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

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, 2015 1

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, 2015 2

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, 2015 3

Structural uses of stainless steel Pedestrian bridge, Sweden, 2013 Dublin Spire, Ireland, 2003 Marina Bay Bridge, Singapore, 2010 November, 2015 4

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, 2015 5

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, 2015 6

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, 2015 7

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, 2015 8

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, 2015 9

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, 2015 10

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 0.2 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, 2015 11

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, 2015 12

CSM for slender cross-sections 𝜀 𝑒,𝑒𝑣 =𝐶 𝜀 𝑐𝑠𝑚 RHS Lipped Channel I-Section SHS November, 2015 13

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, 2015 14

CSM for slender cross-sections (cont…) a=3.03 b= 2.83 All Section types November, 2015 15

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, 2015 16

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 0.2 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 0.2 𝛾 𝑀0 𝑓 𝑐𝑠𝑚 =𝐶 𝜀 𝑐𝑠𝑚 𝐸 𝑜 for 𝜆 𝑝 >0.68 November, 2015 17

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, 2015 18

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, 2015 19

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, 2015 20

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