Mechanical Behaviour of Cold-Formed Hollow Structural ... · Mechanical Behaviour of Cold-Formed Hollow Structural Section Material Min Sun Doctor of Philosophy Graduate Department

Mechanical Behaviour of Cold-Formed Hollow Structural Section Material

by

Min Sun

A thesis submitted in conformity with the requirements

for the degree of Doctor of Philosophy

Graduate Department of Civil Engineering

University of Toronto

© Copyright by Min Sun 2014

ii

Mechanical Behaviour of Cold-Formed Hollow Structural Section Material

Min Sun

Doctor of Philosophy

Graduate Department of Civil Engineering

University of Toronto

2014

Abstract

In this thesis, the static and dynamic properties of cold-formed Rectangular Hollow Sections

(RHS) produced by different manufacturing techniques (direct-forming versus continuous-

forming; heat-treated versus non-heat-treated) were studied comparatively for the first time.

The aim of this research was to quantify the effects of different manufacturing processes on

the mechanical behaviour of RHS such that the implications of using RHS with different

production histories can be better appreciated during the design of structures made of RHS

and their welded joints.

The static properties of seven cold-formed RHS specimens were investigated by performing

tensile coupon tests, stub column tests, and residual stress measurements. Analytical column

curves were generated to reflect their compression behaviour, based on the experimental

results. It was found that, in general, the static properties of a direct-formed RHS are midway

between those of its continuous-formed and continuous-formed plus heat-treated

counterparts.

The Charpy V-notch (CVN) impact toughness properties of six RHS specimens were studied

via 378 CVN coupons. For RHS with different cross-sectional geometries and produced by

different methods, complete CVN toughness-temperature curves of the flat face and the

corner were compared to quantify the decrease of notch toughness from the flat face to the

iii

corner due to uneven degrees of cold-forming. It was also found that heat treatment in

accordance with Canadian standards for “Class H” finishing does not provide improvement in

the CVN toughness.

The high strain rate properties (compressive and tensile) of four RHS specimens

manufactured by different cold-forming methods were examined by performing a total of 166

split Hopkinson pressure/tension bar tests at strain rates ranging from 100 to 1000 s-1

. Their

dynamic yield stresses were compared to their static yield stresses, to characterize the

strength enhancement of cold-formed RHS under such loading rates, which can be used in the

blast- or impact-resistant design of RHS members.

iv

Acknowledgements

First and foremost I would like to thank Professor Jeffrey Packer for his guidance and

expertise. I appreciate the countless hours he has invested in this thesis as well as in my

professional and personal development.

I would like to thank Professor Kaiwen Xia for his technical support in the split-Hopkinson

pressure/tension bar test program and Professor Michael Seica for his expertise in high strain

rate loadings and dynamic structural design. I am also grateful to the discussions and

motivation generously offered by my friends Dr. Michael Simpson, David Ruggiero, Paolo

Calvi, Giorgio Proestos, Drew Cheung, Martin Walker, Tarana Haque, Elena Nuta, Matthew

McFadden, Stephen Perkins, and many officemates and research group members.

Financial support has been provided by the Natural Sciences and Engineering Research

Council of Canada (NSERC), Explora Foundation, the Ontario Graduate Scholarship

program and the University of Toronto. Appreciation is extended to Bull Moose Tube and

Atlas Tube for providing the RHS members.

I am grateful to the staff of the Department of Civil Engineering’s Structural Testing

Facilities – Giovanni Buzzeo, John MacDonald, Renzo Basset and Xiaoming Sun – for their

help with the experiments. Also, I would like to thank Sheng Huang for his help in using the

split-Hopkinson pressure/tension bar apparatus in the Department’s Impact and Fracture

Laboratory.

Finally, I would like to express my profound appreciation to my family, in particular my wife

Yang Yang, for their love, encouragement and patience.

v

Table of Contents

Abstract ii

Acknowledgements iv

Table of Contents v

List of Tables viii

List of Figures xi

Notation xviii

Chapter 1 Introduction 1

1.1 Background 1

1.2 Scope of research 4

Chapter 2 Static Properties 6

2.1 Summary 6

2.2 Background 6

2.3 RHS specimens and geometric measurements 7

2.4 Experimental investigation 12

2.4.1 Tensile coupon tests 12

2.4.2 Stub column tests 16

2.4.3 Longitudinal residual stress measurements 20

2.5 Results and discussions 26

2.5.1 Tensile stress-strain behaviour and ductility around the cross-section 26

2.5.2 Compressive stress-strain behaviour of the entire cross-section 27

2.5.3 Longitudinal residual stresses around the cross-section 28

2.5.4 Column model 30

Chapter 3 Charpy V-Notch Impact Toughness 39

3.1 Summary 39

3.2 Background 39

vi

3.3 Effects of chemical composition on material CVN impact toughness 41

3.4 Toughness anisotropy in HSS 44

3.4.1 Effect of rolling direction of base plate 44

3.4.2 Effect of notch orientation of CVN coupon 44

3.5 CVN toughness in pertinent HSS product standards 44

3.5.1 ASTM A500-13 [ASTM 2013a] 44

3.5.2 ASTM A1085-13 [ASTM 2013b] 45

3.5.3 CAN/CSA G40.20-13/G40.21-13 [CSA 2013] 45

3.5.4 EN 10219:2006 [CEN 2006a; CEN 2006b] and ISO 10799-1 [ISO 2011] 45

3.6 CVN toughness in international design standards 46

3.6.1 Correlation of CVN toughness to fracture mechanics 46

3.6.2 AASHTO [AASHTO 2007] 46

3.6.3 CSA S16-09 [CSA 2009] 47

3.6.4 EN 1993-1-10:2005 [CEN 2005] 47

3.7 Previous toughness investigations on cold-formed products 48

3.8 RHS specimens and chemical compositions 55



3.10.1 Effects of chemical composition 66

3.10.2 Effects of cold-forming and heat-treatment 67

Chapter 4 High Strain Rate Behaviour 71

4.1 Summary 71

4.2 Background 71

4.3 Previous investigations 74

4.4 RHS specimens 79


4.5.1 Tensile coupon tests 79

4.5.2 SHPB tests 80

4.5.2.1 Background 80

4.5.2.2 Compressive SHPB tests 84

vii

4.5.2.3 Tensile SHPB tests 88


4.6.1 Strength increase factor 92

4.6.2 Dynamic increase factor 92

Chapter 5 Conclusions 96

References 101

Appendix A Geometric Measurements and Static Properties 108

A.1 Geometric measurements 108

A.2 Tensile coupon test results 110

A.3 Stub column test results and determination of maximum longitudinal

compressive residual stresses 114

A.4 Measured longitudinal residual stresses 118

A.5 Analytical compressive stress-strain curves based on column models 123

Appendix B Calculations for Analytical Charpy Transition Temperatures 126

B.1 Derivation of equations in Figure 3.7 for determination of εeff in the

bent region of HSS [Feldmann et al. 2012] 126

B.2 Calculation of analytical ∆Tcf-values in Table 3.10 based on the approach

proposed by [Feldmann et al. 2012] using measured cross-sectional dimensions 129

Appendix C Split-Hopkinson Pressure Bar Test Results 144

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List of Tables

Table 2.1 List of RHS specimens 8

Table 2.2 Nominal and measured dimensions of RHS specimens 10

Table 2.3 Measured cross-sectional area of flat faces and corners 12

Table 2.4 Key tensile coupon test results 13

Table 2.5 Full-sectional tensile properties 16

Table 2.6 Key stub column test results 18

Table 2.7 Comparison of full-sectional tensile and compressive properties 18

Table 2.8 Key longitudinal residual stress measurement results 24

Table 3.1 Chemical requirements in ASTM A500 [ASTM 2013a] 42

Table 3.2 Charpy V-notch test acceptance criteria for coupons with different sizes

[ASTM 2009] 45

Table 3.3 Maximum permissible value of element thickness for S355 steel

[CEN 2005] 47

Table 3.4 Maximum permissible value of element thickness for S355 steel

– Table 2.1 of EN 1993-1-10:2005 extended [Feldmann et al. 2012] 53

Table 3.5 Chemical compositions of RHS specimens and effects of chemical

elements on the CVN toughness of low-carbon structural steel

[Roe and Bramfitt 1990; Maranian 2010] 56

Table 3.6 Cutting locations and orientations of CVN coupons 57

Table 3.7 CVN test results: (a) full-sized coupons; (b) sub-sized coupons 59

Table 3.8 Normalized upper-shelf energy (KVus), ductile-to-brittle transition

temperature (DBTT) and nil-ductility temperature (NDT) of all RHS

specimens 65

ix

Table 3.9 Measured cross-sectional dimensions 69

Table 3.10 Comparison of ∆Tcf-values obtained from experiment results

and ∆Tcf-values estimated based on the approach proposed by

[Feldmann et al. 2012] using measured cross-sectional dimensions 69

Table 4.1 DIFy and DIFu values for various structural steels under low pressure

explosion [Gilsanz et al. 2013] 72

Table 4.2 SIFy and SIFu values for RHS specimens 80

Table 4.3 DIFy values for RHS specimens under compression loading ( = 100 s-1

) 93


) 93

Table 4.5 DIFy values for RHS specimens under tension loading ( = 100 s-1

) 93


) 93

Table 4.7 DIFy values for RHS specimens under flexural loading ( = 100 s-1

) 93


) 94

Table A.1 Measured thickness and corner radius of RHS 152x152x12.7

& Domex (DF19) 108

Table A.2 Measured thickness and corner radius of RHS 152x152x6.35 109

Table A.3 Normalized measured longitudinal residual stresses in DF12,

CF12 and CFH12 118

Table A.4 Normalized measured longitudinal residual stresses in DF24,

CF24 and CFH24 119

Table A.5 Calculation of residual force in DF12 120

Table A.6 Calculation of residual force in CF12 120

Table A.7 Calculation of residual force in CFH12 120

Table A.8 Calculation of residual force in DF24 121

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Table A.9 Calculation of residual force in CF24 121

Table A.10 Calculation of residual force in CFH24 122

Table C.1 Key compressive SHPB test results (F = flat face; C = corner) 148

Table C.2 Key tensile SHPB test results (F = flat face; C = corner) 154

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List of Figures

Figure 1.1 Cold-forming processes: (a) direct-forming; (b) continuous-forming 2

Figure 1.2 Flat rollers used in direct-forming process 3

Figure 1.3 Concave rollers used in continuous-forming process 3

Figure 2.1 Thickness and corner radius measurement locations 9

Figure 2.2 Difference between measured and nominal thickness (mm) 9

Figure 2.3 Normalized corner radii for all RHS specimens: (a) outside corner

radii; (b) inside corner radii 10

Figure 2.4 Measurement of corner area 11

Figure 2.5 Average elongations of tensile coupons at failure 14

Figure 2.6 Comparison of typical tensile coupon test results from different RHS:

(a) flat coupons; (b) corner coupons 14

Figure 2.7 Comparison of typical flat and corner tensile coupon test results

from the same RHS: (a) DF24; (b) CF24; (c) CFH24 15

Figure 2.8 Stub column test setup: (a) before testing; (b) after testing 17

Figure 2.9 Normalized compressive stress-strain curves from stub column tests:

(a) RHS152x152x12.7; (b) RHS152x152x6.35 19

Figure 2.10 Relationship between unloading stress and in-situ longitudinal

residual stress 21

Figure 2.11 Locations of strain gauges for longitudinal residual stress

measurement: (a) strain gauges on RHS 152x152x12.7 and

RHS 152x152x6.35; (b) strain gauges on one inside surface

of RHS 152x152x6.35 23

Figure 2.12 Normalized longitudinal residual stresses: (a) RHS 152x152x12.7;

(b) RHS 152x152x6.35 25

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Figure 2.13 Example (DF24) of determination of maximum longitudinal

compressive residual stress based on stub column test result 29

Figure 2.14 Comparison of maximum compressive longitudinal residual

stresses obtained from residual stress measurements and stub column

test results 29

Figure 2.15 Illustration of discretized cross-section column model 32

Figure 2.16 Comparisons of overall compressive stress-strain curves from stub

column tests and column models: (a) CF12; (b) CF24 34

Figure 2.17 Analytical column curves: (a) RHS 152x152x12.7;

(b) RHS 152x152x6.35 35

Figure 2.18 Comparison with column curves as per CSA S16-09, AISC 360-10

and EN 1993-1-1:2005 for direct-formed RHS: (a) DF12 (RHS 152x152x12.7);

(b) DF24 (RHS 152x152x6.35) 36


and EN 1993-1-1:2005 for continuous-formed RHS:

(a) CF12 (RHS 152x152x12.7); (b) CF24 (RHS 152x152x6.35) 37


and EN 1993-1-1:2005 for continuous-formed plus heat-treated RHS:

(a) CFH12 (RHS 152x152x12.7); (b) CFH24 (RHS 152x152x6.35) 38

Figure 3.1 Approximate relationship between the CVN energy-temperature

curve and the fracture behaviour of a steel component

[adapted from Sedlacek et al. 2008] 40

Figure 3.2 Variation in CVN impact energy with temperature for carbon steels

of varying carbon content [adapted from Roe and Bramfitt 1990] 43

Figure 3.3 Variation in CVN impact energy with temperature for 0.30% carbon

steels of varying manganese content [adapted from Roe and Bramfitt 1990] 43

Figure 3.4 Determination of maximum plastic strain due to cold-bending

[adapted from Sedlacek et al. 2008] 48

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Figure 3.5 Change of Charpy V-notch impact energy due to cold-forming,

for S355J2 steel [adapted from VDEh 1992] 49

Figure 3.6 Change of T27J-temperature due to cold-forming, for S355J2 steel

[adapted from VDEh 1992] 50

Figure 3.7 Determination of εeff in the bent region of HSS

[adapted from Feldmann et al. 2012] 54

Figure 3.8 Cutting locations and orientations of CVN coupons:

(a) full-sized coupons; (b) sub-sized coupons 57

Figure 3.9 CVN impact test setup 58

Figure 3.10 Illustration of “tanh” function 60

Figure 3.11 CVN impact energy-temperature curves for DF12 61

Figure 3.12 CVN impact energy-temperature curves for CF12 61

Figure 3.13 CVN impact energy-temperature curves for CFH12 62

Figure 3.14 CVN impact energy-temperature curves for DF24 62

Figure 3.15 CVN impact energy-temperature curves for CF24 63

Figure 3.16 CVN impact energy-temperature curves for CFH24 63

Figure 3.17 Change of DBTT from flat face to corner for all RHS specimens 64

Figure 3.18 Change of NDT from flat face to corner for all RHS specimens 64

Figure 3.19 Normalized KVus (J/cm2) for all RHS specimens 65

Figure 4.1 DIFy values at various strain rates for ASTM A36 and A514 steels in

[adapted from DOD 2008] 73

Figure 4.2 Typical stress-strain curves for steel and dynamic design stress

[adapted from DOD 2008] 74

xiv

Figure 4.3 Relationships between DIFy and strain rate based on previous

investigations at intermediate strain rate level (test strain rate up to 10 s-1

) 77

Figure 4.4 Relationships between DIFy and strain rate based on previous

investigations at high strain rate level (test strain rate up to 2500 s-1

) 78

Figure 4.5 Schematic diagram of compressive SHPB apparatus 80

Figure 4.6 Photograph of compressive SHPB apparatus 81

Figure 4.7 Typical strain gauge data from a compressive SHPB test 81

Figure 4.8 Schematic diagram of tensile SHPB apparatus 83

Figure 4.9 Determination of dynamic yield stress 84

Figure 4.10 Determination of strain rate 84

Figure 4.11 Compressive and tensile SHPB samples 85

Figure 4.12 Cutting location and orientation of compressive and tensile

SHPB samples 85

Figure 4.13 Typical compressive SHPB test results 86

Figure 4.14 Compressive DIFy values of DF12 (12.7 mm thick RHS) 87

Figure 4.15 Compressive DIFy values of CF12 (12.7 mm thick RHS) 87

Figure 4.16 Compressive DIFy values of DF24 (6.35 mm thick RHS) 88

Figure 4.17 Compressive DIFy values of CF24 (6.35 mm thick RHS) 88

Figure 4.18 Schematic diagram of tensile SHPB sample 89

Figure 4.19 Tensile SHPB sample after test 90

Figure 4.20 Typical tensile SHPB test results 90

Figure 4.21 Tensile DIFy values of DF12 (12.7 mm thick RHS) 91

Figure 4.22 Tensile DIFy values of CF12 (12.7 mm thick RHS) 91

xv

Figure A.1 Tensile coupon test results for DF19

(RHS 152x152x7.95, high strength, direct-formed) 110


(RHS 152x152x12.7, regular strength, direct-formed) 110



Figure A.4 Tensile coupon test results for CF12

(RHS 152x152x12.7, regular strength, continuous-formed) 111

Figure A.5 Tensile coupon test results for CFH12

(RHS 152x152x12.7, regular strength, continuous-formed plus heat-treated) 112

Figure A.6 Tensile coupon test results for CF24


Figure A.7 Tensile coupon test results for CFH24


Figure A.8 Stub column test results for DF19

(RHS 152x152x7.95, high strength, direct-formed) 114





Figure A.11 Stub column test results for CF12


Figure A.12 Stub column test results for CFH12


Figure A.13 Stub column test results for CF24


xvi

Figure A.14 Stub column test results for CFH24


Figure A.15 Comparisons of overall compressive stress-strain curves

from stub column tests and column models for DF12 123


from stub column tests and column models for DF24 123


from stub column tests and column models for CF12 124


from stub column tests and column models for CFH12 124


from stub column tests and column models for CF24 125


from stub column tests and column models for CFH24 125

Figure C.1 Dynamic compressive stress-strain curves for flat face of DF12


Figure C.2 Dynamic compressive stress-strain curves for corner of DF12


Figure C.3 Dynamic compressive stress-strain curves for flat face of CF12


Figure C.4 Dynamic compressive stress-strain curves for corner of CF12


Figure C.5 Dynamic compressive stress-strain curves for flat face of DF24


Figure C.6 Dynamic compressive stress-strain curves for corner of DF24


xvii

Figure C.7 Dynamic compressive stress-strain curves for flat face of CF24


Figure C.8 Dynamic compressive stress-strain curves for corner of CF24


Figure C.9 Dynamic tensile stress-strain curves for flat face of DF12


Figure C.10 Dynamic tensile stress-strain curves for corner of DF12


Figure C.11 Dynamic tensile stress-strain curves for flat face of CF12


Figure C.12 Dynamic tensile stress-strain curves for corner of CF12


xviii

Notation

fds Dynamic design stress for tension, compression and bending

fdv Dynamic design stress for shear

fdy Measured dynamic yield stress, or predicted dynamic yield stress

fdu Predicted dynamic ultimate strength

fy Measured static yield strength

fy,avg Average of yield strengths of tensile coupons

fy,nom Nominal yield strength

fu Measured static ultimate strength

fu,avg Average of ultimate strengths of tensile coupons

fu,nom Nominal ultimate strength

ls Length of compressive SHPB sample

q Cowper-Symonds parameter

ri Inside corner radius of RHS, or inside radius of CHS

ri,avg Average of measured inside corner radii of RHS

ro Outside corner radius of RHS

ro,avg Average of measured outside corner radii of RHS

t Measured wall thickness of RHS

tavg Average of measured wall thicknesses of RHS

tnom Nominal wall thickness of RHS

A Cross-sectional area, or curve fitting coefficient in Eq. 3-4

xix

Ab Cross-sectional area of pressure bar

As Cross-sectional area of compressive SHPB sample, or cross-sectional area of the test

region of tensile SHPB sample

B Measured external width of RHS, or curve fitting coefficient in Eq. 3-4

Bavg Average of measured external widths of RHS

Bnom Nominal external width of RHS

C Curve fitting coefficient in Eq. 3-4, or Cowper-Symonds parameter

Cb Longitudinal elastic wave speed in pressure bar

CF Continuous-forming

CFH Continuous-forming and stress-relieved

CHS Circular hollow section(s)

CVN Charpy V-notch

DBTT Ductile-to-brittle transition temperature (°C)

DCF Degree of cold-forming (%)

DF Direct-forming

DIFy Dynamic increase factor for yield stress = measured dynamic yield stress / measured

static yield stress

DIFu Dynamic increase factor for ultimate strength = measured dynamic ultimate strength

/ measured static ultimate strength

E Young’s modulus

F Ratio of flat face area to total cross-sectional area of RHS

HSS Hollow structural section(s)

IE Effective moment of inertia

xx

KV Energy absorbed by the CVN coupon (J)

KVus Upper-shelf energy (J)

L Length of RHS

NDT Nil-ductility temperature (°C)

P Compression load

R2 Coefficient of determination

RHS Rectangular hollow section(s)

Ry Ratio of the expected yield stress to the specified minimum yield stress

SHPB Split-Hopkinson pressure bar

SHTB Split-Hopkinson tension bar

SIFy Strength increase factor for yield stress = measured static yield stress / nominal

yield stress

SIFu Strength increase factor for ultimate strength = measured static ultimate strength /

nominal ultimate strength

T Temperature (°C)

T27J Temperature (°C) at which the energy absorbed by the CVN coupon is 27 J

σb Bending component of theoretical unloading surface stress

σin Theoretical unloading stress on the inside surface of RHS

σm Membrane component of theoretical unloading surface stress

σout Theoretical unloading stress on the outside surface of RHS

σp Proportional limit

xxi

σrs Longitudinal residual stress

σrs,in Longitudinal residual stress on the inside surface of RHS

σrs,out Longitudinal residual stress on the outside surface of RHS

σ(t) Stress-time history of SHPB sample

εeff Average value of the plastic strain (%) in the net section of the CVN coupon

εmax Plastic strain (%) on the surface of HSS

ε(t) Strain-time history of SHPB sample

εi(t) Incident wave in the pressure bar

εr(t) Reflected wave in the pressure bar

εt(t) Transmitted wave in the pressure bar

ε Strain rate

∆Tcf Shift of CVN energy-temperature curve (°C) due to cold-forming

1

Chapter 1 Introduction

1.1 Background

Hollow Structural Sections (HSS) have become an increasingly popular building material

since their introduction in the 1950s due to their torsional rigidity, high compression strength-

to-weight ratio and aesthetic form. HSS are manufactured around the world by either hot-

forming (a hot-finishing or seamless process) or, more commonly, by cold-forming. Hot-

formed HSS have superior mechanical properties compared to their cold-formed counterparts,

but they are either unavailable in much of the world or prohibitively expensive. With cold-

formed HSS, depending on the amount of cold-working, the mechanical properties are

sometimes substantially different from those of the base material. Thus, experimental tests

and numerical analyses have been conducted extensively in the past to investigate the effect

of cold-forming on the structural behaviour of HSS and their welded joints, thereby

encouraging the use of HSS by design engineers.

Although elliptical shapes are available, HSS are predominantly available in two shapes:

circular and rectangular (including square). Among different shapes, Rectangular Hollow

Sections (RHS) are often preferred to Circular Hollow Sections (CHS) due to the ease of

fabrication at the connections.

Internationally, there are two common manufacturing methods for cold-formed RHS: direct-

forming and continuous-forming. For both methods, the coil strip is progressively cold-bent

into the desired shape by passage through a serious of pressure rollers, during which the

rollers introduce a controlled amount of cold-bending (depending on the sizes of the used

rollers) to the coil strip, thus the mechanical properties are theoretically consistent in the

longitudinal direction of the RHS product. However, some gradual variation in the

longitudinal direction will occur – for both production methods – in practice due to the

location of the final RHS member relative to the position in the hot-rolled coil material from

which it was made.

The direct-forming process is illustrated in Figure 1.1(a) and includes: (1) roll-forming a coil

strip directly into an open section with the desired rectangular shape; and (2) joining the

edges of the open section by welding to form a closed rectangular shape. The continuous-

forming process is illustrated in Figure 1.1(b) and includes: (1) roll-forming a coil strip first

into a circular open tube; (2) joining the edges of the open tube by welding to form a closed

2

circular shape; and (3) flattening the circular tube walls to form the desired rectangular shape.

Figure 1.2 shows the flat rollers used in the direct-forming process to form the coil into a

rectangular tube directly. Figure 1.3 shows the concave rollers used in the continuous-

forming process to form the coil into a circular tube before further flattening it into a

rectangular tube.

(a)

(b)

Figure 1.1 Cold-forming processes: (a) direct-forming; (b) continuous-forming

Although the appearance of the sections can be similar, the mechanical behaviours of RHS

produced by different cold-forming methods can be substantially different. For direct-formed

RHS, the cold-working is concentrated at the four corners, thus the flat faces (not containing

the weld) of the final RHS product have similar properties to the coil material. For

3

continuous-formed RHS, the entire cross-section contains high degrees of cold-working, thus

the final RHS product has higher yield and ultimate strengths and lower ductility compared to

the coil material.

The implications of using RHS produced by different cold-forming methods (i.e. different

mechanical behaviours) are often not fully appreciated. Thus, in this thesis, the static and

dynamic properties of cold-formed RHS produced by different manufacturing techniques

(direct-forming versus continuous-forming; heat-treated versus non-heat-treated) were

studied comprehensively.

Figure 1.2 Flat rollers used in direct-forming process

Figure 1.3 Concave rollers used in continuous-forming process

4

1.2 Scope of research

The main aim of this thesis has been to determine experimentally how different

manufacturing techniques (direct-forming versus continuous-forming; heat-treated versus

non-heat-treated) affect the static and dynamic properties of cold-formed RHS. The static

properties of the RHS specimens were investigated by performing tensile coupon tests, stub

column tests, and residual stress measurements. The dynamic properties of the RHS

specimens were investigated by performing Charpy V-notch (CVN) tests, Split-Hopkinson

Pressure Bar (SHPB) tests and Split-Hopkinson Tension Bar (SHTB) tests. The main

parameters considered include: (1) various cross-sectional geometries, which correspond to

different degrees of cold-forming; and (2) different static yield strengths, as steel with higher

static yield strength is in general less susceptible to cold-forming and high strain rate effects.

