the plate (y-direction), hence the integer parameter n = 1,

Timoshenko and Gere (1963). With this, the equation (2.12) may be evaluated to

(2.13)

in which the integer parameter m describes the number of half sinus waves over the length of

the plate (x-direction). The equation (2.13) are more often formed as

(2.14)

w amn

m x

a----------- n y

b--------- m nsinsin

n 1=m 1=

1 2 3= =

Dm

a-------

2 n

b------

2

+2

Nx

m

a-------

2

+ amn

m x

a----------- n y

b---------sinsin 0=

Dm

a-------

2 n

b------

2

+2

Nx

m

a-------

2

+ 0=

Nx

Dm

a-------

2 n

b------

2

+2

m

a-------

2-------------------------------------------------=

Ncr

a2 2

D

m2

---------------- m2

a2

------ 1

b2

-----+=

2

m 1 2 3=

Ncr

kcr

2D

b2

----------=

12

where the dimensionless parameter kcr is the buckling load coefficient and is given by

. (2.15)

Furthermore, with the expression for the flexural rigidity of the plate given in (2.2), inserted

in (2.14) the well known expression for the critical, or bifurcation, stress may be expressed as

(2.16)

with the insight of that

(2.17)

The buckling load coefficient, kcr, is, as can be seen in (2.15), a function of the plate width

b, the length a and the number of sinus half waves over the length, m. For different values of the

plate width and length ratio a / b, the lowest critical stress level will be found for different

numbers of half waves according to Figure 2.6 below.

Figure 2.6: The buckling load coefficient for a simply supported thin plate.

Timoshenko and Gere (1963).

2.2.3. Initial plate imperfections

In section 2.2.1 above, a quite straight forward method for calculating the critical stress level

is presented. However, as always concerning theoretical models describing nature, it is

important to remember the assumptions made for the theory in question. Emphasizing the

assumptions made of a initially perfect flat plate and a perfectly isotropic behaviour in a

homogenous material the understanding of the limitations in the presented theory are obvious.

All materials have different levels inherent imperfections, also steel. A plate delivered from the

steel fabricator has an initial curvature and probably also residual stresses from uneven cooling

kcr

mb

a------- a

mb-------+

2

m 1 2 3= =

cr kcr

2E

12 12

–------------------------- t

b---

2

=

crN

crt=

Plate Buckling - Theory

13

of the material. These facts makes the assumptions made above somewhat untrue, which also

has been proven experimentally and may be found in chapter 3.

Now when the assumptions are found to be a quite utopical description of the real behaviour

of the considered plates, the question arises how these initial imperfections affect the plate

behaviour before, as well as after, the bifurcation point. Figure 2.7 below shows the difference

in the plate behaviour when plate imperfections are considered.

Figure 2.7: The influence of initial plate imperfections in relation to perfect

plates. Farshad (1994).

Considering Figure 2.7 above two conclusions concerning how the imperfection influence

the plate behaviour may be drawn. Firstly, buckling of a plate with inherent imperfections is

gradual and the exact critical load may be difficult to determine. Hence, difficulties arises when

a comparison between theoretically and experimentally determined critical loads are to be

conducted. Secondly, as mentioned before, the plate may accept continued loading after the

bifurcation load is reached. Thus the critical load is shown to be a non-representative measure

on the ultimate resistance of the plate in question, Brush and Almroth (1975).

2.2.4. Geometric imperfections

When considering the initial out-of-plane imperfections, i.e. initial buckles, the influence of

these on the maximal out-of-plane deformation / load correlation are shown in Figure 2.8.

The graph and the calculations behind was made by H. Nylander in 1951 and shows how an

applied initial deformed shape with the amplitude wo (in the same shape as the deformed plate)

affects the magnitude of lateral deformations under applied load. Furthermore, when the

material is assumed to be ideal elastic, the model gives no information concerning the ultimate

load, Johansson (2005). Concluded, the initial geometric imperfections primarily influences the

plate stiffness and becomes more obvious with an increased plate slenderness.

14

Figure 2.8: The effect of initial geometric imperfections. Relation between the

lateral deformation, w, plate thickness, d, and load, N, concerning

different amplitudes of initial imperfections wo. StBK-K2 (1973).

2.2.5. Residual stresses

How residual, or initial, stresses are formed, distributed and under which magnitudes these

may occur is more thoroughly described in chapter 5. However, knowing that residual stresses

are present in all materials, it is evident that this must affect also the elastic plate buckling

theory. Geometrical imperfections and residual stresses in a plate under compression mainly

affects the initial stiffness of the plate. In Figure 2.9 below, a schematical distribution of residual

stresses caused by edge welding a plate is shown.

Figure 2.9: Schematic distribution of residual stresses in an edge welded plate.

Considering Figure 2.9 above, the influence of the initial load due to the present residual

stresses is clear. Since the middle region of the plate before external loads are applied, already

is under compressive stresses, it is obvious that yielding of the plate in question will occur at a

lower external load level compared to a residual stress free plate, see Figure 2.10.

The effect of inherent residual stresses is more marked for stockier or intermediate slender

plates, for which the yielding process of the plate is the governing cause of failure. Concerning

more slender plates, the initial geometric imperfection tend to surpass the influence of residual

Plate Buckling - Theory

15

stresses, Dubas and Gehri (1986). Hence, the influence of residual stresses decreases with

increasing plate slenderness.

Figure 2.10: Schematic influence on the behaviour of a plate with (S) and without

(A) residual stresses.

2.3. Non linear theory / Post buckling behaviour

As shown above, the estimation of the critical load may be done by a straight forward

method. However, the elastic analysis assumes, as described in previous sections, that the plate

in question is perfectly flat and that no initial stresses are present. Because of the presence of

these imperfections non-linear models were evolved. Furthermore, the initial plate

imperfections were not solely the reason to why non-linear theories had to be evolved. The

assumption concerning the constitutive relations, in this case ideal elastic material, is not

suitable to use when the ultimate resistance is sought for.

Another reason why non-linear models were established was that many researchers showed

that the ultimate load of a plate under compression may significantly surpass the critical load

level. This was especially evident concerning more slender plates. Regarding stockier plates the

resistance is often limited by yielding in the material and the ultimate load may be lower than

the critical.

In linear elastic analysis, the distribution of the load is assumed to remain uniform until the

plate buckles. However, when the plate starts to buckle, the stresses are re-distributed in the

plate. The plate behaviour under these large deformations, or post critical behaviour, is a

complicated area to describe. Some differential equations describing the phenomenon were

derived by von Kármán in 1910 but the methods for solving these are complex, Dubas and Gehri

(1986). The finite difference method, fourier series or different perturbation methods are

possible tools for this work.

L / L

cr

16

Other methods may also be used for studying the post critical plate behaviour. One example

is the numerical methods, e.g. the finite element method, FEM, which probably is the most

powerful tool available today. However, other methods have been used during the years of

research. Analytical methods such as the Ritz energy method or a method based on a theory by

Skaloud and Kristek called the “Folded plate theory method” are both excellent examples.

As described above, the theory behind plate buckling is rather complicated due to the

combination between the membrane stresses from the applied load and bending stresses in the

deformed plate, as well as shear stresses due to rotation of the corners of the plate. For design

purposes the above described methods may be too advanced to use. This is why the “Effective

width approach” by von Kármán et al. (1932), is widely spread as the model for determining the

ultimate resistance of plates under compression.

2.3.1. The von Kármán effective-width formula

The starting point for the effective width approach is that the ultimate resistance is reached

when the largest edge stress reaches the yield stress level. Since the formed buckle in the middle

of the plate reduces the plates ability to carry the load, the stresses are re-distributed as shown

in Figure 2.11 below. The real stress distribution in the plate is approximated, or substituted,

with two strips which describes the load carrying effective width of the plate.

Figure 2.11: Stress distribution in a plate before (a) and after buckling (b).The von

Kármán assumption concerning the effective width is presented in (c).

Brush and Almroth (1975).

Plate Buckling - Theory

17

von Kármán’s hypothesis was that the “new” plate with the width of beff would have the

critical stress equal to the yield stress, i.e.

(2.18)

Furthermore, the critical stress according to (2.16) under the condition that the plate is under

uniform compression and simply supported (kcr = 4) the following expression may describe the

relation between effective width and yield stress level:

(2.19)

or with the original plate width equal to b

(2.20)

which is usually referred to as the von Kármán effective-width formula. Furthermore, the

relation

(2.21)

was made as a generalization of the corresponding well known parameter for column buckling

and was called the reference slenderness of the plate. In modern design rules, when design is

done with respect to the ultimate load level, this expression is the only one considering the

critical load. And as expressed in von Kármán et al. (1932) the following may be stated

(2.22)

or

, for (2.23)

under the circumstances that the plate is simply supported and under uniform compressive load.

Although, von Kármán’s theories gained reputation as a good method to use for the

determination of the ultimate load of the plate in question, the method was a strictly theoretical

method based on plates without initial imperfections and when compared to test results it was

found to be true only for large b / t ratios. However, von Kármán still stands as the first

researcher proposing a reduction factor function.

crfy=

42E

12 12

–------------------------- t

beff

--------2

fy=

beff

b cr

fy

-------=

pcr

fy

-------= 1 05b

t---

fy

kcr

E----------=

beff 1 9tE

fy

---=

beff

b-------- 1

p

-----= p 1

18

2.3.2. The Winter function

Theodor von Kármáns work was a milestone concerning the simplified design methods

concerning plate buckling. Many researchers followed his work (Figure 2.12), aiming for an

expression describing a real plate with inherent initial imperfections. One of the more known

and widely spread in design codes, are the one proposed by Winter in 1947. Winter conducted

numerous experimental tests on cold formed specimens and suggested

, for (2.24)

as a suitable function regarding the effective width, Winter (1947). Winters first suggestion

was with the coefficient 0,25 but was later changed to the 0,22 used nowadays. However, it is

interesting to notice the small difference between the “original” equation (2.23) and the

experimentally based (2.24).

Other researcher proposed different solutions, or modifications, of the initial von Kármán

formula. Two reported in Dubas and Gehri (1986) are

, for (2.25)

by Faulkner in 1965 and

(2.26)

suggested by Gerard in 1957.

Figure 2.12: Reduction functions according to Winter, Faulkner, von Kármán and

Gerard as described in the text above.

beff

b-------- 1

p

----- 10 22

p

------------–= p 0 673

beff

b-------- 1 05

p

------------ 10 26

p

------------–= p 0 55

beff

b-------- 0 82

p0 85

------------=

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Winter function

Faulkner function

von Kármán function

Gerard function

Plate Buckling - Theory

19

Even though a lot of effort has been put into this reseach field, the Winter function, based on

the cold formed members survived and is nowadays set as the function used in the present

design regulation in Europe, the Eurocode 3.

In Eurocode 3 the plate slenderness, p, is calculated according to

(2.27)

and is defined according as

. (2.28)

Furthermore the buckling load coefficient, k , for a simply supported plate under uniform

compressive load is determined according to Figure 2.6.

As mentioned above, design with respect to local buckling of flat compression elements is

made through a reduction of the cross sectional area of the plate in question. Concerning internal

compression elements this is, according to Eurocode 3, done through the use of the expression

(2.29)

in which the factor , represents the actual stress distribution over the plate. Concerning uniform

distribution of compressive stress this factor equals 1. Thus, the equation reflects the

original Winter function (2.24) used for these kind of plate elements in Eurocode 3.

p

b t

28 4 k-------------------------=

235fy

---------=

p 0 055 3 +–

p

2-------------------------------------------------- 1 0=

20

Plate Buckling - Survey of Literature

21

Chapter 3:

Plate Buckling - Survey of Literature

The plate buckling phenomena has, as mentioned in previous chapters, been quite thoroughly

investigated. This also on a strictly experimental basis. The research work is forthgoing when

new steel grades and design rules enter the field of constructional applications.

However, to acquire all the test data and experimental reports concerning plate buckling are

difficult and the author to this theses makes no claims of have accomplished this. Though the

work presented below should be sufficient to validate the experiments presented in following

chapter 4.

The articles and papers presented in this chapter have been chosen to be comparable to the

tests in chapter 4. This with respect to specimen layout, welding conditions, support conditions,

steel grades and other comparable similarities. Furthermore, all the test results presented in this

chapter are evaluated with respect to the Winter function discussed in chapter 2 and according

to the Eurocode 3 specifications concerning plate slenderness values.

3.1. “Experimental Investigation of the Buckling of Plates with Residual

Stresses”

An investigation aiming to clarify how residual stresses influence the resistance against local

buckling was presented by Nishino et al. (1967). Specimens used in this research work were

fabricated of plates welded together to form a square cross section, see Figure 3.1, and tested in

as-welded condition.

22

Figure 3.1: Specimen layout and weld detailing. Nishino et al. (1967).

Two different steel grades were used for the specimens, ASTM A7 (sheared specimen plates)

and ASTM A514 (flame-cut specimen plates) with properties according to adjacent Table 3.1.

In addition to the buckling tests the residual stress condition in the specimens were measured

with the sectioning method (described in section 5.4.1).

Table 3.1: Results from tension coupon tests.The average compressive residual

stresses was estimated regarding each plate (side) individually.

Nishino et al. (1967).

3.1.1. Test Setup

The tests of the specimens were divided into four sets, each comprising two specimens with

the same geometrical properties and made of the same steel. The width - thickness ratios were,

according Nishino et al., selected such that the critical loads were reached in either the elastic

range or the elastic-plastic range. Furthermore, the length of the specimens were chosen in such

way that

• the buckling mode corresponding to the lowest critical load would be developed

and

• short enough to prevent column buckling to be the governing failure mode.

The buckling tests were performed with the specimens under uniformly distributed

compressive force as the specimens were equipped with rigid end plates, milled flat to simplify

Specimen

No.

Material Yield Strength,

fy [MPa]

Average compressive

residual stress, rc [MPa]

Ratio

rc / fy

1 A 7 273,0 83 - 97 0,32

2 A 7 266,1 69 - 76 0,27

3 A 514 799,8 76 - 83 0,10

4 A 514 717,1 97 - 103 0,15

Plate Buckling - Survey of Literature

23

the alignment in the test rig. Simply supported conditions were assumed to be valid constraints

for the plates in the welded specimen.

3.1.2. Test results and conclusions

Regarding the conclusions drawn by the authors in their article, the most interesting

concerning this theses were:

• The effect of residual stresses on the buckling strength of a plate is less pronounced

for A 514 steel than it is for A 7 steel.

• Considerable post-buckling strength exists in a plate buckled in the elastic range,

while a plate buckled in the elastic-plastic range has a relatively small reserve of

post-buckling strength.

• The plate elements of square columns of A 514 steel are stronger than those of A 7

steel when compared on a non dimensional basis (compared to the yield strength of

each grade).

Furthermore the test results presented by Nishino et al. were re-evaluated herein with respect

to the Winter function (2.24) and Eurocode 3 and presented in adjacent Figure 3.2.

Figure 3.2: Test results from all the 8 specimens from Nishino et al.(1967). The

results are re-evaluated with respect to the Winter function (2.24).

Plate slenderness according to Eurocode 3.

3.2. “Plate Slenderness Limits for High Strength Steel Sections”

An investigation with the aim of determining if high strength steel with yield stress in the

range 450 - 700 MPa could be designed according to existing Australian design rules was

presented in Rasmussen and Hancock (1992). A test programme comprising box welded

sections and cruciform shaped specimens as well as I-shaped sections were used to examine if

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Specimens of grade A7

Specimens of grade A514

Winter function

24

the design codes had to be modified or if they were usable also for the grades with higher

strength (a similar aim as for this thesis, except the difference in regarded codes). The

investigation focused on whether the yield slenderness limits for welded uniformly compressed

plates supported along one or both longitudinal edges were applicable to the high strength steels.

However, since this thesis solely focus on plates supported along both sides, these test results

are the only ones regarded herein. Furthermore, the intention of the investigation by Rasmussen

and Hancock (1992) may not be completely in line with the aim of this thesis, still the test results

from the paper in question are valuable and re-evaluated with respect to the Winter function

(2.24).

The test programme was divided into three parts; measurement of the material properties

with tension and compression coupons, residual stress measurement through specimen

sectioning and compression tests of the specimens. The specimens were all made of

BISALLOY 80 steel which, according to Rasmussen and Hancock, is equivalent to the ASTM

A514 grade. The through coupon tests measured mechanical properties of the BISALLOY 80

grade are presented in Table 3.2.

Table 3.2: Nominal and measured mechanical properties of BISALLOY 80.

Rasmussen and Hancock (1992).

3.2.1. Test setup

The box specimens used in the test programme were all fabricated by weld joining four plates

(Figure 3.3) with nominal thickness of 5 mm and with 3 different nominal widths (plate

slenderness values in Figure 3.4). Gas metal arc welding with a Lincoln L50 wire were used for

all the welds.

Figure 3.3: Specimen layout and weld detailing. Rasmussen and Hancock (1992).

The specimens were milled flat at the ends to allow a proper seating to the end plates of the

test rig. The bottom plate was fixed against rotation and the top plate was mounted on a

Nominal plate

thickness [mm]

Type of test Nominal values,

fy [MPa]

Youngs modulus,

E [MPa]

Measured values,

fy / fu [MPa]

5 Tension 650 211 670 / 775

5 Compression 650 211 750 / -

Plate Buckling - Survey of Literature

25

spherical seat. Furthermore the length of the specimens were chosen to allow unrestrained

development of local buckles and short enough to prevent overall instability phenomena

(column buckling).

3.2.2. Residual stress measurement

The longitudinal residual stresses were measured with the sectioning method and readings

were made with use of strain gauges. Gauges were applied near the centreline of each plate of

the box specimen and the mean values of the measured compressive stresses on the four plates

are presented for each specimen in Table 3.3.

Table 3.3: Measured residual stresses of box columns. The average compressive

residual stresses was estimated regarding each specimen

individually. Rasmussen and Hancock (1992).

3.2.3. Test results and conclusions

The test results from Rasmussen and Hancock were re-evaluated herein with respect to the

Winter function (2.24) and Eurocode 3 and presented in Figure 3.4.

Figure 3.4: Test results from all the 6 specimens from Rasmussen and Hancock

(1992). The results were re-evaluated with respect to the Winter

function (2.24). Plate slenderness according to Eurocode 3.

Specimen Average compressive

residual stress, rc [MPa]

Yield Strength,

fy [MPa]

Ratio

rc / fy

B1RS 169 670 0,25

B2RS 114 670 0,17

B3RS 73 670 0,11

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Specimens of grade BISALLOY 80

Winter function

26

The investigation of the high strength steel sections presented by Rasmussen and Hancock

rendered in the following conclusions regarding the box sectioned specimens:

• The strength of slender welded high strength steel plates exceeds that of welded

ordinary steel plates when compared on a non dimensional basis (compared to the

yield strength of each grade). The test results suggest that the difference in the non

dimensional strength may be greater for plates supported along one longitudinal

edge than for plates supported along both.

• More slender plates are more affected of the presence of the residual stresses than

stockier ones. This is due to the fact that the more stocky plates may be almost

completely plastified at the ultimate load level.

