Stainless steel structures experts seminar Ascot, UK, 6-7 December 2012 CLASS 4 STAINLESS STEEL I BEAMS SUBJECTED TO FIRE

Transcription

1 Stainless steel structures experts seminar Ascot, UK, 6-7 December CLASS 4 STAINLESS STEEL I BEAMS SUBJECTED TO FIRE Nuno Lopes; Paulo Vila Real LABEST - Universidade de Aveiro

2 Contents Introduction Material behaviour Lateral-torsional buckling fire design recommendations Buckling modes analyses Finite element model description Parametric study Conclusions

3 Introduction Although initially more expensive than conventional carbon steel, stainless steel structures can be competitive because of its bigger fire resistance. Fire design simplified rules importance: rules provided by codes of practice, are of the utmost importance to designers that do not always have access to applications dealing with advanced calculation methods. European codes of practice for stainless steel: Part.4 of EC3 for the fire resistance refers to the Part. of the same EC3. Here, it is stated that members must be checked using the same design formulae developed for carbon steel. However, these two materials have different constitutive laws.

4 Introduction Class 4 members: it was introduced in the French National Annex of the EN993-- new design proposals for Class 4 carbon steel structural elements, acknowledging the conservative nature of the rules in EC3. The manual of EuroInox also proposes the use of different formulae for the fire design of stainless steel elements. Lateral-torsional buckling: the LTB is a very important and common phenomenon in unrestrained steel beams. Thus is of great interest to better understand the behaviour of these thinwalled stainless steel beams with LTB in case of fire. The main objective of this work was to perform a numerical analysis on thinwalled stainless steel structural elements subjected to bending and in case of fire. These numerical results are compared against the buckling curves from the different design approaches.

5 Introduction The influence of geometrical imperfections and residual stresses on the ultimate load bearing capacity of these profiles is evaluated It is presented a parametric study on two class 4 cross sections on three stainless steel grades In this numerical study, it were used the programs: CUFSM (developed at Johns Hopkins University in the United States) SAFIR (developed at the University of Liege in Belgium)

6 Introduction Study Case Simply supported beams with uniform bendiing Grades.43,.43 and.446 Study case dimensions: height 46 mm base 5 mm web thickness 3 mm and 4mm flange thickness 4 mm and 7mm Temperature considered uniform throughout the cross section

7 ,TLmoc Material behaviour Mechanical properties reduction at high temperatures.8.6 Grade.43 Grade.44/.444 Grade.457 Grade.43 Grade.446 Carbon s teel k.p,q qa (ºC)

8 LT,com, Material behaviour Stainless steel Carbon steel.8.6 ke,.4 f u,. f.p, E ct, = tan a (ºC) E a, = tan c, k u,

9 Material behaviour ºC ºC ºC ºC ºC ºC 3 ºC 3 ºC 4 ºC 4 ºC 5 5 ºC ºC 6 6 ºC ºC 7 7 ºC ºC 8 8 ºC ºC 9 ºC ºC ºC ºC ºC ºC stress-strain relationship at high temperatures EC3 part -

10 Material behaviour ºC ºC ºC 3 ºC 4 ºC 5 ºC 6 ºC 7 ºC 8 ºC 9 ºC ºC ºC stress-strain relationship at high temperatures EC3 part -

11 Material behaviour Introduction of D mechanical properties of the stainless steels in FEM code SAFIR The stainless steel hardening rule had to be introduced The stress-strain relationship has two branches. In the second branch: k E g(k) In first branch was necessary to developed an approximation (Mpa).43-6ºC f u, f.p, E ct, = tan 8 E a, = tan 6 4 EC3 Aproximation c, k u,

12 LTB fire design recommendations EC3 (EN 993--) For classes, e 3 sections, due to the fact that a fire is an accident action, the EC3 allows the consideration of bigger deformations. f y, f, stress at % total strain For class 4 sections f f y,. proof, proof strength at.% plastic strain M b, fi, t, Rd LT LT, fi W eff, y LT,, com LT, k. proof, LT,, com.65 LT k f 35/. proof, k y E, M, fi, fi with LT, fi LT,, com LT,, com LT,, com LT,, com f y.5

