1

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Tests on stainless steel

continuous beams

Marios Theofanous, Najib Saliba, Ou Zhao and Leroy Gardner

Imperial College London

Fourth International Experts Seminar

Stainless steel in structures

2

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

• Introduction

• Experiments

• Analysis of results and assessment of design

methods

• CSM with moment redistribution

• Conclusions and suggestions for future research

Presentation overview

3

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Plastic design

Plastic design refers to the method in which

the collapse load of an indeterminate

structure is determined on the basis of

sufficient plastic hinges forming to create a

collapse mechanism

Cross-sections must be capable of reaching

Mpl and maintaining it during plastic

deformation whilst the collapse mechanism is

forming. This is satisfied for Class 1 sections.

Introduction

4

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Current design provisions

Plastic design is not currently permitted for stainless steel, despite a Class 1 slenderness limit being provided in Standards.

Characteristics of stainless-steel

• Rounded stress-strain behaviour

• Substantial strain hardening

• High ductility

• Mu considerably above Mpl for stocky sections

Plastic design

5

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Aim

The aim of this study is to assess the applicability of plastic design procedures to stainless steel indeterminate structures.

Aim

6

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

To examine the applicability of plastic design to

stainless steel structures (grades EN 1.4301 and

EN 1.4162), the following tests were performed:

• Tensile coupon tests

• Simply supported beam tests

• Continuous beam tests to determine plastic

collapse loads of indeterminate assemblages

– Two arrangements considered

Experiments performed

7

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Tested cross-sections:

• Cold-formed RHS/SHS (EN 1.4301)

- SHS (50×50×3, 60×60×3, 100×100×3)

- RHS 60×40×3

• Welded I-sections (EN 1.4162)

- I 200×140×6×6

- I 200×140×8×6

- I 200×140×10×8

- I 200×140×12×8

Experiments performed

8

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

To assess moment capacity, rotation capacity and

effect of moment gradient in determinate systems:

• 5 three-point bending tests on RHS/SHS

• 4 three-point bending tests on I-sections

• 4 four-point bending tests on I-sections

Simple beam tests

9

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Simple beam tests

900 mm100 mm 100 mm

Beam specimen

String

potentiometer Inclinometer

Lateral restraints

Loading jackSpreader beam

900 mm 1000 mm

Lateral restraintsLinear Variable

Displacement

Transducer (LVDT)

Stiffener

1400 mm 1400 mm 100 mm 100 mm

Loading jack Beam

specimen

String

potentiomete

r

Inclinometer

Lateral

restraint

Linear Variable

Displacement Transducer

(LVDT)

Stiffener

10

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Normalised moment-rotation curves

Simple beam test

results

0.0

0.5

1.0

1.5

0 2 4 6 8 10θ/θpl

M/M

pl

50×50×3

60×60×3

100×100×3

60×40×3-MA

60×40×3-MI

11

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Normalised moment-rotation curves

Simple beam test

results

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 2 4 6 8 10 12

M/M

pl

θ/θpl

I-200 140 6 6-1

I-200 140 8 6-1

I-200 140 10 8-1

I-200 140 12 8-1

12

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Normalised moment-curvature curves

Simple beam test

results

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 3 6 9 12 15 18 21

M/M

pl

κ/κpl

I-200 140 6 6-2

I-200 140 8 6-2

I-200 140 10 8-2

I-200 140 12 8-2

13

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

To assess moment capacity, rotation capacity and

collapse loads of indeterminate structures:

• 18 continuous beam tests

• 2 configurations

Continuous beam tests

Loading jack

LVDT6 LVDT5

LVDT3

LVDT4

LVDT1

Spreader beam

Load Cell

LVDT2

1/2

200

1/2 1/2 1/2

Specimen

LVDT7 LVDT8

Continuous

beam test setup

2/3 1/3 1/3 2/3

Configuration 1 Configuration 2

14

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Continuous beam results

15

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Load-rotation curves (60x40x3-MA)

Continuous beam results

0

20

40

60

80

100

0.0 0.1 0.2 0.3 0.4

End rotation θ

Lo

ad

F

60×40×3-MA

First hinge

Plastic collapse

Plastic hinges

16

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Evolution of moment redistribution

0.4

0.6

0.8

1.0

1.2

1.4

0 10 20 30 40 50

Msu

pp

ort/M

span

Displacement (mm)

• SHS 50×50×3 -

loads at mid-span

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35

Msu

pport/M

span

Displacement (mm)

• SHS 50×50×3 -loads

at third points

17

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Design methods for simple beams