3.3. “Basic Compressive Strength of Steel Plates from Test Data”

A comprehensive investigation regarding uniformly compressed steel plates was presented

in a paper by Fukumoto and Itoh (1984). The purpose of the work was to review and store data

of experimental investigations under clearly defined and described conditions. The authors

collected data from 793 individual tests of a variety of cross sections such as single plates,

welded square boxes, square and rectangular tubes, welded rectangular sections and cruciform

specimens. Data concerning specimens in as-welded as well as annealed condition were

regarded. 13 % of the data collected was regarding specimens made of steel with higher yield

strength than 430 MPa (definition of high strength steel in the paper).

Data concerning initial geometrical imperfections, residual stress levels and ultimate loads

were presented in form of histogram plots. Concerning the residual stresses, Fukumoto and Itoh

states that the magnitude of the residual compressive stress may not be influenced of the yield

stress of the base material. This statement was founded on 32 residual stress measurements on

specimens made of high strength steel which showed that the rc / fy ratio was lower for the high

strength steel specimens compared to the rest of the data set.

Fukumoto and Itoh collected results from 383 plates with inherent residual stresses. The

plates were of the type with welds along the unloaded edges (in tubes or as single plates) or as-

welded box sections. The authors made a nonlinear regression analysis with an assumed

uniform variance on the data and the mean function presented with a standard deviation of

0,0871 were

, for (3.1)u

fy

------ 0 968

p

--------------- 0 286

p

2---------------–

0 0338

p

3------------------+= p 0 571

Plate Buckling - Survey of Literature

27

Furthermore, the authors made the same analysis for 172 plates without residual stresses.

These plates were as-cut, annealed or annealed box sections. The results from this analysis were

, for (3.2)

with a standard deviation of 0,104. Herein both the equations (3.1) and (3.2) are compared

to the Winter function (2.24) in Figure 3.5.

Figure 3.5: Mean functions of plates with (3.1) and without (3.2) residual stresses

from Fukumoto and Itoh (1984) compared to the Winter function

(2.24).

Several interesting conclusions were drawn by Fukumoto and Itoh concerning their

experimental data-base approach. Conclusions among others were:

• No clear difference between the plate strengths determined through single plate

tests and square boxes could be pointed out.

• Annealed plates showed larger variations in strength than as-welded plates.

• Further experimental investigations were needed concerning plates of high

strength steel.

3.4. “Local Buckling of Thin-Walled Columns”

The local buckling tests presented in Dwight et al. (1968) comprised tests of square box,

rectangular box and cruciform sections. The square box section tests were conducted with the

aim of filling gaps in previously presented tests reported by J.D. Harrison and also presented by

Dwight and Moxham (1969), see section 3.5.1. A total of 49 columns were tested in as-welded

and stress relived condition. However only 4 specimens, made by T.K. Chin, were used in the

u

fy

------ 1 133

p

--------------- 0 384

p

2---------------–

0 0468

p

3------------------+= p 0 658

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Plates with residual stresses (3.1)

Plates without residual stresses (3.2)

Winter function

28

evaluation in this thesis. These specimens were of square box section type in as-welded

condition.

The mechanical properties of the steel used for fabrication of the specimens were determined

through compression tests. The length of the specimens were set to 3,5 to 4 times the plate width

and tested under uniform compressive stress. In this evaluation the result from four of these tests

were used and the yield stress in compression was measured to 354 respective 403 MPa. The

test results from these tests were re-evaluated herein with respect to the Winter function (2.24)

and Eurocode 3 and presented in adjacent Figure 3.6.

Figure 3.6: Test results from 4 as-welded specimens reported in Dwight et el.

(1968). The results were re-evaluated with respect to the Winter

function (2.24). Plate slenderness according to Eurocode 3.

3.4.1. Conclusions

Dwight et al. concluded that the difference between the resistance of an as-welded specimen

compared to a stress relieved specimen could be in the order of 10 to 15 %. This considering a

considerable range of width to thickness ratios and with the higher resistance concerning the

stress relieved specimens.

3.5. “Welded Steel Plates in Compression”

Another survey of work by different researchers in the field of plate buckling were presented

by Dwight and Moxham (1969). The paper focused on investigating how well the British

standards of 1969 were describing the actual behaviour of plate buckling and was somewhat a

continuation of the work described in section 3.4. Special effort were put into investigating how

the weld induced residual stresses affected the ultimate resistance with respect to local buckling.

Dwight and Moxham gathered test results from over 40 welded column specimens of square

box sections with yield strengths in the range of 232 to 402 MPa. The tests applicable to this

theses are listed below.

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Specimens with fy = 354 MPa

Specimens with fy = 403 MPa

Winter function

Plate Buckling - Survey of Literature

29

3.5.1. Tests made by J.D. Harrison

Dwight and Moxham reported results from 20 experiments made by J.D. Harrison and J.B.

Dwight. These specimens were in as-welded as well as in annealed condition. The length of the

specimens were about 4 times the plate width and the specimens were loaded under uniformly

distributed compressive stress. In this thesis the only regarded specimens are the as-welded

ones. Furthermore, the test results from these tests were re-evaluated with respect to the Winter

function, equation (2.24), and Eurocode 3 to be comparable within this thesis. These re-

evaluated results are presented in Figure 3.7 below.

Figure 3.7: Test results from the 10 as-welded specimens reported in Dwight and

Moxham (1969). The results were re-evaluated with respect to the

Winter function (2.24). Plate slenderness according to Eurocode 3.

3.5.2. Tests made by K.E. Moxham

In Dwight and Moxham (1969) three additional tests were collected for the evaluation. These

tests were made by K.E. Moxham and conducted in a similar way to the one described above.

However, these tests were made in a somewhat larger scale with bigger specimens (plate

thickness of 12,7 mm) but still in as-welded condition and thereby possible to compare with the

other tests reported herein. The re-evaluation of the three specimens, with a yield strength of

312 MPa, are presented in Figure 3.8.

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Specimens with fy = 250 - 281 MPa

Winter function

30

Figure 3.8: Test results from all the 3 specimens of K.E. Moxham presented in

Dwight and Moxham (1969). The results were re-evaluated with

respect to the Winter function (2.24). Plate slenderness according to

Eurocode 3.

3.5.3. Conclusions

Several conclusions were drawn concerning the work presented by Dwight and Moxham

(1969). Concerning this thesis relevant conclusions are:

• Residual stresses caused by welding may reduce the strength of fabricated

members in relation to the size of the welds.

• The load - deformation curve for a web containing residual stresses is less peaky

than that for a stress free web.

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Specimens with fy = 312 MPa

Winter function

Plate Buckling - Survey of Literature

31

3.6. “Buckling Tests on Rectangular Plates made of two Different types of

Weldox 1100 Steel”

Buckling tests on 9 specimens made of two different steel grades were presented by Möller

and Johansson (1995). The aim of the investigation was to determine which one of two grades

made by SSAB Oxelösund was preferable to be sold under the trade name Weldox 1100 with

respect to local buckling. The two candidates had somewhat different mechanical properties,

according to the author one grade had a yield stress of 1130 MPa and the other was 1349 MPa.

The specimens were of stub column type with a box shaped cross section, Figure 3.9, and the

height of the specimens were chosen to 3,5 times the specimen width. This to prevent column

buckling, avoid clampening effects from the end supports and to allow the specimen to buckle

in such a way that the lowest buckling load would be acquired. Furthermore, the specimens were

tested in as-welded condition.

Figure 3.9: Specimen layout and weld detailing. Möller and Johansson (1995).

3.6.1. Test setup

The tests were performed under uniform compression of the specimens between two rigid

end plates. The deformation speed was chosen such that the nominal stress would reach the

yield strength within 30 seconds. Furthermore the deformation of the specimens were carried

on until a 50 % load drop from the ultimate load was acquired. Deformation and load data was

sampled during the tests.

3.6.2. Test results and conclusions

The conclusions drawn by Möller and Johansson were mainly concerning how the two

different types of Weldox 1100 would be classified or used. This made their conclusions

somewhat difficult to use herein. However, the test results could still be re-evaluated to be

comparable in this thesis. The test results from Möller and Johansson (1995) were re-evaluated

with respect to the Winter function (2.24) and Eurocode 3 and presented in Figure 3.10.

32

Figure 3.10: Test results from all the 9 specimens from Möller and Johansson

(1995). The results were re-evaluated with respect to the Winter

function (2.24). Plate slenderness according to Eurocode 3.

3.7. Discussion and Conclusions

Regarding the presented results collected through the literature survey the predominantly

chosen steel grades seems to be of a type with lower strength (i.e. yield strength below 460

MPa). However, with respect to the tests presented later in this thesis (see chapter 4), these

gathered test results are of great importance to be used as a reference to grades included in

Eurocode 3.

Furthermore, the re-evaluation (or use of test data) was made with respect to Eurocode 3 and

the Winter function. This was done in order to be able to do a comparison between the different

experimental results. Even though this procedure was conducted, some differences considering

the results are still present. One obvious difference is that in some case the yield strength of the

steel was measured in compression. Usually the compressive strength is slightly higher

compared to steel in tension. This influences not only the evaluation considering the reduction

factor, but also the plate slenderness. Emphasizing the definition of plate slenderness according

to Eurocode 3, described in equation (2.27) and (2.28), the yield strength of the material in

question is regarded. An increased yield strength implies a higher plate slenderness, i.e. the plate

will be considered more slender than it would be if the yield strength in tension would be used.

Regarding the presented results some conclusions may be drawn when contemplating the

conducted work showed in sections above.

• The effect of the presence of residual stresses are evident to decrease the local

buckling resistance.

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Specimens with fy = 1130 MPa

Specimens with fy = 1349 MPa

Winter function

Plate Buckling - Survey of Literature

33

• Most of the stockier specimens seems to have a resistance surpassing the Winter

function.

• More slender specimens tends to have a lower resistance than predicted by the

Winter function.

34

Plate Buckling - Experimental Work

35

Chapter 4:

Plate Buckling - Experimental Work

The local buckling phenomenon has over the years been quite thoroughly investigated by

numerous of different researchers, e.g. see chapter 3. However, the sphere of local buckling

research concerning members made of steels with higher strength has yet not been fully

evaluated. This topic has been the focus of the experimental work presented herein and, in some

way, a step towards filling these gaps in knowledge and further enhance the possibility of using

high strength steel in the constructional work of today.

4.1. Background

During the winter and spring of 2004 a local buckling test programme, comprising stub

column tests and uniaxial tests, were performed at the division of structural engineering, Luleå

university of technology, LTU. The tests were a part of the RFSC funded project “LiftHigh -

Efficient Lifting Equipment with Extra High Strength Steel” and with focus on the second

project work package: “Global and local buckling of hollow sections and welded boxes”.

With focus on this work package, 48 specimens with box cross section have been tested at

LTU, solely with respect to the local buckling phenomena. This was complemented with

uniaxial tension tests for the determination of the mechanical properties of the steel in question.

Furthermore, measurements of the residual stress state in the specimens (as-welded condition)

was conducted (presented in chapter 7).

The specimens were fabricated by SSAB Oxelösund and made of extra high strength steel,

as well as of a more commonly used steel grade. The specimens were designed to simulate four

individual plates under uniform compression and simply supported along their boundaries.

4.2. Experimental investigation

The aim for the test programme was to investigate if steels with yield strength > 460 MPa

behaves different than ordinary steel grades with respect to local buckling. This is something

that has not been examined to such a great extent before. As an example, steel grades with yield

strength of 460 MPa is nowadays set as the upper limit for the Eurocode 3.This may be

36

preferable to adjust to also comprise grades with strength above this limit. With this aim the

specimens for evaluating the local buckling resistance were fabricated out of three different

steel grades; 3 mm thick Domex 420 (hot rolled) and the two Weldox grades 700 (quenched and

tempered) and 1100 (quenched), both of plates with a nominal thickness of 4 mm. These

measured thicknesses were also used in the evaluation of the results from the buckling tests.

In addition to the buckling tests, 18 coupon tension tests were conducted with the purpose of

determine the properties of the three different grades needed for further evaluation of the

buckling test data.

4.3. Uniaxial tests

The mechanical properties of the steel used for the fabrication of the local buckling

specimens (see section 4.4) were determined through tensile coupon tests. The tests were made

according to the test standardization in EN 10002-1 (2001). A total of 18 coupons were laser-

cut from the same virgin plates as used for the fabrication of the buckling test specimens.

Furthermore, because the rolling direction of the steel was altered between being along and

perpendicular to the loading direction in the buckling tests, the mechanical properties were also

determined in these directions, Figure 4.1.

4.3.1. Specimens

The thicknesses of the plates used for the fabrication of the box specimens, hence also

concerning the coupons, were nominally 3 mm for the Domex grade and 4 mm concerning the

Weldox.

Figure 4.1: Plate with laser-cut coupons along and transverse the rolling

direction.

Prior to each tension test the coupon was measured to determine the geometry of the

specimen. The length of the coupons was 379 mm and the width 39 mm for the gripping part of

the coupon (the ends) and 24,9 mm (mean value for all 18 coupons) for the notched area in the

middle of the coupon specimen. Furthermore the plate thickness was determined to 3,05 mm for

the Domex plates, 4,09 mm for the Weldox 700 and 3,98 mm for the Weldox 1100 plates.

Plate Buckling - Experimental Work

37

4.3.2. Test setup

The tension tests were made in a 600 kN servo - hydraulic DARTEC rig and the test data was

acquired through software enclosed with the rig. The load and axial elongation was measured

until failure of the coupon specimens.

Figure 4.2: The coupon equipped with extensometer in the test rig.

4.3.3. Test results

In Figure 4.3 the typical stress-stain relation is shown for the three different grades and in

Table 4.1 the results from the 18 tested coupons are presented in numbers. The Domex 420

grade shows a classic steel stress - strain relation behaviour, with a distinct yield plateau.

Therefor the yield strength is stated for these specimens. However, the Weldox grades shows a

strongly non-linear behaviour and has no well identifiable yield plateau. In this case the 0,2 %

proof stress are used as the yield criterion. All of the uniaxial stress - strain curves from the 18

coupons are enclosed in Appendix A.1.

Figure 4.3: Typical stress - strain relation for Domex 420, Weldox 700 and 1100.

All specimens oriented along the rolling direction.

0 10 20 30 40

, Strain [%]

0

400

800

1200

1600

, T

en

sile s

tress [

MP

a]

S420, Coupon D1

W700, Coupon W1

W1100, Coupon W7

38

Concerning the material behaviour of the Domex 420 and Weldox 700 it is evident that the

yield or 0,2 % proof stress and ultimate resistance is higher when tested transverse the rolling

direction. The Weldox 1100 seems to behave contradictive to the other two grades, with an

almost equal 0,2 % proof stress and ultimate strength in the both directions, maybe with a

slightly higher strength along the rolling direction. This was also concluded by Gozzi (2004).

Table: 4.1: Results from the uniaxial tensile coupon tests.0o indicates rolling

direction along the loading direction and 90o transverse.

* Indicates failure outside of the range of the extensometer.

4.4. Buckling tests

4.4.1. Specimens

The specimens were made of four identically designed plates, along their edges weld joined,

see Figure 4.4 and Figure 4.5 below. The design of the specimens were conducted with the

purpose to allow the plates to act as simply supported along the longitudinal edges (edges in the

loading direction). Furthermore, the aim is to have these simply supported plates be subjected

to an uniformly distributed compressive stresses. This was achieved through welding flat milled

rigid end plates to the top and bottom of the box section. These end plates were assumed to be

thick enough (thickness > 15 mm) to distribute the applied load evenly to the four plates of the

welded box specimen.

Specimen Yield Strength,

fy [MPa]

Proof Stress,

Rp0.2 [MPa]

Ultimate Strength,

Rm [MPa]

A5 [%]

Dom

ex 4

20 0o

D1

D2

D3

442

439

443

-

-

-

529

526

530

30,1

29,8

30,1

90

o

D4

D5

D6

469

473

471

-

-

-

533

533

532

30,5

28,8

28,7

Wel

do

x 7

00

0o

W1

W2

W3

-

-

-

769

774

775

821

828

826

15,2

15,6

14,4

90

o

W4

W5

W6

-

-

-

791

800

791

824

834

826

14,6

14,7

15,0

Wel

do

x 1

10

0

0o

W7

W8

W9

-

-

-

1345

1350

1357

1477

1480

1489

9,5

8,6

*

90

o

W10

W11

W12

-

-

-

1326

1359

1320

1457

1512

1485

*

8,7

8,6

Plate Buckling - Experimental Work

39

To prevent column buckling, the height of the specimens were limited to 3 times the plate

width. This would also minimize the influence of eventual clamping effects (moment restraints)

from the end plates. Furthermore the rolling direction of the steel was varied between being

along and perpendicular to the loading axis of the specimen.

Figure 4.4: Specimen layout and weld positions.

All specimen fabrication work, along with the production of the Weldox plates, were made

by SSAB Oxelösund. The Domex plates were fabricated by SSAB Tunnplåt in Borlänge. The

test ready box specimens were delivered to LTU along with plates of the three grades for

fabrication of the coupons needed for the uniaxial tests.

Figure 4.5: Specimens S30-0a (left) and W73-0a (right) after test.

The 48 specimens were divided into three sets, each comprising one of the steel grades

Domex 420, Weldox 700 or Weldox 1100. The nominal plate slenderness values, p, were

A - A

AA

40

chosen to 0,7, 0,85, 1,0 and 1,5 and the nominal thickness was 3 mm (Domex) and 4 mm

(Weldox). The width of the plates was then given by Eurocode 3 with respect to the chosen plate

slenderness.

The different slenderness “groups” comprised four specimens for each steel grade. Two of

these had the rolling direction oriented in the axial, or loading, direction of the specimen,

denoted 0o. The other two were designed with the rolling direction perpendicular to the loading

direction, marked 90o. The different specimens setup and geometries are enclosed in Appendix

A.2.

Welds

All welds were of fillet type and had a nominal throat thickness (a) of 4 mm. Gas metal arc

welding was used for the welds and two different electrodes were used with respect to the

different steel grades, see Table 4.2 below for electrode properties.

Table: 4.2: Nominal electrode properties provided by SSAB Oxelösund.

However, the heat input of 0,33 kJ / mm, welding speed 340 mm / min., current 155 A and

the voltage 15,3 V were all the same for all specimens. Mison 25 (77 % Ar and 23 % CO2) was

used as protective gas for all the welds.

4.4.2. Test Setup

All the box specimens were tested in an INSTRON I450, 4,5 MN rig, see adjacent Figure

4.7. The specimens were uniaxially loaded with a deformation speed of 0,072 mm / min. until

the ultimate load had been reached.

The deformation speed was kept until the load response had decreased with 10 % of the

ultimate load. At this point the deformation speed was doubled and the test was run until the

load had decreased to approximately 70 % of the ultimate load.

Electrode

Type

Steel

Grade

Nominal Yield

Strength, fye [MPa]

Nominal Ultimate

Strength, fue [MPa]

Elongation [%]

AWS A5.18-93

(D=1 mm)Domex 470 560 26

AWS A5.28-79

(D=1 mm)Weldox 690 770 20

Plate Buckling - Experimental Work

41

Figure 4.6: A box specimen placed in the INSTRON I450, 4,5 MN test rig.