Since cold-forming increases yield and ultimate strengths but decreases ductility of steel,

theoretically there is a larger cross-sectional variation (i.e. flat face versus corner) of

mechanical properties in a direct-formed RHS than that in its continuous-formed counterpart.

For all RHS specimens, the static tensile stress-strain behaviour and ductility of the flat face

and the corner were measured locally through tensile coupon tests. Using the measured flat

face and corner areas, the full-sectional tensile properties of the RHS specimens with

different production histories are determined and compared.

Column strengths are influenced by the magnitude and distribution of residual stresses. In the

Canadian steel structures design standard [CSA 2009], a single column curve is used for the

determination of column strengths of cold-formed non-stress-relieved HSS (Class C),

regardless of the cold-forming methods. A more favourable column curve is used for the

cold-formed stress-relieved HSS (Class H). However, due to a lower overall residual stress

level, theoretically a direct-formed RHS (Class C) should have a more favourable column

behaviour than its continuous-formed counterpart (Class C). In this study, the overall

compressive behaviours of the RHS specimens with different production histories were

investigated both experimentally (through stub column tests and longitudinal residual stress

measurements) and analytically (through discretized cross-section column models).

For the assessment of RHS for notch toughness, steel product standards normally require

testing of Charpy V-notch (CVN) coupons taken longitudinally in the flat face (away from

the weld seam) of the RHS, which is questionable since the corner in general has lower notch

toughness due to uneven degrees of cold-forming. Thus, when selecting RHS for notch

5

toughness, it is preferable to specify the corner as an alternate measuring location, or to

consider the deterioration from the flat face to the corner if the notch toughness was measured

in the standard location (flat face). In this study, by performing CVN tests, the notch

toughness decrease from the flat face to the corner of RHS specimens with different

production histories is quantified (in terms of degree of cold-forming) and expressed as a

transition temperature shift (∆Tcf). Also, steel product standards are in general ambiguous

about the sampling orientation (i.e. notch orientation) of full-sized CVN coupons (10x10 mm)

from HSS, which in fact affects the test results. Hence, the effect of notch orientation is

investigated in this study as well.

For blast- or impact-resistant design of steel structures, it is important to use realistic

properties of steel under high strain rate. In particular, the substantial rise in yield stress under

high strain rate may have important effects on the dynamic behaviour of a steel structure.

Since investigations on the high strain rate properties of cold-formed HSS are scarce, by

performing split-Hopkinson pressure/tension bar tests at strain rates from 100 to 1000 s-1

, the

local dynamic yield stresses (compressive and tensile) of the flat face and the corner of the

RHS specimens were measured. Using the measured flat face and corner areas, the full-

sectional dynamic yield stresses are determined and compared to the corresponding static

yield stresses to characterize the dynamic yield stress enhancements (compressive and tensile)

of RHS specimens with different production histories.

A secondary aim of this thesis has been to compare the experimental and analytical results

with the respective design rules and recommendations for cold-formed hollow sections, in

international design specifications for steel structures, with a view to improving current

design practice with hollow sections.

6

Chapter 2 Static Properties

2.1 Summary

This chapter compares the static properties of a total of seven cold-formed RHS

manufactured by different methods: (1) direct-forming, (2) continuous-forming, and (3)

continuous-forming plus stress-relieving by heat treatment. The static properties compared

are: (1) tensile stress-strain behaviour and ductility around the cross-section, (2) compressive

stress-strain behaviour of the entire cross-section, and (3) longitudinal residual stress around

the cross-section. The maximum values of longitudinal compressive residual stresses

estimated from the stub column test results are used to check the accuracy of the longitudinal

residual stress measurements from strips. Finally, the measured longitudinal residual stress

gradients are incorporated into column models to study the column behaviour of RHS with

different production histories.

2.2 Background

It is well known that cold-forming causes strain hardening of the steel material, hence its

yield and ultimate strengths increase while its ductility decreases. Early investigations on the

corner properties of cold-formed steel shapes [Chajes et al. 1963; Karren 1967; Karren and

Winter 1967] have shown that, for steel shapes cold-bent from the same virgin steel, values of

yield strength are larger for smaller inside radius-to-thickness ratios since they correspond to

larger degrees of cold-forming. Based on these investigations, equations have been developed

and adopted by AISI S100-07 [AISI 2007], using the material properties of the virgin steel

and the bending radius as input, for estimation of the average yield strength of the cold-

formed section. Of particular interest, similar investigations have been conducted on cold-

formed RHS [Davison and Birkemoe 1983; Key et al. 1988; Zhao and Hancock 1992; Key

and Hancock 1993; Wilkinson and Hancock 1997; Guo et al. 2007; Gardner et al. 2010].

These studies revealed that, depending on the cross-sectional geometry, the mechanical

behaviours of the flat face and the corner are sometimes substantially diverse due to the

different degrees of cold-forming.

Also associated with cold-forming is the generation of residual stress. For the purpose of

compression member design, residual stress in the longitudinal direction is much more

influential than that in the transverse direction. The effect of longitudinal residual stress on

the compression behaviour of a steel member is to cause premature yielding, leading to a loss

7

of stiffness and a reduction in load-carrying capacity. In previous investigations on the

compression behaviour of cold-formed RHS [Davison and Birkemoe 1983; Key et al. 1988;

Key and Hancock 1993; Gardner et al. 2010], the measured longitudinal residual stresses are

commonly considered as two components. The first is the membrane component (tensile or

compressive depending on the measuring location), which is the mean value of the measured

longitudinal residual stress and occurs uniformly through the wall thickness. The second is

the bending component, which is the deviation from the mean value. Due to the existence of

the longitudinal residual stress, tensile coupons cut from the tube walls may exhibit both axial

deformation and curvature, corresponding to membrane and bending residual stresses

respectively. It can be concluded from these investigations that the compression behaviour of

cold-formed RHS is mostly affected by the bending residual stress, while the membrane

residual stress plays a minimal role.

Although the effects of cold-forming on the mechanical properties of cold-formed RHS have

been studied in the past, direct comparisons between RHS produced by different methods are

scarce. Since RHS of similar cross-sectional geometry may exhibit different structural

behaviours due to different strain histories and thermal actions experienced during production,

in this chapter the mechanical properties of RHS manufactured in North America by: (1)

direct-forming, (2) continuous-forming and (3) continuous-forming plus stress-relieving by

heat treatment are compared through a series of investigations.

2.3 RHS specimens and geometric measurements

In this study, continuous-formed square hollow section specimens with different Bnom/tnom

ratios are selected since the Bnom/tnom ratio is a good indicator of the overall amount of cold-

forming contained in the cross-section. The conclusions and recommendations based on the

test results of the square hollow section specimens apply to rectangular hollow sections as

well since the overall amount of cold-forming in a rectangular cross-section can be estimated

based on the average external width-to-wall thickness ratio, or conservatively based on the

smaller external width-to-wall thickness ratio.

On the other hand, the overall amounts of cold-forming contained in the cross-sections of

direct-formed RHS with different Bnom/tnom ratios are similar. For comparison purpose, the

direct-formed square hollow section specimens were chosen to have the same cross-sectional

dimensions as the continuous-formed ones.

8

The nominal sizes and manufacturing standards for the seven RHS examined are summarized

in Table 2.1. Each section is denoted by a section number in which the prefix “DF”, “CF”, or

“CFH” distinguishes the section by its manufacturing method, where DF = direct-formed; CF

= continuous-formed; and CFH = continuous-formed and subsequently stress-relieved by heat

treatment in accordance with Canadian standards for “Class H” finishing (heated to a

temperature of 450 °C or higher, followed by cooling in air) [CSA 2013]. The number after

the prefix is the Bnom/tnom ratio of the RHS specimen.

Table 2.1 List of RHS specimens

RHS ID Nominal sizes Bnom/tnom Manufacturing standard / grade

DF19 152x152x7.95 mm 19 N/A (Domex)

DF12 152x152x12.7 mm 12 CAN/CSA-G40.20-04/G40.21-04 Gr. 350W Class C

DF24 152x152x6.35 mm 24 CAN/CSA-G40.20-04/G40.21-04 Gr. 350W Class C

CF12 152x152x12.7 mm 12 CAN/CSA-G40.20-04/G40.21-04 Gr. 350W Class C

CFH12 152x152x12.7 mm 12 CAN/CSA-G40.20-04/G40.21-04 Gr. 350W Class H

CF24 152x152x6.35 mm 24 CAN/CSA-G40.20-04/G40.21-04 Gr. 350W Class C

CFH24 152x152x6.35 mm 24 CAN/CSA-G40.20-04/G40.21-04 Gr. 350W Class H

The two sets of RHS, (1) DF12, CF12 and CFH12 , and (2) DF24, CF24, and CFH24, with

each set having the same nominal dimensions and including one direct-formed, one

continuous-formed and one continuous-formed plus stress-relieved RHS, enabled the effects

of different cold-forming methods and heat treatment to be directly compared. The inclusion

of DF19 (direct-formed, thin-walled, high-strength RHS) enabled a comparison of its

mechanical properties with the other RHS with different wall thicknesses and strength

properties. Also, the effect of residual stresses due to direct-forming could be further

demonstrated, in conjunction with DF12 and DF24.

Prior to testing the specimens, each RHS was subject to careful geometrical measurement.

For each specimen, the external widths of all four sides, the thicknesses at 16 different

locations, and the outside and inside corner radii of all four corners of the section were

measured. The measurement locations of thickness and corner radius are shown in Figure 2.1.

For corner radius measurement, the cross-section of each specimen was scanned and input

into AutoCAD so that three-point arcs could be drawn to fit the outside and inside surfaces of

all corners, and the corner radii were then determined by measuring the radii of these arcs.

The thickness and corner radius of all measured locations of the RHS specimens are listed in

Appendix A.1.

9

Figure 2.1 Thickness and corner radius measurement locations

The differences between the measured and nominal thickness for all RHS are shown in

Figure 2.2. The averages of measured width and thickness (Bavg and tavg) are compared to the

nominal values (Bnom and tnom) in Table 2.2. The measured outside and inside corner radii (ro

and ri) of all RHS specimens are normalized to their corresponding tavg in Figure 2.3(a) and

(b), respectively. The averages of measured outside and inside corner radii (ro,avg and ri,avg) are

compared to their corresponding tavg in Table 2.2. The dimensions of CF12 and CFH12 are

the same since they were cut from the same tube. Similarly, CF24 and CFH24 have the same

dimensions as well.

Figure 2.2 Difference between measured and nominal thickness (mm)

1

weld

seam

23

16

9 87

10

4

5

6

14

13

12

15

11

-1.20

-0.80

-0.40

0.00

0.40

0.80

1.20

DF19 DF12 DF24 CF12 & CFH12 CF24 & CFH24

10

Table 2.2 Nominal and measured dimensions of RHS specimens

RHS ID Bnom (mm) tnom (mm) Bavg (mm) Bavg / Bnom tavg (mm) tavg / tnom ro,avg / tavg ri,avg / tavg

DF19 152 7.95 153.5 1.010 8.252 1.038 1.892 1.110

DF12 152 12.7 152.4 1.003 12.538 0.987 1.941 0.689

CF12 &

CFH12 152 12.7 151.9 0.999 12.734 1.003 2.310 1.289

DF24 152 6.35 152.4 1.003 6.289 0.990 2.227 1.103

CF24 &

CFH24 152 6.35 152.8 1.005 5.983 0.942 2.195 1.171

(a)

(b)

Figure 2.3 Normalized corner radii for all RHS specimens: (a) outside corner radii; (b) inside

corner radii

1

1.5

2

2.5

3

r o/t

avg


0

0.5

1

1.5

2

r i/t

avg


11

According to Figure 2.2, there are considerable variations in thickness around the cross-

section of the RHS examined. Particularly, for DF24, a small notch near the weld seam was

found such that the local wall thickness was lower than the other locations around the section.

As can be seen in Table 2.2, for all RHS specimens, the Bavg/Bnom ratios range from 0.999 to

1.010, and the tavg/tnom ratios range from 0.942 to 1.038, both of which are within permitted

tolerance ranges for ASTM A500 (± 1% for external width for RHS with a nominal external

width ≥140 mm; ±10% for wall thickness for all RHS) [ASTM 2013a]. However,

CF24/CFH24 have an average measured thickness below CSA [CSA 2013] tolerance (±5%

for wall thickness for all RHS), and this product was supposed to conform to this

manufacturing standard (see Table 2.1).

Although the average outside corner radius-to-thickness ratios (ro,avg/tavg) for all seven RHS,

ranging from 1.89 to 2.31, are within the typical scatter previously found for cold-formed

sections in North America [Packer and Frater 2005], there is quite a variation of both outside

and inside corner radii (ro and ri) around the measured sections, as can be seen in Figure 2.3(a)

and (b). The corner at location 3 of CF12/CFH12 is much “flatter” than the others. For the

corner at location 7 of DF12, the inside surface was severely cold-bent to a very small ri/tavg

value of 0.42, which is likely to cause the local mechanical properties to be quite different

from other parts of the section.

Figure 2.4 Measurement of corner area

The cross-sectional areas of the flat faces and corners of all RHS specimens were measured

by scanning the cross-sections and inputting them into AutoCAD. It is assumed that the

cross-sectional area remains the same in the longitudinal direction of the RHS specimens.

The calibration and area measurement of a typical corner is shown in Figure 2.4. In order to

ensure the accuracy of the AutoCAD measurements, the total cross-sectional areas of all RHS

specimens were also determined by weighing the stub column (further discussion about stub

12

columns can be found in Section 2.4.2), using a steel density of 7850 kg/m3 [CISC 2010].

The measured cross-sectional areas are listed in Table 2.3. The areas measured using both

methods are consistent. It can be seen that as the Bnom/tnom ratio increases, the ratio of corner

area to total cross-sectional area of RHS decreases. Thus, as the Bnom/tnom ratio increases, the

influence of the corner on the full-sectional behaviour of RHS (tensile or compressive)

becomes smaller.

Table 2.3 Measured cross-sectional area of flat faces and corners

Cross-sectional area (mm

2)

Measured in AutoCAD

Measured by

weighing stub

column

RHS ID Bnom/tnom Flat face Corner Total Corner/total Total

DF12 12 5228 1636 6864 24% 6678

CF12 & CFH12 12 4991 1692 6683 25% 6565

DF19 19 3867 708 4575 15% 4662

DF24 24 3240 382 3622 11% 3549

CF24 & CFH24 24 3036 379 3415 11% 3366

2.4 Experimental investigation

2.4.1 Tensile coupon tests

The tensile stress-strain behaviour and ductility around the cross-sections of the investigated

RHS specimens were obtained through tensile coupon tests. For each RHS, three flat tensile

coupons (from locations 1, 5 and 13 in Figure 2.1) and two corner coupons (from locations 3

and 7 in Figure 2.1) were machined and tested in accordance with ASTM A370 [ASTM

2009].

The tensile coupons tended to become curved after being cut from the RHS due to the release

of longitudinal residual stress. Prior to each test, one end of the curved coupon was clamped

by the universal testing machine. Using a prying bar, the curved coupon was straightened by

force, predominantly elastically (i.e. the coupon would go back to the curved shape if the

prying bar was removed), such that the other end of the coupon could be clamped by the

machine. During tests, the curved coupons were thus restored to their original straight shape

so that their in-situ tensile behaviours could be studied.

The tensile stress-strain curves of all coupons are shown in Appendix A.2. The key test

results from the tensile coupon tests are summarized and compared to the nominal values in

13

Table 2.4. The yield stresses are determined by the 0.2% strain offset method. The average

elongations of the flat coupons and corner coupons at failure are shown in Figure 2.5.

Comparisons of typical flat and corner tensile coupon test results from different RHS are

shown in Figures 2.6 and 2.7. Using Eq. 2-1 and the measured flat face and corner areas in

Table 2.3, the full-sectional tensile properties of the RHS specimens are determined in Table

2.5.

( ) (2-1a)

( ) (2-1b)

where F is the ratio of flat face area to total cross-sectional area of RHS

Table 2.4 Key tensile coupon test results

Flat face Corner

RHS ID fy,nom

(MPa)

fy,avg

(MPa)

(fy,avg-fy,nom)

/fy,nom

fy,avg

(MPa)

(fy,avg-fy,nom)

/fy,nom

DF19 690 723 4.80% 770 11.60%

DF12 350 427 22.00% 615 75.70%

DF24 350 402 14.90% 539 54.00%

CF12 350 457 30.60% 590 68.60%

CFH12 350 483 38.00% 570 62.90%

CF24 350 340 -2.90% 483 38.00%

CFH24 350 363 3.70% 463 32.30%

Flat face Corner

RHS ID fu,nom

(MPa)

fu,avg

(MPa)

(fu,avg-fu,nom)

/fu,nom

fu,avg

(MPa)

(fu,avg-fu,nom)

/fu,nom

DF19 N/A 779 N/A 807 N/A

DF12 450 522 16.00% 649 44.20%

DF24 450 473 5.10% 567 26.00%

CF12 450 599 33.10% 676 50.20%

CFH12 450 606 34.70% 637 41.60%

CF24 450 448 -0.40% 528 17.30%

CFH24 450 464 3.10% 531 18.00%

14

Figure 2.5 Average elongations of tensile coupons at failure

(a)

(b)

Figure 2.6 Comparison of typical tensile coupon test results from different RHS: (a) flat

coupons; (b) corner coupons

0%

10%

20%

30%

40%

DF19 DF12 DF24 CF12 CFH12 CF24 CFH24

Flat coupon Corner coupon

0

100

200

300

400

500

600

0 0.005 0.01

Str

ess (

MP

a)

Strain

DF24 CF24 CFH24

0

100

200

300

400

500

600

0 0.005 0.01

Str

ess (

MP

a)

Strain

DF24 CF24 CFH24

15

(a)

(b)

(c)

Figure 2.7 Comparison of typical flat and corner tensile coupon test results from the same

RHS: (a) DF24; (b) CF24; (c) CFH24

0

100

200

300

400

500

600

0 0.005 0.01

Str

ess (

MP

a)

Strain

Flat face Corner

0

100

200

300

400

500

600

0 0.005 0.01

Str

ess (

MP

a)

Strain

Flat face Corner

0

100

200

300

400

500

600

0 0.005 0.01

Str

ess (

MP

a)

Strain

Flat face Corner

16

Table 2.5 Full-sectional tensile properties

Flat face Corner

Entire

cross-section fy,avg difference

between flat

face and entire

cross-section RHS ID Bnom/tnom Area

(mm2)

fy,avg

(MPa)

Area

(mm2)

fy,avg

(MPa)

Area

(mm2)

fy,avg

(MPa)

DF19 19 3867 723 708 770 4575 730 1%

DF12 12 5228 427 1636 615 6864 472 10%

DF24 24 3240 402 382 539 3622 416 4%

CF12 12 4991 457 1692 590 6683 491 7%

CFH12 12 4991 483 1692 570 6683 505 5%

CF24 24 3036 340 379 483 3415 356 5%

CFH24 24 3036 363 379 463 3415 374 3%

Flat face Corner

Entire

cross-section fu,avg difference

between flat

face and entire

cross-section RHS ID Bnom/tnom Area

(mm2)

fu,avg

(MPa)

Area

(mm2)

fu,avg

(MPa)

Area

(mm2)

fu,avg

(MPa)

DF19 19 3867 779 708 807 4575 783 1%

DF12 12 5228 522 1636 649 6864 552 6%

DF24 24 3240 473 382 567 3622 483 2%

CF12 12 4991 599 1692 676 6683 618 3%

CFH12 12 4991 606 1692 637 6683 614 1%

CF24 24 3036 448 379 528 3415 457 2%

CFH24 24 3036 464 379 531 3415 471 2%

2.4.2 Stub column tests

The overall compressive stress-strain behaviour of the investigated RHS specimens and the

influence of longitudinal residual stress were determined by stub column tests.

The stub columns were machined and tested in accordance with internationally accepted

criteria [Ziemian 2010]. For all stub columns, both ends were machined flat, parallel and

normal to the tube axis. As per [Ziemian 2010], the lengths of the stub columns were chosen

to be at least three times the nominal width of the RHS specimens but no more than 20 times

the corresponding radius of gyration. The former was to ensure that the stub columns were

sufficiently long to contain the same initial residual stress pattern as a much longer member

cut from the same stock. The latter was to ensure that the stub columns could resist the yield

load (i.e. Afy).

During testing, each stub column was instrumented with 5 mm long strain gauges at the mid-

height of each tube face and Linearly Varying Differential Transformers (LVDTs) to ensure

17

proper alignment. The criterion for acceptable alignment is for the variation between strains

on any stub column face, relative to the average strain, to be less than 5% [Ziemian 2010].

This requirement is stipulated to ensure concentric, uniform compression over the cross-

section of the stub column. The alignment of each specimen was checked at 25% and 50% of

the expected yield load as per [Ziemian 2010]. All specimens were tested in an MTS machine

with a compression capacity of 4800 kN. The loading rate of all specimens was kept quasi-

static to preclude any dynamic influence on the test results. The tests were continued after the

ultimate load until the load dropped to approximately 80% of the yield load. Figure 2.8 shows

a typical stub column test setup.

(a) (b)

Figure 2.8 Stub column test setup: (a) before testing; (b) after testing

All stub columns failed by local inelastic buckling (squashing) of the RHS walls near the

ends due to restraint from the platens. The average compressive stress over the cross-section

was determined by dividing the compression load by the cross-sectional area in Table 2.3

(measured by weighing the stub columns), and the average strain over the cross-section was

determined by dividing the end shortening by the initial length of the specimen. The

compressive stress-strain curves of all stub columns (up to an average strain of 0.015) are

Local inelastic

buckling

18

shown in Appendix A.3. The key test results from all stub column tests are summarized in

Table 2.6. The overall compressive yield strength is determined by the 0.2% strain offset

method. The Young’s modulus values were determined based on the average strain gauge

data in the elastic range. The overall compressive properties are compared to the overall

tensile properties in Table 2.7.

The compressive stress-strain curves obtained from the stub column tests for RHS with 12.7

mm nominal wall thickness (DF12, CF12 and CFH12) and 6.35 mm nominal wall thickness

(DF24, CF24 and CFH24) are normalized by their overall compressive yield strengths (fy) for

comparison in Figure 2.9(a) and (b), together with their proportional limits. The proportional

limit was determined by fitting a straight line to the elastic portion of the stress-strain curve.

The point from which the stress-strain curve starts to deviate from the straight line is

identified as the proportional limit (i.e. the stress is no longer proportional to the strain).

Table 2.6 Key stub column test results

RHS ID L (mm) A (mm2) E (GPa) fy (MPa) fu (MPa) σp (MPa) σp / fy

DF19 498.0 4662 206.8 720 801 320 44.4%

DF12 499.8 6678 211.5 500 580 240 48.0%

DF24 599.5 3549 217.1 470 482 240 51.1%

CF12 501.5 6565 216.1 550 658 140 25.5%

CFH12 498.3 6565 215.6 580 584 400 69.0%

CF24 599.8 3366 208.5 390 446 150 38.5%

CFH24 599.7 3366 214.8 410 426 340 82.9%

Table 2.7 Comparison of full-sectional tensile and compressive properties

fy,avg fu,avg

RHS ID Bnom/tnom Tensile

(MPa)

Compressive

(MPa)

Tensile /

compressive

Tensile

(MPa)

Compressive

(MPa)

Tensile /

compressive

DF19 19 730 720 1.01 783 801 0.98

DF12 12 472 500 0.94 552 580 0.95

DF24 24 416 470 0.89 483 482 1.00

CF12 12 491 550 0.89 618 658 0.94

CFH12 12 505 580 0.87 614 584 1.05

CF24 24 356 390 0.91 457 446 1.02

CFH24 24 374 410 0.91 471 426 1.11

Note: There are differences between the full-sectional tensile and compressive properties because the full-

sectional tensile properties were calculated based on local tensile properties obtained from tensile coupon tests.

19

(a)

(b)

Figure 2.9 Normalized compressive stress-strain curves from stub column tests: (a)

RHS152x152x12.7; (b) RHS152x152x6.35

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008 0.01

Str

ess / f

y

Strain

DF12 CF12 CFH12

Respective Proportional Limits

0

0.2

0.4

0.6

0.8

1

1.2

0 0.002 0.004 0.006 0.008 0.01

Str

ess / f

y

Strain

DF24 CF24 CFH24

Respective Proportional Limits

20

2.4.3 Longitudinal residual stress measurements

The longitudinal residual stress around the cross-section of the investigated RHS specimens

was measured using the sectioning technique, which has been commonly used by researchers

for the determination of residual stress in all types of steel shapes including hollow sections

[Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993; Gardner et al. 2010;

Jiao and Zhao 2003]. The procedures of the sectioning technique are as follows:

(1) Attach strain gauges to the outside and inside surfaces of the examined section in the

longitudinal direction.

(2) Cut the examined section into longitudinal strips. During cutting, these steel strips will

exhibit both axial deformation and curvature due to the membrane and bending components

of the unloading stress as shown in Figure 2.10(b) and (c).

(3) Measure the changes in strains on the outside and inside surfaces of the steel strips.

(4) Convert the measured changes in strains to the unloading surface stresses, σout and σin, so

that theoretical through-thickness unloading stress due to sectioning, as shown in Figure

2.10(a), can be determined.

