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Topic%20 compression

  1. 1. Dr. Seshu AdluriStructural Steel DesignCompression Members
  2. 2. ColumnsinBuildings Compression members -Dr. Seshu Adluri
  3. 3. Columns in Buildings Compression members -Dr. Seshu Adluri
  4. 4. Columnsupports Compression members -Dr. Seshu Adluri
  5. 5. Compression members in trusses Compression members -Dr. Seshu Adluri
  6. 6. Compression members in trusses Compression members -Dr. Seshu Adluri
  7. 7. Compression members in OWSJ Compression members -Dr. Seshu Adluri
  8. 8. Compression members in bridges Howrah bridge, Kolkata, India Compression members -Dr. Seshu Adluri
  9. 9. Compression members in towersEiffel Tower (1887 - 89) The new Tokyo Tower is set to be completed in 2011. It will stand 610m high. Compression members -Dr. Seshu Adluri
  10. 10. Compression inequipment Compression members -Dr. Seshu Adluri
  11. 11. Introduction Steel Compression members Building columns Frame Bracing Truss members (chords and bracing) Useful in pure compression as well as in beam- columns Design Clauses: CAN/CSA-S16 Over-all strength as per Clause 13.3 Local buckling check: Clause 11 (Table 1) Built-up members: Clause 19 Compression members -Dr. Seshu Adluri
  12. 12. Column erection Compression members -Dr. Seshu Adluri
  13. 13. Differentcolumn c/sshapes Compression members -Dr. Seshu Adluri
  14. 14. Differentcolumn c/sshapes Compression members -Dr. Seshu Adluri
  15. 15. Instability and bifurcation Stable, neutral and unstable equilibriums Compression members -Dr. Seshu Adluri
  16. 16. Buckling Compression members -Dr. Seshu Adluri
  17. 17. Instability and bifurcation Instability effect To compress or not to compress? Energy considerations Long column Compression members -Dr. Seshu Adluri
  18. 18. Compression terminology -review Moment of inertia I x = ∫ y 2 dA A Parallel axis theorem I = I + Ax x′ x 2 Radius of gyration r= I A Effective length kL Symmetric (major) Slenderness ratio kL/r axis h Principal axes (major and minor) Critical Load Pcr b Unsymmetric Factored compressive strength, Cr (minor) axis Compression members -Dr. Seshu Adluri
  19. 19. Compression members Bucking Elastic (Euler) buckling Inelastic buckling Buckling modes Overall buckling Flexural buckling Torsional buckling Torsional-flexural buckling Local buckling Compression members -Dr. Seshu Adluri
  20. 20. Elastic Buckling Equilibrium equation Internal moment + applied moment = 0 d 2wEI 2 + Pw = 0; w = 0 @ y = 0; w=0@ y = L dx πxSolution : w = A sin satisfies the b.c. LSubstituting int o the differential equation,   π 2 EI  − A  sin πx  + P A sin πx  = 0    L L   L  2 π  −   EI + P = 0 L π 2 EI Pcr = 2 L Compression members -Dr. Seshu Adluri
  21. 21. Inelastic Buckling Compression members -Dr. Seshu Adluri
  22. 22. Compression members σpl = σy - κΛ/ρes Moment of inertia σpl = (0.5~1.0)σy Radius of gyration Effective length Slenderness ratio Compression members -Dr. Seshu Adluri
  23. 23. Effective length factorsDifferent endconditionsgive differentlengths forequivalenthalf-sine wave Compression members -Dr. Seshu Adluri
  24. 24. Theoretical Effective length factors Compression members -Dr. Seshu Adluri
  25. 25. Theoretical Effective length factors Compression members -Dr. Seshu Adluri
  26. 26. Effectivelengthfactors US practice Compression members -Dr. Seshu Adluri
  27. 27. Effective lengths in differentdirections Compression members -Dr. Seshu Adluri