4.4.3. Measurements

During testing data was sampled over 6 channels. The load was measured with a load cell

from DARTEC with a measuring range up to 2 MN. The deformation in the loading direction

was measured with four 11 mm LVDT's in four points located at the corners of one of the end

plates. Four LVDT’s were used to be able to calculate the mean axial deformation of the end

plate which in further evaluations was used as the mean axial plate deformation. The out of

plane plate deformation, or buckle growth, was also measured. This was done with a 25 mm

LVDT at the mid point of one side of the specimen, see Figure 4.7.

During all the tests the sample rate of data was 2 Hz and a 600 Hz Spider 8 from HBM was

used for interpreting the signals from the gauges to PC environment. For information

concerning the specifications of the equipment used for acquiring data, see Appendix A.5.

Figure 4.7: The test setup with all the LVDT’s and the load cell. The specimen

was deformed from the lower side and the load measured by the load

cell on the upper side (left). To the right the out of plane deflection

LDVT is pictured.

42

Prior to test start the specimens position in the rig was measured to ensure that the loading

axis was in the centre of the specimens, hence the risk of introducing forces due to eccentricity

of the specimen was minimized. As an extra precaution to eventual unwanted influences, a

small hole was drilled through one of the end plates of the specimens. This was to ensure that

the air pressure inside the closed specimen was equal to the surrounding air at all times during

the deformation of the specimen. Furthermore, eventual pressure differences due to the welding

(heated air) was also avoided through this procedure.

Additional measurements concerning the geometry of the specimens were also conducted.

The plate dimensions were measured prior to the buckling tests and are enclosed in Appendix

A.2. The plate width was measured on three positions on all four plates in every specimen. In

addition to this, the plate height was measured on one position on all four sides. All dimensions

were measured between the weld edges, i.e the effective width and height of the simply

supported plates.

4.4.4. Results

The test data essential to the aim of this investigation was the ultimate load registered

concerning respective specimen. The typical load - mean deformation behaviour for the

specimens made of the three different grades is presented in adjacent Figure 4.8. All of the load

- mean axial deformation curves are enclosed in Appendix A.3.

Figure 4.8: Typical load - mean axial deformation behaviour for the box

specimens made of the three different steel grades.

The cross section area for the stress comparison was calculated from the data enclosed in

Appendix A.2 - Table A.1. The weld area was added to the plate section area. The weld areas

were set to 19 mm2 for the Domex specimens, 34 mm2 for the Weldox 700 specimens and 32

mm2 for the Weldox 1100 specimens. All weld areas were theoretically determined with respect

to their individual measured plate thicknesses. The mean 0,2 % proof stress, Rp0.2, was

calculated from the tension coupon test results presented in Table 4.1.

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

F, A

xia

l lo

ad

[kN

]

S40-0a

W74-0b

W114-0a

Plate Buckling - Experimental Work

43

Three specimens, one from each grade, were removed from the buckling test programme.

These specimens, S20-0b, W72-0b and W112-0b, were put to side to be used for the

measurement of longitudinal residual stresses, presented in chapter 7. Furthermore SSAB

Oxelösund delivered some extra specimens of the stubbier type with a nominal plate

slenderness of 0,7. These specimens were made of the two Weldox grades and the results are

enclosed with the other results from the ordinary specimens.

Figure 4.9: Specimen W74-0a with deformed end plate (left) and specimen W111-

0b with ruptured weld in upper left corner (right).

Unfortunately, the results from the specimen W74-0a had to be removed from the evaluation

because of some problems regarding end plate deformation. The specimen never reached its

ultimate load due to the plastic deformation of one of the end plates. In addition to this, problems

concerning specimen W111-0b occurred. This specimen reached its ultimate load, but shortly

thereafter one weld failed and the load dropped very fast. However, the load - deformation curve

shows a somewhat different behaviour and are enclosed Appendix A, but since the ultimate load

were reached without problems, the results from this specimen was evaluated and enclosed

among the other results.

4.5. Test Evaluation

The test results were evaluated with respect to the Eurocode 3, i.e. equations (2.27) and (2.28)

in section 2.3.2. The calculations are based on the mean values for each specimen, i.e. the mean

width for all four plates and the mean values concerning the mechanical properties. This is also

the case concerning the plate thickness, which is determined through measurement of the

coupons used in the material tests.

In Figure 4.10 and Figure 4.11 the results are plotted as a comparison to the Winter function

(2.24).

44

Figure 4.10: The evaluated results from the 48 specimens along with the Winter

function. Plate slenderness calculated according to Eurocode 3.

Regarding the evaluated test data some things are important to be pointed out. Firstly, the spread

between the results for each group of tests are small for the more slender specimens. Some

differences can be noticed for the slender specimens, especially concerning the slenderness

value of the plates. The origin of these differences is mostly dependent of the different strength

of the steel concerning the rolling direction. Though, these differences seem to be less

pronounced with increasing steel strength. Furthermore, the scatter between each test tend to be

larger for the specimens with p< 0,9.

Figure 4.11: Results presented non-dimensionally with respect to yield strength or

0,2 % proof stress. Ultimate resistance from tests and theoretical

resistance according to Eurocode 3.

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Domex 420

Weldox 700

Weldox 1100

Winter function

0 0.4 0.8 1.2

R / fy

0

0.4

0.8

1.2

u/f y

Domex 420

Weldox 700

Weldox 1100

Plate Buckling - Experimental Work

45

4.6. Discussion and conclusions of test results

Considering Figure 4.10 the evaluated test results seems to be consistent within each test

group, i.e. plate slenderness value concerning each grade. This is even more obvious regarding

the most slender specimens where the four tests of each grade are nearly four repetitions of each

test (the same ultimate load reached for each specimen). Moreover, another conclusion may be

drawn based on this fact and this is simply that the test procedure seems to have been consistent

with small differences between each specimen test.

When comparing the test results with the Winter function (hence Eurocode 3) the more

stocky plates, p < 0,9, seems to coincide with the reduction factor function, see Figure 4.10.

The resistance may even be somewhat higher than predicted through the Winter function.

Considering these more stocky specimens, the ones of the “lower” strength steel seems to

inherent a higher resistance than the high strength steel specimens which is positioned closer or

on the Winter function in Figure 4.10. However, this may have its origin in the difference in

mechanical behaviour and how the material properties are regarded as discussed above.

Regarding the other range of specimens, p > 0,9, the opposite has to be concluded. The

Winter function seems to overestimate the resistance concerning more slender plates. This

completely independent of steel grade. However, if Figure 4.11 is considered along with the

Figure 4.10, the specimens of high strength steel seems to coincide better with the Winter

function.

Considering all of the evaluated and presented test results the following may be concluded:

• The Winter function seems to underestimate the resistance of stockier specimens.

In this case plates with p < 0,9.

• The Winter function overestimates the resistance of more slender plates. In this

case plates with p > 0,9.

• Plates made of high strength steel may be treated in the same way as “ordinary”

grades with respect to the local buckling resistance.

• With respect to the Winter function, no difference between the specimens with

different rolling direction could be concluded.

Considering the evaluation of the test results, one obvious difference, regarding the

mechanical properties of the steel, in the evaluation procedure has to be mentioned. The slight

difference between the specimens of the Domex and Weldox specimens concerns the used

material properties, i.e. yield strength for Domex and 0,2 % proof stress concerning Weldox

specimens. This different approach is dependent of the lack of well defined yield plateau

considering the Weldox grade, still the hardening properties of these grades influences the

evaluation. This in the way that the difference between the ultimate strength and the stress

46

defined as fy is larger for the steels with lower strength, i.e. a well defined yield limit. This leads

to that the calculated critical stress level considering the Weldox specimens will be in an

unfavourable position since the stress level defined as yield stress is closer to ultimate strength

of the steel. In the evaluation of the experimental work, this leads to a lower reduction factor,

hence a lower position if plotted with the Winter function as a reference.

When considering the actual experimental work some things are imported to state. First, the

measurement of the buckling growth has not been implemented nor evaluated in this thesis. This

data was herein excluded due to the fact that this test data was considered to give no further

valuable information or possibilities to conclude with respect to the aim of this thesis.

Furthermore, the measured initial geometric plate imperfections were neither implemented

herein. Regarding these measurements, the reason why these were measured was to be used in

further investigations, i.e. FE-modelling of the presented tests.

Residual Stresses - Theory

47

Chapter 5:

Residual Stresses - Theory

Since the middle of the 19th century it has been known that stresses exists in structures,

members or even in a solitary material, without being under externally applied loads, Alpsten

(1967). These are often called residual stresses, but various other technical terms have been

applied to the residual stresses over the years, such as internal stresses, inherent stresses,

reaction stresses or locked-in stresses, Welding Handbook (1976). The residual stresses may be

seen as a statement, or a reminder, of its historical events, e.g. how the steel plate in question

has been manufactured or how well a joint is fitted.

An other, for the layman more understandable, example of residual stresses is timber being

cut up to planks. The planks are hopefully straight and flat after cut up, though not seldom in a

bent or twisted shape. This new shape has its origin in the, through the cutting, released residual

stresses which were present in the timber due to e.g. different growth in the fibres of the timber.

Moreover, the same type of stresses may be noticed in steel due to the history of the material.

Residual stresses in metallic materials may, as briefly mentioned above, spring from various

different events. The most common cause are the manufacturing, fabrication or refinement

processes of the metal in question. Processes such as casting, welding, machining, shearing,

molding, rolling, bending etc. (Figure 5.1) induces residual stresses of different magnitudes and

distributions in the metal.

Figure 5.1: Examples of how macroscopic residual stresses may be induced in

metals. Welding Handbook (1976).

48

Moreover, residual stresses can also be induced into structural members after assembled to

a finished structure through e.g. ground settlements or repair work under the life cycle of the

structure.

5.1. The origin of residual stresses

It has been shown by numerous different authors that the residual stresses in a member may

reach the extreme stress levels up to, or even beyond the yield stress of the regarded material,

herein steel, see Figure 5.2. Even though extensive work has been put into the cause of establish

rules for estimating the residual stresses in a member, and many suggestions has been presented,

the topic is still somewhat dwelled in fog. Questions have been risen whether the yield stress of

a material is an appropriate way of estimate the residual stresses in, for example a steel plate.

Masubuchi (1977), reports that some researchers have presented results showing that the yield

stress approximation may even be less suitable regarding steels with higher yield strength than

conventionally used steel grades. In some of these reports the measured stress levels were

considerably lower than the yield stress of the steel.

Figure 5.2: Example of failure in a hot rolled profile due to residual stresses.

Alpsten (1967).

The residual stress state in a material is a highly coupled thermal / metallurgical / mechanical

process, Sjöström (1994). This has led to that the classification of residual stresses in a material,

in this case steel, usually sorted into stresses of the first (macro stresses), second or third order

(micro stresses). The first order residual stresses are defined as stresses in a scale corresponding

to the definition of stress used in continuum mechanics, Lagerqvist and Olsson (2001). Residual

stresses with variation in a microscopic range between the grains in the steel are usually put as

the second order. Third order residual stresses are existing in areas near dislocations in the steel.

This thesis is strictly limited to treat residual stresses of the first order.

Residual Stresses - Theory

49

Residual stresses may be divided into groups according to how the stresses are induced into

the steel or structure in question:

• Stresses due to structural mismatch, or

• Stresses caused by the uneven distribution of thermal or plastic strains.

The residual stresses in a material most often shows great variations with respect to the

regarded position in the geometry. Variations through the thickness, across the width and over

the length, e.g. of a plate, may be considerable. Since residual stresses exists without externally

applied loads, the regarded member must be in equilibrium. The resultant force and moment

produced by the residual stresses has to vanish, which implies that the stresses must be varied

in magnitudes over the cross section in order to maintain the state of equilibrium.

5.2. Residual stresses due to structural mismatch

Residual stresses dependent of structural mismatch, see Figure 5.3, can often be avoided

through a more innovative selection of materials or better fitting of joined parts, e.g. a bolted

joint between steel members. Straightening operations of steel members also induces residual

stresses. However, the second category might be more difficult to avoid without making special

operations focused especially on reducing the already induced stresses. As an example is a weld;

it has to be done to join parts and finish the structure in question. As will be described later in

this chapter, welding in steel induces residual stresses, hence formation of stresses can not be

avoided.

Figure 5.3: Figure describing mismatch. Welding Handbook (1976).

5.3. Residual stresses due to thermal or plastic strains

Residual stresses caused by thermal or plastic strains is probably the most studied field

considering residual stress research. This is most likely due to the fact that these induced

stresses are possible to measure in laboratory environments, while residual stresses caused by

mismatch often occur in the field (in a finished structure or similar) which leads to a more

difficult measurement procedure.

50

When a material is heated or cooled uniformly with no temperature gradients, it is free to

expand and shrink without restrictions, hence no residual stresses are induced through the

change of temperature. Hence, change in temperature is not alone the requirement for

introducing residual stresses in a material. In order to induce residual stresses through a mere

change of temperature, the expansion or shrinkage of the material has to be restrained. A simple

example is the cooling of a steel bar fitted between two rigid end supports. If the bar is placed

between the ends in a state were the temperature is higher than the equilibrium temperature of

the surrounding medium (air) and the fitting is exact, stresses will be formed in the bar when the

temperature decreases. These stresses act like any load, and is in this case evenly distributed as

tensile stresses. A bar heated in one end acts analogous to this, but with residual stresses as

result.

Residual stresses can also be induced through an uneven distribution of non-elastic strains,

e.g. a bar subjected to a bending moment which introduces strains at plastic levels into parts of

the bar. However, if the bar is unloaded the elastic part of the strains is released, but the plastic

deformations (strains) remains in the material. No external loads are applied on the bar but still

strains (unevenly distributed) are present in the material. Hence residual stresses have been

formed.

Another very common way to induce residual stresses into a material is through the welding

process. However flame cutting steel plates also induces significant residual stresses. The

theory behind both of these processes are very similar why the emphasis herein is on describing

the former, see section 5.3.3.

5.3.1. Hot rolling

As mentioned above, residual stresses induced through fabrication or manufacturing

processes often have their origin in the uneven cooling of the steel. The main issue concerning

the residual stress state in a hot rolled member is to reduce the temperature gradient in the

material under the cooling process in order to keep the stresses as low as possible. When

fabricating heavy profiles, i.e. with thick material, this is of course a major concern. It has been

indicated that the magnitude of residual stresses tend to increase with an increasing size of the

member in question, Alpsten (1972). This fact is explained through the cooling behaviour which

is a combination between surface heat transfer and internal heat conductivity.

Considerable variations in the stress distribution and magnitudes are often found when

measuring the stress state in heavier members. The stresses may diverge in magnitude as well

in direction concerning all dimensions of the member. A special behaviour concerning the

heavy members are that the stresses can often differ significantly in levels and directions

through the thickness of the steel plate.

Residual Stresses - Theory

51

The behaviour of hot rolled members of thinner material is somewhat the same as described

above for heavier members. Though, the through thickness variations are most often not of the

same magnitudes as for the thicker material.

Considering hot rolled members, straightening is often a contributing cause to the residual

stress state in the members. When the members are fabricated, the residual stresses due to the

cooling of the section may cause the member to twist or bend in a shape with unacceptable

geometry. This is usually solved through a straightening procedure, often done in a cold state

member. The result of the straightening is a member more straighter and more flat. Actually, the

member is deformed plastically to acquire its new more ideal shape. Though, the cost of twisting

and bending the member is that new additional residual stresses are induced.

5.3.2. Cold forming

Profiles made through cold forming steel plates have inherent residual stresses as all other

members. Though, the theory behind the introduction of residual stresses in these members are

fundamentally different than for hot rolled sections, described in section 5.3.1. When cold

forming a member into desired shape, the base material, e.g. a flat thin plate, is deformed in a

cold state to form the desired cross section. This implies that the stresses are not induced through

uneven thermal flow or heat transfer to air, but on a strictly mechanical basis. According to

Ingvarsson (1977) the cold forming mechanism of a flat plate involves two events:

1. The flat plate is elastically and plastically deformed

2. The bent shape is elastically unloaded

The cold forming process may be done through many different methods, e.g. forming by

bending or hydro forming. Though all the different processes introduces plastic deformations in

the base material which causes distortions in the material.

Figure 5.4: Example of residual stress state dependent of cold forming and flame

cutting. Ingvarsson (1977).

52

5.3.3. Weld induced residual stresses

When the welding technique made fast progresses during the 1930’s, the residual stress

research gained speed when a new unexplored area was discovered. This especially due to some

bridge collapses which was claimed to be partly caused by the weld induced residual stresses,

Alpsten (1967), which today has led to an extensive literature quantity. However, this multitude

of reports seems to be somewhat divergent in their conclusions when the correlation between

steel grade and factual residual stress magnitudes caused by welds is still not determined.

When welding in metal, the material is locally heated and a non-uniform temperature

distribution in the member is induced. Furthermore, the temperature changes during the welding

process in terms of cooling and heating of new material. The weld metal, e.g. the electrode, and

the metal in the heat affected zone (HAZ) are at a temperature significantly above the

surrounding material. The welding process adds molten material to the base metal which

immediately starts to solidify through heat transfer to the surrounding material and to the air.

Under this solidification process the molten metal starts to transfer shrinkage stresses to the rest

of the metal.

A weld is usually made progressively, point D to point A in Figure 5.5, which introduces

stresses in the longitudinal (along the weld) direction of the joined material. These

longitudinally directioned residual stresses spring from the fact that the already solidified

portions of the weld resists the shrinkage of the more recently laid parts of the weld, Welding

Handbook (1976). Furthermore, the allowance of transverse movement is often also restricted

which induces stresses transverse to the weld bead. Analogously to this, stresses in the direction

of the plate thickness may also be introduced into the joined plates.

Figure 5.5: Schematic representation of how welding induces residual stresses.

Welding Handbook (1976).

Residual Stresses - Theory

53

Adjacent Figure 5.5 shows how the residual stresses are formed during joining two plates by

welding. The welding arc, moving with speed , adds molten metal at the point O. In front of

point O, the base metal is still more or less unaffected by the heating of the material, and hence

no residual stresses are present in section A-A (if disregarding eventual stresses caused by the

plate fabrication process).The cross hatched area indicates the HAZ region where plastic

deformations occur during the welding. Thus, the region outside the HAZ remains in the elastic

region. Figure 5.5b shows how the temperature changes in the member at different points along

the weld and Figure 5.5c displays how the residual stress distribution varies when the material

is cooling.

In section B-B the molten metal in point O supports no loads. This leads to a stress level in

the centre of the weld is close to zero. Furthermore, the temperature gradient causes the warmer

metal near the weld to expand and compressive stresses are founded because of the restraints

dependent of the surrounding cooler material. Since the temperature in these areas are high and

therefor inherent a lower yield strength, the stresses may be as high as the yield strength.

However, when the stresses must be in equilibrium, the compressive forces near the weld are

balanced with tensile stresses farther from the weld.

Considering section C-C, the molten weld metal and the surrounding base metal near the

weld bead have cooled and the temperature gradient in Figure 5.5b has decreased. When cooling

the metal wants to shrink which causes tensile stresses to form close to the weld. The

equilibrium makes the regions outside these parts to first form compressive stresses which may

pass to tensile farther from the bead.

