Lecturer-10-Plate Girders Design Steps 2

Plate Girder Design

1. Steel structure Plate Girders

2. This lecture will cover Introduction 2. General  Considerations Local   Buckling Flexure   Design Shear   Design Design Examples of Plate  Girders Example  01: Capacity Check of Plate  Girders Example 02: Design of Plate Girders Steel structure

3. Introduction Steel structure

4. introduction A  girder is a flexural member which is required to carry heavy loads on  relatively  long  spans Steel structure

5. introduction Plate girders are typically used as long‐span floor girders in buildings, as  bridge  girders,  and  as crane girders in industrial structures. Commonly  term girder refers to a flexural x‐section made up of a number of  elements . They  are generally considerably deeper than the deepest rolled sections  (W540 and   usually  have  webs  thinner than rolled sections . Modern  plate girders are normally fabricated by welding together two flanges  and  a web  plate . Plate girders are at their most impressive in modern bridge construction where  main spans  of well over 200m are feasible, with corresponding cross‐section  depths ,  haunched over  the supports, in the range of 5‐10m . Because  plate girders are fabricated separately, each may be designed  individually  to  resist  the applied actions using proportions that ensure low self‐weight and high load  resistance . Steel structure

6. introduction Changes in Cross Section There  is also considerable scope for variation of cross‐section in the  longitudinal   direction .  A  designer may choose to reduce the flange thickness (or breadth) in a zone of  \low   applied  moment . Equally , in a zone of high shear, the designer might choose to thicken the web  plate Steel structure

7. introduction Changes in Material  Alternatively , higher grade steel might be employed for zones of high applied  moment   and  shear, while standard grade would be used elsewhere.  So‐called  "hybrid" girders with different strength material in the flanges and the web  offer  another possible means of more closely matching resistance to  requirements . Steel structure

8. introduction Built up vs Rolled  Shapes For hot‐rolled shapes, and for all the standard sections in the Manual, the webs are  compact .  Some  have noncompact flanges, but none have slender flanges.  Plate  girders are large flexural members that are composed of plate  elements—in particular , those with noncompact or slender webs . With  shapes built up from plates, however, both flanges and webs can  be  compact,  noncompact , or slender.  Steel structure

9. introduction AISC  Sections The  AISC Specification covers flexural members with slender webs in Section  F5 ,  “ Doubly Symmetric and Singly Symmetric I‐Shaped Members with Slender Webs  Bent  About Their Major Axis.”  This  is the category usually thought of as plate girders.  Flexural  members with noncompact webs are covered in Section F4, “Other I‐ shaped Members with Compact or Noncompact Webs Bent About Their Major  Axis.”  This  section deals with both doubly and singly symmetric sections.  Steel structure

10. introduction Flexure   Strength Flexural Limit  States Steel structure

11. introduction AISC Sections Interestingly , noncompact webs are more difficult to deal with than slender  webs .  In  a User Note in Section F4, the Specification permits members covered by  Section F4 to be designed by the provisions of Section F5.  We  do this and use Section F5 for girders with either noncompact or slender  webs .  We  refer to both types as plate girders.  Shear  provisions for all flexural members are covered in AISC Chapter G,  “ Design of  Members  for Shear.” Other requirements are given in AISC F13,  “ Proportions  of Beams  and Girders.” Steel structure

12. 2. General Consideration Steel structure

13. General   Consideration Diagonal Compression in Webs At  a location of high shear in a girder web, usually near the support and at or  near   the neutral  axis, the principal planes will be inclined with respect to the  longitudinal  axis of  the  member, and the principal stresses will be diagonal  tension  and diagonal  compression .  The  diagonal tension poses no particular problem, but the diagonal  compression  can  cause  the web to buckle.  This  problem can be addressed in one of three ways:  1.The  depth‐to‐thickness ratio of the web can be made small enough that the  problem  is  eliminated 2. Web  stiffeners can be used to form panels with increased shear strength 3. Web  stiffeners can be used to form panels that resist the diagonal  compression  through  tension‐field  action. Steel structure

14. General   Consideration Steel structure

15. General   Consideration Tension Field  Action Tension field action in plate girder Steel structure

16. General   Consideration Tension Field Action At  the point of impending buckling, the web loses its ability to support the  diagonal   compression , and this stress is shifted to the transverse stiffeners and the flanges.  The  stiffeners resist the vertical component of the diagonal compression, and  the  flanges  resist  the horizontal component.  The  web will need to resist only the diagonal tension, hence the term  tension‐field  action.  Steel structure