  28. 28. Effective length factors Canadian practicek = .65 k = .8 k = 1.2 k = 1.0 k = 2.0 k = 2.0 Compression members -Dr. Seshu Adluri
  29. 29. USrecommended Engrg. Eff. Boundary Theoretical Eff.values Length Conditions Length, LeffT LeffEFree-Free L (1.2·L)Hinged-Free L (1.2·L)Hinged-Hinged L L (Simply-Supported)Guided-Free 2·L (2.1·L)Guided-Hinged 2·L 2·LGuided-Guided L 1.2·LClamped-Free 2·L 2.1·L (Cantilever)Clamped-Hinged 0.7·L 0.8·LClamped-Guided L 1.2·LClamped-Clamped 0.5·L 0.65·L Compression members -Dr. Seshu Adluri
  30. 30. Canadianrecommended Engrg. Eff. Boundary Theoretical Eff.values – LengthAppendix F Conditions Length, LeffTCAN/CSA/S16-01 LeffEFree-Free L (1.2·L)Hinged-Free L (1.2·L)Hinged-Hinged L L (Simply-Supported)Guided-Free 2·L (2.0·L)Guided-Hinged 2·L 2·LGuided-Guided L 1.2·LClamped-Free 2·L 2.0·L (Cantilever)Clamped-Hinged 0.7·L 0.8·LClamped-Guided L 1.2·LClamped-Clamped 0.5·L 0.65·L Compression members -Dr. Seshu Adluri
  31. 31. Effective lengths in frame columns Compression members -Dr. Seshu Adluri
  32. 32. Effective lengths in frame columns Compression members -Dr. Seshu Adluri
  33. 33. Real columns -Factors for considerationPartially plasticbucklingInitial out-of-straightness(L/2000 to L/1000) Compression members -Dr. Seshu Adluri
  34. 34. Real columns -Factors forconsideration Residual stresses in Hot-rolled shapes (idealized) Compression members -Dr. Seshu Adluri
  35. 35. Realcolumns -Factors forconsideration Residual stresses in Hot-rolled shapes (idealized) Compression members -Dr. Seshu Adluri
  36. 36. Perfect column failure Compression members -Dr. Seshu Adluri
  37. 37. Perfect column failure Compression members -Dr. Seshu Adluri
  38. 38. Practical column failure Compression members -Dr. Seshu Adluri
  39. 39. Column curve Compression members -Dr. Seshu Adluri
  40. 40. Intermediate Short Column Long Column Column (Strength (Elastic Stability (Inelastic Limit) Limit) Material Stability Limit) Slenderness Ratio ( kL/r = Leff / r)Structural Steel kL/r < 40 40 < kL/r < 150 kL/r > 150Aluminum Alloy kL/r < 9.5 9.5 < kL/r < 66 kL/r > 66 AA 6061 - T6Aluminum Alloy kL/r < 12 12 < kL/r < 55 kL/r > 55 AA 2014 - T6 Wood kL/r < 11 11 < kL/r < (18~30) (18~30)<kL/r<50 Compression members -Dr. Seshu Adluri
  41. 41. Over-all buckling Flexural Torsional Torsional-flexural Compression members -Dr. Seshu Adluri
  42. 42. Flexural Buckling About minor axis (with higher kL/R) for doubly symmetric shapes About minor axis (the unsymmetric axis) for singly symmetric shapes 1964 Alaska quake, EqIIS collection Compression members -Dr. Seshu Adluri
  43. 43. Flexural Buckling Compression members -Dr. Seshu Adluri
  44. 44. Torsional buckling Short lengths Usually kL/r less than approx. 50 doubly symmetric sections Wide flange sections, cruciform sections, double channels, point symmetric sections, …. Not for closed sections such as HSS since they are very strong in torsion Compression members -Dr. Seshu Adluri
  45. 45. Torsion Torque is a moment that causes twisting along the length of a bar. The twist is also the torsional deformation. For a circular shaft, the torque (or torsional moment) rotates each c/s relative to the nearby c/s. Compression members -Dr. Seshu Adluri
  46. 46. Torsionaldeformation Compression members -Dr. Seshu Adluri