The opposite of the measured unloading stress, as shown in Figure 2.10(d), is a good

indicator of the magnitude of the in-situ surface longitudinal residual stress. As shown in

Figure 2.10(a), (b) and (c), the measured unloading stress equals the algebraic sum of the

membrane and bending components. It shall be noted that, for illustration purposes, the

membrane component is assumed to be compressive in Figure 2.10(b). According to previous

investigations on hollow sections [Davison and Birkemoe 1983; Key et al. 1988; Key and

Hancock 1993; Gardner et al. 2010; Jiao and Zhao 2003], the membrane component can be

either tensile or compressive, depending on the measuring location. Generally, the magnitude

of the membrane component is much smaller than that of the bending component. Previous

investigations [Davison and Birkemoe 1983; Key et al. 1988; Key and Hancock 1993;

Gardner et al. 2010; Jiao and Zhao 2003] have also revealed that, for hollow sections, the

measured unloading stress in Figure 2.10(a) is always compressive on the outside surface and

tensile on the inside surface. In other words, the in-situ longitudinal residual stress is tensile

on the outside surface and compressive on the inside surface.

21

A limitation of the sectioning technique is that the measured unloading stress is only an

approximation of the in-situ longitudinal residual stress. It has been shown [Davison and

Birkemoe 1983; Key and Hancock 1993] that a block sectioned from a cold-formed RHS still

contains compressive longitudinal residual stress on the outside surface and tensile

longitudinal residual stress on the inside surface (Figure 2.10(f)). That is, the measured σout

and σin values are in fact the difference between the in-situ state and the final block state,

rather than the in-situ longitudinal residual stress itself. As shown experimentally by

[Davison and Birkemoe 1983], for RHS containing a high level of longitudinal residual stress

(i.e. with the maximum value approaching the yield stress), the measured σout and σin values

may sometimes exceed the corresponding yield stress. It was also found in this study that the

measured σout and σin values at some locations of the two continuous-formed RHS (CF12 and

CF24) exceeded their corresponding yield stresses.

Figure 2.10 Relationship between unloading stress and in-situ longitudinal residual stress

(a)

Measured

unloading

strain x E

(b)

Membrane

component

(assume

compressive)

(c)

Bending

component

Inside surface

Outside surface

t / 2

t / 2

σout = σb + σm σm σb

σb

– σout

σin = σb + σm

– σin

(d)

Opposite of

measured

unloading

strain x E

σrs,in

t / 3

t / 3

t / 3

(e)

In-situ

longitudinal

residual stress

(assumed)

σrs,out

σm

(f)

Longitudinal residual

stress in released

block (e.g. [Davison

and Birkemoe 1983])

Inside surface

Outside surface

t / 2

t / 2

22

In this chapter, the relationship between the measured values and the in-situ values suggested

by [Davison and Birkemoe 1983] was adopted. This suggested in-situ through-thickness

distribution, as shown in Figure 2.10(e), was later shown both experimentally [Weng and

White 1990] and analytically [Quach et al. 2006] to be representative of the through-

thickness longitudinal residual stress distribution associated with large plastic bending

deformations. In this model, using the measured unloading surface stress data as input, the in-

situ longitudinal residual stresses on the outside and inside surfaces (σrs,out and σrs,in) at an

arbitrary point on the RHS can be determined by Eqs. 2-2 and 2-3, which were derived from

graphs in [Davison and Birkemoe 1983].

m

b

outrs, σ13

σ9σ (2-2)

in which

σb is the bending component of the measured theoretical unloading stress on the outside

surface (compressive and hence negative), as shown in Figure 2.10(c), and

σm is the membrane component of the measured theoretical unloading stress on the outside

surface (either tensile or compressive depending on the measuring location around the cross-

section), as shown in Figure 2.10(b).

mb

rs,in σ13

σ9σ (2-3)

in which

σb is the bending component of the measured theoretical unloading stress on the inside

surface (tensile and hence positive), as shown in Figure 2.10(c), and

σm is the membrane component of the measured theoretical unloading stress on the inside

surface (either tensile or compressive depending on the measuring location around the cross-

section), as shown in Figure 2.10(b).

Since the residual stress increase due to heat input from welding is very local, it is not

considered in this study. A total of 18 strain gauges were mounted on the RHS with nominal

dimensions of 152x152x12.7 mm (DF12, CF12 and CFH12) to monitor the unloading strains

in the longitudinal direction (half on the outside surface and half on the inside surface). For

23

comparison purpose, 26 strain gauges were mounted on the RHS with nominal dimensions of

152x152x6.35 mm (DF24, CF24 and CFH24). Due to physical constraints, these strain

gauges were mounted at a section located 60 mm away from the end of the RHS rather than

the mid-length of the RHS. According to previous research [Jiao and Zhao 2003], residual

stress values at this location would be reasonably close to those at the mid-length of the RHS.

The strain gauge locations are shown schematically in Figure 2.11(a) and photographically in

Figure 2.11(b).

(a)

(b)

Figure 2.11 Locations of strain gauges for longitudinal residual stress measurement: (a) strain

gauges on RHS 152x152x12.7 and RHS 152x152x6.35; (b) strain gauges on one inside

surface of RHS 152x152x6.35

weldseam

1

straingauge

35

2 4

35mm

7

6

8

9

24mm

2 3 5 641 7

8

9

10

13

11

12

RHS 152x152x12.7

weldseam

straingauge

RHS 152x152x6.35

35mm

35mm

35mm

24mm

24mm

24mm

24mm

24mm

24

The procedures for the determination of the longitudinal residual stresses in the examined

RHS are as follows:

(1) After initial readings, cuttings were made around each strain gauge and small blocks with

strain gauges on both sides were taken from each RHS. The differences between the strain

gauge readings before and after the cutting were recorded as the unloading strains;

(2) The theoretical unloading stresses (σout and σin) were obtained by multiplying the

unloading strains by Young’s modulus (E in Table 2.6). It was found that the unloading stress

at some locations of the two continuous-formed Class C RHS (CF12 and CF24) exceeded

their corresponding average compressive yield strengths (fy in Table 2.6);

(3) Calculate σm and σb, using the relationship illustrated in Figure 2.10(a), (b) and (c); and

finally

(4) Calculate the σrs,out and σrs,in, using Eqs. 2-2 and 2-3.

The calculated σrs,out and σrs,in values around the cross-section of all examined RHS are

normalized by their corresponding average compressive yield strength (fy in Table 2.6) and

listed in Appendix A.4, in which the tensile residual stress on the outside surface is positive

and the compressive residual stress on the inside surface is negative. These values are plotted

here in Figure 2.12(a) and (b). The averages of the normalized values (σrs,out/fy and σrs,in/fy)

are listed in Table 2.8. The normalized maximum longitudinal compressive residual stresses

(max. compressive σrs/fy) for all RHS specimens, determined from Figure 2.12, are also listed

in Table 2.8.

Table 2.8 Key longitudinal residual stress measurement results

RHS ID Bnom /

tnom

Average of

σrs,out / fy

(tensile)

Average of

σrs,in / fy

(compressive)

Max. compressive σrs / fy

(from residual stress

measurements)

Max. compressive σrs / fy

(from stub column test

results)

DF12 12 39.0% 37.6% 60.2% 52.0%

DF24 24 36.1% 28.1% 56.7% 48.9%

CF12 12 60.0% 60.0% 91.1% 74.5%

CFH12 12 24.1% 24.5% 37.2% 31.0%

CF24 24 51.8% 47.4% 74.9% 61.5%

CFH24 24 19.4% 16.1% 28.5% 17.1%

25

(a)

(b)

Figure 2.12 Normalized longitudinal residual stresses: (a) RHS 152x152x12.7; (b) RHS

152x152x6.35

-1

-0.5

0

0.5

1

σrs

/ f y

Outside surface of DF12 Inside surface of DF12

Outside surface of CF12 Inside surface of CF12

Outside surface of CFH12 Inside surface of CFH12

-1

-0.5

0

0.5

1

σrs

/ f y

Outside surface of DF24 Inside surface of DF24

Outside surface of CF24 Inside surface of CF24

Outside surface of CFH24 Inside surface of CFH24

26

2.5 Results and discussions

2.5.1 Tensile stress-strain behaviour and ductility around the cross-section

As can be seen in Table 2.4, the spread between the actual yield strength (fy,avg) and the

minimum specified value (fy,nom) is sometimes substantial, up to 38% for the flat face and 76%

for the corner. For RHS specimens with regular yield strength (DF12, DF24, CF12, CFH12,

CF24, CFH24), there is generally a significant variation between the flat face and corner in

yield and ultimate strengths due to the uneven degrees of cold-forming around the cross-

section. For the RHS specimen with a high yield strength (DF19), such variation is minor,

which suggests that steel material with such a chemical composition is less sensitive to cold-

working.

For the effects of cold-forming and heat treatment on the ductility around the RHS cross-

section, it can be seen from Figure 2.5 that:

(1) The flat face is much more ductile than the corner for all direct-formed RHS (DF19, DF12

and DF24). This is because the flat face was not severely cold-formed during production.

(2) For the continuous-formed RHS with Bnom/tnom ratio of 12 (CF12), the ductility difference

between the flat face and corner is minor. However, for the continuous-formed RHS with

Bnom/tnom ratio of 24 (CF24), such difference becomes obvious again. This is because, as

discussed previously, the steel plate is roll-formed into a circular section before reverse

bending it into a rectangular section during the continuous-forming process. Previous

research [Feldmann et al. 2012] suggested that the amount of cold-working at the flat face of

the continuous-formed rectangular section is proportional to the thickness-to-radius ratio of

the circular section. Since the thickness-to-radius ratio of the circular section used to form

CF12 is approximately twice that of CF24, the amount of cold-working at the flat face of

CF12 is approximately twice that of CF24. In other words, the cold-working gradient around

the cross-section (i.e. flat face versus corner) of CF12 is smaller than that of CF24. Thus, the

ductility difference between the flat face and the corner of CF12 is smaller than that of CF24.

(3) Heat treatment is effective in bringing back the ductility of the cold-formed RHS (CFH12

versus CF12, and CFH24 versus CF24).

For the effects of cold-forming and heat treatment on the tensile stress-strain behaviour

around the RHS cross-section, it can be seen from Figure 2.6(a) and (b) that:

27

(1) The tensile stress-strain behaviour of the flat face of the direct-formed RHS is similar to

that of the continuous-formed-stress-relieved RHS, wherein there is a clear yield point.

(2) The tensile stress-strain behaviour of the corner of the direct-formed RHS is similar to

that of the continuous-formed RHS, wherein there is no clear yield point (i.e. the material

starts to yield at a relatively early stage).

For full-sectional tensile properties, it can be seen in Table 2.5 that:

(1) For all RHS specimens, the fy,avg differences between flat face and entire cross-section are

in general larger than the fu,avg differences. This is because, for low carbon structural steel, as

the amount of cold-working increases, the yield strength increases dramatically, while the

ultimate strength increases moderately [Roe and Bramfitt 1990]. This is confirmed by the

results in Table 2.5. Due to uneven degrees of cold-working, generally there are large yield

strength differences between the flat face and corner of the RHS specimens. On the other

hand, the ultimate strength differences between the flat face and the corner are moderate.

(2) For RHS with Bnom/tnom ratio of 12 (DF12, CF12 and CFH12), the corners contribute

approximately 25% of the total cross-sectional area, thus the “corner effect” is obvious. Since

the cold-forming gradient in DF12 is larger than those in CF12 and CFH12, DF12 has a

larger fy,avg difference between flat face and entire cross-section (10%) than CF12 and CFH12

(7% and 5% respectively).

(3) For RHS with Bnom/tnom ratio of 24 (DF24, CF24 and CFH24), although the cold-forming

gradient in DF24 is larger than those in CF24 and CFH24, since the corners only contribute

approximately 11% of the total cross-sectional area, the fy,avg differences between flat and

entire cross-section for DF24, CF24 and CFH24 are small and similar (4%, 5% and 3%

respectively). It can be seen that the “corner effect” becomes less obvious as the Bnom/tnom

ratio increases from 12 to 24.

2.5.2 Compressive stress-strain behaviour of the entire cross-section

Theoretically, the corners and their nearby regions of both direct-formed and continuous-

formed RHS should contain similar amounts of longitudinal residual stress which are

primarily influenced by the corner bending radius. The flat face of direct-formed RHS likely

contains a low level of longitudinal residual stress, since it experiences a small amount of

cold-work during the direct-forming process. The flat face of continuous-formed RHS likely

28

contains a high level of longitudinal residual stress due to the high degree of cold-forming

during the continuous-forming process.

According to Table 2.6, the proportional limit-to-overall compressive yield strength ratios

(σp/fy) for the three direct-formed RHS (DF19, DF12 and DF24) are very similar, regardless

of the dimensional differences. However, for the two continuous-formed RHS (CF12 and

CF24), a relatively larger difference in the σp/fy ratios was observed. This is because, for

continuous-formed RHS, as the Bnom/tnom ratio increases, the overall degree of cold-forming

to the cross-section decreases, leading to a lower level of longitudinal residual stress.

It can be seen in Figure 2.9(a) and (b) that:

(1) For RHS with a low width-to-thickness ratio (Bnom/tnom = 12), the compressive stress-

strain behaviour of the direct-formed RHS is midway between those of its continuous-formed

and continuous-formed-stress-relieved counterparts.

(2) For RHS with an intermediate width-to-thickness ratio (Bnom/tnom = 24), the difference in

compressive stress-strain behaviour between the direct-formed RHS and the continuous-

formed non-stress-relieved RHS becomes smaller.

2.5.3 Longitudinal residual stresses around the cross-section

Before analysing the longitudinal residual stresses measured using the sectioning technique,

the maximum value of the longitudinal compressive residual stress in all RHS specimens was

estimated using the stub column test results. These maximum values were used to check the

accuracy of the longitudinal residual stress measurements.

Since the stub columns tested have very low global slenderness ratios and non-slender cross-

sections, their capacities are achieved when all fibres reach the yield stress. The presence of

longitudinal residual stress in the cross-section implies that some fibres are in a state of

residual compression. Under compression load, these fibres will yield before others, leading

to a loss in column stiffness. Thus, the maximum value of the longitudinal compressive

residual stress within the section can be estimated by evaluating the difference between the

proportional limit stress and the yield stress. An example (DF24) is shown in Figure 2.13. As

can be seen in this figure, the maximum longitudinal compressive residual stress in DF24 is

approximately 50% of its yield stress. Using this method, the maximum longitudinal

29

compressive residual stress values for all RHS specimens are determined and shown in

Appendix A.3, and are listed in Table 2.8.

Figure 2.13 Example (DF24) of determination of maximum longitudinal compressive residual

stress based on stub column test result

Figure 2.14 Comparison of maximum compressive longitudinal residual stresses obtained

from residual stress measurements and stub column test results

Credence was given to the accuracy of the longitudinal residual stress measurement since:

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain

Yield stress = 470 MPa

Proportional limit = 240 MPa

Maximum longitudinal

compressive residual stress = 230 MPa

0%

25%

50%

75%

100%

0% 25% 50% 75% 100%

Max. com

pre

ssive σ

rs/ f y

fro

m resid

ual s

tress m

easure

ments

Max. compressive σrs / f y

f rom stub column test results

DF12

DF24

CF12

CFH12

CF24

CFH24

30

(1) The maximum values of the longitudinal compressive residual stress measured using the

sectioning technique are in general consistent with those estimated based on the stub column

test results. The comparison is shown in Figure 2.14.

(2) Assuming the through-thickness longitudinal residual stress distribution in Figure 2.10(e),

the residual forces (integral of residual stress over the cross-sectional area) in all RHS are

below 5% of their corresponding yield load, thus adequate equilibria were attained. The

calculations of residual forces in the cross-section of the RHS specimens are shown in

Appendix A.4. For each RHS specimen, since the residual stress measurement was performed

on half of the cross-section, it is assumed that the residual stress on the other half of the cross-

section is the same. Thus, the bending moment resulting from the bending component of the

residual stress (i.e. Figure 2.10(e) minus Figure 2.10(b)) at a certain location is balanced by

that at the symmetrical location of the cross-section. Also, the bending component results in

zero axial force. Hence, the residual force in the cross-section equals the integral of the

membrane component (i.e. Figure 2.10(b)) over the cross-sectional area.

It can be seen in Figure 2.12(a) and (b) that:

(1) For all RHS, the maximum longitudinal residual stresses were found between the

centrelines of the flat faces and the corners, which is in good agreement with the

measurements reported by other researchers [Davison and Birkemoe 1983; Key et al. 1988;

Key and Hancock 1993; Gardner et al. 2010].

(2) The continuous-formed RHS (CF12 and CF24) contain the highest level of longitudinal

residual stress. The longitudinal residual stress in continuous-formed-stress-relieved RHS

(CFH12 and CFH24) is not only the lowest but also the most uniform around the cross-

section, due to the heat treatment. The magnitude of the longitudinal residual stress in the

direct-formed RHS (DF12 and DF24) is mid-way between those of its continuous-formed and

continuous-formed-stress-relieved counterparts.

According to Table 2.8, as the Bnom/tnom ratio increases, the average longitudinal residual

stress level decreases for all three types of RHS (DF24 versus DF12, CF24 versus CF12, and

CFH24 versus CFH12).

2.5.4 Column model

In this section, the measured longitudinal residual stress gradients were incorporated into

column models to study the column behaviour of RHS with different production histories.

31

Column behaviour models are commonly based on the tangent modulus theory or the

maximum strength theory [Davison and Birkemoe 1983]. In this section, the tangent modulus

theory, considering the column strength of a perfectly straight member, was used. The initial

crookedness of the column was deemed of minor significance in this study because HSS has a

reputation for very high levels of straightness in practice. The column behaviour was

simplified to a bifurcation problem, and the tangent modulus bifurcation load (P) of a

centrally loaded, perfectly straight, pin-ended column of length L was calculated as:

2

E

2

L

EIπP (2-4)

where E is the Young’s modulus and IE is the effective moment of inertia of the cross-section

at a certain load stage.

The following assumptions were made when applying the tangent modulus theory:

(1) The stress-strain state in any longitudinal fibre at a certain load stage is independent of

that in any other longitudinal fibre, and it is constant along the member length;

(2) The residual stress varies around the cross-section perimeter and through the wall

thickness of the member but is constant in any longitudinal fibre along the member length;

(3) Only the longitudinal residual stress is considered. The interaction with transverse

residual stress is ignored;

(4) Strain hardening of the material is not considered;

(5) For simplification, the corner radius is ignored and a box section is used in the calculation.

Comparing to the actual section with corner radius, the simplified box section ignoring corner

radius has a slightly larger cross-sectional area since it overestimates the corner area.

However, since the cross-sections of all RHS specimens contain much more “flat face” than

“corner” (i.e. the percentages of corner areas are small), the impact of this assumption on the

column model results was found to be very minor.

For each of the RHS specimens, a discretized cross-section column model was built, using

the material properties listed in Table 2.6 (i.e. E and fy). As illustrated in Figure 2.15, the

model contained the through-thickness longitudinal residual stress distribution as shown in

Figure 2.10(e), with the σrs,out and σrs,in values as shown in Figure 2.12(a) and (b) around the

cross-section. The discretized cross-section column models were subjected to uniform strains.

The applied buckling load (P) and the effective moment of inertia (IE) corresponding to a

32

certain applied strain were determined and used to solve for the buckling length (L) under this

buckling load using Eq. 2-4.

Figure 2.15 Illustration of discretized cross-section column model

The analytical stress-strain relationships of the cross-section column models were compared

to the stub column test results and shown in Appendix A.5. Typical comparisons are shown in

Figure 2.16(a) and (b). The maximum stresses for the model stress-strain curves are the fy

values listed in Table 2.6, since strain hardening of the material was not considered. The

analytical stress-strain curves (pre-yielding) generated by the tangent modulus column

models were found to agree with the stub column test results well. Thus, further credence is

given to the longitudinal residual stress measurements and the following deductions.

Layer 2

Layer 3

Layer 4

Layer 5

Layer 6

Layer 7

Layer 8

Layer 9

Layer 10

t / 3

t / 3

t / 3

Layer 1

Layer 11

(tensile)

(compressive)

Corresponding magnitude of

longitudinal residual stress

Outside surface = σrs,out

Inside surface = σrs,in

33

The normalized analytical column curves of the RHS with the same nominal dimensions but

different production histories are compared in Figure 2.17(a) and (b). The data points on the

normalized analytical column curves correspond to those in the analytical compressive stress-

strain curves in Figure 2.16 (i.e. the same applied strain level up to the yield point). It can be

seen in Figure 2.17(a) that for the three RHS 152x152x12.7, the column behaviour of the

direct-formed RHS (DF12) is closer to that of its heat-treated continuous-formed counterpart

(CFH12). On the other hand, Figure 2.17(b) shows that for the three RHS 152x152x6.35, the

column behaviour of the direct-formed RHS (DF24) is closer to that of its non-heat-treated

counterpart (CF24).

Figures 2.18 – 2.20 show the comparisons between the analytical column curves with the

respective column curves for cold-formed and cold-formed stress-relived (CSA Class H)

hollow sections, omitting any resistance or partial safety factor, for CSA S16-09 [CSA 2009],

AISC 360-10 [AISC 2010b], and Eurocode 3 “curve c” [CEN 2010]. It can be seen that (1)

the two direct-formed RHS specimens have analytical column curves close to the CSA “Class

H” curves; (2) among different design curves, the CSA “Class C” curves give the best

predictions for the column behaviours two non-heat-treated continuous-formed RHS

specimens; and (3) all design curves are conservative in predicting the column behaviours of

the two heat-treated continuous-formed RHS specimens. One must bear in mind, however,

that the column design curves in various codes/specifications have further conservatisms and

safety factors included, and relative comparisons between production methods are better

evaluated from Figure 2.17 than Figures 2.18 to 2.20.

34

(a)

(b)

Figure 2.16 Comparisons of overall compressive stress-strain curves from stub column tests

and column models: (a) CF12; (b) CF24

0

100

200

300

400

500

600

700

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain

CF12 stub column test results

CF12 column model results

0

50

100

150

200

250

300

350

400

450

500

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain



35

(a)

(b)

Figure 2.17 Analytical column curves: (a) RHS 152x152x12.7; (b) RHS 152x152x6.35

0.00

0.20

0.40

0.60

0.80

1.00

0 2 4 6 8 10

P/A

f y

L (m)

DF12 CF12 CFH12

0.00

0.20

0.40

0.60

0.80

1.00

0 2 4 6 8 10

P/A

f y

L (m)

DF24 CF24 CFH24

36

(a)

(b)

Figure 2.18 Comparison with column curves as per CSA S16-09, AISC 360-10 and EN 1993-

1-1:2005 for direct-formed RHS: (a) DF12 (RHS 152x152x12.7); (b) DF24 (RHS

152x152x6.35)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

P/A

f y

L (m)

DF12 Class C CSA S16-09

Class H CSA S16-09 AISC 360-10

EN 1993-1-1:2005 curve c

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

P/A

f y

L (m)

DF24 Class C CSA S16-09


EN 1993-1-1:2005 curve c

37

(a)

(b)


1-1:2005 for continuous-formed RHS: (a) CF12 (RHS 152x152x12.7); (b) CF24 (RHS

152x152x6.35)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

P/A

f y

L (m)

CF12 Class C CSA S16-09


EN 1993-1-1:2005 curve c

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

P/A

f y

L (m)

CF24 Class C CSA S16-09


EN 1993-1-1:2005 curve c

38

(a)

(b)


1-1:2005 for continuous-formed plus heat-treated RHS: (a) CFH12 (RHS 152x152x12.7); (b)

CFH24 (RHS 152x152x6.35)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

P/A

f y

L (m)

CFH12 Class C CSA S16-09


EN 1993-1-1:2005 curve c

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6

P/A

f y

L (m)

CFH24 Class C CSA S16-09


EN 1993-1-1:2005 curve c

39

Chapter 3 Charpy V-Notch Impact Toughness

3.1 Summary

This chapter compares the Charpy V-notch (CVN) impact toughness of a total of six cold-

formed RHS manufactured by different methods: (1) direct-forming, (2) continuous-forming,

and (3) continuous-forming plus stress-relieving by heat treatment. A total of 378 CVN

coupons were tested and complete CVN toughness-temperature curves were generated for the

flat face, corner and weld seam regions of the RHS specimens. For RHS with different cross-

sectional geometries and produced by different methods, the CVN toughness-temperature

curves of the flat face and the corner were compared to quantify the decrease of notch

toughness from the flat face to the corner due to uneven degrees of cold-forming, which can

be used by structural designers for the choice of steel material to avoid brittle fracture for

RHS structures.

3.2 Background

The selection of steel for toughness, as specified by international steel product standards and

design specifications, normally requires CVN impact testing of the material. A required

toughness is commonly expressed in terms of the test temperature (e.g. 20 °C) at which a

minimum CVN impact energy value (e.g. 34 J/cm2, which is 27 J for a standard full-sized

CVN coupon) shall be achieved.

As detailed in ASTM A370 [ASTM 2009], a CVN impact test is a dynamic test in which a

notched coupon is struck and broken by a single mechanical impact in a specially designed

apparatus. The measured test value is the energy consumed to break the coupon at the testing

temperature. Testing temperatures other than room temperature are often specified in product

standards. For steel products, the CVN test most commonly uses a standard full-sized

(10x10x55 mm) rectangular beam-type coupon with a machined notch of specified geometry

(2 mm deep). By plotting the energy absorbed by the coupons as a function of the testing

temperatures, as shown in Figure 3.1 [Sedlacek et al. 2008], an energy absorption versus

temperature transition curve can be produced. At temperatures in the upper shelf, CVN

coupons normally fracture in a ductile manner, absorbing relatively large amounts of energy.

At temperatures in the lower shelf, CVN coupons normally fracture in a brittle manner,

absorbing considerably less energy. Within the transition range, the fracture is generally a

mixture of both ductile and brittle fractures. The approximate relationship between the CVN

40

energy-temperature curve and the fracture behaviour of a steel component is also illustrated

in Figure 3.1 [Sedlacek et al. 2008].

