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
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