When the temperature is back to normal, i.e. equal to the surrounding medium (usually air),

the final residual stress state has been reached and is shown in section D-D. The weld bead and

the added material has now cooled down completely and high tensile stresses have been formed.

These are balanced with compressive stresses along the edges of the plate, Figure 5.6. The

example above is described with support of Welding Handbook (1976).

Figure 5.6: Measured residual stresses induced by welding. Spooner et al. (1992).

54

The distribution and magnitudes of the weld induced residual stresses are dependent of many

factors. As stated above, the geometry of the members to be joined are crucial, but the welding

speed, added material (electrode), welding energy and surrounding temperature as well as the

temperature of the base metal are all factors which influence the stress state in the finished

member. Moreover, the number of passes are of great importance considering the weld induced

residual stresses.

One other factor which may introduce secondary residual stresses into a weld joined member

is the geometrical distortions that often occur when welding. The distortions is connected to the

residual stress state in the way that it is dependent of the shrinkage of the heated material during

the cooling process. The distrortion is caused by a non-uniform contraction of the member in

question, Figure 5.7. The distortion of the member may often be straighend to fit other parts in

a structure which further induces stresses into the member.

Figure 5.7: Example of distortion caused by welding. Longitudinal (L) and

transverse (T) shrinkage. Welding Handbook (1976).

5.4. Measurement methods

The measurement of the residual stress state in a material is a somewhat difficult and maybe

even more disturbing, often very time consuming. Concerning the measurement of the stresses,

all of the measurement techniques may be divided into two categories:

• Destructive methods

• Non destructive methods

In the past the former group was the only known method to measure residual stresses. In

order to measure the historically induced stresses in an object, these stresses had to be relaxed

in some fashion in order to measure the difference between a relaxed and a stressed state.

However new strain measurement techniques have been developed allowing the stresses to be

measured without cutting or drilling in the member.

Residual Stresses - Theory

55

5.4.1. Destructive residual stress measurement methods

The destructive methods for measuring residual stresses in a material are all founded on the

removal of material and measuring the up-coming change in strain due to the operation. Hereby

the relieved stresses are possible to estimate.

Sectioning

Measurement of residual stresses with the sectioning method is founded on cutting the

specimen in strips or layers and then measure the strain change over the operation. Sectioning

in strips (Figure 5.8) gives information about the stress levels in the plane of the plate and the

layering shows how the stresses varies through the thickness of the specimen.

Figure 5.8: Example of the sectioning of welded specimen. Tebedge et al. (1973).

The actual measurement may be done with e.g. strain gauges or mechanical tools

determining the elongation of the sectioned strip, see Figure 5.9. Measurement of elongation

mechanically may be done using a Staeger meter where reference points are used for the

determination of the released strains. The distance between the reference points are measured

before and after the sectioning, and the released strain may the be calculated as the difference

between the two measurements. The same procedure is done when strain gauges are used in the

purpose.

56

Figure 5.9: Measurement of distance between reference points before sectioning

(left). Strips equipped with strain gauges from a sectioned specimen

(right).

The sectioning method has its benefits in being reasonably economical and easy understood

but a disadvantage is that the measured relieved strain, is in fact a mean value over the width of

the strip in question.

Hole drilling

The hole drilling method for measuring residual stresses have many different names with

some differences. The deep hole drilling method, centre / blind hole drilling or trepan technique

are all different approaches but still founded on the same theory. Usually the released strains are

measured with a rosette strain gauge, but mechanical measurement methods may also be used.

Figure 5.10: Schematic description of the deep hole method. Smith and Bonner

(1996).

Residual Stresses - Theory

57

The deep hole method (Figure 5.10) is often used when measurements in thick plates are to

be conducted. The measurement is initiated by the drilling of a small reference hole through the

specimen and the diameter of this reference hole is carefully measured. A column of the

material with the reference hole in the middle is trepanned out of the specimen. After this the

diameter of the reference hole is measured once again, and every difference between the two

measurements are used to determine the released residual stresses in diametral direction

(diameter change) as well as in axial direction (the depth of the hole).

The centre or blind hole methods are both versions of the same type of measurement. They

are based on using a rosette strain gauge with the individual strain gauges situated around a hole

positioned in the centre of the gauge. Drilling in the specimen is done either partially through

the thickness or completely through. The removal of the material may be done in increments,

determining the change of strain levels at different layers through the thickness, as well as in

one increment completely through the plate. The method is proven to be accurate if applied

correctly, Procter and Beaney (1987).

Figure 5.11: An example of the blind hole technique. The drilling is done in the

centre of the rosette gauge to a depth of half the plate thickness.

The trepanning technique may be described as the deep hole method without the reference

hole. Instead a rosette strain gauge is placed in the middle of the measurement area. The method

may be used to investigate changes in strains through the thickness with incremental removal

of material.

58

Figure 5.12: Schematic description of the trepan technique. Procter and Beaney

(1987).

Other methods

Other versions of the above described methods to measure residual stresses are available, but

this thesis claims in no way to be a complete coverage of the today existing techniques.

However a somewhat semi-empirical method to measure the residual stress state is to use stress

relieved and specimens as-welded and evaluate the different behaviour between these

specimens.

5.4.2. Non-destructive residual stress measurement methods

The non-destructive methods are much younger than the ones described above. These new

methods are base on advanced technical innovations such as the neutron diffraction method.

However, they are all superior to the destructive methods in the way that they all leave the

specimen in question un-affected by the measurement. Hence it is possible to use these method

on site, e.g. on an existing structure. Of course the equipment for measuring the stresses are

expensive and in some cases not portable.

Neutron diffraction

Some authors claims the neutron diffraction method to be the most accurate for

determination of residual stresses, Walker (2001). However this method is dependent of

neutrons supplied by a nuclear reactor which makes usage of the method somewhat restricted.

Usual specimens measured with this type of method are landing gears and jet engines. The

greatest benefit of this method is that the full stress tensor may be determined.

The measurement of the residual stress state is founded on the reflection of the neutrons

when travelling through the material. The reflection angle gives information about how severe

Residual Stresses - Theory

59

the distortions among the crystals in the material is. The depth penetration are very good with

its 38 mm in steel and a layering depth in the range of grains.

X-Ray measurement

X-ray diffraction measurement also offers a non destructive method to estimate the residual

stresses in a specimen. However the measurement of strains are restricted to a depth of about 8

to 20 m and hence only gives information about the stresses at the surface of the specimen.

Other methods

Other methods used for non-destructive stress measurements are quickly mentioned.

Ultrasonic conduction, photo-stress coating (measuring regions with high stress levels) or laser

speckle-shear techniques. Most of the above described methods, except maybe the X-ray

method, are somewhat since fiction regarding civil engineering applications and hence not

further regarded herein.

5.5. Effects of residual stresses

The presence of residual stresses in a member, plate or structure may be either beneficial or

detrimental. How the residual stresses affect the resistance of the object in question can only be

determined by a careful consideration regarding the way the structure is planned to be used. The

residual stresses are treated like any other load acting on the structure and super positioning

these applied loads and stresses may give a more favourable case when regarding the residual

stresses. However, coinciding directions of external loads and residual stresses are more often

reality concerning structures.

Extensive studies concerning the instability phenomenon in relation to residual stresses in

welded steel structures have been conducted by many researchers, Welding Handbook (1976).

Experimental studies as well as numerical computations have been used in the effort to establish

the relation between the residual stresses and resistance, e.g. with respect to local buckling. It is

well known that residual stresses in welded members decreases the resistance regarding local

buckling. This may easily be concluded studying Figure 5.13 with initial compressive stresses

in the middle of the plate welded into forming a box cross section. When the plate is subjected

to externally applied compressive forces, these are added to the already present stresses. Hence

the ultimate load decreases with increasing residual stress magnitudes in the plate. Furthermore,

the influence of the residual stresses regarding the resistance to local buckling of plates

increases with an increasing plate slenderness (more elastic buckling).

60

Figure 5.13: Measured distribution of residual stresses in a welded box cross

section. Compressive stresses inside the box and tensile outside.

Concluded the following facts may be presented concerning the effects of residual stresses,

Welding Handbook (1976):

• The effect of residual welding stresses on the performance of welded structures is

significant only on phenomena which occur under low applied stress, such as

brittle fracture and stress corrosion cracking

• As the level of applied stress increases, the effect of residual stresses decreases

• The effect of residual stresses is negligible on the performance of welded

structures under applied stress beyond yielding

• The effect of residual stress tends to decrease after repeated loading.

5.6. How to reduce residual stresses

That residual stresses exists in all materials is now concluded. That levels and distributions

may also be altered through welding, heating or other structural operations have also been

described. However, treatments reducing the residual stresses in structural members exists.

These may be or strict mechanical nature or of other typ as thermal processes.

The most common way to reduce residual stresses is to anneal the material or member in

question. However this operation may affect earlier acquired properties of the material and are

not always suitable.

Other methods to reduce residual stresses are the ones based on peening of different types.

Shot peening, laser peening or water peening are used to lower the magnitudes of, mostly weld

induced, residual stresses. These methods are often described as post weld treatments, or PWT.

Residual Stresses - Theory

61

When concerning welding steel, the easiest way to decrease unwanted distortion or high

stress levels in the finished member is to pre-heat the material. This makes the cooling of the

material much more even and hence the stresses are reduced.

However considering the methods available for reducing the residual stresses the time and

effort, most often spelled “economy”, are the governing equation for all construction work. The

residual stresses may be more economical to keep unmodified and instead increase the member

size in order to reach the resistance required for the purpose in question.

62

Residual Stresses - Survey of Literature

63

Chapter 6:

Residual Stresses - Survey of Literature

Residual stresses are present, in some extent and type, in all members used in civil

engineering applications. When designing these structures, usually no special consideration is

paid to the residual stress magnitude and distribution in the member in question. However, the

effect of residual stresses are often implied in other parts of the design. An example is the

Winter function (see chapter 2) which is derived through experimental work on specimens with

residual stresses. This means that the residual stresses are regarded in the design even if not

directly announced. Even though the residual stresses may be treated implicitly in the design,

the determination of the residual stress state may be needed if special load cases are to be

regarded or if design with numerical methods, e.g. finite element analyses, will be used.

Modelling of residual stresses have been shown to be a rather complicated issue to pursue, e.g.

Ueda and Yuan (1991) and Clarin (2003). The modelling of residual stresses will be treated in

section 6.1 below. If special modelling work not is possible to carry out for the designer, the

residual stress state in a welded member are described in most design codes. Though, these

suggestions are schematic and a quite rough instrument to use. Such examples of stress

distributions are presented in Figure 6.1.

Residual stresses may spring from many different origins. However, this chapter is solely

focused on residual stresses caused by welding, or maybe more accurately put, residual stresses

in welded members. Residual stresses along the weld (herein called longitudinal direction or

longitudinal stresses) were the main focus of the survey of literature regarding residual stress

measurements or modelling work presented in this chapter.

The aim of the literature survey was to examine if a correlation between the yield strength of

the material and the tensile stress was possible to derive. In a further perspective, this would

give information whether the stress states presented in Figure 6.1 are suitable to use when

concerning steels with higher strengths. The measurement methods used in the different articles

or papers span from neutron diffraction to sectioning. Furthermore, the steel grades, the welding

characteristics and the specimens used for the residual stress measurements are greatly varied.

Because of this, a rather large amount of specimens with measured longitudinal stresses could

be regarded in the task of examining the actual stress state in welded specimens.

64

Figure 6.1: Residual stress distributions used in the swedish design code BSK 94.

6.1. Modelling of residual stresses

Modelling or determining residual stresses induced by welding in the design phase of

construction work may be a difficult issue. As mentioned, simplified distributions of the stress

state after welding may be estimated by using the suggested distributions according to the used

design code. However, if a more accurate estimation of the residual stresses is required, some

tools are available. Some of these tools are approximate formulations derived from

experimental work, while some are strictly numerical and often on the form of FE analysis.

Numerical modelling of the induction of residual stresses due to welding are most often

based on some thermal elasto-plastic analysis. By considering the problem this way many

different influential factors are possible to regard. Furthermore, the entire mechanical behaviour

during welding is possible to simulate; ending in the welded component with residual stresses

induced due to the welding process, Ueda and Yuan (1991). Even though the numerical

approach of determining the residual stress state after welding seems to be a rather powerful tool

concerning this task, not further regard is paid to this method herein. This due to the fact that

Residual Stresses - Survey of Literature

65

the methods are still quite complicated and not yet really applicable in terms of constructive

work in civil engineering applications. The method still seems to be on a research level.

6.1.1. Analytical models

The models for determining residual stresses induced by welding briefly presented in this

section, called analytical models, are all derived from evaluation of test results. Weld area,

welding characteristics such as welding speed, voltage, current or material properties are

common quantities regarded. Furthermore, the amount of weld passes (single run or multi weld)

also affects the final stress state and are possible to take into account.

However, most of the analytical models derived are assuming that the zone close to the weld

are subjected to tensile stresses equal to the yield strength of the steel. Under this assumption

combined with the knowing of a total equilibrium over the member in question, the formulas

are derived to describe how the residual stresses are distributed over the member. In this section

two examples of formulas for estimation of residual stresses in a welded member are presented.

One is strictly based on the welding characteristics and derived under the assumptions described

above. The other focuses on the weld geometry and the number of weld passes and results in an

estimation of the shrinkage force resultant of the residual stresses induced by the welding.

However the slightly different names of the two models, both of them estimates the tendon force

acting to form the equilibrium to the tensile forces induced by the welding.

“Shrinkage force method”

In the Merrison report (1973) a method for estimation of the residual stresses induced by

welding is presented. The concept was based on the thought that the stresses would be assessed

by considering the shrinkage forces, Fc, induced by all welds attached to the component in

question. Furthermore, the effects of the shrinkage forces was calculated under the assumption

that the forces were uniformly distributed over a specified area. Examples of these

specifications are:

• For welds connecting longitudinal stiffeners to plate in stiffened panel - the gross

sectional area of the stiffened panel should be used.

• For longitudinal seam and panel junction welds - the total cross-section area should

be used.

The estimation of the shrinkage forces were conducted on the basis of the total nominal

cross-sectional area of the weld metal in the joint. The most simple formulations for the

estimation were made concerning single run welds equation (6.1) as

(6.1)

and multi run welds equation (6.2) as

Fc 10 A=

66

(6.2)

where the weld layout giving information concerning the weld area needed in the equations

were presented according to adjacent Figure 6.2 and Figure 6.3.

Figure 6.2: Area definitions concerning a single weld joint. Nominal areas

showed hatched. The Merrison report (1973).

Figure 6.3: Area definitions concerning multi-run weld joints. Total nominal

areas shown hatched. The Merrison report (1973).

More complicated weld layouts were also concerned in the Merrison report but are not

presented herein.

“Tendon force concept”

A printing examining the tendon force concept of estimating residual stresses in welded

plates was written by Bambach and Rasmussen (2001). The authors used 40 welded specimens

to evaluate the tendon force concept, originally presented in 1977 by J.D. White. The model by

White relates welding characteristics to the stress induced as a function of the plate width.

Bambach and Rasmussen used White’s equation (6.3) which is defined with two parameters

describing the type of weld, k, and the process efficiency, p.

(6.3)

Fc 10A

n32

--------------=

F k pQ

v----=

Residual Stresses - Survey of Literature

67

Concerning a plate with a centre weld, according to Figure 6.4a below, the process efficiency

was found to be 0,8 and the weld constant, k, equal to 0,2. The centre weld condition was,

according to the authors applicable to the weld shrinkage induced in a flange plate welded into

a T- or an I-section.

Furthermore, if regarding a plate equipped with a weld along its edge, according to Figure

6.4b, the bending stresses induced due to the eccentricity of the weld offset the tendon force.

According to the theory description by Bambach and Rasmussen (2001), this causes a stress

gradient and increases the magnitude of the tendon force. This is regarded by setting the weld

constant, k, to 0,32 and the process efficiency was found to be 0,42. This condition is applicable

to the web welded to a T-section.

Figure 6.4: Description of residual stress magnitudes and distributions in welded

plates. Bambach and Rasmussen (2001).

Regarding the welding conditions showed in Figure 6.4c, i.e. a plate with welds laid

simultaneously along the edges, the constants used for calculation of the tendon force are the

same as for the centre weld.

However if the welds are placed on the plate consecutive, with allowance of plate cooling

between the runs, the residual stress distribution changes along the plate, see Figure 6.5.

Experiments by White showed that the magnitude of the tendon force was the same (the same

constants) as that for the edge welded plate, Bambach and Rasmussen (2001), however scaled

up or down by a factor, m.

Figure 6.5: Description of residual stress magnitudes and distributions edge

welded plates. Bambach and Rasmussen (2001).

68

Conclusions made in Bambach and Rasmussen (2001), concerning the experimental results

compared to the above described model of estimating the tendon force, was that a good

correlation between the models and the residual stress measurements could be pointed out.

6.2. Measurements of residual stresses

A quite extensive amount of different publications describing measurements of residual

stresses in welded members have been presented over the years. Within this section some of the

publications are described. They surveyed in the purpose of investigating the correlation

between the yield strength of the steel and the tension residual stresses. All of the gathered, to

this task interesting information were enclosed in special data sheets. This to make the

information as available to further evaluations as possible. These data sheets are presented in

Appendix C. The specifications given by the respective authors were shown to be of different

quality, some very extensive and some with less information concerning the experimental work

enclosed.

The literature study presented in this section, shows a big variety of measurement methods,

as well as used specimens and steel grades. One common denominator however, is that all of

the measurement presentations are considering welded members of some sort. Furthermore only

“ordinary” steel grades are regarded (i.e. stainless grades etc. are not included). A total of 47

individual specimens are regarded in this survey and only longitudinal tensile stresses were

evaluated. Furthermore, the welds have to be in as-welded condition and the plate thickness has

to be in a reasonable range considering eventual through-thickness variations.

The used methodology of this evaluation was to estimate the maximum value of the tensile

stresses concerning each specimen, see Figure 6.6. This was done by measuring the magnitudes

in respective case, if not the author had given information regarding the exact values sought for.

Figure 6.6: Collected residual stress data from Appendix C. Specimen ID and

respective measured maximum of tensile stress.

0 10 20 30 40 50 60 70

Specimen number

0

100

200

300

400

500

600

Maxim

um

valu

e,

t,rs

[M

Pa]

1

2

3

4

5

6

1314

15

16

1718

19

2021

22

23

24

28

29

3031

32

33

34

37

38

39

45

48

49

50

51

52

53

54

55

56

57

58

59

60

61

Residual Stresses - Survey of Literature

69

Furthermore, the tensile mean stresses over the welds were normalized to the yield strength

of the steel grade in question, Figure 6.7. The nominal yield strength of the material was used

in the evaluation if not specified by the author through special tests in addition to the residual

stress measurements.

Figure 6.7: Correlation between the yield strength and maximum value of

dimensionless measured tensile residual stresses.