17. General   Consideration Tension Field Action This  behavior can be likened to that of a Pratt truss, in which the vertical web  members   carry  compression and the diagonals carry tension. Since  the tension field does not actually exist until the web begins to buckle, its  contribution to the web shear strength will not exist until the web buckles.  The  total strength will consist of the strength prior to buckling plus the  Post buckling   strength  deriving from tension field action. Steel structure

18. General   Consideration Tension  Field Action This behavior can be likened to that of a Pratt truss, in which the vertical web  members carry compression and the diagonals carry tension. Since the tension field does not actually exist until the web begins to buckle, its  contribution to the web shear strength will not exist until the web buckles.  The total strength will consist of the strength prior to buckling plus the  Post buckling strength deriving from tension field action. Steel structure Diagonal tension field and truss action in plate girders.

19. General   Consideration Intermediate  Stiffeners If  an unstiffened web is incapable of resisting the applied shear, appropriately  spaced   stiffeners  are used to develop tension‐field action.  Cross‐sectional requirements for these stiffeners, called intermediate  stiffeners,are   minimal  because their primary purpose is to provide stiffness rather than  resist  directly  applied  loads. Steel structure

20. 3. Local Buckling Steel structure

21. Local   Buckling Doubly Symmetric I  shapes Whether a girder web is noncompact or slender depends on h/tw , the width‐to thickness ratio of the web, where h is the depth of the web from inside face of flange to inside face of flange and tw is the web thickness . From AISC B4, Table B4.1b , the web of a doubly symmetric I‐shaped section is noncompact if Steel structure compact Non slender noncompact

22. Local buckling Limits for Compact, Non‐compact, and Slender Sections Steel structure

23. Local buckling Limits for Compact, Non‐compact, and Slender Sections Steel structure

24. Local buckling Limits for Compact, Non‐compact, and Slender Sections Steel structure

25. Local   Buckling Singly Symmetric I  Shapes • For singly symmetric I‐shaped sections, the web is noncompact if Steel structure noncompact compact

26. Local   Buckling Web depth-to-thickness ratios for noncompact and slender webs Steel structure

27. Local   Buckling Singly Symmetric I Shapes For  singly symmetric sections, the proportions of the cross section must be  such  that Steel structure

28. Local   Buckling Singly  Symmetric I Shapes hc =  twice the distance from the elastic neutral axis (the  centroidal  axis) to the  inside  face  of  the compression flange.  ( hc /2 defines the part of the web that is in compression for  elastic  bending.  hc = h for girders with equal flanges).  hp = twice the distance from the plastic neutral axis to the inside face of the  compression   flange .  ( hp /2  defines the part of the web in compression for the plastic moment.  hp = h for  girders  with equal flanges). Steel structure

29. Local   Buckling Web Slenderness Limits To  prevent vertical buckling of the compression flange into the web, AISC F13.2 imposes  an  upper limit on the web slenderness.  The  limiting value of  h/tw is  a function of the aspect ratio, a/h, of the girder panels, which  is  the ratio of  intermediate  stiffener spacing to web depth (see Figure 10.6). Steel structure Design; Web   Size Flange   Size Check Flexure  Strength compression flange is compact, noncompact, or slender Capacity; Web   slender Geometric properties Tension flange yield TFY Compression Flange 

30. Local   Buckling Web Slenderness Limits In  all girders without web stiffeners, AISC F13.2 requires that h/tw be  no greater than 260  and  that the ratio of the web area to the compression  flange  area be no greater than 10. Steel structure

31. Local   Buckling Web Slenderness  Limits Steel structure

32. 4. Flexural Design Steel structure

33. Flexural  Design Steel structure

34. Flexural  Design Steel structure Sxc = elastic section modulus referred to the compression side Capacity; Web   slender Geometric properties Tension flange yield TFY Compression Flange  (B/Y) Design; Web   Size Flange   Size Check Flexure  Strength compression flange is compact, noncompact, or  slender compression‐flange   strength (B/Y)

35. Flexural  Design Steel structure Capacity; Web   slender Geometric properties Tension flange yield TFY Compression Flange  (B/Y)

36. Flexural  Design Steel structure Capacity; Web   slender Geometric properties Tension flange yield (TFY) Compression Flange  (B/Y) Lateral Torsional  Buckling (LTB)

37. Flexural   Design Lateral torsional buckling Steel structure

38. Flexural  Design Steel structure

39. Flexural  Design Steel structure

40. Flexural   Design Lateral torsional buckling Steel structure

41. Flexural  Design Steel structure Capacity; Web   slender Geometric properties Tension flange yield TFY Compression Flange  (B/Y)

