Innovative Buckling Design Rules for Structural Hollow Sections

1. Innovative Buckling Design Rules for Structural Hollow SectionsFINAL WORKSHOP, Oslo, 6th June 2019 HOLLOSSTAB is an EU funded programme under RFCS, the Research Fund for Coal and Steel, under grant agreement 709892

2. PROGRAMME 1. Welcome and introduction 2. Trends for hollow sections 3. Physical and numerical test campaign 4. Development of GSRM/CSM Design 5. Software: calculation core 6. Examples 7. Closing statement

3. Motivation 1. What makes Hollow Sections “Slender”? • At the global/member level (“column” or “member buckling”) • Reduced cross-section sizes for minimal visual impact  slender elements in compression • Slenderness globalso depends onyield strength fy •  For High-Strength Steel (S460): Relative increase of relevance of second-order effects Buckling reduction factor  as function of general rule: and crwhen L/b and/or b/t

4. Motivation 1. What makes Hollow Sections “Slender”? • At the cross-sectional level: local instabilities • Thin-walled elements – economy and weight reduction (sustainability+) • Slenderness plate or shell depends on yield strength fy •  For High-Strength Steel:most cross-sections are “(semi-)slender” (class 3 or 4)  Many (HSS) hollowsectionsareslender at thelocal (L), global (G) or L+G level will bechangedto 34 & 38! Classification of cross-section parts acc. to Eurocode 3 – EN 1993-1-1(from CIDECT manuals)

5. Motivation 2. Initial Examples: “Column” / pure compression Cold-formed RHS 200x100x5, weak-axis flexuralbuckling, L=3m S700: A=Aeff (class 4) ; plate,EC3=1.09 EC3 bucklingstrength: Nb,Rk=720 kN S235: A=Agross (class 2) EC3 bucklingstrength: Nb,Rk=457 kN S700, numericalslenderness of CS CS,FEM=1.01 S700, realistic (GMNIA) FEM-based ’’numerical test’’ Nb,Rk=843 kN +17%

6. Motivation 2. Initial Examples: “Beam” / pure bending Cold-formed SHS 200x200x5 S700: W=Welast,eff (class 4) ; plate,EC3=1.09 EC3 bendingstrength: My,Rk=140,4 kNm S235: W=Wplast (class 2) EC3 bendingstrength: My,Rk=65,5 kNm S700, numericalslenderness of CS CS,FEM=0.99 S700, realistic (GMNIA) FEM-based ’’numerical test’’:My,Rk=164 kNm +16%  tendenciesconfirmed by physical tests

7. Motivation 3. Sources of Inaccuracies: 1) Cross-section classification concept leads to discontinuity at class 2-3 border; particularly detrimental for My+Mz  RFCS “SEMICOMP” 2) Plate-by-plate determination of slenderness means that mutual support effects are neglected, slenderness overestimated  k=4,0! k~5÷6

8. Motivation 4. In summary • Design economy and simplicity should be improved: • Removal of strength as function of cross-sectional “classes”- too many issues and inconsistencies, in addition to practical application difficulties. • Interaction formulae for Beam-Columns, Effective Width Method for class 4 sections: tedious and sometimes inaccurate • Particularly for high strength steels sections (fy >460 MPa): many sections fall into the slender range, leading to long and complex calculations • Innovation in cross-sectional shapes and materials hindered • RFCS HOLLOSSTAB: new design methods, based on a Overall Interaction Concept (O.I.C.) and a Generalised Slenderness-based Resistance Method

9. OIC and GSRM Mechanical Background If member is short, section resistance prevails (no buckling) and reaches plastic capacity Npl (resistance limit) If member is long and allowable stress is infinite (no yielding), buckling load Ncr is reached (stability limit) Response of real column results from interaction between resistance and stability + influence of imperfections Basic case of member instability: simply-supported column in compression (capacity N vs. length L)

10. OIC and GSRM Mechanical Background • These principles have been used for decades in major design standards (e.g. in Eurocode 3 for column buckling or beam L.T.B.) • Non-dimensional representation is usually preferred: N – L plots are replaced by c – lrel“buckling curves”, where c stands as the penalty on plastic capacity owing to buckling • In HOLLOSSTAB, a Generalised Slenderness-based Resistance Method (GSRM) is developed for the design of hollow sections. • It relies on this same background and extends it to: • Resistance and stability of sections (“L”ocal buckling) • Situations with combined loading (N + My or N + My + Mz), by means of load ratios Rref(characterizes the attainment of a defined reference resistance, e.g. Rpl or Rel) and Rcr (stability limit, either Rcr,L for sections or Rcr,Gfor members) • The “Overall Interaction Concept” (OIC) is one type of GSRM, which uses the plastic resistance Rpl as reference resistance.