6.3. Discussion and Conclusions

The models for estimation of the weld induced residual stresses were tested with respect to

the presented measurement results (Figure 6.7). However, concerning the, in some cases,

limited information concerning welding characteristics the results are not included herein.

However, the correlation between the test results and the models was not convincing. Though,

the correlation would probably become better if a special test programme, done for the purpose

of investigating the models, was used to measure the residual stresses. This way, gathering

information for several different sources, was proven to be a too uncertain path of investigating

the models.

Regarding the surveyed literature, presented in section 6.2 and Appendix C, the scatter

between the test results and conclusions are obvious. This may be dependent of the fact that the

measurement of residual stresses is, as mentioned earlier herein, a difficult piece of work. Both

with respect to the actual measurement work, which requires patience and precise handling, and

the evaluation of the test results, which may be done in several different ways. However, if

disregarding the actual aims for the different presented measurements and only the test data is

regarded, some obvious conclusions are possible to do.

First, residual stress measurements regarding steels with yield strength above 400 - 450 MPa

are not too usual. Though, this may be due to the fact that these steels still are somewhat “new”

to the market and not used in such a large extent.

0 200 400 600 800 1000

Yield strength, fy [MPa]

0

0.4

0.8

1.2

1.6

2

t,rs

/f y

70

Second, some of the results from the measured stresses seems to be somewhat difficult to

trust. Measured residual stresses 1,6 times higher than the yield strength of the steel in question

is hard to believe. The problem behind this issue may be the lack of actual measurements of the

mechanical properties of the steel. As stated before, if no mechanical properties of the material

was given by the author, the nominal values were used and this affects the outcome of the ratio

between the residual stresses and the yield strength.

Third, when considering the steels grades with higher yield strengths, the tensile residual

stresses seems to be lower in comparison to the yield strength. The majority of measured tensile

stresses in the specimens with yield strength above 400 MPa were significantly lower than the

yield strength in question.

Residual Stresses - Experimental Work

71

Chapter 7:

Residual Stresses - Experimental Work

To measure residual stresses has been, and will be in the future, an interesting and

challenging task to take upon ones shoulders. As mentioned before in the literature survey

(chapter 5) and the description of the experimental work (chapter 6), the measurement of

residual stresses in materials has proven to be an extremely time consuming and often a difficult

topic to master. The changes of stress magnitudes and distribution over the three dimensions of

a body makes the evaluation of the test results a demanding work. The methods of measurement

are often base on quite simple and theoretically graspable methods. However, the understanding

of what was measured and how to interpret the sampled data may be a somewhat intriguing

piece of work. Despite this, an effort in measuring the residual stress state in three welded box

sections was made within the LiftHigh project, funded partially by RFSC.

7.1. Background

How residual stresses are formed and why has been covered earlier herein. However,

although the origin of the stresses are known, the actual magnitudes and distributions of residual

stresses in different members most often has to be measured to be fully determined. As

discussed in chapter 6 different model approaches are available to pre-define up coming

residual stresses due to different processes, in this case welding. Though, setting up a finite

element model may be as time consuming as measuring the actual stresses in a “blind”

specimen.

Residual stress magnitudes and distributions has been measured in numerous applications

and in a multitude of specimens, mainly during the 1970’s. However, the development of steels

with higher strength and their introduction on the market has, in some way actualized the need

for residual stress measurements concerning these “new” grades. Therefor three welded

specimens with box cross-sections were withdrawn from the local buckling test programme (see

chapter 4) to be used for residual stress measurements. Through this, the residual stresses could

be determined and in a further evaluation compared to the residual stress distributions used in

some design codes (see chapter 6). Furthermore, the suggestions in the codes convenience could

also be investigated with respect to the measured stresses in the high strength steel.

72

The specimens were of the same three different steel grades as described in chapter 4, i.e.

Domex 420, Weldox 700 and 1100. The method for determining the residual stress distribution

and magnitudes was blind hole drilling and the released strains were measured with rosette

strain gauges. The method is explained further in Appendix B.

7.2. Experimental work

The measurement of the residual stresses was done at TESTLAB, LTU, during a 3 week

period in october 2004. Relieving of strains were measured in a total of 15 positions on the three

welded box specimens S20-0b, W72-0b and W112-0b. As the specimen notation indicates, the

rolling direction of the plates was along the welds. For further details concerning the specimens

and the fabrication of these see chapter 4. The blind hole measuring technique provides a

possibility to measure relieved strains in the x-y-plane to evaluate the principal stresses relaxed

in the direction of these. The evaluation method are presented in detail in Appendix B along

with the measured strains of each specimen. However, only longitudinally oriented stresses

(along the welds) are regarded in this thesis.

7.2.1. Test setup

The residual stresses relaxed through the hole drilling were measured over one side on each

of the three specimens. All of the rosette strain gauges were positioned on the mid-line of the

plate, see adjacent Figure 7.1. The tensile stresses induced by the welding of the plates were of

special interest to measure. Hence two rosettes were placed on each side of the plate, as close

to the weld bead as possible, Figure 7.2. Furthermore, one rosette gauge was placed in the mid-

point of the plate and the two remaining gauges were distributed between the weld bead and the

mid-point. The position of each of the measurement point is displayed in each graph presenting

the measured stress levels in section 7.3.

Figure 7.1: Specimen W72-0b with fixed air supplied high speed drill.

Residual Stresses - Experimental Work

73

The rosette gauges were glued to the plate surface with the individual strain gauges

positioned along and perpendicular to the weld bead. The third strain gauge was directed with

an angle of 135o referring to the weld direction.

The hole drilling was done in increments of which the first two were drilled 0,127 mm and

followed by 5 increments each removing a material layer of 0,254 mm. The hole was finished

with a last increment of 0,533 mm to the full depth of 2,06 mm. The measurement method is

base of the measurement of the change in strain in the x-y-plane between each increment. Hence,

strains were registered after each increment. With this information of the change in strain the

relaxed residual stresses may be estimated by Hooke’s law.

Figure 7.2: Rosette strain gauge glued to the specimen. The drill diameter was

1,59 mm.

The actual drilling process was proven to be a quite time consuming undertaking; one days

work was required for drilling one hole.

7.3. Test evaluation and test results

The relieved residual strains in the three specimens were evaluated according to the

measurement manual published by Measurements Group, Tech Note 503-4 (1993). The

procedure of the transformation of the measured strains to released stresses are described along

with the actual sampled data in Appendix B.

Even though the blind holes were drilled to a depth of nearly half the plate thickness of the

specimens (Weldox specimens) the relieved strains used in the evaluation was regarded only to

the depth of approximately 1 mm (the fifth increment). The reason was that FE studies has

shown that the change in strain produced in drilling through any depth beyond the first, is caused

only partly by the residual stress in that increment. Due to the change in stress distribution and

material compliance, most of the relieved strains at a given depth is in a large extent generated

by preceding increments. Hence, the relative contribution from a particular increment to the

total relieved strain at full hole depth decreases rapidly with the distance to the plate surface and

74

the strain gauge. This resulting in the fact that in full hole depth, the estimated released stresses

are dominated by stresses measured closer to the surface. Because of this, Measurements Group

states that little, if any, quantitative result interpretation can safely be done for readings below

1,03 mm with the equipment used for the tests described herein.

The results from the evaluation of the tests are enclosed in Appendix B regarding each

specimen individually. However the compiled results from all the three specimens normalized

with respect to the measured yield strength or 0,2 % proof stress (see chapter 4) are presented

in Figure 7.3 below. The reason of the normalization is to be able to compare the measured

longitudinal stresses to the schematical distributions described in the design codes which

implies that the tensile residual stress should be in the magnitude of the yield strength.

Furthermore, the position of the gauges, x, were made dimensionless with respect to the plate

width, b.

Figure 7.3: The measured longitudinal normalized to the measured yield or 0,2 %

proof strength of respective grade. Positive sign equals measured

tensile stress.

As mentioned above, the estimation of the residual stresses is based on the use of Hooke’s

law. The required modulus of elasticity was evaluated from the uniaxial tension tests presented

in Appendix A. However, no consideration was made to eventual difference in the modulus

regarding the rolling direction of the plates in question. The modulus used in the evaluation was

estimated from the specimens with rolling direction along the loading axis (notation 0). The

estimation of the elasticity modulus rendered in values of 200 GPa concerning the Domex 420

grade and 190 GPa for the two Weldox grades.

Domex 420

Weldox 700

Weldox 1100

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

X / b

-0.4

0

0.4

0.8

1.2

rs / f

y

Residual Stresses - Experimental Work

75

7.4. Discussion and conclusions of test results

When comparing the normalized results in Figure 7.3 the tensile stresses close to the weld

beads seems to be significantly lower than the 0,2 % proof stress concerning the high strength

steel grades Weldox 700 and 1100. Furthermore, the ratio residual stresses / material strength

seems to decrease with increasing material strength. The absolute values of the measured

stresses are lowest concerning the Domex specimen, however the Figure 7.3 concludes that the

residual stress magnitude does not increases linearly with respect an increasing material

strength.

Regarding the evaluation of the measured relieved strains some things are important to

comment. First, the modulus of elasticity has a huge influence on the estimation of the residual

stresses present in the regarded specimen. Furthermore, no consideration has been taken to the

eventual mechanical anisotropies in the material.

The measured strains were, as mentioned, only evaluated to a depth of approximately 1 mm.

This gives some uncertainties considering the fact that no information regarding eventual

fluctuations over the whole plate thickness could be concluded.

The ideal position of the measurement point may be closer to the weld bead. However the

size of the rosette gauges made it impossible to place the point closer to the weld than what was

done. Furthermore, additional measurement point over the plate width could make the

distribution of the stresses more even.

The non-linear material behaviour of the Weldox grades may influence the estimation of the

stresses. Ideal elasto-plastic material behaviour was an initial assumption concerning the

evaluation model (see Appendix B). However, with stress levels below the 0,2 % proof stress

of the Weldox grades, the non-linear behaviour are of moderate level and hence not too

influential on the presented results.

Furthermore, when regarding the presented measurements in Figure 7.3 one of the data

points are questionable. This is the point close to the weld in the Domex 420 specimen, which

shows residual stresses more than 20 % above the yield strength of the steel. When only elastic

strains can be measured (relieved through the drilling) this seems to be a rather large strain

measured. The reason why this has occurred is somewhat hard to conclude in any other way than

the human factor or a measurement error of an other type.

However, considering the rest of the data acquired, the magnitudes and the distribution of the

residual stresses seems to be trustable. A common way of investigating if the results from

residual stress measurements seems convenient may be an equilibrium analysis. However, this

is difficult to perform in this case when the stresses along one side of four are measured on the

specimen. Furthermore, additional measurement points would be desired in anything certain

regarding the equilibrium would be possible to conclude.

76

Considering the compressive stresses measured on the plates a comparison between the

specimens are not done herein. This due to the fact that the plate width are of great importance

when the stresses are induced through the welding process. If emphasizing the cause of the

compressive stresses described in chapter 5, the compressive stresses are formed as a reaction

to the tensile stresses near the weld. When the plate width increases, the compressive stress

magnitude decreases and vice versa. This makes a comparison between the differently sized

specimens and their inherent compressive stresses somewhat difficult to do properly without

this uncertainty. However, this fact should not influence the tensile stresses in same extent

which makes these possible to compare as stated above.

Discussion and Conclusions

77

Chapter 8:

Discussion and Conclusions

Since discussions regarding the retrieved data from the literature and the actual test

procedures were held in respective chapter, this chapter will focus on discussing the results with

respect to underlaying phenomena. The results from previous chapters are compared to design

codes and concluded to be useful in the future.

8.1. Residual Stresses

That the measurement of residual stresses is a complicated task, has already been mentioned

in this thesis. The large scatter between the different results, both from literature and by the

experimental work at LTU, may be a cause of this fact. Nevertheless, when evaluating test

results with different origins covering different steel grades, measurement methods as well as

specimens, a trend of these test results may be visible; as is the case displayed in Figure 8.1.

Considering the 53 individual measurements (47 from literature and 6 measured at LTU) a mean

value of the tensile residual stresses for respective grade, seems to decline with an increasing

yield strength. However, a majority of tests are made grades with lower strength (fy < 600 MPa),

but still, all of the test data over this “limit” shows tensile yield stresses lower than the yield

strength. This will also be evident if disregarding the data showing less reliable results, i.e.

relaxed stresses beyond the yield limit or extremely low readings.

Regarding the suggested residual stress distribution for design purposes, the experimental

work presented herein along with results from the literature survey, points towards that the usual

assumption of longitudinal tensile stresses reaching a magnitude of the yield strength seems to

be a bit to pessimistic regarding steels with higher strength. Studying Figure 8.1, this seems to

be significantly marked for steels with fy > 600 MPa. However, since the welding characteristics

have been proven to influence the magnitudes of weld induced residual stresses, this may differ

greatly if a larger test programme was carried out with the purpose to establish a relation

between steel grade and actual residual stress state. Another important thing to point out is the

fact that welding in high strength steels is often done with under-matching electrodes, i.e.

electrodes with lower strength than the base material. This fact may also influence the results.

78

Figure 8.1: Measured tensile longitudinal residual stresses in Domex 420,

Weldox 700 and 1100 specimens along with gathered test results from

relevant literature.

Furthermore, the actual mechanical properties of the base material of each specimen strongly

influences the outcome of experimental work. This with respect to how strongly non-linear the

behaviour of the considered grade is. When measuring residual stresses through relaxation

methods, the only possible measurable inherent stress in the steel is of elastic type. These

methods gives no information regarding eventual plastic strains present in the material. So, if

the material behaves strongly non-linear, even for low strains, the actual stress magnitude

present in the steel may very well be larger than what is evaluated. However, if the measured

stresses are shown to be lower than the yield stress (or other chosen reference stress level) the

evaluated results should be trustworthy if the material is linear-elastic up to this level. The

Weldox grades tested trough tensile coupon tests (enclosed in Appendix A), seems to be nearly

linear-elastic up to the 0,2 % proof stress used in the evaluations, the measured relaxed stresses

in these specimens should not be questioned with respect to this. However, when considering

the Domex grade, some uncertainties may rise due to the measured relived strains

corresponding to stress levels equal to or above the yield strength. The only certain statement

considering these readings is that the stress magnitudes reaches at least the yield strength.

8.2. Local Buckling

The Winter function used for design with respect to local buckling in some design codes,

such as the Eurocode 3, is based on tests of cold-formed specimens, Winter (1947). When cold-

forming profiles, one do not only produce the wanted profile without welding, but also changes

the material properties as well as inducing and residual stresses. The induction of these changes

into the very basis of the material, may lead to an incompatibility issue when compared directly

with welded plates. Even though the boundary conditions of the respective plates are the same,

i.e. simply supported around all edges in this case, the differences on a deeper level may leave

0 200 400 600 800 1000 1200 1400

Yield strength, fy [MPa]

0

0.4

0.8

1.2

1.6

2

t,rs

/f y

Domex 420

Weldox 700

Weldox 1100

Tests from literature (Ch. 6)

Discussion and Conclusions

79

the researcher astonished when comparing their test results with the Winter function. The cause

of this may be the different residual stress state between welded plates and cold-formed.

Furthermore, cold-forming induces plastic strains into the material. Experimental work has

shown that cold-formed profiles inherent significantly higher proof stresses and ultimate

strength levels in the area of forming, i.e. corners of a box section, Gardner (2002) and Talja

(2002). These increases in the material resistance of course affects the over-all behaviour of

such a specimen.

Furthermore, if considering the residual stress state in a cold-formed profile compared to a

welded section of the same dimensions, the magnitudes of compressive stresses in the sides

(webs) of the former seems to be lower than the corresponding ones in the welded profile,

Ingvarsson (1977). Lower levels of compressive residual stresses increases the resistance. Thus,

the Winter function may not on a phenomenological basis be comparable with welded plates.

However, the influence of the residual stresses in the plates should have less influence on the

resistance when the plate slenderness is lower (more plastic buckling).

Veljkovic and Johansson (2001) comprises FE studies of plates with and without residual

stresses and concluded that the Winter function is more suitable to use for plates without

significant residual stresses or stress relieved. This is not the case concerning plates in as-

welded condition. Similar conclusions were also drawn by Rusch and Lindner (2001).

When considering Figure 8.2, comprising the collected data from the literature (chapter 3)

and the experimental results presented in chapter 4, the outcome seem to coincide with the

results discussed above. Regarding plates of different steel grades, it seems like the Winter

function may be a more suitable function to use when the plate slenderness is lower. Regarding

more slender plates, > 0,9 the Winter function may overestimate the resistance.

Figure 8.2: The evaluated test data from 48 box specimens along with data

acquired from relevant literature.

0 0.5 1 1.5 2 2.5

p , Plate slenderness

0

0.4

0.8

1.2

, R

ed

ucti

on

facto

r

Domex 420

Weldox 700

Weldox 1100

Tests from Literature (Ch. 3)

Mean function (eq. 3.1)

Winter function

80

Nevertheless, the results presented in this report shows that steel with higher strength may

be treated in the same way as “ordinary” steel grades. The high strength steel may even coincide

a bit better with the Winter function than steels with lower strength (fy < 460 MPa), see chapter

4.

8.3. Conclusions

The following conclusions are drawn from the work presented in this thesis:

• The absolute magnitudes of the tensile residual stresses in welded plates of high

strength steels seems to be higher than compared to corresponding low strength

steel plates. Nevertheless, if made dimensionless with respect to yield strength or

Rp0.2 stress, the ratio is lower regarding the high strength steels.

• The Winter function may need some adjustments concerning more slender plates,

(approx. p > 0,9), since it seems to overestimate the resistance with respect to

local buckling.

• Concerning stockier plates (approx. p < 0,9) the Winter function seems to

underestimate or coincide with test results.

• No significant difference in the behaviour could be concluded when comparing

simply supported plates made of high strength steel with corresponding plates of

steel with lower strength. This with sole respect to local buckling resistance.

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81

Chapter 9:

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3rd International Conference on Trends in Welding Research, Gatlinburg, USA, June

1-5, 1992. (ISBN: 0-87170-476-5).

Rusch, A. and Lindner, J. (2001). “Tragfähigkeit von beulgefährdeten Querschnittselementen unter Berücksichtigung von Imperfektionen”, Stahlbau 70,

Heft 10, 2001. (In German).

Sjöström, S. (1994). “Physical, Mathematical and Numerical Modelling for Calculation of Residual Stress. Fundamentals and Applications”, Proceedings of the 4th Int.

Conference on Residual Stresses, Baltimore, USA, June 8-10, 1994.

84

Smith, D.J. and Bonner, N.W. (1996). “Measurement of Residual Stresses Using the Deep

Hole Method”, PVP-Vol. 327, Residual Stresses in Design Fabrication, Assessment and Repair, ASME, 1996.

Spooner, S., David, S.A., Root, J.H., Holden, T.M., Bourke, M.A.M. and Goldstone, J.A. (1992). “Residual Stress and Strain Measurements in an Austenitic Steel Plate Containing a Multipass Weld”, Proceedings of the 3rd International Conference on

Trends in Welding Research, Gatlinburg, USA, June 1-5, 1992.

(ISBN: 0-87170-476-5).

