1. Rehabilitation and maintenance of buildings - 02 Karel Mikeš

2. 2 Contents  Properties of material  Failures of steel structures  Types of refurbishment  Methods of reliability verification  Basis of member design of steel structures  Basis of joint design  Assessment of steel structures  Strengthening of members  Strengthening and refurbishment of structures  Refurbishment of masonry structures using steelwork  Seismic upgrading using steel structure

3. 3 Methods of reliability verification  Design based on experience  Empirical attitude  Allowable stress method  One safety factor  Reduction of strength  Actions not affected  Method of limit states  Real probabilistic methods  Method of partial safety factors  Semi-probabilistic method

4. 4 Method of partial safety factors Partial safety factors:  material factors  M  load factors  F  Ultimate Limit States...  M ≥ 1,  F > 1  Serviceability limit states...  M = 1,  F = 1  Basis of Eurocodes

5. 5 Partial safety factors  Characteristic values  Partial factors  M,  F  Reduction factors   Design values  Partial factors  cover:  Disadvantageous deviations from characteristic values  Inaccuracy of action model  Inaccuracy of structural model for analysis  Inaccuracy of transformation factors

6. 6 Eurocodes  Design codes (Eurocodes)  European codes from1980  European Comittee for Standartization (CEN) from 1990  CR - member from 1998  Preliminary codes (ENV)  European codes (EN)  ENV - National application document (NAD) – national specials  EN - National annex, limited clauses  Since 3/2010 should be valid in all CEN countries

7. 7 Eurocodes – EN  EN 1990 Eurocode 0 Basis of Structural Design  EN 1991 Eurocode 1 Actions on structures  EN 1992 Eurocode 2 Design of concrete structures  EN 1993 Eurocode 3 Design of steel structures  EN 1994 Eurocode 4 Design of composite steel and concrete structures  EN 1995 Eurocode 5 Design of timber structures  EN 1996 Eurocode 6 Design of masonry structures  EN 1997 Eurocode 7 Geotechnical design  EN 1998 Eurocode 8 Design of structures for earthquake resistance  EN 1999 Eurocode 9 Design of aluminium structures

8. 8 Eurocodes – EN Partial safety factors   M = 1,00 (for steel)   M2 = 1,25 LoadingEffectService load (SLS) Extreme load (ULS) Deadfavourable  G = 1,0  G,min = 1,0 unfavourable  G = 1,0  G,max = 1,35 Variable  Q = 1,0  Q = 1,50

9. 9 Contents  Properties of material  Failures of steel structures  Types of refurbishment  Methods of reliability verification  Basis of design of steel structures  Assessment of steel structures  Strengthening of members  Strengthening and refurbishment of structures  Refurbishment of masonry structures using steelwork  Seismic upgrading using steel structure

10. 10 Basis of design of steel structures  Eurocode EN 1993 Design of steel structures  Method of partial safety factors  Utilization of bi-linear stress-strain relation of steel  Axial tension  Axial compression  Bending  Shear  Combination

11. 11 Axial tension Stress distribution: (direct stress)

12. 12 Axial tension Resistance:  full cross-section (plastic resistance) N pl.Rd = A f y /  M0  net cross-section at holes for fasteners N u.Rd = 0,9 A net f u /  M2

13. 13 Axial compression Design buckling resistance  Buckling factor  :  covers the effect of buckling    (  depends on cross-section type)

14. 14 Axial compression Buckling  Stability collapse  buckling before f y is reached along cross-section  Most frequent reason for collapse of S.S.  Perfect (ideal) member- stability problem  Real member - buckling resistance

15. 15 Axial compression Stability of perfect member  Straight member  Pinned ends  Centric loading  Solution  Euler –1744

16. 16 Axial compression Critical (Euler’s) Force  Critical Stress  Slenderness

17. 17 Axial compression Buckling of Member  flexural or torsional  Double axis symmetric profiles  Slenderness y, z, zw  flexural or flexural-torsional  Uniaxial symmetric profiles  Slenderness y, yzw  flexural-torsional  Non-symmetrical profiles  Slenderness yzw  It is taken into account in simplified form