Figure 3.1 Approximate relationship between the CVN energy-temperature curve and the

fracture behaviour of a steel component [adapted from Sedlacek et al. 2008]

There are various methods for the determination of the transition temperature [Roe and

Bramfitt 1990; Barsom and Rolfe 1999; Sedlacek et al. 2008; ASTM 2009]. As shown in

Figure 3.1, in this study the Ductile-to-Brittle Transition Temperature (DBTT) is defined as

the temperature corresponding to half of the upper-shelf energy value [Barsom and Rolfe

1999]. The 34 J/cm2 temperature, commonly defined as the beginning of the lower-shelf

region in international steel product standards, is defined as the Nil-Ductility Temperature

(NDT) in this study. Below the NDT, the material is considered to be brittle under impact

loading [Sedlacek et al. 2008].

The modern design of structures made of cold-formed HSS and their welded joints is largely

dependent on the redistribution of stress in the inelastic range. Thus, the selection of HSS for

CVN toughness is critical if low temperature or dynamic loading is a design consideration.

For RHS, previous research [Kosteski et al. 2005] has shown that the CVN toughness around

the cross-section is sometimes highly heterogeneous due to the uneven degree of cold-

forming. However, for the assessment of notch toughness of RHS, steel product standards

[CEN 2006a; CEN 2006b; ISO 2011; ASTM 2013b; CSA 2013] normally require testing of

Charpy V-notch (CVN) coupons taken longitudinally from one of the flat faces not

containing the weld. This tends to lead to the most optimistic notch toughness result for the

cross-section. As discussed previously, there are two common manufacturing methods

Lower shelf Transition

region

Upper shelfCVN

Energy

(J/cm2)

Temperature( C)

σ

ε

σ

ε

σ

ε

34

Ro

om

tem

pe

ratu

re

DBTT

NDT

41

internationally for cold-forming RHS: direct-forming and continuous-forming. For direct-

formed RHS, the cold-working is concentrated at the four corners only. For continuous-

formed RHS, the entire cross-section may contain high degrees of cold-working. Thus, it can

be expected that there is a larger variation of CVN toughness between the flat face and the

corner of direct-formed RHS than for continuous-formed RHS, as cold-forming reduces the

CVN toughness of steel [Sedlacek et al. 2008].

Failures of cold-formed RHS members due to cracking in the corners have been reported

around the world. During the 1994 Northridge, California earthquake, there were incidents

involving damage to RHS bracing (including local buckling, tearing of steel at corners and

complete rupture of braces) due to cracking initiated from the corner as a result of low CVN

toughness [Maranian 2010].

Thus, the use of cold-formed RHS for low temperature or dynamic applications is

questionable if the selection of the member is based on the CVN toughness at the flat face

only, as required by international standards [CEN 2006a; CEN 2006b; ISO 2011; ASTM

2013b; CSA 2013]. Hence, there is a need to incorporate the CVN toughness differences

between the flat face and other locations around the RHS, for various member types and sizes,

so that the selection of RHS can be based on better judgement. In this study, CVN tests were

performed on coupons taken from various locations around the cross-sections of six RHS

specimens with different production histories, to investigate the effects of different cold-

forming methods and heat treatment.

3.3 Effects of chemical composition on material CVN impact toughness

The control of chemical composition is one of the methods to obtain the desired mechanical

properties of structural steels. Product standards normally specify the ranges or limits of

chemical elements which are considered necessary for the proper production of steel

materials covered by the scope of the standards. For example, the chemical requirements for

cold-formed HSS produced to ASTM A500 [ASTM 2013a] are shown in Table 3.1.

Low-carbon structural steels, commonly referred to as mild steels, normally have up to 0.25%

carbon, 0.4% - 0.7% manganese, 0.1% - 0.5% silicon and some residuals of sulphur,

phosphorus, and some other elements. They are not deliberately strengthened by alloying

elements other than carbon and contain manganese for sulphur stabilization and silicon for

42

deoxidation, thus their yield strengths cannot be increased beyond approximately 690 MPa

without significant loss in toughness and ductility [Roe and Bramfitt 1990]. Although the

effects of a single chemical element on the mechanical properties of steel are sometimes

influenced by the effects of other elements, for simplification, the common elements and their

effects on the CVN toughness of steel are usually discussed individually.

Table 3.1 Chemical requirements in ASTM A500 [ASTM 2013a]

Element

Composition, %

Grade A, B, and D Grade C

Heat Analysis Product Analysis Heat Analysis Product Analysis

Carbon, max 0.26 0.3 0.23 0.27

Manganese, max 1.35 1.4 1.35 1.4

Phosphorus, max 0.035 0.045 0.035 0.045

Sulphur, max 0.035 0.045 0.035 0.045

Copper, min 0.2 0.18 0.2 0.18

The CVN impact energy – temperature curves for carbon steels of varying carbon content,

and 0.30 % carbon steels of varying manganese content are shown in Figures 3.2 and 3.3,

respectively [Roe and Bramfitt 1990]. As can be seen in Figure 3.2, for the steels investigated,

the increasing carbon content (from 0.11% to 0.80%) increases the transition temperature

(from -46 °C to 150 °C) and decreases the upper-shelf energy (from 204 J to 33 J) primarily

as a result of the increased strength. Despite the importance of strength, CVN toughness must

also be considered when selecting a structural steel, thus a compromise has to be made.

Manganese is the principal element for increasing toughness in carbon structural steels. As

can be seen in Figure 3.3, for the steels investigated, the increasing manganese content (from

0.30% to 1.55%) decreases the transition temperatures (from 36 °C to -23 °C) while its effect

on the upper-shelf energy is less obvious (increased from 128 J to 141 J). For applications

involving exposure to low temperatures ranging from 0°C to -200°C, low-carbon and high-

nickel steels are typically used. The effect of nickel content is to reduce the ductile-to-brittle

transition temperature, therefore improving the toughness of the steel material at low

temperature. Phosphorous is generally considered an impurity but sometimes is added for

atmospheric corrosion resistance. It increases the strength and hardness of steel but

significantly decreases its ductility and toughness. Silicon is primarily a deoxidizing agent

and it tends to reduce steel ductility. Sulphur is considered an impurity which significantly

reduces the fracture toughness of steels. It is necessary to keep sulphur content low, which is

usually done by adding manganese to form manganese sulphides. However, the MnS

43

inclusion may increase the susceptibility of the steel to lamellar tearing [Roe and Bramfitt

1990]. Investigations on the effects of these chemical elements on the CVN toughness of

various steels have been brought together in ASM Handbook Vol. 1 [Roe and Bramfitt 1990].

Figure 3.2 Variation in CVN impact energy with temperature for carbon steels of varying

carbon content [adapted from Roe and Bramfitt 1990]

Figure 3.3 Variation in CVN impact energy with temperature for 0.30% carbon steels of

varying manganese content [adapted from Roe and Bramfitt 1990]

0

50

100

150

200

250

-100 0 100 200 300

Absorb

ed e

nerg

y (

J)

Temperature ( C)

0.11% C 0.20% C 0.31% C 0.41% C

0.49% C 0.60% C 0.69% C 0.80% C

0

20

40

60

80

100

120

140

160

-100 -50 0 50 100

Absorb

ed e

nerg

y (

J)

Temperature ( C)

1.55% Mn 1.01% Mn 0.39% Mn 0.30% Mn

44

3.4 Toughness anisotropy in HSS

3.4.1 Effect of rolling direction of base plate

Steels can acquire strongly anisotropic microstructures as a result of rolling, leading to the

anisotropy of mechanical properties, particularly notch toughness [Roe and Bramfitt 1990].

For as-rolled low carbon steel plate, previous research [Puzak et al. 1952] has shown that

CVN coupons taken parallel to the rolling direction have better impact toughness than those

taken perpendicular to the rolling direction. Similarly, for cold-formed RHS, previous

research [Kosteski et al. 2005; Stranghöner et al. 2010] found that CVN coupons taken from

the flat face (not containing the weld) in the longitudinal direction of the RHS absorb greater

amounts of energy then their transverse counterparts. This is because the rolling direction of

the steel plate, which is later used to form the RHS, is the same as the longitudinal direction

of the tube.

3.4.2 Effect of notch orientation of CVN coupon

For as-rolled low carbon steel plate, previous investigations [Puzak et al. 1952; Roe and

Bramfitt 1990] have shown that CVN coupons with notches lying in the plane of the plate

surface tend to absorb greater amounts of energy than those with notches perpendicular to the

plate surface. However, the temperature range over which the ductile-to-brittle transition

occurs is the same, regardless of notch orientation. For cold-formed RHS, such comparison is

scarce, and most previous investigations have used CVN coupons with notches lying in the

plane of the RHS surface [Kosteski et al. 2005; Puthli and Herion 2005; Stranghöner et al.

2010; Ritakallio 2012; Stranghöner et al. 2012]. Thus, it is also desirable to study the effect of

different notch orientations within RHS.

3.5 CVN toughness in pertinent HSS product standards

3.5.1 ASTM A500-13 [ASTM 2013a]

The prime American standard for cold-formed HSS [ASTM 2013a] has no notch toughness

requirement, and within its scope it states that …“products manufactured to this specification

may not be suitable for those applications such as dynamically loaded elements in welded

structures, etc., where low-temperature notch-toughness properties may be important”.

Although cold-formed HSS with a notch toughness grade is not commonly produced in North

America, this has not inhibited its widespread use for all structural applications [Kosteski et

al. 2005; Packer et al. 2010].

45

3.5.2 ASTM A1085-13 [ASTM 2013b]

This recent American standard was developed to include cold-formed HSS in dynamically

loaded structures. For the preparation of CVN test coupons, it refers to ASTM A370 [ASTM

2009] which specifies that the CVN coupon be taken longitudinally from one of the flat faces

not containing the weld. When the tube wall thickness is greater than or equal to 11 mm,

standard full-sized coupons (10x10 mm) shall be tested and conform to a minimum CVN

impact energy of 34 J at 4 °C. When the material is less than 11 mm thick, the largest feasible

standard sub-sized coupons shall be tested. Standard sub-sized test coupon sizes are 10x7.5

mm, 10x6.7 mm, 10x5 mm, 10x3.3 mm and 10x2.5 mm. It is specified that the notch shall be

made on the narrow face of the standard sub-sized coupon so that the notch is perpendicular

to the 10 mm wide face [ASTM 2009]. When sub-sized coupons are tested, the minimum

CVN impact energy requirement is to be modified according to Table 3.2, in which the

required impact energy for acceptance is proportional to the net cross-sectional area (i.e. the

area of notched cross-section) of CVN coupons with various sizes.

Table 3.2 Charpy V-notch test acceptance criteria for coupons with different sizes

[ASTM 2009]

Size (mm) Charpy V-notch test acceptance criteria for full-sized coupon (J)

10x10 54 48 41 34 27 22 20 18 16 14 10

Size (mm) Equivalent Charpy V-notch test acceptance criteria for sub-sized coupon (J)

10x7.5 41 35 30 26 20 16 15 14 12 11 7

10x6.7 37 31 27 23 18 15 14 12 11 10 7

10x5 27 24 20 16 14 11 11 8 8 7 5

10x3.3 18 16 14 11 10 7 7 5 5 4 3

10x2.5 14 12 11 8 7 5 5 4 4 3 3

3.5.3 CAN/CSA G40.20-13/G40.21-13 [CSA 2013]

This Canadian structural steel product standard specifies minimum CVN requirements (20 J,

27 J, or 34 J for full-sized specimens) for notch tough base material with different grades

(Grade AT, QT or WT), according to four standard temperature categories (0 °C, -20 °C, -

30 °C or -45 °C). For the preparation and testing of both full-sized and sub-sized CVN

coupons, the Canadian standard also refers to ASTM A370 [ASTM 2009].

3.5.4 EN 10219:2006 [CEN 2006a; CEN 2006b] and ISO 10799-1 [ISO 2011]

In Europe, cold-formed HSS is most commonly produced to Grade S255J2H as per EN

10219. This standard and grade guarantees a minimum CVN impact energy of 27 J at -20 °C

46

from full-sized CVN coupons taken either longitudinally or transversely, at the discretion of

the manufacturer, from one of the flat faces not containing the weld. For HSS with wall

thickness less than 10 mm, EN 10219 [CEN 2006a] specifies that the CVN impact test shall

be carried out using sub-sized coupons of depth less than 10 mm, but not less than 5 mm, and

the minimum CVN energy requirement shall be reduced in direct proportion to the actual net

cross-sectional area of the coupon compared to that of a full-sized CVN coupon. ISO 10799-1

has the same requirements as EN 10219.

3.6 CVN toughness in international design standards

3.6.1 Correlation of CVN toughness to fracture mechanics

Although the CVN impact test is used worldwide across many industries to indicate the

ductile-to-brittle transition of steel materials, the CVN test results cannot be directly applied

in structural design since the potential for brittle fracture of a steel component depends on

multiple factors: (1) steel strength, (2) material thickness, (3) loading rate, (4) minimum

service temperature, (5) material toughness and (6) type of structural element [Roe and

Bramfitt 1990]. Thus, correlations of the CVN impact toughness of steel material to the

fracture toughness of a steel component have been developed using fracture mechanics, and

design criteria based on these correlations have been adopted by international specifications

such as the AASHTO bridge design specification [AASHTO 2007], CSA S16 [CSA 2009],

and EN 1993-1-10 [CEN 2005] to minimize failure of steel components subjected to dynamic

loading. For different service temperatures, these specifications require minimum values of

CVN impact energy at certain testing temperatures.

3.6.2 AASHTO [AASHTO 2007]

The AASHTO bridge design specification [AASHTO 2007] has CVN impact energy

requirements for three service temperatures zones, including Zone 1: -18 °C and above; Zone

2: -18 °C to -34 °C; and Zone 3: -35 °C to -51 °C. For different service temperature zones,

different minimum CVN impact energy values are required for steel plates manufactured as

per various ASTM standards. For example, a carbon steel ASTM A36 plate (thickness less

than 102 mm) would require 34 J for full-sized CVN coupons at the following CVN test

temperatures: 21 °C for Zone 1; 4 °C for Zone 2; and -12°C for Zone 3. The effect of cold-

forming is not explicitly considered in this specification.

47

3.6.3 CSA S16-09 [CSA 2009]

In Annex L of the Canadian steel structures design standard [CSA 2009], the required notch

toughness to prevent brittle fracture is expressed in terms of different testing temperatures

(from 20 °C to -75 °C) and a minimum CVN impact energy (20 J or 27 J) for four different

service temperature ranges (above 0 °C, 0 °C to -30 °C, -30 °C to -60 °C, and below -60 °C).

In general, for notch tough steel material, plates are more readily available than shapes [CSA

2009]. Due to this limited availability of notch tough steel sections, the Canadian standard

permits steel which is not specifically designated as notch-tough (e.g. cold-formed HSS) to be

substituted if the minimum CVN impact energy requirement is satisfied. For the preparation

and testing of both full-sized and sub-sized CVN coupons, the Canadian standard also refers

to ASTM A370 [ASTM 2009]. Similar to the AASHTO specification [AASHTO 2007], the

effect of cold-forming is not explicitly considered in the Canadian standard.

3.6.4 EN 1993-1-10:2005 [CEN 2005]

The design rules for the selection of material for fracture toughness given in EN 1993-1-10

[CEN 2005] are related to welded structures made by plates and rolled sections [Sedlacek et

al. 2008; Feldmann et al. 2012]. Table 2-1 of EN 1993-1-10 [CEN 2005] gives the maximum

permissible values of element thickness to avoid brittle fracture depending on the following

parameters: (1) steel grade and T27J (temperature for a full-sized CVN coupon to absorb an

impact energy of 27 J), (2) service temperature and (3) stress level for the design situation.

Part of the table, for S355 steel with a design stress level of 0.75fy, is shown as Table 3.3.

Table 3.3 Maximum permissible value of element thickness for S355 steel [CEN 2005]

Stress level: σ/fy = 0.75

Steel

grade

Sub

-grade

Charpy test

energy

Service temperature (°C)

10 0 -10 -20 -30 -40 -50

at T (°C) Jmin Maximum permissible thickness (mm)

S355

JR 20 27 40 35 25 20 15 15 10

J0 0 27 60 50 40 35 25 20 15

J2 -20 27 90 75 60 50 40 35 25

K2,M,N -20 40 110 90 75 60 50 40 35

ML,NL -50 27 155 130 110 90 75 60 50

Since Table 2-1 of EN 1993-1-10 [CEN 2005] is for non-cold-formed steel, to account for the

reduction of toughness from the cold-forming of plates, EN 1993-1-10 specifies that the

tabulated values may be used by altering the service temperature by deducting ∆Tcf (°C) (i.e.

48

the maximum permissible element thickness decreases as the degree of cold-forming

increases), where

∆Tcf = 3 x DCF (3-1)

in which DCF = degree of cold-forming (%), and ∆Tcf = adjustment for the degree of cold-

forming (°C).

The method for determination of DCF is not included in EN 1993-1-10 [CEN 2005]. It was

recommended in the Commentary and Worked Examples to EN 1993-1-10 [Sedlacek et al.

2008] that DCF due to cold-bending can be calculated using Eq. 3-2. [Sedlacek et al. 2008]

suggest that ∆Tcf equals zero for DCF ≤ 2% and ∆Tcf is constant (45°C) for DCF ≥ 15%. The

development and validity range of Eq. 3-1 are further discussed in Section 3.7.

DCF = εmax – 0.02 (3-2)

in which εmax is the maximum plastic strain (%) on the surface of the bent region, which can

be calculated using Figure 3.4.

Figure 3.4 Determination of maximum plastic strain due to cold-bending

[adapted from Sedlacek et al. 2008]

3.7 Previous toughness investigations on cold-formed products

As documented by the German Iron and Steel Institute (VDEh) [VDEh 1992], early

investigations on the effect of cold-forming on the toughness of various steels were

conducted by performing German DVM-notch impact tests on pre-strained (constant through

thickness) steels. It was concluded that, for pre-strain up to 10%, the T27J-temperature (for

Determination of maximum plastic strain εmax

𝜀𝑚𝑎𝑥 =𝑡

2𝑟𝑖 + 𝑡

Determination of εeff

t (mm) Plastic strain distribution εeff

≥ 20

𝜀𝑚𝑎𝑥 1 10

𝑡

< 20

≥ 10

𝜀𝑚𝑎𝑥 𝑡

40+ 20 𝑡 2

40𝑡

< 10


20

εmax

ri

1

t

ri

εmax εmax εmax

t t t

10

10<10

εmax εmax εmax

t t t

10

10<10

εmax εmax εmax

t t t

10

10<10

49

full-sized 10x10 coupons) increases linearly as the pre-strain increases, and a 10% pre-strain

leads to an increase in the transition temperature of approximately 30 °C for various types of

steel materials. For S355J2 steel, which is the grade most commonly used to produce cold-

formed HSS in Europe, CVN impact tests were performed. The changes in CVN impact

energy and T27J-temperature with various degrees of cold-forming (i.e. pre-straining) are

shown in Figures 3.5 and 3.6, respectively. It can be seen that both changes become

insignificant with a degree of cold-forming (DCF) higher than 15% [VDEh 1992]. The design

rule in EN 1993-1-10 [CEN 2005] for the reduction of toughness due to cold-forming of steel

plates (i.e. Eq. 3-1) was developed based on these investigations [VDEh 1992]. However, it

shall be noted that the pre-strains applied in the above research were constant through the

thickness of the coupons, while for HSS the through-thickness strain input during production

is non-uniform.

Figure 3.5 Change of Charpy V-notch impact energy due to cold-forming, for S355J2 steel

[adapted from VDEh 1992]

For research on the notch toughness of cold-formed hollow sections, an early investigation by

[Dagg et al. 1989] studied the CVN toughness difference between coupons sampled from the

flat face (not containing the weld) and the corner of Australian cold-formed RHS

203x203x9.5 and RHS 76x76x6.3. Sub-sized 5 x 10 mm CVN coupons were machined in the

0

40

80

120

160

200

-100 -75 -50 -25 0 25 50

Energ

y (J

)

Temperature (°C)

DCF=0 DCF=5% DCF=7%

DCF=10% DCF=15% DCF=20%

DCF=30%

50

longitudinal direction of the RHS and notched on the narrow face so that the notch was

perpendicular to the RHS surface. Little difference was observed between the energy-

temperature results of CVN coupons sampled from the flat face versus the corner for both

RHS, regardless of cross-sectional geometry. Although there was no information regarding

the cold-forming method used to produce the above RHS specimens, it is likely that the two

tubes were continuous-formed as this is the normal production method in Australia.

Figure 3.6 Change of T27J-temperature due to cold-forming, for S355J2 steel

[adapted from VDEh 1992]

Later, [Soininen 1996] also conducted an investigation on the CVN toughness of cold-formed

European RHS with different cross-sectional geometries. All tubes were continuous-formed.

The CVN coupons were sampled from the following locations and delivery states: (1) base

material with CVN coupons longitudinal and transverse to the rolling direction of the coil; (2)

flat face of the RHS with CVN coupons longitudinal and transverse to the rolling direction of

the coil; (3) longitudinal and transverse from the flat face of the RHS after artificial ageing at

250 °C for 30 minutes; and (4) longitudinal from the corner of the RHS, in the delivery

condition and after artificial ageing at 250 °C for 30 minutes. For RHS with wall thickness

more than 10 mm, full-sized CVN coupons were made. For RHS with wall thickness less

than 10 mm, sub-sized CVN coupons were made using the full wall thickness. All notches

-120

-90

-60

-30

0

0% 5% 10% 15% 20% 25% 30% 35%

T27J ( C

)

Degree of cold-forming

51

were made perpendicular to the plane of the RHS surfaces. The 34 J/cm2-temperatures (e.g.

27 J for full-sized 10x10 mm coupon with a notch depth of 2 mm) were determined based on

the CVN test results. It was reported that the transverse coupons had, on average, 19°C higher

34 J/cm2-temperatures both in the base material and in the flat face of the RHS, compared to

the longitudinal coupons. The average 34 J/cm2-temperatures of longitudinal coupons from

the flat face and corner of the RHS were 15 °C and 23 °C higher than those of longitudinal

coupons from the base material. Similar to [Dagg et al. 1989], [Soininen 1996] reported a

relatively small difference (8 °C) between the average 34 J/cm2-temperatures of the flat face

and corner of the tested RHS. One of the principal conclusions of [Soininen 1996] was that in

order to fulfil a certain Charpy toughness requirement in the finished cold-formed RHS, at a

certain temperature, the base material had to fulfil the same notch toughness at a temperature

at least 30 °C lower.

However, as discussed previously, for continuous-formed RHS the plate is first bent into a

circular tube before further flattening it into the rectangular shape, thus the degree of cold-

forming to the flat face decreases as the wall slenderness (Bnom/tnom) ratio increases, and the

differences in the mechanical behaviours between the flat face and corner become larger as

the Bnom/tnom ratio of the tube increases. Hence, it is not logical to average the transition

temperatures for RHS with different cross-sectional geometries.

The Australian and Finnish RHS specimens studied in the above investigations are not

necessarily representative of those produced in other parts of the world. Thus, [Kosteski et al.

2005] conducted a study of the CVN toughness of various RHS manufactured in North

America, South America, and Europe. The specimens included hot-formed RHS, cold-formed

RHS, and stress-relieved cold-formed RHS. CVN impact tests were performed on CVN

coupons with different orientations (longitudinal versus transverse), different cross-section

location (flat face, corner, and weld seam), and different notched face exposures (interior face

of RHS versus exterior face). In total, 557 CVN coupons were tested. All coupons had the

notch parallel to the tube surface. It was found by [Kosteski et al. 2005] that: (1) hot-formed

RHS has excellent CVN toughness at all locations around the cross-section and in both the

longitudinal and transverse directions; (2) the European cold-formed RHS generally have

better CVN toughness than the North American ones; (3) for cold-formed RHS, there is little

improvement in CVN toughness achieved by stress-relieving the section by heat treatment

according to CSA “Class H” requirements [CSA 2013]; and (4) for cold-formed RHS,

transverse CVN coupons from the weld regions have a particularly poor CVN toughness.

52

Thus, [Kosteski et al. 2005] concluded that to guarantee high values of inherent toughness at

any location or orientation in the cross-section, hot-formed RHS are more reliable. The

excellent CVN toughness of hot-formed RHS has again been demonstrated by [Stranghöner

et al. 2012].

Although European cold-formed HSS produced to EN10219 [CEN 2006a; CEN 2006b] in

general exhibit good toughness properties [Kosteski et al. 2005; Ritakallio 2012; Ritakallio

2013], limits in applying the toughness-related rules for the choice of steel material in EN

1993-1-10 [CEN 2005] to cold-formed HSS still constitute barriers to their utilization.

According to [Feldmann et al. 2012], the design rules in EN 1993-1-10 [CEN 2005] may not

be sufficient for the specific case of cold-formed HSS due to the high degrees of cold-

forming since the design rules in EN 1993-1-10 are related to welded structures made by

plates and rolled section (i.e. not severely cold-formed). Also, Eq. 3-1 is limited by the

following factors: (1) the linear relation only applies to DCF-values below 15%; and (2) it

assumes an equal distribution of degree of cold-forming across the thickness of the material

since, as discussed at the beginning of this section, the equation was developed based on the

notch impact test results of uniformly pre-strained specimens, while in the case of cold-

forming of HSS by bending the strain distribution varies over the cross-section and contains

both tensile and compressive strains.

In order to include cold-formed HSS in the rules for the choice of steel to avoid brittle

fracture in EN 1993-1-10 [CEN 2005], an amendment was proposed by [Feldmann et al.

2012], in which an approach was developed to consider the reduction in material toughness in

the bent areas of HSS due to the cold-forming process. For the degradation of these toughness

properties an appropriate temperature shift ΔTcf was derived for both circular and rectangular

hollow sections. In order to guarantee the proper application of this temperature shift, Table

2.1 in EN 1993-1-10 (part of which is shown as Table 3.3 in this thesis) was extended to

lower temperatures down to -120 °C. Part of the extended table, for S355 steel with a design

stress level of 0.75fy, is shown here as Table 3.4. It was suggested by [Feldmann et al. 2012]

that:

(1) since the extended table is intended for structural components made of steel plate and

rolled sections (i.e. non-cold-formed steels), it could be used without a temperature shift

when determining the maximum permissible wall thickness of hot-formed HSS, since it is

53

believed that the toughness properties in the flat face and corner of hot-finished HSS are close

to its base material.