13 LTB fire design recommendations EC3 French national annex formulae For classes, e 3 sections, due to the fact that a fire is an accident action, the EC3 allows the consideration of bigger deformations. f y, f, stress at % total strain For class 4 sections f f y,. proof, proof strength at.% plastic strain M b, fi, t, Rd LT, fi with LT, fi LT,, com LT,, com LT, fi W LT,, com eff, y LT, k. proof, LT k f. proof, k y E, M, fi. LT, LT, LT, obtained from EN993-- for hot rolled sections equals.34 for the case study.5

14 LTB fire design recommendations EuroInox manual proposal M b, fi, t, Rd LT, fi W eff, y k. proof, f y M, fi f f y,. proof, proof strength at.% plastic strain LT, fi with LT, fi LT,, com LT,, com LT,, com. LT, LT, 4 LT, Higher which equals.76 for the case study LT, LT k. proof, k E,.5

15 Buckling modes analyses Elastic critical ultimate load determination and respective instability modes 46x5x3x4 Load factor mm 5 mm Length (mm)

16 Buckling modes analyses Load factor 3.5 Elastic critical ultimate load determination and respective instability modes 46x5x3x mm 5 mm Length (mm)

17 Buckling modes analyses Elastic critical ultimate load determination and respective instability modes 46x5x4x7 Load factor mm mm Length (mm)

18 Finite element model description loads restritions

19 Finite element model description Local imperfections Global imperfections

20 LT,com, Finite element model description M/Mfi,,Rd.6.4. y= EN No imp Local imp Global imp Local+Global imp ºC LT,,com Local plus Global imperfections

21 LT,com, h Finite element model description. M/Mfi,,Rd y= EN Without residual stresses With residual stresses Residual stresses ºC LT,,com f y T C C.5 f y T f y C T b

22 LT,com, LT,com, Parametric study grade.43 M/Mfi,,Rd y= EN EN french annex EuroInox Manual SAFIR-35ºC SAFIR-5ºC SAFIR-6ºC 46x5x3x M/Mfi,,Rd y= EN EN french annex EuroInox Manual SAFIR-35ºC SAFIR-5ºC SAFIR-6ºC LT,,com.6 46x5x4x LT,,com

23 Parametric study grade.43

24 LT,com, LT,com, Parametric study grade.43 M/Mfi,,Rd y= EN EN french annex EuroInox Manual SAFIR-35ºC SAFIR-5ºC SAFIR-6ºC 46x5x3x M/Mfi,,Rd y= EN EN french annex EuroInox Manual SAFIR-35ºC SAFIR-5ºC SAFIR-6ºC LT,,com.6 46x5x4x LT,,com

25 Parametric study grade.43

26 LT,com, LT,com, Parametric study grade.446 M/Mfi,,Rd y= EN EN french annex EuroInox Manual SAFIR-35ºC SAFIR-5ºC SAFIR-6ºC 46x5x3x M/Mfi,,Rd y= EN EN french annex EuroInox Manual SAFIR-35ºC SAFIR-5ºC SAFIR-6ºC LT,,com.6 46x5x4x LT,,com

27 Parametric study grade.446

28 Conclusions In this work it was presented a numerical study on the behaviour of thin walled stainless steel I beams with Class 4 cross sections in case of fire. The elastic critical loads and buckling modes of those profiles were determined through CUFSM program. From this analysis it was possible to better predict the behaviour of the analysed beams and to apply those buckling modes shapes on the initial geometric imperfections considered on the numerical parametric analysis. The influence of initial geometrical imperfections (local, global, and both added) on the determination of the ultimate loads of these elements at high temperatures was analysed. It was concluded that these imperfections are relevant to the determination of those ultimate loads, and that they should be considered the expected collapse mode. Finally, it was also performed a comparison between the obtained finite element results from the program SAFIR for the determination of ultimate loads and different design approaches as the requirements prescribed in Part - of EC3, the French national annex of the same Part of the EC3 and the EuroInox manual proposal, concluding that some small adjustments could be made to each of the proposals to improve the approximations to the numerical results.

29 Stainless steel structures experts seminar Ascot, UK, 6-7 December CLASS 4 STAINLESS STEEL I BEAMS SUBJECTED TO FIRE Nuno Lopes; Paulo Vila Real nuno.lopes@ua.pt Thank you