11. Basic Application Steps of the GSRM – CS resistance Step 1: Rref reference resistance without instabilities(e.g. Rpl or Rel) Step 2: Rcr linear buckling load • Step 1: calculation of the reference resistance at a local, cross-sectional level • Step 2: calculation of the critical, elastic bifurcation load • Step 3: calculation of the corresponding overall slenderness • Step 4: derivation of the buckling knock-down factor • Step 5: ultimate buckling resistance NOTE: «R» alwaysdenotes a load amplification factor

12. Advantages and features • Economy: • Accuracy is improved compared to current Eurocode 3 rules • Positive strain-hardening effects can be accounted for: capacities higher than plastic • Cross-section treated as a whole: positive interaction between plates (flanges and webs) accounted for • Simplicity: • Same concept and reference for sections (local L) and members (global G) • Coupled instabilities (local/global) dealt with consistently (high strength steel) • No section classification for strength checks (avoid many inconsistencies) • Thus, no discontinuities along resistance: smooth transition from plastic to slender • No need for effective properties, procedure simpler • Use of dedicated, small software for the calculation of Rcr and Rpl

13. RFCS Project HOLLOSSTAB Objectives: • Give alternatives to conventional EC3 methods (classification, interaction formulae) for Hollow Section design (CHS, EHS, RHS, SHS, other shapes...) • Define accurate, easily applicable and economical buckling rules for slender (class 4) cylindrical sections (CHS & EHS) • Determine new buckling reduction factors for the local (L) and global (G) as well as the L+G buckling cases, as a “Generalised Slenderness-based Resistance Method” (GSRM) for all HS-shapes mentioned above  “Direct Strength” for N+M • Take advantage of strain hardening and plasticity in compact to (locally) slender cross-sections. • Take advantage of mutual interaction of plate or shell parts in determining the local slenderness. • Develop easily applied tools and design methods for the industry • Prepare the industry for increased use of innovative (HSS) hollow sections.

14. RFCS Project HOLLOSSTAB Structureand Partners: WP1: Project Management (UNIBWM) WP2: Industrial applications : market analysis and case studies (Condesa, CTICM, ECCS) WP3: Cross-sectional resistance of HSS CHS & EHS (UNIBWM, ICL, IST, ULaval, holl. sec. producers) WP4: Cross-sectional resistance of HSSRHS & SHS (ICL, UNIBWM, IST, ULaval, holl. sec. producers) ForGMNIAwithrandominputvar. • WP5: Buckling resistance of hollow-section beam-columns • (ULaval, UniBWM, ICL, hollow section producers) WP7, Task 7.1: statistical data collection(Condesa, CTICM, ECCS) WP7, Task 7.2: statistical verificationof design rule proposals (CTICM, UNIBWM) Experimental & numericalbackgroundfrom WP3 to 5 WP6: Elastic buckling of hollow section members (IST, ICL) Rulemodificationsifnecessary WP8: Design rules and software tool (IST, UNIBWM, ICL, ULaval) WP9: Design Guidelines & Workshop (ECCS, all)

15. PROGRAMME 1. Welcome and introduction 2. Trends for hollow sections 3. Physical and numerical test campaign 4. Development of GSRM/CSM Design 5. Software: calculation core 6. Examples 7. Closing statement

16. Trends for hollow sections Czech Republic France Germany Luxembourg Norway Poland Portugal Romania Spain Sweden Switzerland The Netherlands UK Survey amongStructure Designers and Tube Manufactures

17. Trends for hollow sections * Not higher than S460 Current use/production of hollow sections

18. Trends for hollow sections Advantages and disadvantages of usinghollow sections

19. Trends for hollow sections * An increase in either mass or steel grade will mean an increase in price • Difficulties of using high strength steel hollow sections • For production  Multiplying stock • For design  Non-optimum depending on the profile size • Example: alternatives to CHS 219,1x8 S275 column (6m height, buckling coefficient 0,7) • CHS 244,5x8  increase in capacity ≈ 18%; increase in mass ≈ 11% • CHS 273x6  increase in capacity ≈ 9%; reduction in mass ≈ 0,5% • CHS 323,9x5  increase in capacity ≈ 10%; reduction in mass ≈ 6% • CHS 323,9x6  increase in capacity ≈ 30%; increase in mass ≈ 11% • CHS 219,1x8 S355  increase in capacity ≈ 20%; increase in mass = 0%

20. Trends for hollow sections • Conclusions • In order to boost the use of hollow sections, their advantages should be fostered and their drawbacks softened. HOLLOSSTAB works doubly on it, helping exploit – even more – the buckling resistance of the hollow sections and, by optimizing the sizes, leading to a (price) reduction of the tubular structural solution for members subjected to compression or compression + bending • No big changes are expected in the use of both hollow section cross-sections and steel grades, less common ones remaining as a solution for specific structures (bridges, singular buildings, etc.). • In order to boost a greater use of high strength steel tubes, a substitution of lower grades (S235) by higher ones (S420 or S460) should be happening.

21. THANK YOU!