Table 3.4 Maximum permissible value of element thickness for S355 steel – Table 2.1 of EN

1993-1-10:2005 extended [Feldmann et al. 2012]

Stress level: σ/fy = 0.75

Steel grade Sub-grade Charpy energy


10 0 -10 -20 -30 -40 -50


S355

JR 20 27 43 35 29 24 20 16 14

J0 0 27 63 52 43 35 29 24 20

J2 -20 27 92 76 63 52 43 35 29

K2,M,N -20 40 109 91 75 62 51 42 35

ML,NL -50 27 155 131 110 92 76 63 52

Steel grade Sub-grade Charpy energy


-60 -70 -80 -90 -100 -110 -120


S355

JR 20 27 11 10 8 7 6 5 5

J0 0 27 16 14 11 10 8 7 6

J2 -20 27 24 20 16 14 11 10 8

K2,M,N -20 40 28 23 19 16 13 11 9

ML,NL -50 27 43 35 29 24 20 16 14

Note: Values based upon slightly different parameters to Table 3.3.

(2) when determining the maximum permissible wall thickness of structural components

made of cold-formed HSS, the extended table could be used with a shift of the service

temperature to allow for the reduction in material toughness due to cold-forming (i.e. the

maximum permissible thickness decreases as the degree of cold-forming increases). The shift

in service temperature of the structural component is considered to be the same as the shift of

the T27J-temperature due to cold-forming.

It is assumed by [Feldmann et al. 2012] that the effect of coiling and uncoiling of the base

material is minor, hence the steel plate used for production of cold-formed HSS is considered

to be in a non-cold-formed state. Thus, the degree of cold-forming contained in the cross-

section of the CVN coupon can be estimated based on the cross-sectional dimensions of the

cold-formed HSS and the sampling location of the CVN coupon. Similar to Eq. 3-1, for the

reduction of toughness from cold-forming plates into HSS, Table 3.4 can be used by altering

the service temperature by deducting ∆Tcf (°C), where:

54

∆Tcf = 3 x εeff ≤ 45 °C (3-3)

in which εeff = the average value of the plastic strain (%) in the net section of the CVN

coupon, with the longitudinal position taken adjacent to the surface of the HSS, which is the

most severely cold-worked region; and ∆Tcf = adjustment for the degree of cold forming (°C).

The temperature shift is limited to 45°C since, as discussed previously, ∆Tcf equals zero for

DCF ≤ 2% and ∆Tcf is constant for DCF ≥ 15% [Sedlacek et al. 2008].

Note: The shaded areas represent the cross-section of a CVN coupon

Figure 3.7 Determination of εeff in the bent region of HSS

[adapted from Feldmann et al. 2012]

For cold-formed Circular Hollow Sections (CHS), ∆Tcf was calculated by assuming that: (1)

tensile and compressive strains have equal effects on toughness; and (2) the effect of unequal

Determination of maximum plastic strain εmax

𝜀𝑚𝑎𝑥 =𝑡

2𝑟𝑖 + 𝑡

Determination of εeff

t (mm) Plastic strain distribution εeff

≥ 20

𝜀𝑚𝑎𝑥 1 10

𝑡

< 20

≥ 10


40+ 20 𝑡 2

40𝑡

< 10


20

εmax

ri

1

t

ri

εmax εmax εmax

t t t

10

10<10

εmax εmax εmax

t t t

10

10<10

εmax εmax εmax

t t t

10

10<10

55

strain distribution over the net cross-section of the CVN coupon is equivalent to the effect of

the mean strain-value of that distribution, εeff, which can be determined based on the

geometry of the cross-section and the sampling location of the CVN coupon, using Figure 3.7.

The derivations of the equations in Figure 3.7 are shown in Appendix B.1. As a conclusion

from the calculation method, [Feldmann et al. 2012] suggested that for CHS with external

radius-to-thickness ratio greater than 16, the cold-forming effects may be neglected, and the

maximum ∆Tcf may be taken as 20 °C.

For cold-formed RHS, εeff needs to be determined based on the corner geometry only since it

is the most severely cold-worked area. Following the same assumptions as CHS, εeff can be

determined using Figure 3.7. Based on the relationship between the inside radius and the wall

thickness for RHS corners according to EN 10219 [CEN 2006b], the conclusion from this

approach is that, for cold-formed RHS, the temperature shift ΔTcf is about 35 °C for wall

thickness ≤ 16 mm and 45 °C for wall thickness > 16 mm. This conclusion is consistent with

the experimental results (all RHS specimens are continuous-formed) reported by [Feldmann

et al. 2012] and has been implemented in reference tables [Puthli and Packer 2013]. However,

as stated in the JRC report [Feldmann et al. 2012], since the tests have been carried out

mainly with HSS made of EN 10219 S355J2H material, the conclusions refer to this material

type only (i.e. are not necessarily applicable to HSS produced in North America).

It can be seen from the above studies that research on the effects of cold-forming and heat

treatment on the CVN impact toughness of North American cold-formed RHS is still

insufficient and none of the previous investigations have included direct-formed RHS.

3.8 RHS specimens and chemical compositions

In this chapter, CVN impact tests were performed on RHS specimens DF12, DF24, CF12,

CFH12, CF24, and CFH24 in Table 2.1. The chemical compositions of the six RHS

specimens are listed in Table 3.5. The chemical analysis (Optical Emission Vacuum

Spectrometric Analysis) was performed at Acuren Group Inc. (2421 Drew Road, Mississauga,

Ontario, L5S 1A1). The effects of the listed chemical elements on the CVN toughness of low-

carbon structural steel, according to [Roe and Bramfitt 1990; Maranian 2010] are also shown

in Table 3.5.

56

Table 3.5 Chemical compositions of RHS specimens and effects of chemical elements on the

CVN toughness of low-carbon structural steel [Roe and Bramfitt 1990; Maranian 2010]

Nominal

sizes 152x152x12.7 mm 152x152x6.35 mm

RHS

specimen DF12

CF12 &

CFH12 DF24

CF24 &

CFH24

Ch

emic

al e

lem

ents

an

d t

he

effe

cts

of

hig

h a

mo

un

ts o

n C

VN

to

ug

hnes

s

of

low

-car

bo

n s

tru

ctu

ral

stee

l

No

te:

“+ +

” =

in

crea

ses

it s

ign

ific

antl

y,

“+”

= i

ncr

ease

s it

mo

der

atel

y,

“– –

” =

dec

reas

es i

t si

gn

ific

antl

y,

“–”

= d

ecre

ases

it

mo

der

atel

y,

“~”

= h

as a

neg

lig

ible

eff

ect

C – –

Ch

emic

al a

nal

ysi

s re

sult

s (%

by

wei

gh

t)

0.066 0.049 0.058 0.182

Si – 0.052 0.353 0.023 0.013

Mn + + 0.715 0.871 0.647 0.761

P – – 0.013 0.016 0.01 0.009

S – – <0.005 0.005 0.015 0.008

Cr ~ 0.095 0.447 0.058 0.035

Mo – 0.021 0.018 0.019 0.006

Ni + 0.068 0.173 0.062 0.008

Al + 0.025 0.014 0.026 0.03

Cu ~ 0.137 0.36 0.136 0.035

Nb + 0.023 0.004 0.025 0.006

Ti + <0.005 <0.005 <0.005 <0.005

V + <0.005 0.034 <0.005 <0.005

Sn – 0.017 <0.005 0.021 <0.005

As – 0.006 0.006 0.006 0.004

Zr + <0.005 <0.005 <0.005 <0.005

Ca + 0.001 0.002 0.001 <0.001

Sb + 0.003 0.003 0.005 0.003

B + <0.0005 <0.0005 <0.0005 <0.0005


The objective of the CVN impact test program was to generate the complete toughness-

temperature transition curves for CVN coupons sampled from various cross-section locations

(flat face, corner and weld seam) with different coupon orientations (longitudinal and

transverse) and notch face exposures (in the plane of, and perpendicular to, the RHS surface),

for the six North American RHS. The cutting locations and orientations of the CVN coupons

are summarized in Table 3.6, and illustrated in Figure 3.8.

For the three RHS with a nominal wall thickness of 6.35 mm (DF24, CF24 and CFH24), 162

sub-sized coupons (10x3.3x55 mm) with notch perpendicular to the RHS surface were made

since, as specified in ASTM A370 [ASTM 2009], due to the fact that the width of the sub-

sized coupon is reduced, the sub-sized coupon has to be notched on the narrow side to have

enough cross-sectional area. As discussed in Section 3.4.2, it has been shown by previous

investigations [Puzak et al. 1952; Roe and Bramfitt 1990] that different notch orientations

57

result in different CVN energy absorption levels but the same DBTT. For the three RHS with

a nominal wall thickness of 12.7 mm (DF12, CF12 and CF12), 216 full-sized coupons

(10x10x55 mm) were made as per ASTM A370 [ASTM 2009] with notches lying in the

plane of the RHS surface as most of the previous investigations [Kosteski et al. 2005; Puthli

and Herion 2005; Stranghöner et al. 2010; Ritakallio 2012; Stranghöner et al. 2012] used

CVN coupons with such notch orientations.

Table 3.6 Cutting locations and orientations of CVN coupons

Location Full-sized coupons Sub-sized coupons

A Flat face not containing the weld,

longitudinal, notch facing outside surface

Flat face not containing the weld,

longitudinal, notch through thickness

B Corner, longitudinal, notch facing

outside surface

Corner, longitudinal, notch through

thickness

C Flat face containing the weld, transverse,

notch facing outside surface

Flat face containing the weld, transverse,

notch through thickness

D Corner, longitudinal, notch facing inside

surface N/A

(a) (b)

Figure 3.8 Cutting locations and orientations of CVN coupons: (a) full-sized coupons; (b)

sub-sized coupons

The CVN coupons from DF12, CF12 and CFH12 were tested using a “Riehle” pendulum

impact tester with a 325 J direct-reading scale. The CVN coupons from DF24, CF24 and

CFH24 were tested using a “Tinius Olsen” pendulum impact tester with a 406 J direct-

reading scale. Before testing, 20 self-verification coupons (10 low-energy ones and 10 high-

energy ones) supplied by the National Institute of Standards and Technology (NIST) were

weld

seam

D B

A

CB

weld

seam

A

C

weld

seam

D B

A

CB

weld

seam

A

C

58

used to check the calibrations of both testing machines and the results were consistent with

the expected values provided by NIST.

For DF12, CF12 and CFH12, the CVN specimens were cooled by a freezer and an additional

thermometer was used to ensure the accuracy of the desired testing temperatures for the CVN

specimens. For DF24, CF24 and CFH24, the specimens were thermally conditioned in a dry

ice-methanol liquid coolant mixture for a sufficiently long time before being tested. A

thermometer was used to monitor the temperature of the dry ice-methanol mixture. The dry

ice, which has an ambient temperature of -87.5°C, was proportioned by trial and error in the

methanol bath to achieve the desired testing temperatures for the CVN specimens. The test

setup is shown in Figure 3.9.

Figure 3.9 CVN impact test setup

The CVN impact tests were performed in accordance with ASTM A370 [ASTM 2009]. Prior

to the tests, the coupons and the tongs for handling coupons were held in the conditioning

medium for a sufficiently long time (at least 5 minutes in liquid media and 30 minutes in

gaseous media as per ASTM A370 [ASTM 2009]) to ensure that the intended testing

temperature was reached in both of them. During the tests, the coupon was carefully centered

in the anvil and the pendulum was released to break the coupon. For all tests, the pendulum

was released within 5 seconds after removing the coupon from the conditioning medium.

59

Table 3.7 CVN test results: (a) full-sized coupons; (b) sub-sized coupons

(a)

Energy absorption (J) for full-sized CVN coupons (10x10x55 mm)

RHS DF12 CF12 CFH12

Temperature (°C)

A flat

B corner

C weld

D corner

A flat

B corner

C weld

D corner

A flat

B corner

C weld

D corner

20 - 225.7 107.1 269.8 265.7 240.0 127.4 277.3 276.6 214.2 200.7 283.4

20 - 244.0 116.6 267.1 264.4 273.9 161.3 269.8 292.9 193.9 130.2 282.0

20 - 271.2 242.0 273.9 257.6 265.7 146.4 252.2 260.3 197.9 81.3 273.9

10 - 203.4 254.2 271.2 258.3 234.6 134.2 282.0 238.6 192.5 83.4 168.8

10 - 248.8 21.7 268.4 296.9 223.7 136.9 151.8 265.7 203.4 40.7 127.4

10 - 265.7 276.6 279.3 296.9 233.2 287.4 271.2 226.4 181.7 48.8 218.3

0 - 254.9 253.5 276.6 283.4 233.2 135.6 211.5 187.1 173.5 67.8 119.3

0 - 272.5 219.6 282.0 299.6 251.0 123.4 202.0 287.4 179.6 28.5 174.9

0 - 246.8 275.2 265.7 287.4 212.9 120.7 276.6 216.9 149.1 92.2 235.9

-10 - 232.5 292.2 212.0 180.3 216.9 116.6 116.6 126.1 179.0 89.5 103.0

-10 - 250.8 263.0 219.1 188.5 202.0 100.3 43.4 72.5 180.3 15.6 25.8

-10 - 210.1 29.8 216.9 162.7 203.4 105.8 52.9 21.0 160.0 20.3 22.4

-20 274.5 132.9 12.2 108.5 62.4 141.0 135.6 20.3 16.3 119.3 16.3 12.2

-20 286.8 162.7 40.7 103.0 63.7 132.9 54.2 16.3 35.3 59.7 13.6 16.3

-20 297.6 127.4 12.2 105.8 58.3 119.3 107.1 46.1 29.8 173.5 81.3 24.4

-30 134.2 21.7 17.6 61.8 12.9 48.8 32.5 48.8 19.0 25.8 81.3 29.8

-30 273.9 14.9 5.4 9.8 75.9 51.5 94.9 12.2 33.9 15.6 29.8 21.7

-30 284.7 6.8 100.3 28.2 51.5 10.8 38.0 13.6 19.0 15.6 30.5 23.7

Note: CVN coupons from the flat face (location A) of DF2 did not fully break at 20 °C, 10 °C, 0 °C and -10 °C

(b)

Energy absorption (J) for sub-sized CVN coupons (10x3.3x55 mm)

RHS DF24 CF24 CFH24

Temperature (°C)

A flat

B corner

C weld

A flat

B corner

C weld

A flat

B corner

C weld

20 44.6 37.7 33.7 34.9 34.5 21.0 39.4 31.0 16.7

20 44.7 37.3 35.6 37.6 30.4 16.1 42.1 35.5 17.0

20 49.5 35.1 34.6 37.1 33.5 18.6 35.2 36.1 19.8

-15 34.6 39.5 38.5 38.2 30.9 7.3 34.8 36.3 19.4

-15 45.7 38.1 34.3 38.4 32.5 7.3 38.8 32.8 17.5

-15 47.9 40.4 34.0 39.1 31.2 8.0 37.4 32.7 18.4

-30 42.3 39.5 40.3 35.2 35.1 7.1 43.0 32.7 16.0

-30 42.6 39.3 32.4 36.4 24.7 15.2 34.3 33.6 16.1

-30 46.4 40.5 38.3 38.0 34.7 13.6 33.5 26.5 19.5

-45 44.9 34.7 33.6 35.4 4.0 4.6 32.9 30.3 18.7

-45 41.8 38.7 35.7 34.5 20.3 4.4 32.3 32.1 17.0

-45 44.0 34.6 36.5 33.9 20.9 5.5 30.3 30.8 16.4

-60 40.2 28.5 31.3 22.0 2.6 2.8 24.7 2.4 8.8

-60 42.9 32.4 29.4 27.8 2.5 4.9 23.9 2.0 4.1

-60 41.3 34.5 34.2 20.9 1.6 6.1 26.2 2.2 8.6

-75 40.9 24.7 24.5 1.4 1.4 2.8 2.9 1.9 1.7

-75 38.8 28.0 23.1 3.1 1.7 2.0 1.9 2.2 2.4

-75 42.9 24.4 22.8 2.2 1.7 2.3 6.6 2.5 3.5

60

Three replicate specimens were tested at each target temperature. All test results are listed in

Table 3.7. The test results in Table 3.7 are normalized and plotted against the testing

temperatures in Figures 3.11 – 3.16. CVN coupons from the flat face (location A) of DF12

did not fully break at 20 °C, 10 °C, 0 °C and -10 °C, therefore the “Riehle” testing machine

capacity (325 J / 0.8 cm2 = 406 J/cm

2) was used to plot these points.


The evaluation of the data in Figures 3.11 – 3.16 is performed by using Eq. 3-4, a hyperbolic

tangent “tanh” function commonly used for assessment of CVN data [Feldmann et al. 2012].

Research has shown that among different curve fitting methods, the “tanh” function gives the

best approximation of the mean of the CVN data in the upper-shelf, the lower-shelf and the

transition regions [Cao et al. 2012]. As shown in Figure 3.10, the “tanh” function is a

convenient S-shaped curve whereby the point of contra-curvature (KV = half of upper-shelf

energy) can be taken to represent the DBTT.

[

] (3-4)

where KV is the absorbed energy (J), T is the temperature (°C), and A, B and C are fitting

coefficients.

Figure 3.10 Illustration of “tanh” function

Curve-fitting is performed using a non-linear least squares method. The best fit lines for the

groups of data are shown in Figures 3.11 – 3.16. As shown in Figure 3.11, some data points

for location C (weld) of DF12 have very low CVN toughness possibly due to very small

welding defects, which are inherent in welding processes. The four circled data points were

considered as outliers and were not used when determining the best fit line. The normalized

KV

(J)

T (°C)

tanh𝑥 =e𝑥 e 𝑥

e𝑥 + e 𝑥

DBTT

Upper-shelf

Lower-shelf

KV = A [1 + tanh T B

C ]

where x =T B

C

61

upper-shelf energy (KVus), DBTT and NDT for all flat face and corner curves were

determined and shown in Table 3.8 and Figures 3.17 – 3.19.

Figure 3.11 CVN impact energy-temperature curves for DF12

Figure 3.12 CVN impact energy-temperature curves for CF12

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

D (corner)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

Possibly

due to

very

small

welding defects

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

D (corner)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

D (corner)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

62

Figure 3.13 CVN impact energy-temperature curves for CFH12

Figure 3.14 CVN impact energy-temperature curves for DF24

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

D (corner)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

63

Figure 3.15 CVN impact energy-temperature curves for CF24

Figure 3.16 CVN impact energy-temperature curves for CFH24

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

-90 -60 -30 0 30

0

100

200

300

400

A (flat)

B (corner)

C (weld)

No

rma

lize

d E

ne

rgy (

J/c

m2)

Temperature (°C)

64

Figure 3.17 Change of DBTT from flat face to corner for all RHS specimens

Figure 3.18 Change of NDT from flat face to corner for all RHS specimens

-140

-120

-100

-80

-60

-40

-20

0

A (flat) B (corner) D (corner)

DB

TT

( C

)

DF12 CF12 CFH12 DF24 CF24 CFH24

-160

-140

-120

-100

-80

-60

-40

-20

0


ND

T ( C

)


65

Figure 3.19 Normalized KVus (J/cm2) for all RHS specimens

Table 3.8 Normalized upper-shelf energy (KVus), ductile-to-brittle transition temperature

(DBTT) and nil-ductility temperature (NDT) of all RHS specimens

DF12


KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

406 -38 -56 310 -21 -28 345 -17 -30

CF12


KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

356 -15 -25 300 -22 -33 314 -7 -15

CFH12


KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

305 -8 -15 233 -22 -29 335 0 -22

0

50

100

150

200

250

300

350

400

450

A (f lat) B (corner) D (corner)


No

rmaliz

ed

Kv

us

(J/c

m2)

66

Table 3.8 (continued)

DF24

A (flat) B (corner)

N/A* KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

130 -123 -134 112 -85 -97

CF24

A (flat) B (corner)

N/A* KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

112 -60 -67 100 -45 -48

CFH24

A (flat) B (corner)

N/A* KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

KVus

(J/cm2)

DBTT

(°C)

NDT

(°C)

112 -63 -69 103 -53 -54

* N/A = not available, because no coupons were machined from location D of the DF24, CF24 and CFH24.

3.10.1 Effects of chemical composition

As discussed previously, for the same nominal size, the corners and their nearby regions of

both direct-formed and continuous-formed RHS should theoretically contain similar amounts

of cold-working which are primarily influenced by the corner bending radius. Hence, in order

to study the effects of chemical composition on the CVN toughness of RHS, the corner test

results of RHS specimen DF12 (152x152x12.7 mm) were compared to those of CF12

(152x152x12.7 mm), and the corner test results of DF24 (152x152x6.35 mm) were compared

to those of CF24 (152x152x6.35 mm), to exclude the effect of cold-forming.

According to the effects of chemical elements on the CVN toughness of low-carbon structural

steel shown in Table 3.5 [Roe and Bramfitt 1990; Maranian 2010], it can be deduced based

on the test results that:

(1) As can be seen in Figures 3.17 – 3.19, the corners of CF12 and DF12 have similar CVN

toughness properties, including DBTT, NDT and KVus. Comparing the chemistry of CF12

and DF12 in Table 3.5, although CF12 has a much higher silicon content than DF12 (0.353%

versus 0.052%), the detrimental effect of silicon is offset by the relatively higher contents of

the beneficial elements in CF12 than those in DF12, including manganese (0.871% versus

0.715%), nickel (0.173% versus 0.068%), and vanadium (0.034% versus <0.005%).

67

(2) As discussed previously, the carbon content has the most significant effect on the CVN

toughness of steel. As can be seen in Table 3.5, the carbon content of DF24 (0.058%) is much

lower than that of CF24 (0.182%), hence the DBTT and NDT of the corner of DF24 is much

lower than those of CF24 in Figures 3.17 and 3.18, which is consistent with the findings in

Figure 3.2.

3.10.2 Effects of cold-forming and heat-treatment

For the effects of cold-forming and heat-treatment on the CVN toughness of RHS, the

following deductions were made based on the test results:

(1) Comparing CF12 to CFH12, and CF24 to CFH24 in Figures 3.17 – 3.18, it can be seen

that stress-relieving the section by heat treatment in accordance with Canadian standards for

“Class H” finishing [CSA 2013] results in little, if any, change in the DBTT, NDT and KVus,

which is consistent with the test results by [Kosteski et al. 2005].

(2) For CF12 and CFH12 in Figures 3.17 and 3.18, it can be seen that for thick-walled

continuous-formed RHS (Bnom/tnom = 12), the DBTT and NDT of the flat face are not

significantly different than those of the corner, which is consistent with the test results by

[Soininen 1996; Kosteski et al. 2005], as the whole cross-section is severely cold-formed

during production.

(3) For CF24 and CFH24 in Figures 3.17 and 3.18, it can be seen that for the thin-walled

continuous-formed RHS (Bnom/tnom = 24), the DBTT and NDT of the flat face are

approximately 15 °C and 20 °C lower than those of the corner, since the amount of cold-

forming to the flat face decreases as the Bnom/tnom ratio increases during the continuous-

forming process, leading to better CVN toughness.

(4) For DF12 in Figures 3.17 and 3.18, it can be seen that for the thick-walled direct-formed

RHS (Bnom/tnom = 12), the DBTT and NDT of the flat face are approximately 20 °C and

30 °C lower than those of the corner. The spread is larger compared to its continuous-formed

counterparts (CF12 and CFH12) because theoretically the flat face of DF12 was not cold-

formed during the direct-forming process.

(5) For DF24 in Figures 3.17 and 3.18, it can be seen that for the thin-walled direct-formed

RHS (Bnom/tnom = 24), both the DBTT and NDT of the flat face are approximately 40 °C

68

lower than those of the corner. Again, the spread is larger compared to its continuous-formed

counterparts (CF24 and CFH24).

(6) As shown in Figure 3.19, the CVN coupons with notch lying in the plane of the RHS

surface (DF12, CF12 and CFH12) result in much higher normalized KVus-values than those

with notch perpendicular to the RHS surface (DF24, CF24 and CFH24), which is consistent

with previous investigations on as-rolled steel plate [Puzak et al. 1952; Roe and Bramfitt

1990].

(7) Figures 3.11 – 3.16 show that the weld seam region has the lowest CVN toughness around

the cross-section for all RHS specimens tested. Thus, for dynamically loaded connections,

fabricated from cold-formed HSS, it is preferable to keep the weld seam region away from

the connecting face, as suggested by [Kosteski et al. 2005].

Using the measured cross-sectional geometries of the six RHS specimens listed in Table 3.9,

the analytical ∆Tcf-values from the flat face to the corner due to the extra amount of cold-

forming were determined and are listed in Table 3.10, using the approach proposed by

[Feldmann et al. 2012]. The equations in Figure 3.7 were slightly modified for the calculation

since the CVN coupons in this study were taken at the mid-thickness of the tube wall. For the

continuous-formed RHS specimens (CF12, CFH12, CF24, CFH24), the temperature shift

from the coil plate to the flat face and the temperature shift from the coil plate to the corner

were both determined, and the difference between the two temperature shifts was taken as the

analytical ∆Tcf-value from the flat face to the corner due to the extra amount of cold-working.

For the direct-formed RHS (DF12 and DF24), the temperature shift from the coil plate to the

corner was taken as the ∆Tcf-value from the flat face to the corner. The calculations for all the

analytical ∆Tcf-values are shown in Appendix B.2. The analytical ∆Tcf-values for the all six

RHS specimens are compared to the experimentally obtained ∆Tcf-values (i.e. difference

between DBTTs (or NDTs) of the flat face and the corner) in Table 3.10. It can be seen that,

for the RHS specimens investigated in this study, the approach proposed by [Feldmann et al.