Spooner, S., Fernandez Baca, J.A., David, S.A. and Hubbard, C.R. (1994). “Investigation of Residual Stresses in a Multipass Weld in 1’’ Stainless Steel Plate”, Proceedings of the

4th Int. Conference on Residual Stresses, Baltimore, USA, 8-10 June, 1994.

Spooner, S., Wang, X.L., Hubbard, C.R., David, S.A.(1994). “Residual Stresses in a Multipass Weld in an Austenitic Stainless Steel Plate Before and After Thermal Stress Relief”, Proceedings of the 4th Int. Conference on Residual Stresses, Baltimore, USA,

8-10 June, 1994.

StBK-K2, “Knäckning, Vippning och Buckling”, kommentarer till Stålbyggnadsnorm 70.

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Tech Note 503-4. (1993) “Residual Stress Measurement”, Measurements Group, Inc. Raleigh, USA.

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References

85

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White, J.D. (1977). “Longitudinal Shrinkage of a Single Pass Weld”, University of Cambridge, Report CUED/C-Struct/TR.57.

Winter, G. (1947). “Strength of Thin Steel Compression Flanges”. Transactions, American Society of Civil Engineers, 1947, Vol. 112, pp. 527-554.

Wohlfahrt, H. (1987). “Residual Stresses as a Consequence of Welding”, Advances in

Surface Treatments: Technology-Applications-Effects, Vol. 4, International

Guidebook on Residual Stresses. First edition. Oxford: Pergamon Press, Cop. (ISBN: 0-08-034062-8).

86

APPENDIX A: Plate Buckling - Experimental Work

87

APPENDIX A:

Plate Buckling - Experimental Work

In Appendix A.1 the stress - strain curves from the tensile coupon tests described in

chapter 4 are enclosed. This in the form of 6 figures containing the results from three

coupon tests each.

Appendix A.2 contains the measured dimensions of the 48 box specimens used for

the local buckling tests. Furthermore, for each specimen, the calculated plate slenderness

according to Eurocode 3 is provided.

All of the load - mean axial deformation graphs are enclosed in Appendix A.3. This

in the form of 14 figures describing the behaviour of all the 48 specimens tested.

In Appendix A.4 the evaluated test results from the local buckling tests are enclosed. Furthermore, the cross section areas with included weld areas are shown along with

measured ultimate loads and evaluated ultimate stress levels.

The Appendix A.5 displays the measurement equipment used in the experimental

work. All of the gauges and other equipment are described individually.

88

APPENDIX A: Plate Buckling - Experimental Work

89

A.1: Stress - strain curves from uniaxial tests

Figure A.1: Stress - strain curves from tension tests along the rolling direction on

Domex 420.

Figure A.2: Stress - strain curves from tension tests transverse the rolling

direction on Domex 420.

0 10 20 30 40

, Strain [%]

0

200

400

600

, T

en

sile s

tress [

MP

a]

D1

D2

D3

0 10 20 30 40

, Strain [%]

0

200

400

600

, T

en

sile s

tre

ss [

MP

a]

D4

D5

D6

90

Figure A.3: Stress - strain curves from tension tests along the rolling direction on

Weldox 700.

Figure A.4: Stress - strain curves from tension tests transverse the rolling

direction on Weldox 700.

0 4 8 12 16

, Strain [%]

0

200

400

600

800

1000

, T

en

sil

e s

tre

ss [

MP

a]

W1

W2

W3

0 4 8 12 16

, Strain [%]

0

200

400

600

800

1000

, T

en

sile s

tre

ss [

MP

a]

W4

W5

W6

APPENDIX A: Plate Buckling - Experimental Work

91

Figure A.5: Stress - strain curves from tension tests along the rolling direction on

Weldox 1100.

Figure A.6: Stress - strain curves from tension tests transverse the rolling

direction on Weldox 1100.

0 4 8 12

, Strain [%]

0

400

800

1200

1600

, T

en

sil

e s

tre

ss [

MP

a]

W7

W8

W9

0 4 8 12

, Strain [%]

0

400

800

1200

1600

, T

en

sile s

tre

ss [

MP

a]

W10

W11

W12

92

A.2: Measured dimensions - Box specimens

Table A.1: Specimen dimensions, measured mechanical properties and

according to Eurocode 3, calculated plate slenderness values.

Specimen Mean

Width,

bw [mm]

Mean

Height,

h [mm]

Mean Plate

Thickness,

t [mm]

Yield

Strength,

fy [MPa]

Proof Stress,

Rp0.2 [MPa]

Plate

Slenderness,

p

Dom

ex 4

20

S10-0a

S10-0b

S10-90a

S10-90b

S20-0a

S20-90a

S20-90b

S30-0a

S30-0b

S30-90a

S30-90b

S40-0a

S40-0b

S40-90a

S40-90b

82,4

82,5

82,5

82,1

101,3

101,3

101,2

119,4

119,5

119,5

119,4

181,3

180,8

181,5

181,1

268,1

268,0

268,1

268,3

325,5

327,6

323,5

379,7

380,8

379,8

380,7

571,1

571,1

570,1

571,2

3,05

441,3

441,3

471,0

471,0

441,3

471,0

471,0

441,3

441,3

471,0

471,0

441,3

441,3

471,0

471,0

-

0,65

0,65

0,67

0,67

0,80

0,83

0,83

0,94

0,95

0,98

0,98

1,43

1,43

1,48

1,48

Wel

do

x 7

00

W71-0a

W71-0b

W71-0c

W71-90a

W71-90b

W71-90c

W72-0a

W72-90a

W72-90b

W73-0a

W73-0b

W73-90a

W73-90b

W74-0a

W74-0b

W74-90a

W74-90b

89,4

90,0

89,5

90,0

89,5

89,5

109,3

109,5

109,7

129,6

129,6

129,2

129,4

196,2

196,0

195,4

195,2

276,7

276,1

276,6

276,7

277,3

277,1

336,6

335,9

336,7

395,8

396,8

396,0

396,6

593,8

594,8

593,0

594,0

4.09 -

772,7

772,7

772,7

794,0

794,0

794,0

772,7

794,0

794,0

772,7

772,7

794,0

794,0

772,7

772,7

794,0

794,0

0,70

0,70

0,70

0,71

0,71

0,71

0,85

0,87

0,87

1,01

1,01

1,02

1,02

1,53

1,53

1,55

1,54

Wel

do

x 1

10

0

W111-0aW111-0bW111-0c

W111-90aW111-90bW111-90cW112-0a

W112-90aW112-90W113-0aW113-0b

W113-90aW113-90bW114-0aW114-0b

W114-90aW114-90b

70,370,469,870,169,469,585,585,585,3101,3101,3101,3101,2154,9154,9154,8155,2

220,2221,3220,6218,8220,3220,2266,8265,2267,6312,4312,2312,1312,1471,9469,6472,2472,2

3,98 -

1350,71350,71350,71335,01335,01335,01350,71335,01335,01350,71350,71335,01335,01350,71350,71335,01335,0

0,750,750,740,740,730,730,910,900,901,071,071,071,071,641,641,631,64

APPENDIX A: Plate Buckling - Experimental Work

93

A.3: Load - mean axial deformation curves

Figure A.7: Load - mean deformation curves for Domex 420 specimens with

nominal plate slenderness of 0,7.

Figure A.8: Load - mean deformation curves for Domex 420 specimens with

nominal plate slenderness of 0,85. S20-0b saved for residual stress

measurements.

0 2 4 6

, Mean deformation [mm]

0

200

400

600

Lo

ad

[kN

]

S10-0a

S10-0b

S10-90a

S10-90b

0 2 4 6

, Mean deformation [mm]

0

200

400

600

Lo

ad

[k

N]

S20-0a

S20-90a

S20-90b

94

Figure A.9: Load - mean deformation curves for Domex 420 specimens with

nominal plate slenderness of 1,0.

Figure A.10: Load - mean deformation curves for Domex 420 specimens with

nominal plate slenderness of 1,5.

0 2 4 6

, Mean deformation [mm]

0

200

400

600L

oa

d [

kN

]

S30-0a

S30-0b

S30-90a

S30-90b

0 2 4 6

, Mean deformation [mm]

0

200

400

600

Lo

ad

[k

N]

S40-0a

S40-0b

S40-90a

S40-90b

APPENDIX A: Plate Buckling - Experimental Work

95

Figure A.11: Load - mean deformation curves for Weldox 700 specimens with

nominal plate slenderness of 0,7.

Figure A.12: Load - mean deformation curves for Weldox 700 specimens with

nominal plate slenderness of 0,85. W72-0b saved for residual stress

measurements.

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

Lo

ad

[k

N]

W71-0a

W71-0b

W71-90a

W71-90b

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

Lo

ad

[k

N]

W72-0a

W72-90a

W72-90b

96

Figure A.13: Load - mean deformation curves for Weldox 700 specimens with

nominal plate slenderness of 1,0.

Figure A.14: Load - mean deformation curves for Weldox 700 specimens with

nominal plate slenderness of 1,5. Specimen W72-0a removed due to

testing problems.

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600L

oa

d [

kN

]

W73-0a

W73-0b

W73-90a

W73-90b

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

Lo

ad

[kN

]

W74-0b

W74-90a

W74-90b

APPENDIX A: Plate Buckling - Experimental Work

97

Figure A.15: Load - mean deformation curves for Weldox 700 specimens with

nominal plate slenderness of 0,7. Extra tests.

Figure A.16: Load - mean deformation curves for Weldox 1100 specimens with

nominal plate slenderness of 0,7. W111-0b failed in weld after

ultimate load was reached.

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

Lo

ad

[k

N]

W71-0c

W71-90c

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

2000

Lo

ad

[k

N]

W111-0a

W111-0b

W111-90a

W111-90b

98

Figure A.17: Load - mean deformation curves for Weldox 1100 specimens with

nominal plate slenderness of 0,85. W112-0b saved for residual stress

measurements.

Figure A.18: Load - mean deformation curves for Weldox 1100 specimens with

nominal plate slenderness of 1,0.

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

2000L

oa

d [

kN

]

W112-0a

W112-90a

W112-90b

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

2000

Lo

ad

[kN

]

W113-0a

W113-0b

W113-90a

W113-90b

APPENDIX A: Plate Buckling - Experimental Work

99

Figure A.19: Load - mean deformation curves for Weldox 1100 specimens with

nominal plate slenderness of 1,5.

Figure A.20: Load - mean deformation curves for Weldox 1100 specimens with

nominal plate slenderness of 0,7. Extra tests.

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

Lo

ad

[kN

]

W114-0a

W114-0b

W114-90a

W114-90b

0 2 4 6 8 10

, Mean deformation [mm]

0

400

800

1200

1600

2000

Lo

ad

[kN

]

W111-0c

W111-90c

100

A.4: Test Results - Buckling Tests

Table A.2: Evaluated test results. Cross section areas with included weld areas.

Yield strength used for Domex 420 and 0,2 % proof stress for Weldox

specimens.

Specimen Ultimate

Load [kN]

Area of cross

section [mm2]

Ultimate strength,

u [MPa]

Ratio u/fy or

u/Rp0.2

Dom

ex

42

0

S10-0a

S10-0b

S10-90a

S10-90b

S20-0a

S20-90a

S20-90b

S30-0a

S30-0b

S30-90a

S30-90b

S40-0a

S40-0b

S40-90a

S40-90b

502,3

502,2

514,9

530,6

505,9

517,6

492,6

468,4

484,0

496,1

487,1

502,4

484,2

492,1

493,9

1023,9

1025,1

1024,5

1020,5

1254,5

1254,9

1253,2

1475,7

1476,1

1476,6

1474,9

2230,1

2224,5

2232,9

2228,6

490,5

489,9

502,6

520,0

403,3

412,4

393,1

317,4

327,9

336,0

330,3

225,3

217,7

220,4

221,6

1,11

1,11

1,07

1,10

0,91

0,88

0,83

0,72

0,74

0,71

0,70

0,51

0,49

0,47

0,47

Wel

do

x 7

00

W71-0a

W71-0b

W71-0c

W71-90a

W71-90b

W71-90c

W72-0a

W72-90a

W72-90b

W73-0a

W73-0b

W73-90a

W73-90b

W74-0b

W74-90a

W74-90b

1186,5

1193,5

1191,6

1254,4

1246,3

1216,8

1269,8

1289,2

1310,8

1182,6

1192,7

1228,1

1222,6

1241,1

1253,4

1260,4

1496,2

1505,3

1497,7

1505,2

1497,2

1497,6

1820,8

1824,5

1828,5

2153,0

2154,0

2146,7

2150,9

3239,6

3231,0

3227,4

793,0

792,9

795,6

833,4

832,4

812,5

697,4

706,6

716,8

549,3

553,7

572,1

568,4

383,1

387,9

390,5

1,03

1,03

1,03

1,05

1,05

1,02

0,90

0,89

0,90

0,71

0,72

0,72

0,72

0,50

0,49

0,49

Wel

do

x 1

10

0

W111-0a

W111-0b

W111-0c

W111-90a

W111-90b

W111-90c

W112-0a

W112-90a

W112-90

W113-0a

W113-0b

W113-90a

W113-90b

W114-0a

W114-0b

W114-90a

W114-90b

1433,5

1490,8

1428,7

1378,5

1413,4

1523,5

1650,6

1607,1

1667,7

1529,7

1543,2

1522,1

1551,0

1591,6

1560,9

1538,6

1557,4

1151,0

1151,9

1142,2

1147,0

1136,0

1138,1

1393,6

1392,6

1389,0

1645,1

1644,8

1643,8

1643,2

2497,6

2497,8

2496,8

2502,5

1245,4

1294,2

1250,8

1201,9

1244,1

1338,6

1184,4

1154,1

1200,7

929,9

938,2

925,9

943,9

637,3

624,9

616,2

622,4

0,92

0,96

0,93

0,90

0,93

1,00

0,88

0,86

0,90

0,69

0,69

0,69

0,71

0,47

0,46

0,46

0,47

APPENDIX A: Plate Buckling - Experimental Work

101

A.5: Gauges used in Tests

All 5 position gauges (LVDT) were from Measurements Group, U.K. LTD., Vishay.

The specifications for the 4 Welwyn HS10B LDVT’s used for

measurement of axial displacement are:

Gauge No. 9554: L = 11,0 mm, Non.linearity 0,1 %,

Sensibility 4,9 mV/V.

Gauge No. 9556: L = 11,0 mm, Non.linearity 0,1 %,

Sensibility 5,1 mV/V.

Gauge No. 9952: L = 10,9 mm, Non.linearity 0,1 %,

Sensibility 4,8 mV/V.

Gauge No. 10544: L = 11,1 mm, Non.linearity 0,1 %,

Sensibility 4,9 mV/V.

The specifications for the Welwyn HS25B LVDT used for the

measurement of buckle growth is:

Gauge No. 10168: L = 25,8 mm, Non.linearity 0,1%,

Sensibility 6,4 mV/V.

A SPIDER 8, 600 Hz from HBM were used to

sample and translate measurements to PC-

environment. Serial No. F02439.

The load cell from DARTEC used for load measurement was

calibrated in 2004 with a measurement error of < 0,6 % in the

whole measurement range up to 2 MN. Serial No. 89086/A.

102

APPENDIX B: Residual Stresses - Experimental Work

103

APPENDIX B:

Residual Stresses - Experimental Work

In Appendix B.1 the theory and expressions used for the tests result evaluation of the

residual stress measurement is presented. The theory is completely based on information

provided by Measurements Group, Inc. (Tech Note 503-4).

Appendix B.2 encloses the measured strains from the residual stress experiments.

Furthermore, the data converted to released residual stresses in the plane of the plate is

presented concerning each of the three specimens.

104

APPENDIX B: Residual Stresses - Experimental Work

105

B.1: Test evaluation methodology

The blind hole measurement method was previously described in chapter 5. However the

method for evaluation of test results is described in this section. All of the following text is

based on the residual stress measurement guide published by Measurements Group from 1993.

As presented in chapter 7 the released strains were measured with rosette strain gauges.

However, the strain data needs to be related to the real strains released in the hole (circular

shape). I.e. the measured strains in the plane has to be transformed to polar coordinates to

determine the actual strain released through the material removal. Furthermore, the strains

expressed in polar coordinates are transformed back to cartesian coordinates to describe the

longitudinal residual stress state in the specimen.

B.1.1: Strain transformation and basic relationshipsThe following section describes how the measured strains were evaluated to give information

concerning the plane stress state in the welded specimens. The description of the method of test

data evaluation may seem to be over the top, however hopefully it will provide the reader with

an insight regarding the difficulties connected to the task of measuring residual stresses and the

amount of possible uncertainties included in the measurement evaluations.

Figure B.1: Stress states at P(R, ), before and after the introduction of a hole.

Measurements Group, Tech Note 503-4 (1993)

In Figure B.1a a local area of a plate under uniform distributed residual stress is described.

In any arbitrary chosen point, the initial stress state may be expressed in polar coordinates as

(B.1)'rx

2----- 1 2cos+=

106

(B.2)

(B.3)

When material is removed by drilling the small hole into the plate, the stress state around the

hole is changed and the stresses on the hole surface must be equal to zero. The change in the

stresses, or strains gives information about the magnitude of the released residual stresses.

Solutions to this case has been obtained by G.Kirsch in 1898, and with the help of his work the

expressions for the relieved strains may be obtained. However, some very important

assumptions are made in this step of the theory. The material is assumed to be homogeneous

and isotropic in its mechanical properties. Furthermore linear-elastic stress - strain behaviour is

assumed.

Under this assumptions the following two expressions may be used with Hooke’s law to

calculated the relived stresses:

(B.4)

(B.5)

wherein

. (B.6)

However, the above stated expressions may be simplified by using constants for the material

properties of the material and the ratio, r, according to

(B.7)

(B.8)

It has been concluded in the considered printing by Measurements Group, that the radial

strain is considerably greater than the tangential strain. This has led to that commercial rosette

gauges for residual stress measurements are designed to measure this radial strain changes.

Hence, the radial strain is used for further evaluation.

The above described treatment of a plate under residual stresses consider only a uniaxial

stress state. However, in this case, the plane stress state was desired to be evaluated. This may

' x

2----- 1 2cos–=

'rx

2-----– 2sin=

rx 1 +

2E----------------------- 1

r2

---- 3

r4

---- 24

r2

1 +---------------------- 2cos+cos––=

x 1 +

2E----------------------- 1

r2

----–3

r4

---- 24

r2

1 +----------------------– 2coscos+–=

rR

Ro

------ R Ro=

r x A B 2cos+=

x A– C 2cos+=

APPENDIX B: Residual Stresses - Experimental Work

107

be done by using the superposition principle which gives the following expressions for the

relieved radial strains in the x-y-plane:

(B.9)

The expression above (B.9) describes the basic relationship between measured strains and

the actual residual stress state in the considered plate. However, the expression has to be

inverted to give the wanted information; the principal stresses in the x-y-plane and the angle ,

according to Figure B.2 below, which gives the orientation of the principal stresses referring to

the strain gauges.

Figure B.2: Strain gauge rosette arrangement for determining residual stress.

Measurements Group, Tech Note 503-4 (1993).