  47. 47. Torsion of non-circular sections Torsion of non-circular sections involves torsional shear and warping. Torsional shear needs the use of torsion constant J. J is similar to the use of polar moment of inertia for circular shafts. J=Σbt3/3 Warping calculation needs the use od the constant Cw. Both J and Cw are listed in the Handbook In addition, we need to use the effective length in torsion (kzLz). Usually, kz is taken as 1.0 Compression members -Dr. Seshu Adluri
  48. 48. Torsional buckling of open sections Buckling in pure torsional mode (not needed for HSS or closed sections): Kz is normally taken as 1.0. Cw, J, rx, ry are given in the properties tables, x and y are the axes of symmetry of the section. E= 200 000 MPa (assumed), G=77 000 MPa (assumed). 1  π 2 ECw  Fez =  + GJ  ro2 = xo + yo + rx2 + ry2 2 2 Aro  ( K z L ) 2 2    Fy ( ) −1 n λ= Cr = φ AFy 1 + λ 2n Fe Compression members -Dr. Seshu Adluri
  49. 49. Shear centre Sections always rotate about shear centre Shear centre lies on the axis of symmetry Compression members -Dr. Seshu Adluri
  50. 50. Torsional-flexuralbucklingFor of singlysymmetricsections, aboutthe major axisForunsymmetricsections, aboutany axisRotation isalways aboutshear centre Compression members -Dr. Seshu Adluri
  51. 51. Torsional-flexural buckling Compression members -Dr. Seshu Adluri
  52. 52. Shear flow Compression members -Dr. Seshu Adluri
  53. 53. Shear flow Compression members -Dr. Seshu Adluri
  54. 54. Shear flow Compression members -Dr. Seshu Adluri
  55. 55. Shear centre Compression members -Dr. Seshu Adluri
  56. 56. Shear flow effect Compression members -Dr. Seshu Adluri
  57. 57. Shear centre Compression members -Dr. Seshu Adluri
  58. 58. Shear centre Compression members -Dr. Seshu Adluri
  59. 59. Local (Plate) buckling Compression members -Dr. Seshu Adluri
  60. 60. Plate buckling Compression members -Dr. Seshu Adluri
  61. 61. Plate buckling Effective width concept Compression members -Dr. Seshu Adluri
  62. 62. Plate buckling Different types of buckling depending on b/t ratio end conditions for plate segments Table 1 for columns Table 2 for beams and beam-columns Compression members -Dr. Seshu Adluri
  63. 63. Web buckling Compression members -Dr. Seshu Adluri
  64. 64. Plate buckling b/t ratio effect Compression members -Dr. Seshu Adluri
  65. 65. Built-up columnsTwo or more sections Stitch bolts Batten plates Lacing Combined batten & lacing Perforated cover plates Compression members -Dr. Seshu Adluri
  66. 66. Built-up columns Two or more sections Stitch bolts Batten plates Lacing Combined Compression members -Dr. Seshu Adluri
  67. 67. Built-upcolumns Compression members -Dr. Seshu Adluri
  68. 68. Built-upcolumns Closely spaced channels Compression members -Dr. Seshu Adluri
  69. 69. Built-up columns Built-up member buckling is somewhat similar to frame buckling Batten acts like beams Battens get shear and moment due to the bending of the frame like built-up member at the time of buckling Compression members -Dr. Seshu Adluri
  70. 70. Battened column Compression members -Dr. Seshu Adluri
  71. 71. Built-up columns Design as per normal procedure Moment of inertia about the axis which shifts due to the presence of gap needs parallel axis theorem Effective slenderness ratio as per Cl. 19.1 Compression members -Dr. Seshu Adluri
  72. 72. References AISC Digital Library (2008) ESDEP-the European Steel Design Education Programme - lectures Earthquake Image Information System Hibbeler, R.C., 2008. “Mechanics of Solids,” Prentice-Hall Compression members -Dr. Seshu Adluri

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