2012] gives safe estimations for the thick-walled RHS (DF12, CF12 and CFH12), but unsafe

estimations for the thin-walled RHS (DF24, CF24 and CFH24). This (unsafe) difference is

probably because [Feldmann et al. 2012] assumed a linear relationship between ∆Tcf and εeff

(i.e. ∆Tcf = 3 x εeff within the range of validity). However, for DF24, CF24 and CFH24, the

calculated εeff-values are very small due to their high Bnom/tnom ratio = 24, thus the calculated

∆Tcf-values in Table 3.10 are small. It is possible that the linear relationship in [Feldmann et

69

al. 2012], which was developed based on the test results of European RHS, does not apply to

North American RHS. For DF24 in Table 3.10, the experimental ∆Tcf-values are very large,

exceeding the recommended value of 35 °C in [Feldmann et al. 2012], because DF24 was

direct-formed, while [Feldmann et al. 2012] assumes that all RHS are continuous-formed.

Table 3.9 Measured cross-sectional dimensions


RHS t (mm) t (mm) ri (mm) t (mm) ri (mm)

DF12 Not used* 12.89 5.31 13.03 8.09

CF12 & CFH12 12.62 13.01 17.10 12.96 14.44

DF24 Not used* 6.45 8.46 N/A**

CF24 & CFH24 5.91 6.22 7.32

* The wall thicknesses of the flat face of DF12 and DF24 are not used for the calculation of ∆Tcf.

** N/A = not applicable. No coupons were machined from location D of the DF24, CF24 and CFH24, thus the

wall thickness and inside corner radius are not included in the table.

Table 3.10 Comparison of ∆Tcf-values obtained from experiment results and ∆Tcf-values

estimated based on the approach proposed by [Feldmann et al. 2012] using measured cross-

sectional dimensions

DF12

Based on experimental results

Based on

[Feldmann et al.

2012]


Based on

[Feldmann et al.

2012]

∆Tcf for DBTT

from A (flat) to

B (corner)

∆Tcf for NDT

from A (flat) to

B (corner)

∆Tcf from A

(flat) to B

(corner)

∆Tcf for DBTT

from A (flat) to

D (corner)

∆Tcf for NDT

from A (flat) to

D (corner)

∆Tcf from A

(flat) to D

(corner)

17 °C 28 °C 45 °C (safe) 21 °C 26 °C 44 °C (safe)

CF12


Based on

[Feldmann et al.

2012]


Based on

[Feldmann et al.

2012]

∆Tcf for DBTT

from A (flat) to

B (corner)

∆Tcf for NDT

from A (flat) to

B (corner)

∆Tcf from A

(flat) to B

(corner)

∆Tcf for DBTT

from A (flat) to

D (corner)

∆Tcf for NDT

from A (flat) to

D (corner)

∆Tcf from A

(flat) to D

(corner)

-7 °C -8 °C 14 °C (safe) 8 °C 10 °C 18 °C (safe)

CFH12


Based on

[Feldmann et al.

2012]


Based on

[Feldmann et al.

2012]

∆Tcf for DBTT

from A (flat) to

B (corner)

∆Tcf for NDT

from A (flat) to

B (corner)

∆Tcf from A

(flat) to B

(corner)

∆Tcf for DBTT

from A (flat) to

D (corner)

∆Tcf for NDT

from A (flat) to

D (corner)

∆Tcf from A

(flat) to D

(corner)

-14 °C -14 °C 14 °C (safe) 8 °C -7 °C 18 °C (safe)

70

Table 3.10 (continued)

DF24


Based on

[Feldmann et al.

2012]

N/A* ∆Tcf for DBTT

from A (flat) to

B (corner)

∆Tcf for NDT

from A (flat) to

B (corner)

∆Tcf from A

(flat) to B

(corner)

38 °C 37 °C 7 °C (unsafe)

CF24


Based on

[Feldmann et al.

2012]


from A (flat) to

B (corner)

∆Tcf for NDT

from A (flat) to

B (corner)

∆Tcf from A

(flat) to B

(corner)

15 °C 19 °C 6 °C (unsafe)

CFH24


Based on

[Feldmann et al.

2012]


from A (flat) to

B (corner)

∆Tcf for NDT

from A (flat) to

B (corner)

∆Tcf from A

(flat) to B

(corner)

10 °C 15 °C 6 °C (unsafe)

* N/A = not available. No coupons were tested from location D of the DF24, CF24 and CFH24, thus the ∆Tcf-

values from location A to location D were not calculated.

71

Chapter 4 High Strain Rate Behaviour

4.1 Summary

This chapter compares the high strain rate properties of four cold-formed RHS specimens

manufactured by two different methods: direct-forming versus continuous-forming. Their

compressive and tensile dynamic properties were obtained by performing 128 split-

Hopkinson pressure bar tests and 38 split-Hopkinson tension bar tests respectively. The test

strain rates ranged from 100 to 1000 s-1

and the dynamic yield stresses were compared to the

corresponding static yield stresses, to characterize the strength enhancement of cold-formed

RHS under such loading rates. For simplification and consistency purposes, in this chapter

the abbreviation “SHPB” is used for both split-Hopkinson pressure bar and split-Hopkinson

tension bar.

4.2 Background

Recently, blast and impact loadings have been taken into consideration for the design of

critical infrastructure. For structures under these severe loadings, their responses at high

strain rates from 100 to 1000 s-1

are often sought [Malvar and Crawford 1998; Paik and

Thayamballi 2003; Luecke et al. 2005; Razaqpur et al. 2009; Astaneh-Asl 2010]. It is

estimated that the strain rates on the World Trade Centre steels, due to the aircraft impacts,

were up to 1000 s-1

[Luecke et al. 2005]. For blast- or impact-resistant design of steel

structures, Strength Increase Factors (SIFy) are commonly used to consider the difference

between the nominal static yield stress and the probable static yield stress, and Dynamic

Increase Factors (DIFy and DIFu) are commonly used to consider the dynamic increase of

yield stress and ultimate strength.

According to AISC Steel Design Guide 26 [Gilsanz et al. 2013], for steel grades of 345 MPa

or less, the average yield stress of steels currently produced is approximately 10% larger than

the nominal yield stress specified by the American Society for Testing and Materials (ASTM)

specification. Hence, for blast design the nominal yield stress would be multiplied by a SIFy

of 1.10. For higher grades this average is claimed to be smaller than 5%, so no factor is used

on those grades. Ultimate strength is not factored in any case. The same suggestions are given

in [DOD 2008; ASCE 2010; ASCE 2011; CSA 2012]. It should be noted that the SIFy value

of 1.10 is intended for non-cold-formed steels. For cold-formed hollow sections, the ratio

between the actual yield stress and the nominal value is typically higher. For example, SIFy is

72

taken as 1.4 (Ry factor) for cold-formed hollow sections in the AISC Seismic Provisions for

Structural Steel Buildings [AISC 2010a].

The mechanical properties of steel material vary with strain rate. Compared to the static

values normally used in design, the properties vary for dynamic loading as follows: (1) the

yield stress increases substantially; (2) the ultimate strength increases slightly; and (3) both

modulus of elasticity and the elongation at rupture remain nearly constant [Luecke et al. 2005;

Gilsanz et al. 2013]. Thus, DIFy and DIFu are commonly used to consider the increases in

yield stress and ultimate strength due to blast loading [Gilsanz et al. 2013; DOD 2008; ASCE

2010; ASCE 2011; CSA 2012]. The DIFy and DIFu values for various structural steels

suggested by [Gilsanz et al. 2013] are listed in Table 4.1. The values are based on an average

strain rate of 0.1 s-1

which is characteristic of low pressure explosions. It can be seen in Table

4.1 that the ultimate strengths of various steels are in general less sensitive to the strain rate

effect, compared to the yield stresses. Similar constant DIFy and DIFu values, independent of

the strain rate, are given in [DOD 2008; ASCE 2010; ASCE 2011; CSA 2012]. If the strain

rate can be determined, UFC 3-340-02 [DOD 2008] recommends that the DIFy for strain rates

up to 100 s-1

, for ASTM A36 and A514 steels, be determined using Figure 4.1. Another

important effect of high strain rate on steel members is that the cross-section classification,

and hence member behaviour, may be affected. The yield strength increase from the static to

the dynamic value may cause a downgrading of cross-section classification, for example

changing a section from compact to slender [Liew 2008].

Table 4.1 DIFy and DIFu values for various structural steels under low pressure explosion

[Gilsanz et al. 2013]

ASTM

specifications

DIFy DIFu

Bending / Shear Tension / Compression

A36 1.29 1.19 1.10

A588 1.19 1.12 1.05

A514 1.09 1.05 1.00

A446/A653 1.10 1.10 1.00

A572 1.19 1.10 1.00

A992 1.19 1.10 1.00

73

Figure 4.1 DIFy values at various strain rates for ASTM A36 and A514 steels in

[adapted from DOD 2008]

Based on the expected ductility ratio (ratio between the maximum displacement and the

elastic displacement) or the expected support rotation angle (tangent angle at the support

formed by the maximum beam deflection), it is suggested by AISC Steel Design Guide 26

[Gilsanz et al. 2013] that the dynamic design stress for tension, compression and bending (fds)

can be calculated as follows, for non cold-formed steel:

For ductility ratio ≤ 10 or support rotation angle ≤ 2 degrees,

( ) (4-1)

For ductility ratio > 10 or support rotation angle > 2 degrees,

(4-2)

where

(4-3)

The dynamic design stress for shear is given as:

. (4-4)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0.001 0.01 0.1 1 10 100

DIF

y

Strain rate (s-1)

ASTM A36

ASTM A514 plate thickness ≤ 63.5 mm ASTM A514 platethickness > 63.5 mm

74

The dynamic design stress for tension, compression and bending (fds), calculated using Eqs.

4-1 and 4-2, is illustrated in Figure 4.2, for hot-formed (or hot-finished) steel. As can be seen,

Eq. 4-2 considers the strain hardening effect when the expected ductility ratio (i.e. the

damage allowed in the structural member) is large.

Figure 4.2 Typical stress-strain curves for steel and dynamic design stress

(adapted from DOD 2008)

It should be noted that the constant DIFy and DIFu values suggested by the above design

guides and technical manuals are in general intended for low pressure explosions (for strain

rates in the order of 10-1

s-1

). Thus, they may not be accurate for blast loading in close

proximity or impact loading where the strain rate may be much higher (in the order of 102 to

103 s

-1).

4.3 Previous investigations

The effect of strain rate on the mechanical properties of steels, particularly yield strength, has

long been a subject of interest to researchers. It was found that the yield strength of steel

increases as the strain rate increases. This is because as the material dislocation velocity

fdu

fdy

fy

fu

fds = fdy + (fdu – fdy)/4fds = fdy

Str

ess

Strain

Quasi-static strain rate

High strain rate

Dynamic design stress (fds)

Strain corresponding to

a ductility ratio = 10

Strain corresponding to

a ductility ratio = 20 (incipient failure of member)

75

increases, cross slip becomes increasingly difficult and the flow stress at any given strain

increases, thus increasing the yield strength of steel [Davis 2004]. Early research on the

influence of strain rate on the yield stresses of three structural steels (ASTM A36 and A441

steels and one quenched and tempered steel) was conducted by [Rao et al. 1966]. Tensile

coupons were tested quasi-statically and dynamically to obtain the experimental results. The

measured static tensile yield stresses of the steels tested ranged from 238 MPa to 778 MPa.

The dynamic test strain rates were up to 1.4 x 10-3

s-1

. Based on 189 tests on A36 steel, 39

tests on A441 steel and 29 tests on the quenched and tempered steel (Q-T), Eqs. 4-5 to 4-7

were established to describe the relationships between DIFy and strain rate for the three tested

steels. The equations are functions of the strain rates only.

(4-5)

(4-6)

(4-7)

Later, the mechanical properties of various steels at different strain rates were studied by

[Soroushian and Choi 1987]. Dynamic test results on structural steels, reinforcing bars and

deformed wires were collected. All tests (approximately 60 tests based on the number of data

points in the publication figure) were performed in tension. The measured static tensile yield

stresses of the steels tested ranged from 180 MPa to 684 MPa. The dynamic test strain rates

were up to 10 s-1

and Eq. 4-8 was established for prediction of the DIFy. The equation is a

function of both the strain rate and the actual static yield stress (in MPa) of the steel.

( ) (4-8)

The effects of cold-working and strain rate on the mechanical properties of three types of

sheet steels were investigated by [Kassar and Yu 1992]. The three sheet steels were

designated 35XF, 50XF and 100XF. The numbers “35”, “50” and “100” distinguish the three

sheet steels by their nominal yield stresses (100 ksi = 689 MPa, 50 ksi = 345 MPa, and 35 ksi

= 241 MPa). A total of 124 tensile coupons and 54 compressive coupons were tested. The

measured static tensile yield stresses of the steels tested ranged from 227 MPa to 950 MPa,

and the measured static compressive yield stresses ranged from 206 MPa to 853 MPa. For the

tension tests, the specimens were subjected to uniform cold stretching of 2% and 8% before

testing. By comparing the dynamic yield stresses (obtained from tests at a strain rate of 1 s-1

)

76

to the static yield stresses (obtained from tests at a strain rate of 1x10-4

s-1

), the dynamic

increases in yield stress for the three steels tested in tension were: 12 – 29% for the 241 MPa

(nominal yield stress, same for the following) steel, 4 – 15% for the 345 MPa steel, and 4%

for the 689 MPa steel, while the dynamic increases in yield stress for the three steels tested in

compression were: 24 – 33% for the 241 MPa steel, 9 – 10% for the 345 MPa steel, and 7%

for the 689 MPa steel. For tension tests with different amounts of cold stretching, the strain-

rate sensitivity decreased as the amount of prior cold stretching increased. Comparing the

average value of the measured static tensile yield stresses (in the non-cold-stretched condition)

and the measured dynamic tensile yield stresses under different strain rates, three equations

were established for prediction of dynamic yield stress for the three tested sheet steels. The

three original equations in [Kassar and Yu 1992] are herein divided by the corresponding

average value of the measured static tensile yield stress (in the non-cold-stretched condition),

and are shown as Eqs. 4-9 to 4-11 so that they can be used for prediction of the DIFy.

(4-9)

(4-10)

(4-11)

Recently, [Filiatrault and Holleran 2001] studied experimentally the uniaxial tensile

behaviours of reinforcing steel bars under various combinations of earthquake-level strain

rates (quasi-static to 0.1 s-1

) and temperatures typical of summer and winter conditions in cold

urban regions (+20 °C to -40 °C). A total of 36 coupons were machined from a single

reinforcing bar with a nominal yield stress of 400 MPa. The test results revealed that, when

the strain rate increased from quasi-static (80x10-6

s-1

) to 0.1 s-1

and the temperature dropped

from +20 °C to -40 °C, the yield stress and ultimate strength increased by 22% and 12%

respectively.

Using Eqs. 4-5 to 4-11, for various steels in the above investigations the relationships

between DIFy and test strain rates, together with extrapolations beyond the test strain rates,

are shown in Figure 4.3. It was suggested by [Kassar and Yu 1992] that Eqs. 4-9 to 4-11

could be used for strain rates beyond the test strain rates. However, since there is no test data

to justify this suggestion, the accuracy of the extrapolations is unknown. It can be seen in

Figure 4.3 that the sensitivities for various steels to the strain rate effect are quite different,

thus it is hard to establish a single equation to describe the DIFy versus strain rate relationship

77

for various steels. Nevertheless, there is a strong correlation of the DIFy to the logarithm of

the strain rate.

Figure 4.3 Relationships between DIFy and strain rate based on previous investigations at

intermediate strain rate level (test strain rate up to 10 s-1

)

Investigation into the dynamic strength increase for steel reinforcing bars at higher strain

rates, up to 225 s-1

, was conducted by [Malvar and Crawford 1998]. The static and dynamic

tensile behaviours were studied for reinforcing bars satisfying ASTM A615, A15, A432,

A431, and A706, with the nominal yield stresses ranging from 290 to 710 MPa. The test

results revealed that, under dynamic loading, the yield stresses of these rebars increase by up

to 60% for strain rates of up to 10 s-1

, and up to 100% for strain rates of 225 s-1

. Based on the

experimental data, [Malvar and Crawford 1998] proposed Eqs. 4-12 and 4-13 that give DIFy

and DIFu as functions of the strain rate and the measured static yield stress, fy (MPa). These

two equations have been adopted by CSA S850-12 [CSA 2012] for prediction of the dynamic

strength increase of rebar.

(4-12)

1

1.2

1.4

1.6

1.8

2

2.2

1E-05 0.001 0.1 10 1000

DIF

y

Strain rate (s-1)

A36 in [Rao et al. 1966]

A441 in [Rao et al. 1966]

Q-T in [Rao et al. 1966]

[Soroushian and Choi 1987], fy=350 MPa

35XF in [Kassar and Yu 1992]



78

(4-13)

Recently, in order to study the aircraft impact and the resulting damage to the World Trade

Center (WTC), [Luecke et al. 2005] investigated the dynamic properties of the WTC steels

for strain rates up to 2500 s-1

. Test coupons (tensile and compressive) were machined from

perimeter column steels and core column steels (welded box sections, rolled wide flange

sections and spandrel plates). The nominal yield stresses of the examined steels ranged from

248 MPa to 621 MPa. Based on the experimental data, [Luecke et al. 2005] proposed a

modified Cowper-Symonds [Cowper and Symonds 1957] model for prediction of DIFy of

various steels under high strain rates. Since the original equations are in ksi (unit-dependent),

they are modified hereby as Eqs. 4-14 and 4-15 where fy is in MPa.

(4-14)

(4-15)

Figure 4.4 Relationships between DIFy and strain rate based on previous investigations at

high strain rate level (test strain rate up to 2500 s-1

)

1

1.2

1.4

1.6

1.8

2

2.2

1E-05 0.001 0.1 10 1000

DIF

y

Strain rate (s-1)

[Malvar and Crawford 1998], fy=300 MPa



[Luecke et al. 2005], fy=300 MPa



79

Using Eqs. 4-12 to 4-15, the relationships between DIFy and strain rate suggested by [Malvar

and Crawford 1998; Luecke et al. 2005] are shown in Figure 4.4. Similar to Figure 4.3,

Figure 4.4 also indicates that the sensitivities for different steels to the strain rate effect are

quite different.

Based on Figures 4.3 and 4.4, it can be seen that the DIFy values in Table 4.1, which are

intended for low pressure explosion (strain rates in the order of 10-1

s-1

), may be too

conservative for blast loading in close proximity or impact loading (strain rates in the order of

102 to 10

3 s

-1).

Since (1) test results on structural steel properties under high strain rate are still highly

insufficient [Astaneh-Asl 2010], (2) the high strain rate behaviours of various types of steels

are quite different, and (3) previous investigations are mostly on non-cold-formed steels,

there is a need to investigate the high strain rate behaviour of cold-formed hollow structural

sections, especially as these are favoured for building columns.

4.4 RHS specimens

In this chapter, the dynamic compression and tensile behaviours (at strain rates ranging from

100 to 1000 s-1

) of four RHS specimens (DF12, DF24, CF12 and CF24 in Table 2.1) are

examined by SHPB tests. The dynamic test results are compared to the static tensile coupon

test results to characterize the strength enhancement of cold-formed RHS under such high

strain rate loading.


4.5.1 Tensile coupon tests

The SIFy and SIFu values around the cross-sections of the investigated RHS specimens were

obtained through tensile coupon tests. For each RHS, five tensile coupons (three from three

different flat faces and two from two different corners) were machined and tested quasi-

statically in accordance with ASTM A370 [ASTM 2009] (see Chapter 2). The static yield

stresses are determined by the 0.2% strain offset method. The averages of the measured static

yield stresses (fy,avg in Table 2.4) and the averages of the measured static ultimate strengths

(fu,avg in Table 2.4) are compared to the nominal values (fy,nom and fu,nom), and the SIFy and

SIFu values are listed in Table 4.2.

80

Table 4.2 SIFy and SIFu values for RHS specimens

Flat face Corner

RHS ID SIFy = fy,avg/fy,nom SIFu = fu,avg/fu,nom SIFy = fy,avg/fy,nom SIFu = fu,avg/fu,nom

DF12 1.22 1.16 1.76 1.44

DF24 1.15 1.05 1.54 1.26

CF12 1.31 1.33 1.69 1.50

CF24 0.97 1.00 1.38 1.17

Avg 1.16 1.14 1.59 1.34

4.5.2 SHPB tests

4.5.2.1 Background

Testing using SHPB apparatus is the most common method of determining the high strain

rate behaviour of engineering materials. The determination of the high strain rate behaviour

of a material being tested using SHPB, whether it is loaded in compression or tension, is

based on the same principles of one-dimensional elastic wave propagation within the pressure

loading bars. The detailed historical background and principles of SHPB apparatus can be

found in the ASM Handbook Volume 8 [Gray 2000].

Figure 4.5 Schematic diagram of compressive SHPB apparatus

While there is no universal standard design for SHPB apparatus, all facilities share common

design elements [Gray 2000]. The University of Toronto compressive SHPB apparatus used

in this study is shown schematically in Figure 4.5 and photographically in Figure 4.6. It

consists of two cylindrical bars (incident bar and transmitted bar), a gas gun and a striker.

Strain gauges are mounted on both bars to measure the elastic strains. During a compressive

Gas gun

Incident bar Transmitted bar

Strain gauge

Striker bar

Sample sandwiched

between bars

Strain gauge

81

SHPB test, the sample (usually a cylinder) is sandwiched between the incident bar and the

transmitted bar. The elastic strains measured in the bars are used to determine the stress-strain

relationship of the examined material. The bars used in the SHPB apparatus are made of high

strength steel since the yield strength of the selected pressure bar material determines the

maximum stress attainable within the sample material, given that the pressure bars must

remain elastic.

Figure 4.6 Photograph of compressive SHPB apparatus

Figure 4.7 Typical strain gauge data from a compressive SHPB test

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003

Str

ain

Time (s)

Incident wave

Transmitted wave

Reflected wave

82

The compressive SHPB test starts with accelerating the striker, from the gas gun towards the

incident bar. At impact, a compressive strain wave (incident wave), εi(t), is created within the

incident bar which travels towards the sample. At the boundary between the incident bar and

the sample, part of the pulse reflects as a tensile strain wave (reflected wave), εr(t), back into

the incident bar while the rest transmits as a compressive strain wave (transmitted wave), εt(t),

into the specimen and eventually the transmitted bar [Gray 2000]. The strain-time histories of

the two bars recorded by the strain gauges can be analysed to extract the compressive stress-

time curve and the compressive strain-time curve for the sample tested. These data can then

be combined to obtain the rate-dependent compressive stress-strain relationship of the tested

material. Typical strain gauge data from a compressive SHPB test is shown in Figure 4.7.

Note that for calculation purpose the three waves are truncated so that they start from the

same time. During a test, there are time delays between the waves due to the distance

between the strain gauges.

According to one dimensional elastic wave propagation theory [Gray 2000], the dynamic

compressive stress-time history and the dynamic compressive strain-time history (σ(t) and

ε(t)) of the sample can be determined using Eqs. 4-16 and 4-17.

σ

ε (4-16)

ε

∫ ε

(4-17)

where Ab and As are the cross-sectional areas of the bars and the sample, respectively, ls is the

length of the cylinder sample and Cb is the longitudinal elastic wave speed in the pressure bar.

The longitudinal elastic wave speed in the pressure bar (Cb) can be determined by striking the

pressure bars with no sample. It is the result of dividing the distance between the two strain

gauges by the time difference between the starting points of the incident wave and

transmitted wave. Cb equalled 4790 m/s in this study.

The principles for the tensile SHPB test are similar to those for the compressive SHPB test.

The most commonly used tensile SHPB test method uses a dumb-bell-shaped sample

threaded directly into the ends of the incident and transmitted bars. A tensile force can be

generated by direct impact on a flange at the end of the incident bar, using a hollow striker

83

tube accelerated along the incident bar from a gas gun [Gray 2000]. The tensile SHPB

apparatus used in this study is shown schematically in Figure 4.8.

In the tensile SHPB test, the incident, reflected and transmitted waves recorded by the strain

gauges are in the opposite directions to those in the compressive SHPB test, as shown in

Figure 4.7. Data analysis for the tensile SHPB test is essentially identical to that of the

compressive SHPB test. The same equations (Eqs. 4-16 and 4-17) can be used to determine

the dynamic tensile stress-time history and the dynamic tensile strain-time history.

Figure 4.8 Schematic diagram of tensile SHPB apparatus

In the SHPB test of steel material, the elastic region of the test result (tensile or compressive)

is commonly considered non-reliable, since Eqs. 4-16 and 4-17 assume that the sample is in

force equilibrium, while at strains below the yield point this assumption is not valid [Luecke

et al. 2005; Gray 2000]. Thus, in this study the test results were analysed as follows:

(1) Truncate the data at the elastic region.

(2) Fit a straight line to the yield plateau and determine the dynamic yield stress using the 0.2%

strain offset method, as illustrated in Figure 4.9.

(3) Fit a straight line to the strain-time curve for determination of the average strain rate

experienced by the sample, as illustrated in Figure 4.10.

Gas gun

Incident bar Transmitted bar

Strain gauge

Sample threaded

into bars

Strain gauge

Hollow striker bar

84

Figure 4.9 Determination of dynamic yield stress

Figure 4.10 Determination of strain rate

4.5.2.2 Compressive SHPB tests

The dynamic compressive stress-strain behaviours of all the RHS specimens, under high


, were obtained by compressive SHPB tests. The selection of

0.00 0.01 0.02 0.03 0.04 0.05

0

200

400

600

800

1000

0.002

1

E

Intercept = 762, Slope = 2209

Str

ess (

MP

a)

Strain

Dynamic yield stress = 775 MPa

0.00000 0.00004 0.00008 0.00012

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Strain rate = Slope = 858 s-1

Str

ain

Time (s)

85

sample size is dependent on the strain rate desired. The compressive SHPB sample sizes in

this study were selected following ASM Handbook Volume 8 [Gray 2000], which suggests a

cylinder sample with length-to-diameter ratio from 0.5 to 1.0. The diameters of the samples in

this study were made almost the full wall thickness of the RHS specimens to ensure

measurement of the bulk properties of the RHS specimens.