Considering Figure B.2 the expression (B.9) may be written three times, once for each strain

gauge in the rosette:

(B.10)

(B.11)

(B.12)

When these three expressions are solved simultaneously for the principal stresses and their

direction, the results may be expressed as:

(B.13)

and the direction, , as

(B.14)

r x A B 2cos+ y A B– 2cos+=

1 A x y+ B x y– 2cos+=

2 A x y+ B x y– 2 45o

+cos+=

3 A x y+ B x y– 2 90o

+cos+=

max min1 3+

4A---------------- 1

4B-------

3 1–2

1 3 2 2–+2

+=

2tan 1 2 2– 3+

3 1–------------------------------=

108

Regarding equation B.13, the Measurements Group pointed out some important comments.

The coefficients A and B not only inherent the elastic properties of the material, but also reflects

the severe attenuation of the relieved strains relative to the relaxed stresses. Since the

coefficients always are defined with negative signs, the expression with the subtraction in B.13

always represents the maximum principal stress.

Concerning the direction of the principal stresses, the angle, , must be interpreted

differently dependent of the relation between the measured strains. The following rules points

out how the principal stresses are directed:

(B.15)

and if the latter is the case, then

(B.16)

Furthermore, the coefficients A and B are determined with the use of special data reduction

coefficients determined from specifications by Measurements Group.

3 1 refers to max

3 1 refers tomin

3 1 45o

=

2 1 maxat 45

o

2 1 maxat 45

o–

+

APPENDIX B: Residual Stresses - Experimental Work

109

B.2: Experimental data

Table B.1: Measured strains in specimen S20-0b. Relived strains down to 1,016 mm

depth presented. Positions measured from weld edge.

Figure B.3: Measured longitudinal residual stresses in specimen S20-0b (Steel

grade Domex 420). Plate width was measured between the weld edges

to 101,8 mm.

Position

[mm] [ Str] [ Str] [ Str] [ o]

max

[MPa]

min

[MPa]

5,60 162 -135 -416 -1 432 -70

20,88 0 52 109 1 -30 -125

36,31 -28 50 131 1 -4 -143

51,44 -46 28 149 7 14 -161

95,84 243 -220 -565 -4 584 -126

0 20 40 60 80 100

Plate Width [mm]

-200

0

200

400

600

Rele

ased

str

ess [

MP

a]

110

Table B.2: Measured strains in specimen W72-0b. Relived strains down to 1,016 mm

depth presented. Positions measured from weld edge.

Figure B.4: Measured longitudinal residual stresses in specimen W72-0b (Steel

grade Weldox 700). Plate width was measured between the weld

edges to 109,9 mm.

Position

[mm] [ Str] [ Str] [ Str] [ o]

max

[MPa]

min

[MPa]

5,53 259 -177 -625 0 613 -118

21,51 67 78 197 20 -109 -248

38,37 93 152 268 9 -168 -320

54,86 60 154 244 -1 -130 -282

104,49 155 -121 -589 7 611 -24

0 20 40 60 80 100

Plate Width [mm]

-400

-200

0

200

400

600

800

Rele

ased

str

ess [

MP

a]

APPENDIX B: Residual Stresses - Experimental Work

111

Table B.3: Measured strains in specimen W112-0b. Relived strains down to 1,016

mm depth presented. Positions measured from weld edge.

Figure B.5: Measured longitudinal residual stresses in specimen W112-0b (Steel

grade Weldox 1100). Plate width was measured between the weld

edges to 85,9 mm.

Position

[mm] [ Str] [ Str] [ Str] [ o]

max

[MPa]

min

[MPa]

5,42 430 -227 -815 -2 776 -255

17,19 -45 -17 -10 -15 54 20

30,15 -6 90 177 -1 -40 -191

42,17 -27 92 199 -2 -23 -210

80,08 387 -299 -966 0 951 -167

0 20 40 60 80

Plate Width [mm]

-400

0

400

800

1200

Rele

ased

str

ess [

MP

a]

112

APPENDIX C: Residual Stresses - Survey of Literature

113

APPENDIX C:

Residual Stresses - Survey of Literature

Enclosed in Appendix C is data sheets containing the information used in the

literature survey presented in chapter 6. The used specimens are individually numbered

from 1 to 61. Nevertheless, not all of the enclosed measurements are used in this thesis.

This is due to e.g. incompatible experiments, lack of information or other causes. The

data sheets provides information concerning mechanical properties, specimen layout,

used measurement technique and of course the reference to the published material in

question.

114

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

115

ASTM A36, A441

H-profile

Sectioning / Hole Drilling

G.Alpsten and L.Tall.

March 1970

-

Submerged-arc welding

See Table 1 for details

See Table 1 for details

19mm (web),38mm (flange)

[MPa]

414 0 -345

[MPa]

414 0 -345

No. 3 No. 4

[MPa]

414 0 -345

No. 1 No. 2

[MPa]

414 0 -345

No. 5

[MPa]

414 0 -345

No. 6

Above: Stresses in 15H290, A441 steel. 12.7 mm (1/2 in.) fillet welds (left) resp. 28 mm (11/10 in.) (right) groove welds. All plates flame cut

Above: Stresses in 15H290, A36 steel. 12.7 mm (1/2 in.) fillet welds (left) resp. 28 mm (11/10 in.) (right)

groove welds. All plates flame cut

Above: Stresses in 15H290,A441 steel. 12.7 mm (1/2 in.)fillet welds (left) resp. 28 mm(11/10 in.) (right) groovewelds. Universal milledplates

[MPa]

414 0 -345

1 ksi = 6.895 MPa

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

116

Residual stresses can have a significant influence at the load-carrying behaviour of structuralsteel members subjected to compressive loads. Previous experimental research on residual stressesand the strength of columns was related to small and medium-size shapes. In today’s large structures,increasingly heavy shapes are being used extensively, very little information has been available on theresidual stresses and strength of such members. This paper presents the results of the first phase of amajor investigation into the residual stresses in, and the behaviour of, thick plates and heavy shapesused in compression members. The shapes considered in this initial study are a 15H290 shape and a23H681 shape, as well as two loose component plates, PL16x2 inches (406.4x50.8 mm) andPL24x3.5 inches (609.6x88.9 mm). For the smaller shape, compressive tests were carried out fordifferent manufacturing conditions of the component plates (universal-mill and flame-cut plates),different weld type (penetration) and different yield strengths of the material.

Alpsten, G. and Tall, L. (1970). Residual Stresses in Heavy Welded Shapes. In: Welding Journal,Supplement, Vol. 49, No.3., March 1970. pp. 93-105.

A36: fy = 248 MPa (Nominal)

A441: fy = 345 MPa (Nominal)

See Fig on the previous page.

0 254 508 762 [mm]

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

117

[MPa]

138 0 -138

[MPa]

138 0 -138

No. 13

ASTM A36

H-profile

Sectioning / Hole Drilling

G.Alpsten and L.Tall.

March 1970

-

Automatic beam welding w. 2 electrodes

See Table 1 for details

See Table 1 for details

50.8mm (web), 88.9mm (flange)

[MPa]

414 0 -345

Right: Formation of thestresses in a 23H681

Left: Stresses in 23H681,A36 steel. 12.7 mm (1/2 in.)fillet welds, flame cut plates

[MPa]

138 0 -138

1 ksi = 6.895 MPa

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

118

Residual stresses can have a significant influence at the load-carrying behaviour of structuralsteel members subjected to compressive loads. Previous experimental research on residual stressesand the strength of columns was related to small and medium-size shapes. In today’s large structures,increasingly heavy shapes are being used extensively, very little information has been available on theresidual stresses and strength of such members. This paper presents the results of the first phase of amajor investigation into the residual stresses in, and the behaviour of, thick plates and heavy shapesused in compression members. The shapes considered in this initial study are a 15H290 shape and a23H681 shape, as well as two loose component plates, PL16x2 inches (406.4x50.8 mm) andPL24x3.5 inches (609.6x88.9 mm). For the smaller shape, compressive tests were carried out fordifferent manufacturing conditions of the component plates (universal-mill and flame-cut plates),different weld type (penetration) and different yield strengths of the material.

Alpsten, G. and Tall, L. (1970). Residual Stresses in Heavy Welded Shapes. In: Welding Journal,Supplement, Vol. 49, No.3., March 1970. pp. 93-105.

A36: fy = 248 MPa (Nominal) See Fig on the previous page.

0 254 508 762 [mm]

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

119

S490 - S690

I-profiles

10 - 15 mm

Above: Idealized distribution of residual stresses

Below: Idealized distribution of residual stresses in the flanges considering the influence of flame-cutting

Sectioning and strain gauges

D. Beg and L. Hladnik

1994

Very high strain gradient over the flange thickness of 15 mm. Other sources show only smallgradient for 8 mm thickness.

Residual compressive stresses seems to be independent of the yield strength of the base material.

MMA, pre-heating

Tencito 80 4 mm, EVB NiMo 4 mm

3 passes, a = 7-8 mm

Left: Measured residual stresses

No. 56 No. 57

No. 58 No. 59

No. 60 No. 61

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

120

The article presents the experimental analysis of the distribution of residual stresses developeddue to welding. The measurements have been performed on six welded I-profiles of high strengthsteels Nionicral 70 and Niomol 490. It has been found that in the area of welds through the thicknessof the flange an explicit stress gradient develops. It influences also the decrease of compressiveresidual stresses in the flange. On the basis of the measured residual strains the idealised distributionsof residual stresses over the cross-section which are appropriate for nonlinear analysis of steelstructures have been determined.

Beg, D. and Hladnik, L. (1994). Eigenspannungen bei geschwei ten I-Profilen aus hochfestenStählen. In: Stahlbau 63, Heft 5, 1992.

Nionicral 70: fy = 810 MPa (t = 10)Nionicral 60: fy = 580 MPa (t = 15)

Niomol 490: fy = 525 MPa (t = 12)Niomol 490: fy = 540 MPa (t = 15)

Maximum tensile stress 80-90% timesflange yield strength in average over the flangethickness with a large gradient.

Maximum compressive stress 12-18% offlange yield strength (roughly 100 MPa).

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

121

ASTM A36

Welded Plates

Sectioning

J. Brozzetti, G.Alpsten and L.Tall.

August 1971

-

Semi-automatic

AWS class E7018

See Table above, a = 9.5 mm

50.8 mm (2 in.)

Above: Stresses in a 609.6x50.8 mm (24x2 in.). flame-cut plate. Center welded 2 passes, Left: CW-3 400 dgr.F preheated, Right: CW-4 400 dgr.F locally preheated

Right: Stresses in a universal-milled plate 609.6x50.8 mm (24x2 in.) Center welded, 200 dgr.F preheat, 2 passes.

Above: Stresses in a 609.6x50.8 mm (24x2 in.) flame-cut plate. Center welded, CW-1(left) and CW-2 (right), 200 dgr.F preheat, 1 pass.

-276

[MPa] 0

414

-276

[MPa] 0

414

-276

[MPa] 0

414

-276

[MPa] 0

414

-276

0

[MPa]

414

1 ksi = 6.895 MPa

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

122

See Fig on the previous page.

This paper presents a study of the influence of different welding parameters on the magnitude anddistribution of residual stresses in oxygen-or-flame-cut plates 609.6x50.8 mm (24x2 in.) made of A36steel. The residual stress diagrams obtained after complete sectioning and after slicing are related tothe original conditions of manufacture and fabrication. The welded flame-cut plates studied have beenused as base metal plates of a built-up section 24H428, and the strength of this heavy section isanalyzed theoretically. The differences observed in the theoretical column strength of this simulatedsection 24H428, built up with flanges of 609.6x50.8 mm (24x2 in.) flame-cut center-welded platesand a web of a 508x38.1 mm (20x1.5 in.) flame-cut edge-welded plate, is correlated to the differentheat inputs caused by the different fabrication processes. Conclusion are drawn with respect to theeffect of the different welding parameters on the strength of the column.

Brozzetti, J., Alpsten, G. and Tall, L. (1970). Welding Parameters, Thick Plates, and ColumnStrength. In: Welding Journal, Supplement, Vol. 50, No.8., August 1971. pp. 331-342.

1 ksi = 6.895 MPa

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

123

ASTM A36

Welded Plates

Sectioning

R.Bjorhovde, J.Brozzetti, G.Alpsten andL.Tall

August 1972

-

NA

E7018

1 pass / see table above

38.1 - 152.4 mm (1.5 - 6 in.)

Above: A:Center welded plate B: Edge welded plate

Right: Average residual stresses in “type A” oxygen-

cut plates

Right: Average residual stresses in “type B” oxygen-cut

plates

1 inch = 25.4 mm

No. 19 to 24

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

124

This report presents the results of an experimental investigation of the magnitude and distributionof residual stresses in heavy steel plates. Twenty-six plates were investigated, of which twenty hadoxygen-cut (OC) edges, and the remaining six were universal mill (UM) plates with as-rolled edges.The plate width varied from 228.6 mm (9 in.) to 609.6 mm (24 in.) and the thickness from 38.1 mm(1.5 in.) to 152.4 mm (6 in.). Some of the plates were studied in the as-manufactured condition,whereas others had weld beads placed along the center or along the edges, so as to simulate thecomponent plates of welded built-up shapes. It was found that for as-manufactured UM plates, themaximum compressive residual stress could be determined using the width-factor , a measure of therate of cooling after rolling, and that it increased with increasing plate size. Comparison withtheoretical results showed good correlation between experiment and theory. The variation of theresidual stress through the thickness was negligible in plates thinner than one inch (25.4 mm).

Bjorhovde, R.,Brozzetti, J., Alpsten, G. and Tall, L. (1970). Residual Stresses in Thick WeldedPlates. In: Welding Journal, Supplement., Vol. 51, No.8., August 1972. pp. 392-405.

fy = 248 MPa (Nominal) See Fig on the previous page.

1 inch = 25.4 mm

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

125

Hot rolled, fy = 411 MPa

I-Sections

Sectioning

A.J. Davids and G.J. Hancock

May 1986

The three different slenderness sections showed significantly different distributions of residualstrain in the flange outstands. The 310 section showed a reduction of approximately 40% in theresidual compressive strain from the maximum value to the value at the tip flange.

-

-

One pass bead, a = 3 mm

5 mm

Measured residual strains. “Tension Block” indicates the required magnitude of the tensile residual stresses for achieving cross-sectional

equilibrium.

No. 28

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

126

See Figures on the previous page.

The local buckling and post-buckling behaviour of short length I-section columns fabricated bywelding high tensile steel plate is described. Six sections of three different section geometries weretested to destruction by loading between rigid end plattens mounted on freely rotating bearings in acompression testing machine. Accurate measurements of welding residual strains and geometricimperfections were taken prior to testing and are presented in the paper. Comparisons of the test localbuckling loads are made with a finite strip buckling analysis including welding residual strain.Comparisons of the measured axial stiffnesses and stress distributions were made with a nonlinearfinite strip analysis, which includes geometric imperfections and welding residual strain. The testloads are compared with those on the Winter effective formulas.

Davids, A.J. and Hancock, G.J. (1986). Compression Tests of Short Welded I-Sections. In:Journal of Structural Engineering. Volume 112, No. 5, May 1986.

fy = 411 MPa

E = 202 GPa

See Figures on the previous page.

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

127

fy = 300 - 360 MPa

Box

Hole drilling

J.B. Dwight, T.K. Chin and A.T. Ractliffe

May 1968

Tests carried out to investigate the effect of welding speed produced residual stresses that wereabout equal for plates welded with medium and fast speeds of travel, but 50% higher in the case ofvery slow travel. This suggested that the box specimens may have contained somewhat high residualcompression by practical standards.

Auto. machine welding, bare-wire

-

235 amps. 16 in./min. for t = 3/16 in.285 amps. 14,5 in./min. for t = 1/4 in.

4.8 and 6.4 mm (3/16, 1/4 in.)

Effect of weld speed on residual stress

Residual stress patterns for boxes

0 138 276 [MPa]

0 127 254 [mm]

0 138 276 [MPa]

0 127 254 [mm]

414

2

76

13

8

0

[MP

a]

No. 29

No. 30

No. 31

No. 34

No. 33

No. 32

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

128

The locked-in stresses in the as-welded columns were measured with a Demec extensometer of200 mm (8 in.) gauge length. The measurements were made in the central portion of each long lengthof section. Pairs of 1 mm (0.04 in.) holes 200 mm (8 in.) apart longitudinally were drilled at 25.4 mm(1 in.) spacing across the plates, before welding. Extensometer readings were taken: (i) Beforewelding, (ii) After welding, but before separating the column specimens and (iii) (Box-sections only).After the central portion had been cut into 25.4 mm (1 in.) wide strips.

Comparison of readings (i) and (ii) enabled the residual compressive stresses induced by thewelding to be calculated. The tensile stresses close to the welds, however, could not be obtained inthis way, since the extreme local heat and plastic deformation in these zones made the observedchanges of strain meaningless. Comparison of readings (ii) and (iii) gave the complete residual stresspattern right up to the weld in the columns tested, due to both rolling and welding. Readings were onlytaken on one side of each plate, a probable source of error.

Dwight, J.B., Chin, T.K. and Ractliffe, A.T. “Local buckling of thin-walled columns, effect oflocked-in welding stresses”. CIRIA, Res.Rep. No. 12 (Pt.1), May 1968.

fy = 300 - 360 MPa (22.9-26.1 ton/sq.in )

WF, WJ : 360 MPaWH : 359 MPaWL : 319 MPaWG : 316 MPaWK : 301 MPa

Maximum between 15 - 26% of fy

Specimens for observing effect of welding speed. (Fig. 12 in paper)

Specimens used for measurement of residual stresses are shown on the previous page.

1 inch = 25.4 mm

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

129

S690, fy = 794 MPa

U-Sections, welded to HP

Sectioning

L.Ingvarsson

July 1977

If two cold-formed channel sections welded together are used as a box column both theory andtests show that the resulting residual stress distribution has a positive effect on the local bucklingstrength as well as the overall buckling one in comparison with corner welded box columns.Originally flame-cut plates.

Arc weld, half-automatic, inert-gas

OK Autrod 13.12 and 12.51

2 passes, 138 A/20.9 V, 2 - 4.2 mm/s

7 mm

Measured longitudinal residual stress distributions.

Results of uniaxial tensile tests of welding electrode material.

No. 35 No. 36

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Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

130

This work is the result of an investigation at the Dept. of building Statics and StructuralEngineering at The royal Institute of Technology, Stockholm, Sweden, concerning cold-formingresidual stresses and their effect on buckling strength. In particular the possibility of using quenchedand tempered high strength steel (with a yield strength of about 700 N/mm2) in box columns built upby two thick channel sections welded together is studied. An analysis according to the incrementaltheory of plasticity has been carried out to determine cold-forming residual stresses. An idealized casewas studied. By using von Mises’ yield criterion, Prandtl-Reuss equations, Hooke’s law and anequilibrium equation as well as geometrical relations it was possible to put a system of equationstogether for the increments of stresses and strains in a polar coordinate system. A computer programwas developed solving this system for each incremental increase of curvature (100 steps) and for eachincremental change of the radial position (100 steps) in a bent plate. The calculations were done forboth an ordinary strain-hardening steel and a high strength ideally elastic-plastic steel.