• EN 1993-1-4 (classification, σmax=σ0.2)

• Revised slenderness limits (classification,

σmax=σ0.2)

• Continuous strength Method (CSM)

18

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

• Uses a continuous measure of deformation

capacity to define strength:

Slenderness

Deformation

Continuous Strength Method

In place of section classification

y

u

3.6

csy

csm

ε

0.1ε15;minbut

λ

0.25

ε

ε

Base curve

19

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

• Bilinear elastic-hardening model to account for

strain-hardening at cross-sectional level

0.002)(ε0.016ε

ffE

yu

yu

sh

0

100

200

300

400

500

600

700

0.000 0.004 0.008 0.012 0.016 0.020

Strain

Str

ess

(N/m

m2)

Carbon steel

Stainless steel

2

y

csm

pl

el

y

csm

pl

elsh

pl

csm

ε

ε

W

W11

ε

ε

W

W

E

E1

M

M

Continuous Strength Method

20

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Design methods for simple beams

Specimen EN 1993-1-4 (2006)

Revised slenderness

limits CSM

Class Mpred/Mu Class Mpred/Mu εcsm/εy Mpred/Mu

SHS 50×50×3 1 0.71 1 0.71 0.35 10.8 0.97

SHS 60×60×3 1 0.73 1 0.73 0.37 10.7 0.95

SHS 100×100×3 4 0.65 4 0.68 0.66 10.4 0.81

RHS 60×40×3-MA 1 0.67 1 0.67 0.28 4.3 0.90

RHS 60×40×3-MI 3 0.60 1 0.71 0.42 0.8 0.86

I-200×140×6×6-1 4 0.72 4 0.76 0.65 1.2 0.85

I-200×140×8×6-1 4 0.69 3 0.70 0.51 2.7 0.79

I-200×140×10×8-1 1 0.69 1 0.69 0.38 8.5 0.83

I-200×140×12×8-1 1 0.69 1 0.69 0.31 15.0 0.90

I-200×140×6×6-2 4 0.73 4 0.77 0.65 1.2 0.86

I-200×140×8×6-2 4 0.79 3 0.81 0.51 2.7 0.91

I-200×140×10×8-2 1 0.85 1 0.85 0.37 8.9 1.00

I-200×140×12×8-2 1 0.80 1 0.80 0.31 15.0 1.06

MEAN 0.72 0.74 0.90

COV 0.09 0.08 0.09

21

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Continuous beams

Prediction of ultimate capacity based on:

• Elastic analysis – failure when cross-sectional

capacity is reached at the most heavily

stressed cross-section – no allowance for

moment redistribution

• Collapse mechanism – moment redistribution

is allowed for (plastic design for Class 1 cross-

sections is attmpted)

22

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Continuous beams-elastic analysis

Specimen

EN 1993-1-4 (2006) Revised slenderness limits CSM

Class Fpred/Fu Class Fpred/Fu Mpred/Mu

SHS 50×50×3-1 1 0.60 1 0.60 0.81

SHS 50×50×3-2 1 0.49 1 0.49 0.67

SHS 60×60×3-1 1 0.64 1 0.64 0.83

SHS 60×60×3-2 1 0.67 1 0.67 0.87

SHS 100×100×3-1 4 0.68 4 0.71 0.85

SHS 100×100×3-2 4 0.68 4 0.72 0.85

RHS 60×40×3-MA-1 1 0.56 1 0.56 0.75

RHS 60×40×3-MA-2 1 0.56 1 0.56 0.75

RHS 60×40×3-MI-1 3 0.52 1 0.61 0.75

RHS 60×40×3-MI-2 3 0.43 1 0.51 0.62

I-200×140×6×6-1 4 0.64 4 0.68 0.76

I-200×140×8×6-1 4 0.65 3 0.66 0.74

I-200×140×10×8-1 1 0.70 1 0.70 0.81

I-200×140×12×8-1 1 0.64 1 0.64 0.83

I-200×140×6×6-2 4 0.53 4 0.56 0.62

I-200×140×8×6-2 4 0.57 3 0.57 0.65

I-200×140×10×8-2 1 0.60 1 0.60 0.70

I-200×140×12×8-2 1 0.59 1 0.59 0.77

MEAN 0.60 0.61 0.76

COV 0.12 0.11 0.10

23

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Continuous beams-plastic design