42. Flexural  Design Steel structure

43. Flexural   Design Lateral torsional buckling Steel structure

44. Flexural  Design Steel structure Section Modulus Of Tension Flange Is Greater Then The Section Modulus Of Compression Flange Tension Flange Yielding Does Not Apply Capacity; Web   slender Geometric properties Tension flange yield TFY Compression Flange  (B/S)

45. Flexural  Design Steel structure

46. Flexural  Design Steel structure

47. 5. Shear Design Steel structure

48. Shear   Design The shear strength of a plate girder is a function of the depth‐to‐thickness ratio of the web and the spacing of any intermediate stiffeners that may be present . The shear capacity has two components: the strength before buckling and the post buckling strength . The post buckling strength relies on tension‐field action, which is made possible by the presence of intermediate stiffeners . If stiffeners are not present or are spaced too far apart, tension‐field action will not be possible , and the shear capacity will consist only of the strength before buckling . The AISC Specification covers shear strength in Chapter G, “Design of Members for Shear.” Steel structure

49. Shear   Design Kv factor • AISC defines  kv , which is a plate‐buckling coefficient, in Section G2 as follows: Steel structure Capacity; Web   slender Flexural strength Geometric properties Tension flange yield (TFY) Compression Flange  (B/Y) Lateral Torsional  Buckling (LTB) Shear strength Conditions of Tension Field  Action kv , h/tw and  Cv

50. Shear   Design Kv factor • AISC defines  kv , which is a plate‐buckling coefficient, in Section G2 as follows: Steel structure

51. Shear   Design Cv Factor   • For   Cv , which can be defined as the ratio of the critical web shear stress to the  web  shear  yield  stress, Steel structure

52. Shear   Design Cv Factor   • For   Cv , which can be defined as the ratio of the critical web shear stress to the  web  shear  yield  stress, Steel structure

53. Shear   Design 1. Web Shear Yielding  Whether  the shear strength is based on web shear yielding or web shear  buckling depends on the web width‐to‐thickness ratio h/tw . for Steel structure Capacity; Web   slender Flexural strength Geometric properties Tension flange yield (TFY) Compression Flange  (B/Y) Lateral Torsional  Buckling (LTB) Shear strength Conditions of Tension Field  Action kv , h/tw and  Cv web shear yielding or web shear  buckling post‐buckling  strength Design; Web   Size Flange   Size Check Flexure  Strength compression flange is compact, noncompact, or  slender compression‐flange   strength (B/Y ) Check Shear Strength‐End Panel  Spacing

54. Shear   Design Steel structure  post‐buckling strength. web shear buckling strength  2.  Web buckling  with  Shear Field Action Capacity; Web   slender Flexural strength Geometric properties Tension flange yield (TFY) Compression Flange  (B/Y) Lateral Torsional  Buckling (LTB) Shear strength Conditions of Tension Field  Action kv , h/tw and  Cv web shear yielding or web shear  buckling post‐buckling  strength

55. Shear   Design Steel structure 3. Web buckling without Shear Field Action

56. Shear   Design Steel structure

57. Shear   Design Steel structure

58. Shear   Design Design shear strength with diagonal tension field action ( i.e., post-buckling strength considered) Steel structure

59. Shear   Design Conditions for NO tension field Action Steel structure Capacity; Web   slender Flexural strength Geometric properties Tension flange yield (TFY) Compression Flange  (B/Y) Lateral Torsional  Buckling (LTB) Shear strength Conditions of Tension Field  Action Design; Web   Size Flange   Size Check Flexure  Strength compression flange is compact, noncompact, or  slender compression‐flange   strength (B/Y ) Check Shear Strength‐End Panel  Spacing Check Shear Strength‐Stiffener Spacing outside End  Panel Check Conditions   for  tension field Action

60. Shear   Design Increasing Shear Strength Two options are available for increasing the shear strength: either decrease the  web  slenderness (probably by increasing its thickness) or decrease the aspect  ratio of each end panel by adding an intermediate stiffener.  Steel structure Capacity; Web   slender Flexural strength Geometric properties Tension flange yield (TFY) Compression Flange  (B/Y) Lateral Torsional  Buckling (LTB) Shear strength φ vVn Conditions of Tension Field  Action kv , h/tw and  Cv web shear yielding or web shear  buckling post‐buckling  strength In order to increase shear strength (if needed) Shear strength ( φ vVn ) web shear yielding or web shear buckling Cv and kv Location of Intermediate Stiffener