Ingvarsson, L. (1977). Cold-Forming Residual Stresses and Box Columns Built Up by two Cold-Formed Channel Sections Welded Together. Bulletin No. 121 of The Department of Building Staticsand Structural Engineering, The Royal Institute of Technology, Stockholm, Sweden, July 1977.

fy = 794 MPa

fu = 822 MPa

rc = Average stress for the mid parts of theunwelded sides.

rc = Bending stress (added to rc for theouter and inner surfaces, respectively.

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grades:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

131

Weldox 700, 1.4301

and 1.4462

Welded I-Girders

Sectioning

O. Lagerqvist and A. Olsson

June 2001

The girder RS4301 inherited compressive stresses of the order 20-30% (flange) 40-50% (web) ofRp0.2. The residual stresses in girder RS4465 were measured to be approx. 50% of the stresses inRS4301. Furthermore the measurements showed that the high strength steel girder had even lowerresidual stresses than the two other girders.

MMA, 4 mm fillet weld

E308LTO-4, 2209T0-4

1 pass

4 mm

RS4301 made of 1.4301, RS4462 made of Stainless Steel 1.4462 and B2 made of QT-steel Weldox 700

Measured average residual stresses for flanges andweb for girders. Expressed as the ratio between theaverage residual stresses and Rp0.2 or fy above thecentre line of the web and as stresses in MPa below thecentre line. The tensile stresses (positive) are shownabove the flanges and on the right side of the webs.* marks that the residual stress is only measured on theoutside of the flange in this point.

No. 37 No. 38 No. 39

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

132

See Figures on the previous page.

It is well known that residual stresses can have a considerable influence on the resistance ofwelded and rolled steel elements. Among other things they are added to stresses caused by externalloading and thereby contribute to yielding in some parts of the element and hence a reduction of thestiffness occurs at a lower external load level than if residual stresses were not present. The truemagnitude of the residual stress distribution over the cross section are on the other hand not so wellknown, especially not for welded girders made of stainless steel. This paper presents results frommeasurements of residual stresses in welded I-girders made of austenitic and austenitic-ferriticstainless steel as well on a welded girder made of high strength quenched and tempered steelperformed at the Division of Steel Structures, Luleå University of Technology. Based on the results,the influence of the residual stresses on the resistance for slender structural elements in compressionand on material modelling for FE-analysis is discussed.

Lagerqvist, O. and Olsson, A. (2001). Residual stresses in welded I-girders made of stainless

steel or carbon steel, 9th Nordic Steel Construction Conference, Helsinki, 18-20 June, 2001

1.4301:Rp0.2 = 285(Flange), 297(Web) MPa

1.4362Rp0.2 = 525(Flange), 573(Web) MPa

E = 200 GPa for both 1.4301 and 1.4362

Weldox 700fy = 846(Flange), 815(Web) MPa

E = 210 GPa

See Figures on the previous page.

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grades:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

133

A36, A441 and A514

H-shaped beams

Sectioning

N.R. Nagarajarao, P. Marek and L. Tall

September 1972

The residual stress distributions are similar in all three shapes with A514 steel flanges. The tensileresidual stress at the flame-cut flange tips ranges from 207-483 MPa, and about 172 MPa at the welds.The compressive residual stress is about 138 MPa. The webs have high tensile residual stress in theimmediate vincinity of the welds and compressive stresses about 69 MPa over the rest of the web.

NA

NA

NA

13 mm (Fl) 9,5 mm (W)

(1/2 in. resp. 3/8 in.)

Left: Residual stress distribution in hybrid H-shapes (A441 flanges).

Below: Residual stress distribution in hybrid H-shapes (A514 flanges).

[MPa]0 345

[MPa]0 345

No. 43 No. 44

No. 40 No. 41 No. 42

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Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

134

See Figures on the previous page.

This report presents the analysis and results of a theoretical and experimental investigation todetermine the strength of hybrid steel columns. The investigation was made on centrally-loadedwelded H-shaped columns with high-strength steel flanges and low-strength steel webs. The tangentmodulus and ultimate load, the mechanical properties of the materials, the actual residual stressdistribution and local buckling were taken into consideration for the theoretical analyses of columncurves. The predictions were verified by tests. The experimental study included five hybrid shapes,fabricated from flame-cut or universal-mill plates. The following tests were conducted: tensionspecimen coupon, residual stress measurements, stub column tests and pinned-end column tests witha slenderness ratio of 65. The study showed that the column strength of hybrid shapes can be predictedfrom the actual residual stress distribution by assuming a hypothetical residual stress in the web equalto the difference in yield strength of the flange and the web. The investigation was completed by adiscussion of approximate estimation of residual stress distribution and its magnitude, local bucklingconsiderations and elastic stress of webs at the “working” load.

Nagarajarao, N.R., Marek, P. and Tall, L. (1972). Welded Hybrid Steel Columns. In: Welding

Journal, Volume 51, No 9, Page 462-472, September 1972.

Properties in the order: A514, A441UM,A441 and A36:

fy = 720-760, 345, 340-365, 270-275 MPa(104-110, 50, 49-53, 39-40 ksi)

See Figures on the previous page.

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grades:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

135

S355, S690, S890

Welded plates

X-Ray

Th. Nitschke-Pagel and H. Wohlfahrt

June 1991

The magnitude of the tensile residual stresses in the weld seam can become as high as the yieldstrength of the filler material or the base material. It could be shown that in a material with extremelyhigh yield strength the magnitudes of the residual stresses remain quite moderate.

TIG

Various, see Figures

Various, see Figures

9.5 - 20 mm

Distribution of longitudinal residual stresses at the surface of a dummy weld. Quenched and tempered steel S690 welded with different

values of heat input.

Distribution of longitudinal residual stresses at the surface of a dummy weld. Quenched and tempered steel S890 welded with different

values of heat input.

Distribution of longitudinal residual stresses at the surface of a dummy weld (heat input

W=19.80 kJ/cm) and at the surface of a double-V-weld (8 passes, filler material:

Re=830 N/mm2).

S355

S690

S890

No. 45

No. 46

No. 47

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

136

As preceding papers /1-11/ pointed out various sources contribute to the residual stress state afterwelding and therefore extremely different residual stress patterns can arise as a consequence ofwelding. The aim of this paper is

To clarify the predominance of one or the other of the residual stress generating processes,to show how these processes interact and thusto explain the influence of the type of the base material and filler material and welding parameters

as heat input, welding velocity and cooling conditions an typical residual stress distributions afterwelding.

Nitschke-Pagel, Th. and Wohlfahrt, H. (1991). Residual Stress Distributions After Welding as aConsequence of the Combined Effect of Physical, Metallurgical and Mechanical Sources. In:Mechanical Effects of Welding. IUTAM Symposium Luleå/Sweden, June 10-14, 1991. ISBN 3-540-55240-5.

S355: fy = 355 MPa (Nominal)

S690: fy = 690 MPa (Nominal)

S890: fy = 890 MPa (Nominal)

See Figures on the previous page.

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

137

2,5% Cr, 1% Mo

Plates with V-butt weld

Neutron diffraction

J.H. Root, T.M. Holden, J. Schröder, S. Spooner, C.A. Hubbard, T.A. Dodson and S.A. David..

June 1992

According to the authors the measurement errors lies in the range of MPa.20

Semi-automatic gas tungsten arc (GTA)

NA

6 passes in a V-butt weld

13 mm

Residual stress distribution in the mid-

length plane of the welded plate. The contours have units of MPa. Distances

are to scale. Stress components are longitudinal (L),

transverse (T) and normal (N).

Longitudinal ( ), normal ( ) and transverse (O) strains measured along a locus 1.5mm inside the bottom surface of the plate. Continuous lines are

guides to the eye. The typical uncertainty is the size of the plotting symbols.

No. 48

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

138

The distribution of residual stresses associated with a multipass, gas-tungsten arc weld, joiningtwo 2.5%Cr 1%Mo steel plates of thickness 13 mm, has been measured non-destructively by neutrondiffraction. The large tensile longitudinal stresses (400-500 MPa) in adjacent to the weld are balancedby compressive stresses (-150 MPa) in the periphery of the plate. The stress components normal tothe surface are transverse to the weld everywhere equal in magnitude. In the fusion zone of the weld,these components are tensile at the top surface and middle of the plate and zero at the back surface ofthe plate (i.e., near the root pass of the weld).

Root, J.H., Holden, T.M., Schröder, J., Spooner, S., Hubbard, C.A., Dodson, T.A. and David,S.A. (1992). Residual Stresses in a Multipass Ferritic Weldment. In: Proceedings of the 3rd

International Conference on Trends in Welding Research, Gatlinburg, Tennessee, USA, June 1-51992. ISBN 0-87170-476-5.

fy = 700 MPa (Nominal)

E = 225 GPa

= 0,276

Maximum approximately 500 MPa (tens.)Minimum approx. 150 MPa (compr.)

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

139

304 Stainless

Plates, V-butt welded

Neutron Diffraction

Spooner, S., Fernandez Baca, J.A., David,S.A. and Hubbard, C.R.

8-10 June 1994

This study of 304-type stainless steel plates indicates that the residual stresses in theconventionally welded plate and in the vibratory-treated plate exhibit small differences which arecomparable to the estimate of experimental error

Arc welding

308 stainless steel filler

14 passes

25 mm

The stresses in the as-welded plate are shown as a function of the distance from

the weld centre. The error bars are staggered for clarity of presentation.

The stresses in the plate with the vibration treated weld are most different near the

centre where the errors are large.

No. 49

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

140

Diagram of a transverse section of a welded plate showing the location of the sampling grid on a section through the middle of the welded plate. The fusion zone is schematized by the region capped

by the rounded top. The dotted lines in the background show how the lattice parameter specimens were cut.

Residual stresses and strains were measured in two welded 25-mm thick plates of type 304stainless steel by the neutron diffraction technique. the filler metal was type 308 stainless steel and theweld zone had a two phase microstructure in which the austenitic phase lattice parameter differs fromthe base metal. In these circumstances strain-free samples were taken from the weld zone area foranalysis of the lattice parameters and ferrite content using neutron powder diffraction. Corrections forlattice parameter variation were applied permitting the calculation of residual strains and stresses inthe weld zone, the heat affected zone (HAZ) and base metal. One of the two welds was examinedwithout stress relief and the other was given a stress relief treatment consisting of vibration at afrequency below the resonant condition during welding. In both plates the largest residual stresscomponent (longitudinal) is found in the fusion zone near the boundary between the weld zone andthe heat affected zone. This longitudinal component is 400E50 MPa.

Spooner, S., Fernandez Baca, J.A., David, S.A. and Hubbard, C.R.. (1994). Investigation of

Residual Stresses in a Multipass Weld in 1” Stainless Steel Plate, In: Proceedings of the FourthInternational Conference on Residual Stresses, Baltimore, Maryland, 8-10 June, 1994

E = 196 GPa approx. 350 MPa (tensile)approx. 80 MPa (compr.)

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

141

304 stainless steel

V-butt welded plates

Neutron diffraction

S. Spooner, S.A. David, J.H. Root, T.M. Holden, M.A.M Bourke and J.A. Goldstone

June 1992

According to the authors the measurement precision is 50 MPa. The longitudinal stresses varyfrom close to the yield stress in tension, near the weld zone boundary, to compressive stresses in thecenter of the weld zone. These stresses are asymmetric due to the welding sequence and the annealingeffects on earlier deposited material.

Semiaut. gas tungsten arc weld (GTA)

308 stainless steel filler

11 passes

2.5 cm

Residual stresses through the plate at 40mm from the weld center. Note the small rise in the

stresses with increasing depth.

Residual stresses calculated from the measured strains 4mm from the top surface. Note the

asymmetry across the center line of the weld.

No. 50

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

142

No Figure available.

Residual stresses and strains in a type 304 stainless steel plate containing a multiple-pass gastungsten arc weld were measured with the neutron diffraction technique at a reactor (Chalk River) anda pulsed source (Los Alamos). At Chalk River, three orthogonal strain components were obtained ateach sampling point from the average of the strains measured with (111) and (200) Bragg peaks.Points along the top and bottom of the plate running transverse to the welding direction and pointsalong a through-thickness path in the weld and in the heat affected zone were measured. At the top,the longitudinal stress reached 260 MPa in tension at the fusion line. All three components becamecompressive in the fusion zone. Measurement of the longitudinal and normal strains through thethickness in the fusion zone was difficult because of the large grain size and preferred orientation.However, the transverse strains in the fusion zone were measured as a function of depth at the LosAlamos pulsed source and were compared with corresponding results obtained at Chalk River.

Spooner, S., David, S.A., Root J.H., Holden, T.M., Bourke, M.A.M. and Goldstone, J.A. (1992).Residual Stress and Strain Measurements in an Austenitic Steel Plate Containing a Multipass Weld.In: Proceedings of the 3rd International Conference on Trends in Welding Research, Gatlinburg,Tennessee, USA, June 1-5 1992. ISBN 0-87170-476-5.

E = 196 GPa

= 0.25

Maximum approx. 260MPaMinimum approx. -220MPa

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

143

304 stainless steel

Plate with multipass weld

Neutron Diffraction

Spooner, S., Wang, X.L., Hubbard, C.R., David, S.A.

8-10 June 1994

The region of the last pass in the weld exhibits the largest tensile stresses and strains. Thermalstress relief reduces the largest longitudinal stress by a factor three and leaves the annealed plate in acondition of uniaxial longitudinal stress. The spatial extent of longitudinal stress region is alsoreduced by a factor nearly two.

Gas Tungsten Arc Welding

Type-308 stainless steel

12 passes, 180 Amps, 1143 mm/min.(45 in./min.)

12.7 mm (1/2 in.)

The averaged stresses in the as-welded plate are determined from the average

strains.

The averaged stresses in the stress relieved plate are determined from the average

strains.

Residual stress component maps for the as-welded plate (a) longitudinal, (b) transverse and (c) normal. The stress

contours are incremented by 50 in units of MPa.

No. 51

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

144

Points used in the as-welded plate measurements. The points are on a perpendicular planebisecting the length of the weld line.

The changes in residual stresses due to thermal stress relief were determined in a welded 1/2”thick 304 stainless steel plate from two residual stress maps determined with the neutron diffractiontechnique. The 304 stainless plate was made from two 6” x 12” x 1/2” pieces joined along the lengthby a gas tungsten arc welding process. Multi-pass welds were made with a semiautomatic weldingmachine employing cold-wire feed of type 308 stainless steel filler alloy. The thermal stress relieftreatment consisted of heating to 1150 F, holding for one hour at temperature and then air cooling.Strain components were measured along the weld direction (longitudinal), and perpendicular to theweld line in the plate (transverse), and normal to the plate.(normal) Measurements were confined tothe plane bisecting the weld at the centre of the plate. The strain components were converted to stressassuming that the measured strains were along the principal axes of the strain tensor. The parametersused in the calculation were E=224 GPa and =0.25. The as-welded longitudinal stresses arecompressive in the base metal and become strongly tensile through the heat affected zone......(cont.)

Spooner, S., Wang, X.L., Hubbard, C.R., David, S.A., Residual Stresses in a Multipass Weld in

an Austenitic Stainless Steel Plate Before and After Thermal Stress Relief, In: Proceedings of theFourth International Conference on Residual Stresses, Baltimore, Maryland, 8-10 June, 1994

E = 224 GPa

= 0.25

Maximum:approx. 400 MPa (tensile)

After stress relief:approx. 140 MPa (tensile)

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

145

ASTM A36

H-profile

Sectioning / Hole Drilling

N.Tebedge, G.Alpsten and L.Tall. (1973)

February 1973

-

NA

NA

12,7 mm (1/2 in.) fillet welds

19mm (web),38mm (flange)

Right: Measured stresses using the

hole-drilling method.

Comparison with the sectioning

method.

Below: Comparison of stresses at the two ends, A and B. H14x202

profile.

Above: Stress distribution at location A in the H14x202 profile.

138

[MPa] 0

-138

-138

0

[MPa]

552

207

0

[MPa]

-138

207

0

[MPa]

-138

0 102 203

[mm]

0 102 203

[mm]

-552

[MPa]

0

-138

No. 52

No. 53

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

146

The measurement of residual stresses by the sectioning method has been used for decades tomeasure residual stresses in structural members. This method has proven itself adequate, accurate andeconomical if proper care is taken in the preparation of the specimen and the procedure ofmeasurement. However, a standard procedure to carry out such measurement does not exist in thepublished literature. In this paper a detailed description is presented on the procedure of testing,preparation of specimen, the required tools and measuring devices and working conditions.

For a specific comparison of results, measurements of residual stresses were performed on aspecimen having a uniform residual-stress distribution along its length. On the same specimen, twodifferent hole-drilling methods were also performed to investigate application and comparison ofdifferent methods. Other methods of residual-stress measurement which may be of general interestare discussed in brief.

Tebedge, N., Alpsten, G. and Tall, L. (1973). Residual-stress Measurement by the SectioningMethod. In: Proceedings of the Society for Experimental Stress Analysis, Vol. 30, No. 1. 1973. pp.88-96.

fy = 248 MPa (Nominal) See Fig on the previous page.

Gage-hole location and sectioning detail

1 inch = 25.4 mm

Profile:

Material Thickness:

Author:

Measurement Method:

Date of Publication:

Conclusions / Misc.:

Grade:

Longitudinal Residual Stresses,

Magnitudes and Distribution.

Welding Characteristics

Method:

Material:

No. of Passes in Mulitiweld / Energy / Speed:

147

S690

Plates joined with weld

Dissection / Sectioning

H. Wohlfahrt

1987

In this paper residual stresses due to welding were compared to calculations. Transformationstresses, shrinkage stresses and quenching stresses were also defined and described.

Arc weld

“Similar to base material”

Single

4.5 mm

Weld pattern. structure of the weld zone and of the HAZ and distribution of hardness values and of longitudinal residual stresses in 4.5 mm thick sheets of structural steel arc welded with electrodes of a

composition similar to the base metal.

No. 54

Printed Reference:

Abstract From Reference:

Misc. Material Properties: Measured Extreme Values of Longitudinal Residual Stresses:

Specimen Setup:

148

See Figure on the previous page.

The expression “residual stresses due to welding” is an all-embracing concept including all theresidual stress states arising as a consequence of all the different welding techniques. Furthermore,even in the case of one and the same technique there may be a variety of causes contributing to theoverall residual stress state. Therefor individual authors report on totally different welding stressdistributions. Only by understanding the different processes that can give rise to welding stresses andthe factors that influence them is it possible to gain a grasp of the diverse and complex findings. Hencemodel-type discussions for single pass welds including computed data are useful in this respect. Theresidual stress distributions anticipated from model-type discussions shall be compared withmeasured residual stress distributions in single pass welds as well as multi-pass welds.

Wohlfahrt, H. (1987). Residual Stresses as a Consequence of Welding. In: Advances in Surface

Treatments: Technology-Applications-Effects. Vol. 4, International Guidebook on Residual Stresses.

First edition. Oxford: Pergamon, Cop. ISBN 0-08-034062-8

fy = 690 MPa (Nominal) Maximum approx. 135 MPa (tens.)Minimum approx. -65 MPa (compr.)