1. Presented by : Shameem Ahmed Co-author : Mahmud Ashraf
School of Engineering and Information Technology
COMPRESSION CAPACITY OF SLENDER STAINLESS STEEL CROSS-SECTIONS
Presented by : Shameem Ahmed
Co-author : Mahmud Ashraf
School of Engineering and Information Technology
UNSW, Canberra
November, 2015

2. Outline What is stainless steel?
Advantages and disadvantages of Stainless Steel
Structural uses of stainless steel
Current design approach
Basic concept of CSM
CSM for slender cross-section
Performance of the proposed method
Conclusion
November,

3. What is Stainless steel?
C≤ 1.2% Fe
Cr ≥ 10.5%
Ferrous alloy containing Cr  10.5% and C  1.2%
Other alloy material: Ni, Mn and Mo
Martensitic
(11-18:0-2)
Strain (%) 10 20 30 40 50 60
Stress (MPa)
200
400
600
Duplex (18-27:4-7)
Chromium content (%) 4 8 12 16 20
0.1
0.2
0.3
Corrosion rate (mm/year)
Austenitic
(16-30:8-35)
Ferritic
(12-28:0-5)
November,

4. Advantages and disadvantages of Stainless Steel
Compare to the carbon steel stainless steel exhibits
Better corrosion resistance
Negligible maintenance cost
Higher recyclability
Better performance in fire
Attractive appearance
The only disadvantage is…… High material cost!!!!
However … life cycle cost of a stainless steel structure could be significantly less than the corresponding carbon steel structure!
November,

5. Structural uses of stainless steel
Pedestrian bridge, Sweden, 2013
Dublin Spire, Ireland, 2003
Marina Bay Bridge, Singapore, 2010
November,

6. Stainless Steel Vs Carbon Steel
0.002
Strain ε
Stress σ
Stainless steel E
σ0.2
Carbon steel
0.005
0.010
0.015
Nonlinear stress-strain behavior
No sharply defined yield point
Pronounced strain hardening
November,

7. Australia/ New Zealand
Current design approach
Design Codes for Cross –Sections
Australia/ New Zealand
AS/NZS 4673 (2001)
North America
SEI/ASCE 8-02 (2002)
Europe
Eurocode 3 Part 1.4 (2006)
Rotation
Moment
Mpl
Mel
All current international design rules are analogies with Carbon Steel
Class 1
Class 2
Class 3 sy
Class 4
Stress
Strain
Effective width approach is used for slender sections
November,

8. Current design approach (cont...)
In Effective Width approach
Due to local buckling some part of the section are assumed to be ineffective for slender cross-section section
Design are based on effective section
Effective section
Compression
Bending
November,

9. Basic concept of CSM
The Continuous Strength Method (CSM) is a strain based approach that provides a continuous relationship between the cross-section slenderness β and the deformation capacity LB of a cross-section.
It incorporates
Material nonlinearity
strain hardening
Continuous treatment of local buckling
1st Proposed by Gardner in 2002 for stainless steel hollow sections.
Later modifications by Ashraf (2006), Theofenous (2008) and Afshan (2013)
November,

10. Normalised deformation capacity
Basic concept of CSM u Fu
Deformation
Load
Cross-section slenderness 
Normalised deformation capacity
LB/0
Buckling stress fLB can be calculated from εLB with appropriate material model
𝑁 𝑢 = 𝑓 𝐿𝐵 × 𝐴 𝑔
November,

11. Basic concept of CSM Stress Stress Strain Strain Predicted
Stocky section
Material coupon
eLB,2
fLB,2 (actual)
fLB,2
eLB,2
fLB,2 (pred.)
Material Coupon
Stocky section
fLB,1 (pred.)
eLB,1
fLB,1
eLB,1
fLB,1 (actual)
Slender section
Slender section
Predicted
Observed in tests
November,

12. Basic concept of CSM (cont...)
Effective width Method
Strain Ratio, εcsm/ε0 25 20 15 10 5
0.2
0.4
0.6
0.8
1.0
1.2
Cross-section slenderness, λ 𝒑
Slender Section
Stocky Section
λ 𝒑 =0.68
Afshan (2013) modified the basic design curve only for stocky sections
Include element interaction in cross-section slenderness λ 𝑝
𝜆 p = 𝜎 𝜎 𝑐𝑟,𝑐𝑠
Bi-linear material model is proposed with a strain hardening stiffness Esh
Strains, ε
Stress, σ E0
Esh εy fy
εCSM
fCSM
0.002
𝑓 𝑐𝑠𝑚 = 𝑓 𝑦 + 𝐸 𝑠ℎ 𝜀 𝑦 𝜀 𝑐𝑠𝑚 𝜀 𝑦 −1
for 𝜆 𝑝 ≤0.68
Slender section use traditional codes
November,