61. Shear   Design Design  Procedure Note  that there is no requirement that tension‐field behavior must be used,  although  its  use  will result in a more economical design. This  same procedure also is used for determining the shear strength of hot‐rolled shapes  with  unstiffened webs . For those shapes, a/h does not apply ,   kv = 5, and there is no  tension  field. Steel structure

62. Design Examples of Plate Girders Steel structure

63. Design Examples of Plate  Girders Example  01 The plate girder shown in Figure 10.10 must be investigated for compliance with the AISC Specification . The loads are service loads with a live‐load–to–dead‐load ratio of 3.0.The uniform load of 4 kips/ ft includes the weight of the girder. The compression flange has lateral support at the ends and at the points of application of the concentrated loads. The compression flange is restrained against rotation at these same points. Bearing stiffeners are provided as shown at the ends and at the concentrated loads. They are clipped 1 inch at the inside edge, both top and bottom, to clear the flange‐to‐web welds. There are no intermediate stiffeners, and A36 steel is used throughout. Assume that all welds are adequate and check a. Flexural strength b . Shear strength Steel structure

64. Design Examples of Plate  Girders Example  01 Service loads shown. DL  = 10k, LL = 30 Factored  Load 1.2*10+1.6*30 = 60 k Steel structure

65. Design Examples of Plate  Girders Example 01 Local Buckling Parameters Steel structure Case 15 in Table B4.1b on Page 75 T herefore , the web is slender and the provisions of AISC F5 apply.

66. Limits for Compact, Non‐compact, and Slender Sections Steel structure

67. Design Examples of Plate  Girders Example 01 Flexure Strength‐Geometric  Properties Steel structure

68. Design Examples of Plate  Girders Example 01 Flexure Strength‐Tension Flange  Yielding From  AISC Equation F5‐10, the tension flange strength based on yielding is Steel structure

69. Design Examples of Plate  Girders Example 01 Flexure Strength‐Compression Flange  Steel structure

70. Limits for Compact, Non‐compact, and Slender Sections Steel structure

71. Design Examples of Plate  Girders Example 01 Flexure Strength‐Compression Flange  Steel structure

72. Design Examples of Plate  Girders Example 01  Lateral Torsional Buckling  Steel structure

73. Design Examples of Plate  Girders Example 01  Lateral Torsional  Buckling Since  Lp  <  Lb <  Lr , the girder is subject to inelastic lateral‐torsional buckling. From  AISC Equation F5‐3,  Steel structure

74. Design Examples of Plate  Girders Example 01  Lateral Torsional  Buckling Since  Lp  <  Lb <  Lr , the girder is subject to inelastic lateral‐torsional buckling. From  AISC Equation F5‐3,  Steel structure

75. Design Examples of Plate  Girders Example 01  Flexure  Strength The  nominal flexural strength is therefore based on yielding of the compression  flange ,  and Steel structure

76. Design Examples of Plate  Girders Example 01  Shear Strength‐Conditions of Tension Field Action Steel structure Therefore tension‐field action can be used.

77. Design Examples of Plate  Girders Example 01 Shear Strength‐ kv and  Cv Steel structure

78. Design Examples of Plate  Girders Example 01 Design Shear Strength Steel structure

79. Design Examples of Plate  Girders Example 01 Design Shear Strength Steel structure

80. Design Examples of Plate  Girders Example 01 Increasing Shear Strength Two  options are available for increasing the shear strength: either decrease the  web   slenderness  (probably by increasing its thickness) or decrease the aspect  ratio  of each  end  panel by adding an intermediate stiffener.  Stiffeners  are added in this example. The location of the first intermediate stiffener will be determined by the following strategy: First, equate the shear strength from AISC Equation G2‐1 to the required shear strength and solve for the required value of Cv. Next, solve for kv from Equation G2‐5, then solve for a/h. Steel structure

81. Design Examples of Plate  Girders Example 01 Shear Strength‐Location of Intermediate  Stiffener Steel structure

82. Design Examples of Plate  Girders Example 01 Shear Strength‐Location of Intermediate  Stiffener The required stiffener spacing  is Although a is defined as the clear spacing, we will treat it conservatively as a center‐to‐ center spacing and place the first intermediate stiffener at 54 inches from the end of the girder. This placement will give a design strength that approximately equals the maximum factored load shear of 234 kips . No additional stiffeners will be needed, since the maximum factored load shear outside of the end panels is less than the design strength of 237 kips. Steel structure