Specimen EN 1993-1-4 (2006) Revised slenderness limits

Class Fpred/Fu Class Fpred/Fu

SHS 50×50×3-1 1 0.68 1 0.68

SHS 50×50×3-2 1 0.68 1 0.68

SHS 60×60×3-1 1 0.72 1 0.72

SHS 60×60×3-2 1 0.76 1 0.76

SHS 100×100×3-1 4 0.68 4 0.71

SHS 100×100×3-2 4 0.68 4 0.72

RHS 60×40×3-MA-1 1 0.63 1 0.63

RHS 60×40×3-MA-2 1 0.63 1 0.63

RHS 60×40×3-MI-1 3 0.52 1 0.69

RHS 60×40×3-MI-2 3 0.43 1 0.71

I-200×140×6×6-1 4 0.64 4 0.68

I-200×140×8×6-1 4 0.65 3 0.66

I-200×140×10×8-1 1 0.79 1 0.79

I-200×140×12×8-1 1 0.72 1 0.72

I-200×140×6×6-2 4 0.53 4 0.56

I-200×140×8×6-2 4 0.57 3 0.57

I-200×140×10×8-2 1 0.84 1 0.84

I-200×140×12×8-2 1 0.82 1 0.82

MEAN 0.66 0.70

COV 0.16 0.11

24

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Observations from comparisons with test results:

The comparisons indicate that plastic design is safely applicable to stainless steel structures, but is rather conservative.

The revised slenderness limits give more accurate results than those in EN 1993-1-4

However, limiting the maximum moment to Mpl restricts the accuracy of the design method

Observations

25

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Outline of the method

Assumptions:

• Failure occurs when a sufficient number of

plastic hinges forms

• The moment resistance at the critical (i.e. with

the highest deformation capacity) plastic hinge

is based on CSM and accounts for strain-

hardening

• The required deformation capacity at

subsequent hinges relates to their relative

plastic rotations as derived from the collapse

mechanism considered

2

26

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Outline of the method

Assumptions:

• Failure occurs when a sufficient number of

plastic hinges forms

2

27

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Outline of the method

•

•

2

F 1

F δ

L1 L2 L2 L1

MHinge1

MHinge2 MHinge

2 2

Mechanism Collapse BMD

iy

csm

crity

csm

crit

i

iy

csm

ε

ε

ε

ε

α

α

ε

ε

iy

csm

iii

ε

ε

hθα

28

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Comparison with test data

Specimen

CSM for indeterminate

structures

Class εcsm/εy Fpred/Fu

SHS 50×50×3-1 1 10.5 0.91

SHS 50×50×3-2 1 11.1 0.91

SHS 60×60×3-1 1 8.9 0.93

SHS 60×60×3-2 1 8.9 0.98

SHS 100×100×3-1 4 1.1 N/A

SHS 100×100×3-2 4 1.1 N/A

RHS 60×40×3-MA-1 1 10.2 0.84

RHS 60×40×3-MA-2 1 10.2 0.85

RHS 60×40×3-MI-1 1 5.6 0.84

RHS 60×40×3-MI-2 1 5.6 0.85

I-200×140×6×6-1 4 1.2 N/A

I-200×140×8×6-1 3 2.7 N/A

I-200×140×10×8-1 1 8.5 0.91

I-200×140×12×8-1 1 15.0 0.93

I-200×140×6×6-2 4 1.2 N/A

I-200×140×8×6-2 3 2.7 N/A

I-200×140×10×8-2 1 8.9 0.95

I-200×140×12×8-2 1 15.0 1.02

MEAN 0.91

COV 0.06

29

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Evolution of moments with

increasing load • I-200×140×10×8 - loads at mid-span

30

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Evolution of moments with

increasing load • I-200×140×10×8 - loads at third-points

31

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Conclusions

Conclusions

• 13 simple and 18 continuous beams tested

• Plastic design is applicable to stainless steel

• Revised slenderness improve predictions

• Accuracy of predictions is limited by design

framework (i.e. classification, M ≤ Mpl)

• Strain-hardening at cross-sectional level and

moment redistribution at sructure level

• CSM allows for strain hardening at cross-

sectional level and provides very accurate

capacity predictions when moment

redistribution is allowed for

32

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Future research

• Required slenderness (i.e. deformation

capacity) for moment redistribution

• Assessment of basic assumptions and

accuracy for various configurations of

indeterminate structures

• Effect of incorporating falling branch of

moment-deformation response

33

Introduction

Experiments

Assessment of

design methods

CSM with moment

redistribution

Conclusions and

future research

Tests on stainless steel

continuous beams

Marios Theofanous, Najib Saliba, Ou Zhao and Leroy Gardner

Imperial College London

Fourth International Experts Seminar

Stainless steel in structures