13. CSM for slender cross-sections
Failure of slender sections are dominated by:
elastic local buckling below the material yield stress
significant post buckling
fpredicted
factual
εcsm
Slender section
Material property
Strain
Stress
𝜀 𝑒,𝑒𝑣 = 𝑁 𝑢 𝐸 𝐴 𝑔
εe,ev
Equivalent Elastic Deformation Capacity εe,ev : elastic strain at ultimate load
November,

14. CSM for slender cross-sections
𝜀 𝑒,𝑒𝑣 =𝐶 𝜀 𝑐𝑠𝑚
RHS
Lipped Channel
I-Section
SHS
November,

15. CSM for slender cross-sections (cont…)
𝐶=𝑎 𝜆 𝑝 𝑏
Proposed coefficients a and b for different types of cross sections
Section Type a b
Channel
2.75
2.83
Lipped Channel
3.04
3.15
I Section
3.01
2.79
SHS
2.85
2.50
RHS
3.18
2.90
November,

16. CSM for slender cross-sections (cont…)
a=3.03
b= 2.83
All Section types
November,

17. CSM for slender cross-sections (cont…)
Strain
Stress
Cross-section compression resistance
Buckling Stress fcsm
fcsm
𝑓 𝑐𝑠𝑚 = 𝜀 𝑒,𝑒𝑣 𝐸 0 =𝐶 𝜀 𝑐𝑠𝑚 𝐸 𝑜
for 𝜆 𝑝 >0.68
εe,ev
cross-section compression resistance Nc,Rd
Material model
𝑁 𝑐,𝑅𝑑 = 𝑓 𝑐𝑠𝑚 𝐴 𝑔 𝛾 𝑀0
November,

18. CSM for slender cross-sections (cont…)
The cross section resistance against compression Nc,Rd
Eurocode
CSM
𝑁 𝑐,𝑅𝑑 = 𝐴 𝑔 𝑓 𝑐𝑠𝑚 𝛾 𝑀0
for Class 1, 2 and 3 cross-sections
𝑁 𝑐,𝑅𝑑 = 𝐴 𝑔 𝜎 𝛾 𝑀0
𝑓 𝑐𝑠𝑚 = 𝑓 𝑦 + 𝐸 𝑠ℎ 𝜀 𝑦 𝜀 𝑐𝑠𝑚 𝜀 𝑦 −1
for 𝜆 𝑝 ≤0.68
for Class 4 cross-sections
𝑁 𝑐,𝑅𝑑 = 𝐴 𝑒𝑓𝑓 𝜎 𝛾 𝑀0
𝑓 𝑐𝑠𝑚 =𝐶 𝜀 𝑐𝑠𝑚 𝐸 𝑜
for 𝜆 𝑝 >0.68
November,

19. Performance of the proposed method
Verification of the proposed model and comparison with EC3
(a) RHS
(b) Lipped Channel
(c) I-Section
(d) SHS
November,

20. Performance of the proposed method (cont…)
CSM predictions for cross-section resistances are more accurate and less scattered
All Sections
Section Type
No. of test
Using coefficient according to section types
Using same coefficient for all section types
EC3
Average Ncsm/Ntest
COV
Channel 7
1.001
0.040
1.098
0.041
1.135
0.071
Lipped Channel 27
1.000
0.048
0.997
0.074
0.963
0.066
I Section 25
0.999
0.070
0.996
0.978
0.076
SHS
1.002
0.115
1.016
0.137
0.793
0.149
RHS
0.073
0.948
0.075
0.845
0.092
All Section
109 -
0.995
0.094
0.896
0.129
November,

21. Conclusion
Equivalent Elastic Deformation Capacity e,ev can deal with the observed buckling behaviour of slender sections and can be used to predict the buckling stress.
Performance of the proposed method is more accurate and consistent.
The suggested extension allows CSM to deal with all cross-section slenderness.
Eliminates the necessity of lengthy traditional process of calculating effective cross-sectional properties.
November,

22. November, 2015

23. November, 2015