18. 18 Axial compression Buckling (effective) length  Using Euler‘s formula for general bar Buckling length:  Length of basic member (pinned ends, constant compression force) of the same cross-section with equal critical force as examined member  L cr =  L

19. 19 Axial compression Buckling length Example - Cantilever  Euler  Cantilever L cr = 2 L   =2

20. 20 Axial compression Buckling resistance of real member Imperfections  Geometric imperfections  Initial curvature of the member axis,  excentricity of the loading position  Deviation from the theoretical shape of the cross-section  Material imperfections  Residual stresses  Due to the welding, straightening or cooling  Structural imperfections  Imperfect function of hinges or fixed connections

21. 21 Axial compression Results of experiments of compression members

22. 22 Axial compression Buckling factor   … imperfection factor  depends on type of cross-section

23. 23 Axial compression Buckling factor

24. 24 Global analysis of structure  Statically determinate structures  Statically indeterminate structures  Elastic analysis  Plastic analysis  Plastification of the part of the structure Idealised stress-strain relation

25. 25 Global analysis of structure Elastic analysis  Material satisfies Hooke’s law   =  E  For steel under the yield point f y Ideal stress-strain diagram

26. 26 Global analysis of structure Plastic analysis Two steps:  Plastic check of governing cross-section  Plastic global analysis  At redundant structures  Development of plastic mechanism

27. 27 Global analysis of structure Step by step plastification of I cross section  Development of plastic mechanism  Sufficient rotation capacity of cross section

28. 28 Global analysis of structure Utilization of cross section

29. 29 Global analysis Utilization of cross section  Elasto-elastic  Distribution of internal forces based on elastic analysis  Utilization of structural cross section elastic  Elasto-plastic  Distribution of internal forces based on elastic analysis  Maximally loaded cross section utilized plastically  Plasto-plastic  Distribution of internal forces based on plastic analysis  At plastic joints is cross section plastified

30. 30 Classification of cross section  class 1:  Plastic hinges  Plastic redistribution of inner forces  Plasto-plastic analysis  class 2:  Fully plastified  Limited rotation capacity  Elasto-plastic analysis  class 3:  It is possible to reach the yield point at edge fibres  Elasto-elastic analysis  class 4:  slender, at compression stresses buckle earlier before the yield is reached  Elasto-elastic analysis

31. 31 Classification of cross section Definition of cross-section class  Classification for all parts with compression stress  For every compressed part according to b/t ratio  b... width of sheet  t... thickness of sheet  Maximum class (  cr,min ) governs

32. 32

33. 33 Classification of cross section Cross section of class 4 Plate buckling  Ideal cross-section  Replacement of real width with effective widths

34. 34 Bending, shear  Bending resistance M Rd  Shear resistance V Rd

35. 35 Bending, shear Design bending resistance  Influence of cross-section class  1., 2. class  3. class  4. class f yd = f y /  M0

36. 36 Bending, shear Design shear resistance  A v … shear area  Small shear:  V Ed  0,5 V pl,Rd  combination M+V is neglected  Large shear  V Ed > 0,5 V pl,Rd  combination M+V is considered

37. 37 Bending, shear M+V - Large shear  Reduction of strength on shear area:  for symmetrical cross-section along y-y :

38. 38 Bending Lateral-torsional buckling

39. 39 Relative slenderness Bending Resistance with lateral-torsional buckling for cross section of class 1 a 2 for cross section of class 3 for cross section of class 4

40. 40 Bending Beams not subjected to lat.-torsional buckling  Lateral restraint of compression flange  Beam bended in the direction of smaller rigidity  Torsional rigidity of beam is high (closed cross section)

41. 41 Serviceability limit states  check relevant especially for beams  Deflections  Vibrations  Reversible behaviour is required  Elastic behaviour

42. 42 Serviceability limit states Deflections  Bending stiffness: E I   max... resultant deflection   2... deflection due to variable load   0... chamber of beam   1... deflection due to dead load

43. 43 Serviceability limit states Recommended limit deflections  Limits should be agreed  Just recommendations in National annexes  Refurbishment – proper judgement of designer  Limits according to ENV: Loadingfloorsroofs totalL/250L/200 variableL/300 (L/350)L/250