Figure 4.11 Compressive and tensile SHPB samples

Figure 4.12 Cutting location and orientation of compressive and tensile SHPB samples

Cylinder samples with length of 5 mm or 10 mm and a diameter of 10 mm were machined

from the RHS specimens with nominal thickness of 12.7 mm (DF12 and CF12). Cylinder

samples with length of 2.5 mm or 5 mm and a diameter of 5 mm were machined from the

RHS specimens with nominal thickness of 6.35 mm (DF24 and CF24). In both cases, the

longer samples were intended for strain rates from 100 – 200 s-1

, and the shorter samples

Tensile SHPB

sample

Compressive

SHPB samples

weld

seam

86

were intended for strain rates from 200 – 1000 s-1

. Typical compressive SHPB samples are

shown in Figure 4.11. The cutting location and orientation of the compressive samples are

illustrated in Figure 4.12. The circular surface of the compressive sample is normal to the

longitudinal direction of the RHS specimen. For all four RHS specimens, a total of 128

compressive SHPB samples were tested. During the compressive SHPB test, the loading

direction is normal to the circular surface of the cylinder sample (i.e. in the longitudinal

direction of the RHS specimen), since RHS is usually loaded longitudinally (under

compression, tension or flexural loading). As discussed above, Eqs. 4-16 and 4-17 are valid

when the sample is in force equilibrium. Thus, in this study the pulse shaping technique

suggested by ASM Handbook Volume 8 [Gray 2000] was used to modify the pulse shape of

the incident wave through the placement of a copper disk at the front of the incident bar. The

aim was to obtain dynamic equilibrium in the sample at an earlier stage of a test such that the

data would be valid at an earlier strain.

Figure 4.13 Typical compressive SHPB test results

Typical dynamic compressive stress-strain curves are shown in Figure 4.13 and the full set is

given in Appendix C. Using the procedures illustrated in Figures 4.9 and 4.10, and Eqs. 4-16

and 4-17, the dynamic compressive yield stresses at the flat faces and corners of the RHS

specimens were determined. The compressive DIFy values, obtained by dividing the dynamic

compressive yield stresses by the corresponding static yield stresses (obtained from testing

the tensile coupon machined from the same location), are shown in Figures 4.14 – 4.17. It is

0.00 0.01 0.02 0.03 0.04 0.05

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain

Strain rate = 135 s-1



87

assumed in this study that at the location where the tensile coupon was machined (flat face or

corner) the local static compressive yield stress equals the local static tensile yield stress. Key

compressive SHPB test results are listed in Appendix C.

Figure 4.14 Compressive DIFy values of DF12 (12.7 mm thick RHS)

Figure 4.15 Compressive DIFy values of CF12 (12.7 mm thick RHS)

100 1000

0.8

1.2

1.6

2.0

2.4

2.8

Corner: C=5931, q=1.92

R2=0.948

Flat face

Corner

DIF

y

Strain rate (s-1)

Flat face: C=2318, q=2.83

R2=0.960

100 1000

0.8

1.2

1.6

2.0

2.4

2.8

Corner: C=2271, q=0.48

R2=0.727Flat face: C=1997, q=0.46

R2=0.838

Flat face

Corner

DIF

y

Strain rate (s-1)

88

Figure 4.16 Compressive DIFy values of DF24 (6.35 mm thick RHS)

Figure 4.17 Compressive DIFy values of CF24 (6.35 mm thick RHS)

4.5.2.3 Tensile SHPB tests

The dynamic tensile stress-strain behaviours of RHS specimens DF12 and CF12 under high


were obtained by tensile SHPB tests. No tensile samples

100 1000

0.8

1.2

1.6

2.0

2.4

2.8

Corner: C=118552, q=10.65

R2=0.643

Flat face: C=11494, q=5.96

R2=0.805

Flat face

Corner

DIF

y

Strain rate (s-1)

100 1000

0.8

1.2

1.6

2.0

2.4

2.8

Corner: C=70926, q=12.43

R2=0.523


R2=0.491

Flat face

Corner

DIF

y

Strain rate (s-1)

89

were made from RHS specimens DF24 and CF24 since the tube walls are too thin (nominal

thickness = 6.35 mm). In this study, the dumb-bell-shaped sample with threads on both ends

suggested by ASM Handbook Volume 8 [Gray 2000] was used, as shown in Figure 4.11. The

cross-section of the test region of the tensile SHPB sample is circular with a diameter of 5

mm. A schematic diagram of the tensile SHPB sample is shown in Figure 4.18.

Figure 4.18 Schematic diagram of tensile SHPB sample

The longitudinal direction of the tensile sample is the same as that of the mother tube, such

that during the tensile SHPB test the samples are loaded in the longitudinal direction of the

RHS specimen. The cutting location and orientation of the tensile samples are illustrated in

Figure 4.12. Similar to the compressive SHPB tests, during the tensile SHPB tests pulse

shaping was achieved using copper disks, with the selection of pulse shapers based on

experience [Gray 2000]. By trial and error, best test results were achieved by placing two

copper disks at the symmetrical locations on the impact surface of the flange with the striker

bars in this study. A photograph of a typical tensile SHPB sample after testing is shown as

Figure 4.19.

Typical dynamic tensile stress-strain curves are shown in Figure 4.20 and the full set is given

in Appendix C. Similar to the compressive SHPB tests, using the procedures illustrated in

Figures 4.9 and 4.10, and Eqs. 4-16 and 4-17, the dynamic tensile yield stresses at the flat

faces and corners of the RHS specimens were determined. The tensile DIFy values, obtained

by dividing the dynamic tensile yield stresses by the corresponding static yield stresses

12 mm

A

A

B

B

Section A-ASection B-B

d=12 mm d=5 mm

d=

8 m

m

2.5 mm

12 mm 12 mm

90

(obtained from testing the tensile coupon machined from the same location), are shown in

Figures 4.21 and 4.22. Key tensile SHPB test results for 38 samples are listed in Appendix C.

Figure 4.19 Tensile SHPB sample after test

Figure 4.20 Typical tensile SHPB test results

0.00 0.01 0.02 0.03 0.04 0.05

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain




91

Figure 4.21 Tensile DIFy values of DF12 (12.7 mm thick RHS)

Figure 4.22 Tensile DIFy values of CF12 (12.7 mm thick RHS)

100 1000

0.8

1.2

1.6

2.0

2.4

2.8

Corner: C=3666, q=0.91

R2=0.930


R2=0.923

Flat face

Corner

DIF

y

Strain rate (s-1)

100 1000

0.8

1.2

1.6

2.0

2.4

2.8

Corner: C=2256, q=1.55

R2=0.990


R2=0.972

Flat face

Corner

DIF

y

Strain rate (s-1)

92


4.6.1 Strength increase factor

It can be seen in Table 4.2 that for all RHS specimens the SIFy and SIFu values of the corner

are larger than those of the flat face due to the uneven degrees of cold-forming around the

cross-sections. The spread between the actual yield stress and the nominal specified value is

sometimes substantial. The SIFy values are up to 1.31 for the flat faces and 1.76 for the

corners. The SIFu values are in general smaller than the SIFy values.

4.6.2 Dynamic increase factor

The evaluation of the data in Figures 4.14 – 4.17, 4.21 and 4.22 is performed by fitting the

scatters using the Cowper-Symonds [Cowper and Symonds 1957] model, shown as Eq. 4-18

here. The Cowper-Symonds model has been frequently used for prediction of DIFy for

various metals including steel [Luecke et al. 2005; Astaneh-Asl 2010]. It is also available in

commercial finite element software packages such as LS-DYNA [LSTC 2013]. The Cowper-

Symonds best fit lines for the groups of data, together with the material parameters (C and q)

and the coefficients of determination (R2), are shown in Figures 4.14 – 4.17, 4.21 and 4.22.

(4-18)

where C and q are the Cowper-Symonds parameters.

The compressive and tensile DIFy values of the flat faces and corners at the strain rates of 100

s-1

and 1000 s-1

, calculated by Eq. 4-18 using the material parameters C and q in Figures 4.14

– 4.17, 4.21 and 4.22, are listed in Tables 4.3 – 4.6. Using Eq. 4-19, the measured flat face

and corner areas in Table 2.3 and the compressive DIFy values of the flat faces and corners,

the average DIFy values of the entire cross-section of the RHS specimens under compression

loading were determined and shown in Tables 4.3 and 4.4. Similarly, the average DIFy values

of the RHS specimens under tension loading were determined and shown in Tables 4.5 and

4.6. The average DIFy values of the RHS specimens under flexural loading, as shown in

Tables 4.7 and 4.8, were determined using the average of the corresponding compressive and

tensile DIFy values.

( ) (4-19)

where F is the ratio of flat face area to total cross-sectional area of RHS

93


)

Compression, = 100 s-1

RHS ID Bnom /

tnom

Flat face Corner Average DIFy of

entire

cross-section fy

(MPa) Area (mm

2) DIFy

fy

(MPa) Area (mm

2) DIFy

DF12 12 450 5228 1.33 650 1636 1.12 1.28

DF24 24 490 3240 1.45 550 382 1.51 1.46

CF12 12 420 4991 1.00 520 1692 1.00 1.00

CF24 24 355 3036 1.69 465 379 1.59 1.68


)

Compression, = 1000 s-1

RHS ID Bnom /

tnom


entire

cross-section fy

(MPa) Area (mm

2) DIFy

fy

(MPa) Area (mm

2) DIFy

DF12 12 450 5228 1.74 650 1636 1.40 1.66

DF24 24 490 3240 1.66 550 382 1.64 1.66

CF12 12 420 4991 1.22 520 1692 1.18 1.21

CF24 24 355 3036 1.88 465 379 1.71 1.86


)

Tension, = 100 s-1

RHS ID Bnom /

tnom


entire

cross-section fy

(MPa) Area (mm

2) DIFy

fy

(MPa) Area (mm

2) DIFy

DF12 12 450 5228 1.22 650 1636 1.02 1.17

CF12 12 420 4991 1.31 520 1692 1.13 1.26


)

Tension, = 1000 s-1

RHS ID Bnom /

tnom


entire

cross-section fy

(MPa) Area (mm

2) DIFy

fy

(MPa) Area (mm

2) DIFy

DF12 12 450 5228 1.60 650 1636 1.24 1.51

CF12 12 420 4991 1.72 520 1692 1.59 1.69


)

Flexural, = 100 s-1

RHS ID Bnom /

tnom


entire

cross-section fy

(MPa) Area (mm

2) DIFy

fy

(MPa) Area (mm

2) DIFy

DF12 12 450 5228 1.28 650 1636 1.07 1.23

CF12 12 420 4991 1.16 520 1692 1.07 1.14

94


)

Flexural, = 1000 s-1

RHS ID Bnom /

tnom


entire

cross-section fy

(MPa) Area (mm

2) DIFy

fy

(MPa) Area (mm

2) DIFy

DF12 12 450 5228 1.67 650 1636 1.32 1.59

CF12 12 420 4991 1.47 520 1692 1.39 1.45

As discussed previously, during the direct-forming process the cold-working is concentrated

in the corners while the flat faces receive only a small amount of cold-working. Thus,

theoretically the overall degree of cold-working to the cross-section of direct-formed RHS

does change substantially as cross-sectional size changes. On the other hand, during the

continuous-forming process, the steel plate is roll-formed into a circular tube before reverse

bending it into a rectangular tube, thus the overall degree of cold-working to the cross-section

of continuous-formed RHS increases as the Bnom / tnom ratio of the RHS decreases.

For CF12 (continuous-formed, Bnom / tnom ratio = 12) and CF24 (continuous-formed, Bnom /

tnom ratio = 24), it can be seen in Tables 4.3 and 4.4 that the compressive DIFy values around

the cross-section of CF12 are much lower than those of CF24. This is probably because (1)

the measured static yield stresses of the flat face and corner of CF12 are higher than those of

CF24, which is consistent with the conclusions from other research on cold-formed products

[Malvar and Crawford 1998; Luecke et al. 2005; Rao et al. 1966; Soroushian and Choi 1987;

Kassar and Yu 1992; Filiatrault and Holleran 2001], and (2) CF12 has a smaller Bnom / tnom

ratio which corresponds to a higher overall degree of cold-working, which is consistent with

the conclusions by [Kassar and Yu 1992].

For DF12 (direct-formed, Bnom / tnom ratio = 12) and DF24 (direct-formed, Bnom / tnom ratio =

24), it can be seen in Tables 4.3 and 4.4 that such a difference becomes smaller (or non-

existent) since the overall degree of cold-working to the cross-section of direct-formed RHS

does not change substantially as the cross-sectional size changes. The compressive DIFy

values of the flat face of DF12 are close to those of DF24 due to similar measured static yield

stresses. The compressive DIFy values for the corner of DF12 are smaller than those of DF24

due to a higher measured static yield stress.

Comparing the compressive DIFy values of the direct-formed and continuous-formed RHS

with the same Bnom / tnom ratio of 12 in Tables 4.3 and 4.4, it can be seen that the flat face of

CF12 (continuous-formed) is less susceptible to the strain rate effect than that of DF12

95

(direct-formed) since it experienced a higher level of cold-working. The compressive DIFy

values for the corner of CF12 are closer to those of DF12 since theoretically they experienced

similar amounts of cold-working. For DF24 (direct-formed, Bnom / tnom ratio =24) and CF24

(continuous-formed, Bnom / tnom ratio = 24), it can be seen in Tables 4.3 and 4.4 that their

compressive DIFy values are relatively close. This is probably because, although CF24 still

contains a higher overall amount of cold-working, its measured static yield stresses are lower.

Comparing Tables 4.3 – 4.6 it can be seen that, for the same strain rate, the compressive and

tensile dynamic strength increase levels are different for the RHS specimens tested. Thus, for

blast- or impact-resistant design of RHS member, different DIFy values should be used for

compression, tension and flexural loadings.

Comparing the entire cross-sectional DIFy values in Tables 4.3 – 4.8 (based on measured

SHPB values at strain rates of 100 and 1000 s-1

) to the DIFy values in Table 4.1 (for strain

rates in the order of 10-1

s-1

), it can be seen that the DIFy values given by AISC Design Guide

26 [Gilsanz et al. 2013], which are intended for low pressure explosion and non-cold-formed

steel, may be too conservative for blast loading in close proximity or impact loading on RHS.

Thus, realistic DIFy values in Tables 4.3 – 4.8 should be used in such cases.

Since RHS is usually loaded longitudinally (under compression, tension or flexural loading),

this study focused on the high strain rate behaviour of RHS in the longitudinal direction. The

above results and conclusions may not apply to the dynamic material properties in the

transverse direction.

96

Chapter 5 Conclusions

In this study, the static and dynamic properties of cold-formed Rectangular Hollow Sections

(RHS) produced by different manufacturing methods (direct-forming versus continuous-

forming; heat-treated versus non-heat-treated) were investigated comprehensively and

compared directly for the first time.

Static properties:

Through tensile coupon tests, the principal tensile properties (yield strength, ultimate

strength and ductility) around the cross-sections of the RHS specimens due to uneven degrees

of cold-forming were quantified. It can be concluded that:

1) Since the flat face of a direct-formed RHS is not severely cold-formed during the

production process, its tensile stress-strain behaviour is similar to the flat face of its

heat-treated continuous-formed counterpart (i.e. with a clear yield point). On the other

hand, the corner of a direct-formed RHS has tensile stress-strain behaviour similar to the

corner of its non-heat-treated continuous-formed counterpart (i.e. the material starts to

yield at a relatively early stage), since the amounts of cold-forming in both corners are

similar (i.e. similar corner bending radius).

2) The cross-sectional yield strength gradient (flat face versus corner) in a direct-formed

RHS is larger than that of its continuous-formed and continuous-formed plus heat-

treated counterparts. However, the full-sectional yield strength depends on not only the

yield strength gradient but also the cross-sectional dimensions. When determining the

full-sectional yield strength of RHS with small Bnom/tnom ratios, it is necessary to

perform tensile coupon tests on both the flat face and the corner, since the cross-section

has a high proportion of corner region. The “corner effect” is particularly obvious for

direct-formed RHS with small Bnom/tnom ratios. On the other hand, when determining the

average yield strength of RHS with large Bnom/tnom ratios, since the “corner effect” is

minor (i.e. the cross-section has a low proportion of corner region), it may not be

necessary to perform tensile coupon tests on the corner and the full-sectional yield

strength may be estimated based on the tensile coupon test result of the flat face only.

Also, for large Bnom/tnom ratios it is not necessary to distinguish direct-formed RHS from

continuous-formed RHS.

3) The cross-sectional ductility gradient (flat face versus corner) in RHS with different

production histories and different cross-sectional dimensions is quite different. For

97

direct-formed RHS with different Bnom/tnom ratios, the flat face is always much more

ductile than the corner. For continuous-formed RHS, the ductility difference between

flat face and the corner decreases as the Bnom/tnom ratio increases. To be conservative, the

selection of RHS for ductility should be based on the ductility of the corner (i.e. the

weak spot) such that the entire cross-section is “fit for purpose”.

The overall compressive behaviours of the RHS specimens were investigated both

experimentally (through stub column tests and longitudinal residual stress measurements) and

analytically (through discretized cross-section column models). It can be concluded that:

1) In general, the longitudinal residual stress level in a direct-formed RHS is midway

between those in its continuous-formed and continuous-formed plus heat-treated

counterparts. The difference between a direct-formed RHS and its non-heat-treated

continuous-formed counterpart decreases as the Bnom/tnom ratio increases.

2) Columns with intermediate lengths are most common in steel structures. Failures of

columns with intermediate lengths are greatly influenced by the magnitude and pattern

of longitudinal residual stress. According to a comparison of the analytical column

curves of the RHS specimens, for column lengths from 2 metres to 8 metres the direct-

formed RHS with Bnom/tnom ratio of 12 has column behaviour close to its heat-treated

continuous-formed (CSA “Class H”) counterpart, while the direct-formed RHS with

Bnom/tnom ratio of 24 has column behaviour similar to its non-heat-treated continuous-

formed (CSA “Class C”) counterpart. Thus, when determining the compressive

resistance of intermediate length columns made from RHS with small or intermediate

Bnom/tnom ratios (e.g. Bnom/tnom ratios = 8, 12, or 16), one can distinguish direct-formed

RHS from non-heat-treated continuous-formed RHS since the former has a more

favourable column behaviour, although, for simplicity, both of them would be assigned

to a common “Class C” column curve per CSA S16. The effect of longitudinal residual

stress is less severe for columns with length outside the intermediate range.

Dynamic properties:

The notch toughness of cold-formed RHS, at low temperatures or in dynamic loading

applications, has been a concern in North America for some time, since failures of RHS due

to cracking at the corner as a result of low notch toughness have been reported. By testing a

total of 378 Charpy V-notch (CVN) coupons, the notch toughness gradients around the cross-

98

section of the RHS specimens were investigated quantitatively, in terms of degree of cold-

forming. It can be concluded that:

1) The notch toughness requirements for RHS in current steel product standards (i.e. the

use of CVN toughness of the flat face to assess the CVN toughness of the cross-section)

are questionable since the CVN test results in this study indicate that the notch

toughness of the corner is sometimes substantially lower than that of the flat face.

2) When selecting RHS for notch toughness, serious consideration should be given to the

deterioration from flat face to corner (i.e. the weak spot) such that the entire cross-

section is “fit for purpose”. This can be done by either specifying the corner as an

alternate measuring location, or considering the deterioration from the flat face to the

corner (i.e. the shift in transition temperature ∆Tcf) if the CVN toughness was measured

in the standard location (flat face). When using the latter method, it is necessary to

distinguish direct-formed RHS from continuous-formed RHS. Based on the CVN test

results in this study, it is recommended that if the CVN toughness was measured in the

standard location (flat face), as specified by international steel product standards, a ∆Tcf

of 20 °C from the flat to the corner may be conservatively used for any continuous-

formed RHS, and a ∆Tcf of 40 °C from the flat face to the corner may be conservatively

used for any direct-formed RHS. Such “temperature shifts” can be implemented by a

designer when specifying the flat face CVN toughness if a certain toughness level is

required to be met in the corner (e.g. a specification of 27 J at -40 °C in the flat region of

a continuous-formed RHS would ensure a CVN rating of 27 J at -20 °C in the corner

regions).

3) Heat treatment in accordance with Canadian standards [CSA 2013] for “Class H”

finishing does not provide improvement in the CVN toughness.

4) For thick-walled RHS, where full-sized CVN coupons are possible, current

specifications permit the test coupon notch to be either on the RHS surface or through

the RHS wall thickness. Since the latter produces a lower CVN toughness reading, it is

recommended that testing requirements in HSS product specifications/standards specify

through-thickness notches.

For comparison of the high strain rate properties, a total of 166 split Hopkinson

pressure/tension bar tests were performed on compressive and tensile samples machined from

the flat face and the corner of the RHS specimens. By evaluation of the dynamic properties

relative to the measured static properties at the same test location, local dynamic increase

99

factors for yield stress (DIFy) have been determined. Using the measured flat face and corner

areas, the full-sectional DIFy values were calculated for the RHS specimens. It can be

concluded that:

1) RHS experience a greater dynamic increase in yield stress with increasing strain rates.

2) RHS with higher static yield stress are generally less susceptible to the strain rate effect.

3) For direct-formed RHS, the full-sectional DIFy value does not change substantially as

the cross-sectional geometry changes. For continuous-formed RHS, the full-sectional

DIFy value increases as the Bnom/tnom ratio increases.

4) For the same strain rate, the compressive and tensile DIFy values for identical RHS may

differ.

5) Representative full-sectional DIFy values (for RHS with different cross-sectional

geometries and produced by different forming methods) generated in this study could be

used in the blast- or impact-resistant design of RHS members under compression,

tension and flexural loadings when high strain rates are present.

Future work:

1) In general, the mechanical properties of RHS (especially continuous-formed RHS) with

various Bnom/tnom ratios are different, thus it is necessary to test more RHS specimens

with different Bnom/tnom ratios to further investigate the effect of different cross-sectional

dimensions (i.e. different degrees of cold-forming). Ratios ranging from 8 to 40

ultimately need to be studied (i.e. the range of Bnom/tnom ratios which are typically found

in bridges, buildings and other structures).

2) For overall compressive behaviour, it is desirable to perform column tests on the direct-

formed and continuous-formed RHS specimens investigated in this study (RHS

152x152x12.7 and RHS 152x152x6.35). Different column effective lengths from 2

metres to 8 metres would be appropriate. The column test results could then be

compared to the analytical column curves generated in this study to further validate the

effect of different cold-forming methods on the global column behaviour of RHS.

3) For the high strain rate behaviour, it was found in this study that for continuous-formed

RHS, the full-sectional DIFy value increases as the Bnom/tnom ratio increases. Thus, it is

desirable to perform more high strain rate tests on continuous-formed RHS with

different Bnom/tnom ratios to further capture this trend.

100

4) The dynamic strain rates studied ranged from 100 to 1000 s-1

. Extending the test range

down to ~10 s-1

would be very useful, and relevant to large stand-off blast loadings.

5) Both direct-forming and continuous-forming processes can be modeled using non-linear

finite element methods to study the generation of residual stress. Unlike measuring local

material properties at discrete locations, the effects of different cold-forming processes

on the mechanical behaviour of the entire cross-section of RHS can be studied

analytically. The overall section performance can then be related to various structural

applications.

101

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108

Appendix A Geometric Measurements and Static Properties

A.1 Geometric measurements

Table A.1 Measured thickness and corner radius of RHS 152x152x12.7 & Domex (DF19)

Location

Thickness (mm) Corner radius (mm)

DF19 DF12 CF12 CFH12 DF19 DF12 CF12 CFH12

Outside Inside Outside Inside Outside Inside Outside Inside

1 8.15 12.51 12.62 12.62 - - - - - - - -

2 8.19 12.40 13.04 13.04 - - - - - - - -

3 8.28 12.33 12.88 12.88 18.13 10.53 23.04 9.20 37.77 20.49 37.77 20.49

4 8.14 12.36 12.53 12.53 - - - - - - - -

5 8.08 12.48 12.47 12.47 - - - - - - - -

6 8.21 12.55 12.76 12.76 - - - - - - - -

7 8.49 12.89 13.01 13.01 13.58 9.28 24.96 5.31 29.17 17.10 29.17 17.10

8 8.13 12.59 12.95 12.95 - - - - - - - -

9 8.26 12.60 12.45 12.45 - - - - - - - -

10 8.27 12.54 12.92 12.92 - - - - - - - -

11 8.73 13.03 12.96 12.96 15.46 6.13 25.58 8.09 28.75 14.44 28.75 14.44

12 8.20 12.67 12.61 12.61 - - - - - - - -

13 8.18 12.43 12.39 12.39 - - - - - - - -

14 8.22 12.45 12.46 12.46 - - - - - - - -

15 8.31 12.31 12.96 12.96 15.29 10.73 23.75 11.93 21.98 13.62 21.98 13.62

16 8.19 12.47 12.73 12.73 - - - - - - - -

Average 8.25 12.54 12.73 12.73 15.62 9.16 24.33 8.63 29.42 16.41 29.42 16.41

1

weld

seam

23

16

9 87

10

4

5

6

14

13

12

15

11

109

Table A.2 Measured thickness and corner radius of RHS 152x152x6.35

Location

Thickness (mm) Corner radius (mm)


Outside Inside Outside Inside Outside Inside

1 6.30 5.91 5.91 - - - - - -

2 6.35 5.90 5.90 - - - - - -

3 6.64 6.20 6.20 13.56 6.99 13.87 7.65 13.87 7.65

4 6.28 5.84 5.84 - - - - - -

5 6.22 5.79 5.79 - - - - - -

6 6.25 5.85 5.85 - - - - - -

7 6.45 6.22 6.22 15.30 8.46 13.91 7.32 13.91 7.32

8 6.27 5.86 5.86 - - - - - -

9 5.47* 5.98 5.98 - - - - - -

10 6.29 5.86 5.86 - - - - - -

11 6.48 6.24 6.24 13.26 5.62 12.49 6.88 12.49 6.88

12 6.28 5.93 5.93 - - - - - -

13 6.28 5.95 5.95 - - - - - -

14 6.29 6.04 6.04 - - - - - -

15 6.44 6.26 6.26 13.91 6.67 12.27 6.18 12.27 6.18

16 6.33 5.90 5.90 - - - - - -

Average 6.29 5.98 5.98 14.01 6.94 13.14 7.01 13.14 7.01

*Decrease in thickness near weld seam

1

weld

seam

23

16

9 87

10

4

5

6

14

13

12

15

11

110

A.2 Tensile coupon test results

Figure A.1 Tensile coupon test results for DF19 (RHS 152x152x7.95, high strength, direct-

formed)

Figure A.2 Tensile coupon test results for DF12 (RHS 152x152x12.7, regular strength, direct-

formed)

0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain

Corner#2 Corner#1 Flat face#3

Flat face#1 Flat face#2

0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain



111

Figure A.3 Tensile coupon test results for DF24 (RHS 152x152x6.35, regular strength, direct-

formed)

Figure A.4 Tensile coupon test results for CF12 (RHS 152x152x12.7, regular strength,

continuous-formed)

0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain



0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain



112

Figure A.5 Tensile coupon test results for CFH12 (RHS 152x152x12.7, regular strength,

continuous-formed plus heat-treated)

Figure A.6 Tensile coupon test results for CF24 (RHS 152x152x6.35, regular strength,

continuous-formed)

0

100

200

300

400

500

600

700

800

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain



0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain



113

Figure A.7 Tensile coupon test results for CFH24 (RHS 152x152x6.35, regular strength,


0

100

200

300

400

500

600

700

800

900

0 0.005 0.01 0.015 0.02

Str

ess (

MP

a)

Strain



114

A.3 Stub column test results and determination of maximum longitudinal compressive residual stresses

Figure A.8 Stub column test results for DF19 (RHS 152x152x7.95, high strength, direct-

formed)

Figure A.9 Stub column test results for DF12 (RHS 152x152x12.7, regular strength, direct-

formed)

0

100

200

300

400

500

600

700

800

900

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





0

100

200

300

400

500

600

700

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





115

Figure A.10 Stub column test results for DF24 (RHS 152x152x6.35, regular strength, direct-

formed)

Figure A.11 Stub column test results for CF12 (RHS 152x152x12.7, regular strength,

continuous-formed)

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





0

100

200

300

400

500

600

700

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





116

Figure A.12 Stub column test results for CFH12 (RHS 152x152x12.7, regular strength,


Figure A.13 Stub column test results for CF24 (RHS 152x152x6.35, regular strength,

continuous-formed)

0

100

200

300

400

500

600

700

800

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





0

50

100

150

200

250

300

350

400

450

500

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





117

Figure A.14 Stub column test results for CFH24 (RHS 152x152x6.35, regular strength,


0

50

100

150

200

250

300

350

400

450

500

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Str

ess

(M

Pa)

Strain





118

A.4 Measured longitudinal residual stresses

Table A.3 Normalized measured longitudinal residual stresses in DF12, CF12 and CFH12

DF12 CF12 CFH12

Location 1 σrs,out / fy 0.346 0.380 0.214

σrs,in / fy -0.280 -0.308 -0.209


σrs,in / fy -0.541 -0.888 -0.372


σrs,in / fy -0.121 -0.494 -0.221


σrs,in / fy -0.525 -0.724 -0.337


σrs,in / fy -0.294 -0.315 -0.147


σrs,in / fy -0.602 -0.911 -0.177


σrs,in / fy -0.254 -0.515 -0.169


σrs,in / fy -0.504 -0.800 -0.353


σrs,in / fy -0.263 -0.441 -0.223

119

Table A.4 Normalized measured longitudinal residual stresses in DF24, CF24 and CFH24

DF24 CF24 CFH24


σrs,in / fy -0.299 -0.474 -0.050


σrs,in / fy -0.507 -0.719 -0.258


σrs,in / fy -0.282 -0.459 -0.178


σrs,in / fy -0.253 -0.499 -0.166


σrs,in / fy -0.294 -0.466 -0.181


σrs,in / fy -0.567 -0.749 -0.285


σrs,in / fy -0.276 -0.472 -0.096


σrs,in / fy -0.408 -0.518 -0.236


σrs,in / fy -0.114 -0.230 -0.100


σrs,in / fy -0.094 -0.267 -0.106


σrs,in / fy -0.070 -0.253 -0.114


σrs,in / fy -0.362 -0.592 -0.245


σrs,in / fy -0.127 -0.463 -0.078

120

DF12

σm = [σrs,out / fy+σrs,in / fy]/2

Corresponding percentage of

cross-sectional area

Residual force =

σm x area

Location 1 3.26% of yield stress 6.25% of entire cross-section 0.20% of yield load

Location 2 -6.39% of yield stress 12.50% of entire cross-section -0.80% of yield load








Total 100% of entire cross-section 0.34% of yield load

Table A.5 Calculation of residual force in DF12

CF12




Residual force =

σm x area










Total 100% of entire cross-section -0.58% of yield load

Table A.6 Calculation of residual force in CF12

CFH12




Residual force =

σm x area










Total 100% of entire cross-section -0.34% of yield load

Table A.7 Calculation of residual force in CFH12

121

DF24




Residual force =

σm x area















Table A.8 Calculation of residual force in DF24

CF24




Residual force =

σm x area















Table A.9 Calculation of residual force in CF24

122

CFH24




Residual force =

σm x area















Table A.10 Calculation of residual force in CFH24

123

A.5 Analytical compressive stress-strain curves based on column models

Figure A.15 Comparisons of overall compressive stress-strain curves from stub column tests

and column models for DF12


and column models for DF24

0

100

200

300

400

500

600

700

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain

DF12 stub column test results

DF12 column model results

0

100

200

300

400

500

600

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain

DF24 stub column test results

DF24 column model results

124


and column models for CF12


and column models for CFH12

0

100

200

300

400

500

600

700

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain



0

100

200

300

400

500

600

700

800

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain

CFH12 stub column test results

CFH12 column model results

125


and column models for CF24


and column models for CFH24

0

50

100

150

200

250

300

350

400

450

500

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain



0

50

100

150

200

250

300

350

400

450

0 0.002 0.004 0.006 0.008 0.01

Str

ess (

MP

a)

Strain

CFH24 stub column test results

CFH24 column model results

126

Appendix B Calculations for Analytical Charpy Transition Temperatures

B.1 Derivation of equations in Figure 3.7 for determination of εeff in the bent region of HSS [Feldmann et al. 2012]

When t ≥ 20 mm, use full-sized CVN coupon.

Note: The shaded areas represent the cross-section of a full-sized CVN coupon

𝜀 𝜀

𝑡

𝑡

𝜀 𝑡

𝑡 𝜀

𝜀 𝜀 𝜀

𝜀 (

𝑡 𝑡 ) 𝜀

𝜀

𝑡

𝑡 𝜀

𝑡

εmax

t

10

10<10

εmax εmax

εmax εmax εmax

t t

ε1

ε1

εeff

127

When 10 mm ≤ t < 20 mm, use full-sized CVN coupon.

Note: The shaded areas represent the cross-section of a full-sized CVN coupon

𝜀 𝜀

𝑡

𝑡

𝜀 𝑡

𝑡 𝜀

𝜀 (𝜀 ) (

𝑡 ) (

𝜀

) (𝑡 )

( 𝑡 𝑡 ) 𝜀 (

𝑡 ) (

𝜀

) (𝑡 )

𝜀

𝑡

𝑡

𝜀

𝑡 𝑡

𝑡

𝑡

𝑡

𝑡

𝜀 𝑡

𝑡

𝑡

εeff

εmax

t

10

10<10

εmax εmax

εmax εmax εmax

t tε1

ε1

128

When t < 10 mm, use sub-sized CVN coupon.

Note: The shaded areas represent the cross-section of a sub-sized CVN coupon

Eq. 3-1 in EN 1993-1-10 [CEN 2005] and Eq. 3-3 in the JRC report [Feldmann et al. 2012]

were developed based on CVN test results on full-sized coupons. Thus, when calculating the

εeff-value of a sub-sized CVN coupon for use in Eq. 3-3, the calculated average value of the

plastic strain (%) in the net section of a sub-sized CVN coupon shall be normalized as

follows according to [Feldmann et al. 2012] such that it is consistent with a full-sized CVN

coupon.

𝜀 (𝜀

)

𝑡

𝜀 𝑡

εmax

t

10

10<10

εmax εmax

εmax εmax εmax

t tε1

ε1

εeff

129

B.2 Calculation of analytical ∆Tcf-values in Table 3.10 based on the approach proposed by [Feldmann et al. 2012] using measured cross-sectional dimensions

DF12:

Since DF12 is direct-formed (i.e. the flat face is not severely cold-worked), the temperature

shift from the coil plate to the corner determined using the approach proposed by [Feldmann

et al. 2012] was taken as the analytical ∆Tcf-value from the flat face (location A) to the corner

(Location B or D) due to the uneven degree of cold-forming.

Cutting locations and orientations of CVN coupons

Measured cross-sectional dimensions

Location B: t = 12.89 mm, ri = 5.31 mm

Location D: t = 13.03 mm, ri = 8.09 mm

weld

seam

D B

A

CB

weld

seam

A

C

130

Calculation of εeff at location B

As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

𝜀

𝜀

𝜀 (𝜀 )

(𝜀 )

Determination of analytical ∆Tcf from coil strip to Location B

As per Eq. 3-3,

𝑟 𝑚 𝑖 𝑡𝑟𝑖 𝑡 𝑎𝑡𝑖


2 mm notch

12.89mm

1.445 mm

3 mm

5 mm

1.445 mm

ε2

ε1

εmax

(inside surface of RHS)

(outside surface of RHS)εmax

131

Determination of analytical ∆Tcf from Location A to Location B

Since DF12 is direct-formed, Location A has similar material properties to the coil strip.

𝑟 𝑚 𝑎𝑡𝑖 𝑡 𝑎𝑡𝑖 𝑟 𝑚 𝑖 𝑡𝑟𝑖 𝑡 𝑎𝑡𝑖

Calculation of εeff at location D

As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

𝜀

𝜀

𝜀 (𝜀 )

(𝜀 )

13.03mm

1.515 mm

2 mm notch

3 mm

5 mm

1.515 mm

ε2

ε1

εmax



132

Determination of analytical ∆Tcf from coil strip to Location D

As per Eq. 3-3,



Determination of analytical ∆Tcf from Location A to Location D



133

DF24:

Since DF24 is direct-formed (i.e. the flat face is not severely cold-worked), the temperature

shift from the coil plate to the corner determined using the approach proposed by [Feldmann

et al. 2012] was taken as the analytical ∆Tcf-value from the flat face (location A) to the corner

(Location B) due to the uneven degree of cold-forming.




weld

seam

D B

A

CB

weld

seam

A

C

134


As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

𝜀 (𝜀 )


As per Eq. 3-3,






6.45mm

1.575 mm

3.3 mm

1.575 mmε1

εmax



135

CF12 and CFH12:

Since CF12 and CFH12 are continuous-formed (i.e. both flat face and the corner are severely

cold-worked), the temperature shift from the coil plate to the flat face and the temperature

shift from the coil plate to the corner were both determined, and the difference between the

two temperature shifts was taken as the analytical ∆Tcf-value from the flat face (location A)

to the corner (Location B or D) due to the extra amount of cold-forming.



Bavg = 151.9 mm

Location A: t = 12.62 mm


Location D: t = 12.96 mm, ri = 14.44 mm

weld

seam

D B

A

CB

weld

seam

A

C

136

Calculation of εeff at location A

As per [Feldmann et al. 2012],

𝑟

𝑖 𝑖 𝑟𝑎 𝑖 𝑖𝑟 𝑎𝑟 𝑡 𝑟 𝑟𝑡 𝑟 𝑎𝑡𝑡 𝑖 𝑖𝑡 𝑖 𝑡 𝑟 𝑡𝑎 𝑎𝑟 𝑡

𝑡

𝑚𝑚

As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

𝜀

𝜀

As per [Feldmann et al. 2012], since the coil strip is roll-formed into a circular tube before

flattening it to the desired rectangular tube, the degree of cold-forming at the flat face is

roughly 2 x the degree of cold-forming for the equivalent round tube.

𝜀 (𝜀 )

(𝜀 )

2 mm notch

12.62mm

1.31 mm

3 mm

5 mm

1.31 mm

ε2

ε1

εmax



137

Determination of analytical ∆Tcf from coil strip to Location A

As per Eq. 3-3,




As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

𝜀

𝜀

𝜀 (𝜀 )

(𝜀 )

2 mm notch

13.01mm

1.505 mm

3 mm

5 mm

1.505 mm

ε2

ε1

εmax



138


As per Eq. 3-3,




𝑟 𝑚 𝑎𝑡𝑖 𝑡 𝑎𝑡𝑖

( 𝑟 𝑚 𝑖 𝑡𝑟𝑖 𝑡 𝑎𝑡𝑖 )


Calculation of εeff at location D

As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

12.96mm

1.48 mm

2 mm notch

3 mm

5 mm

1.48 mm

ε2

ε1

εmax



139

𝜀

𝜀

𝜀

𝜀

𝜀 (𝜀 )

(𝜀 )

Determination of analytical ∆Tcf from coil strip to Location D

As per Eq. 3-3,



Determination of analytical ∆Tcf from Location A to Location D




140

CF24 and CFH24

Since CF24 and CFH24 are continuous-formed (i.e. both flat face and the corner are severely

cold-worked), the temperature shift from the coil plate to the flat face and the temperature

shift from the coil plate to the corner were both determined, and the difference between the

two temperature shifts was taken as the analytical ∆Tcf-value from the flat face (location A)

to the corner (Location B) due to the extra amount of cold-forming.



Bavg = 152.8 mm

Location A: t = 5.91 mm


weld

seam

D B

A

CB

weld

seam

A

C

141

Calculation of εeff at location A

As per [Feldmann et al. 2012],

𝑟

𝑖 𝑖 𝑟𝑎 𝑖 𝑖𝑟 𝑎𝑟 𝑡 𝑟 𝑟𝑡 𝑟 𝑎𝑡𝑡 𝑖 𝑖𝑡 𝑖 𝑡 𝑟 𝑡𝑎 𝑎𝑟 𝑡

𝑡

𝑚𝑚

As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

As per [Feldmann et al. 2012], since the coil strip is roll-formed into a circular tube before

flattening it to the desired rectangular tube, the degree of cold-forming at the flat face is

roughly 2 x the degree of cold-forming for the equivalent round tube.

𝜀 (𝜀 )

5.91mm

1.305 mm

3.3 mm

1.305 mmε1

εmax



142

Determination of analytical ∆Tcf from coil strip to Location A

As per Eq. 3-3,




As per Figure 3.7,

𝜀 𝑡

𝑟 𝑡

𝜀

𝜀

𝜀 (𝜀 )


As per Eq. 3-3,

6.22mm

1.46 mm

3.3 mm

1.46 mmε1

εmax



143







144

Appendix C Split-Hopkinson Pressure Bar Test Results

Figure C.1 Dynamic compressive stress-strain curves for flat face of DF12 (RHS

152x152x12.7, regular strength, direct-formed)

Figure C.2 Dynamic compressive stress-strain curves for corner of DF12 (RHS


0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000S

tre

ss (

MP

a)

Strain

Strain rate from 108 s-1 to 987 s

-1

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain


-1

145

Figure C.3 Dynamic compressive stress-strain curves for flat face of CF12 (RHS

152x152x12.7, regular strength, continuous-formed)

Figure C.4 Dynamic compressive stress-strain curves for corner of CF12 (RHS 152x152x12.7,

regular strength, continuous-formed)

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

Str

ess (

MP

a)

Strain

Strain rate from 100 s-1

to 1016 s-1

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

Str

ess (

MP

a)

Strain


-1

146

Figure C.5 Dynamic compressive stress-strain curves for flat face of DF24 (RHS


Figure C.6 Dynamic compressive stress-strain curves for corner of DF24 (RHS


0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain


-1

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

1200

Str

ess (

MP

a)

Strain


-1

147

Figure C.7 Dynamic compressive stress-strain curves for flat face of CF24 (RHS

152x152x6.35, regular strength, continuous-formed)

Figure C.8 Dynamic compressive stress-strain curves for corner of CF24 (RHS 152x152x6.35,


0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

1200

Str

ess (

MP

a)

Strain


-1

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

1200

Str

ess (

MP

a)

Strain


-1

148

Table C.1 Key compressive SHPB test results (F = flat face; C = corner)

No. Cutting

location

Strain

rate (s-1

)

fdy

(MPa)

fy

(MPa) DIFy

1 DF12-F 108 620 450 1.38

2 DF12-F 115 620 450 1.38

3 DF12-F 135 640 450 1.42

4 DF12-F 254 640 450 1.42

5 DF12-F 290 660 450 1.47

6 DF12-F 290 650 450 1.44

7 DF12-F 301 655 450 1.46

8 DF12-F 348 640 450 1.42

9 DF12-F 363 680 450 1.51

10 DF12-F 577 730 450 1.62

11 DF12-F 579 730 450 1.62

12 DF12-F 632 740 450 1.64

13 DF12-F 766 770 450 1.71

14 DF12-F 779 780 450 1.73

15 DF12-F 783 770 450 1.71

16 DF12-F 851 760 450 1.69

17 DF12-F 856 760 450 1.69

18 DF12-F 987 770 450 1.71

19 DF12-C 144 720 650 1.11

20 DF12-C 150 730 650 1.12

21 DF12-C 161 770 650 1.18

22 DF12-C 218 750 650 1.15

23 DF12-C 303 780 650 1.20

24 DF12-C 424 810 650 1.25

25 DF12-C 437 830 650 1.28

26 DF12-C 583 860 650 1.32

27 DF12-C 591 870 650 1.34

28 DF12-C 595 870 650 1.34

29 DF12-C 789 870 650 1.34

30 DF12-C 790 880 650 1.35

31 DF12-C 957 900 650 1.38

32 DF12-C 987 870 650 1.34

33 DF12-C 1001 910 650 1.40

34 CF12-F 100 460 490 0.94

35 CF12-F 108 450 490 0.92

36 CF12-F 115 460 490 0.94

37 CF12-F 140 470 490 0.96

38 CF12-F 140 460 490 0.94

39 CF12-F 151 470 490 0.96

40 CF12-F 403 500 490 1.02

149

Table C.1 (continued)

No. Cutting

location

Strain

rate (s-1

)

fdy

(MPa)

fy

(MPa) DIFy

41 CF12-F 421 510 490 1.04

42 CF12-F 579 540 490 1.10

43 CF12-F 584 530 490 1.08

44 CF12-F 594 520 490 1.06

45 CF12-F 764 550 490 1.12

46 CF12-F 774 550 490 1.12

47 CF12-F 776 550 490 1.12

48 CF12-F 777 540 490 1.10

49 CF12-F 853 590 490 1.20

50 CF12-F 1009 600 490 1.22

51 CF12-F 1016 590 490 1.20

52 CF12-C 45 520 550 0.95

53 CF12-C 117 600 550 1.09

54 CF12-C 118 600 550 1.09

55 CF12-C 130 520 550 0.95

56 CF12-C 161 560 550 1.02

57 CF12-C 166 540 550 0.98

58 CF12-C 357 550 550 1.00

59 CF12-C 435 570 550 1.04

60 CF12-C 452 560 550 1.02

61 CF12-C 588 590 550 1.07

62 CF12-C 591 570 550 1.04

63 CF12-C 593 580 550 1.05

64 CF12-C 759 630 550 1.15

65 CF12-C 762 610 550 1.11

66 CF12-C 767 600 550 1.09

67 CF12-C 986 640 550 1.16

68 CF12-C 998 650 550 1.18

69 CF12-C 1001 650 550 1.18

70 DF24-F 43 500 420 1.19

71 DF24-F 75 610 420 1.45

72 DF24-F 95 620 420 1.48

73 DF24-F 158 680 420 1.62

74 DF24-F 165 670 420 1.60

75 DF24-F 343 660 420 1.57

76 DF24-F 457 690 420 1.64

77 DF24-F 606 690 420 1.64

78 DF24-F 665 660 420 1.57

79 DF24-F 725 670 420 1.60

80 DF24-F 780 670 420 1.60

150


No. Cutting

location

Strain

rate (s-1

)

fdy

(MPa)

fy

(MPa) DIFy

81 DF24-F 814 650 420 1.55

82 DF24-F 828 700 420 1.67

83 DF24-C 89 780 520 1.50

84 DF24-C 111 810 520 1.56

85 DF24-C 133 840 520 1.62

86 DF24-C 186 800 520 1.54

87 DF24-C 204 920 520 1.77

88 DF24-C 232 820 520 1.58

89 DF24-C 241 730 520 1.40

90 DF24-C 261 880 520 1.69

91 DF24-C 340 830 520 1.60

92 DF24-C 413 820 520 1.58

93 DF24-C 430 850 520 1.63

94 DF24-C 754 820 520 1.58

95 DF24-C 808 790 520 1.52

96 DF24-C 818 830 520 1.60

97 DF24-C 1221 800 520 1.54

98 CF24-F 149 680 355 1.92

99 CF24-F 255 680 355 1.92

100 CF24-F 439 570 355 1.61

101 CF24-F 487 700 355 1.97

102 CF24-F 528 730 355 2.06

103 CF24-F 572 630 355 1.77

104 CF24-F 578 720 355 2.03

105 CF24-F 584 470 355 1.32

106 CF24-F 637 700 355 1.97

107 CF24-F 639 670 355 1.89

108 CF24-F 646 630 355 1.77

109 CF24-F 723 680 355 1.92

110 CF24-F 737 680 355 1.92

111 CF24-F 798 670 355 1.89

112 CF24-F 857 640 355 1.80

113 CF24-F 944 590 355 1.66

114 CF24-F 1407 650 355 1.83

115 CF24-F 132 800 465 1.72

116 CF24-F 187 810 465 1.74

117 CF24-F 200 870 465 1.87

118 CF24-F 202 810 465 1.74

119 CF24-F 222 800 465 1.72

120 CF24-F 283 760 465 1.63

151


No. Cutting

location

Strain

rate (s-1

)

fdy

(MPa)

fy

(MPa) DIFy

121 CF24-F 372 830 465 1.78

122 CF24-F 492 690 465 1.48

123 CF24-F 592 720 465 1.55

124 CF24-F 605 750 465 1.61

125 CF24-F 698 800 465 1.72

126 CF24-F 773 740 465 1.59

127 CF24-F 843 700 465 1.51

128 CF24-F 1047 780 465 1.68

152

Figure C.9 Dynamic tensile stress-strain curves for flat face of DF12 (RHS 152x152x12.7,

regular strength, direct-formed)

Figure C.10 Dynamic tensile stress-strain curves for corner of DF12 (RHS 152x152x12.7,

regular strength, direct-formed)

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

Str

ess (

MP

a)

Strain


-1

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain


-1

153

Figure C.11 Dynamic tensile stress-strain curves for flat face of CF12 (RHS 152x152x12.7,


Figure C.12 Dynamic tensile stress-strain curves for corner of CF12 (RHS 152x152x12.7,


0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain


-1

0.00 0.01 0.02 0.03 0.04

0

200

400

600

800

1000

Str

ess (

MP

a)

Strain


-1

154

Table C.2 Key tensile SHPB test results (F = flat face; C = corner)

No. Cutting

location

Strain

rate (s-1

)

fdy

(MPa)

fy

(MPa) DIFy

1 DF12-F 255 590 450 1.31

2 DF12-F 265 580 450 1.29

3 DF12-F 321 620 450 1.38

4 DF12-F 335 630 450 1.40

5 DF12-F 379 660 450 1.47

6 DF12-F 496 650 450 1.44

7 DF12-F 686 650 450 1.44

8 DF12-F 794 720 450 1.60

9 DF12-F 842 720 450 1.60

10 DF12-F 888 680 450 1.51

11 DF12-C 167 650 650 1.00

12 DF12-C 351 700 650 1.08

13 DF12-C 391 720 650 1.11

14 DF12-C 497 710 650 1.09

15 DF12-C 638 760 650 1.17

16 DF12-C 654 730 650 1.12

17 DF12-C 684 760 650 1.17

18 DF12-C 820 790 650 1.22

19 DF12-C 891 780 650 1.20

20 DF12-C 970 790 650 1.22

21 CF12-F 181 710 490 1.45

22 CF12-F 219 700 490 1.43

23 CF12-F 292 690 490 1.41

24 CF12-F 384 730 490 1.49

25 CF12-F 588 780 490 1.59

26 CF12-F 680 780 490 1.59

27 CF12-F 821 820 490 1.67

28 CF12-F 888 820 490 1.67

29 CF12-F 997 870 490 1.78

30 CF12-C 156 650 550 1.18

31 CF12-C 232 680 550 1.24

32 CF12-C 267 680 550 1.24

33 CF12-C 448 750 550 1.36

34 CF12-C 614 770 550 1.40

35 CF12-C 683 800 550 1.45

36 CF12-C 794 850 550 1.55

37 CF12-C 850 850 550 1.55

38 CF12-C 1028 870 550 1.58

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Mechanical Behaviour of Cold-Formed Hollow Structural ... · Mechanical Behaviour of Cold-Formed Hollow Structural Section Material Min Sun Doctor of Philosophy Graduate Department