83. Design Examples of Plate  Girders Example  02 • Use LRFD and design a simply supported plate girder to span 60 feet and support the service loads shown in Figure 10.16a. The maximum permissible depth is 65 inches. Use A36 steel and E70XX electrodes and assume that the girder has continuous lateral support. The ends have bearing‐type supports and are not framed . Steel structure

84. Design Examples of Plate  Girders Following are the step-by-step procedure for Plate  Girders design Select the overall depth Select a trial web size. Estimate the flange size . Check the bending strength of the trial section Check shear. Steel structure

85. Design Examples of Plate  Girders Example  02 Select  an Overall Depth Some  authors recommend an overall depth of 1⁄10 to 1⁄12 of the span length  ( Gaylord,  et  al., 1992). Others suggest a range of 1⁄6 to 1⁄20 ( Galambos , et al.,  1980). Salmon , et al. (2009) and Blodgett (1966) give procedures for determining the  depth  that  incorporate  the required moment strength and a specified h/tw ratio.  As  with any beam design, constraints on the maximum depth could establish  thedepth   by  default.  Building  code limitations on the depth‐to‐span ratio or the deflection could also  influence   the  selection.  Use  the maximum permissible depth of 65 inches. Steel structure

86. Design Examples of Plate  Girders Example 02 Estimate the Web  Size • Try a flange thickness of  tf = 1.5 inches and a web depth of Steel structure

87. Design Examples of Plate  Girders Example 02 Estimate the Web  Size Steel structure

88. Design Examples of Plate  Girders Example 02 Estimate the Flange  Size Steel structure

89. Design Examples of Plate  Girders Example 02 Estimate the Flange  Size Steel structure

90. Design Examples of Plate  Girders Example 02 Estimate the Flange  Size Steel structure

91. Design Examples of Plate  Girders Example 02 Trial Section Steel structure

92. Design Examples of Plate  Girders Example 02 Weight of Girder Steel structure

93. Design Examples of Plate  Girders Example 02 Adjusted Bending Moment Steel structure

94. Design Examples of Plate  Girders Example 02 Check Flexure Strength An examination of AISC Equations F5‐7 and F5‐10 shows that for a girder with a  symmetrical cross section, the flexural strength will never be controlled by  tension  flange  yielding ; therefore only compression‐flange buckling will be  investigated .  Furthermore , as this girder has continuous lateral support, lateral‐torsional  buckling  need  not  be considered. Steel structure

95. Design Examples of Plate  Girders Example 02 Check Flexure Strength Checking  Compactness Determine whether the compression flange is compact, noncompact, or slender. Since   𝜆 < 𝜆p there  is no flange local buckling. The compression‐flange strength is  therefore   based  on yielding, and  Fcr =  Fy  = 36  ksi . Steel structure

96. Design Examples of Plate  Girders Example 02 Check Flexure Strength Strength Reduction  Factor Steel structure

97. Design Examples of Plate  Girders Example 02 Check Flexure  Strength Although this capacity is somewhat more than needed, the excess will  compensate  for  the  weight of stiffeners and other incidentals that we have not  accounted  for. Steel structure

98. Design Examples of Plate  Girders Example 02  Check Shear Strength‐End Panel  Spacing Steel structure

99. Design Examples of Plate  Girders Example 02  Check Shear Strength‐End  Panel   Spacing Steel structure

100. Design Examples of Plate  Girders Example 02  Check Shear Strength‐Stiffener Spacing outside End Panel At  a distance of 36 inches from the left end, the shear is Steel structure

101. Design Examples of Plate  Girders Example 02  Check Shear  Strength‐ outside End   Panel   Spacing Steel structure

102. Design Examples of Plate  Girders Example 02  Check Shear Strength‐Stiffener Spacing outside End  Panel Steel structure

103. Design Examples of Plate  Girders Example 02  Check Shear Strength‐Check Conditions of Tension Field  Action check the conditions of AISC G3.1 to be sure that tension‐field action can be  used  for this  girder  and this stiffener  spacing. Conditions a and b are automatically satisfied by staying within the boundaries  defined  by  the  upper curve and the lower solid curve of Manual Table 3‐16b.) Steel structure

104. Design Examples of Plate  Girders Example 02  Check Shear Strength‐Check Conditions of Tension Field  Action Steel structure

105. Design Examples of Plate  Girders Example 02  Check Shear  The  following spacing will be used from each end of the girder: one at 36 inches and four  at  81 inches, as shown in Figure. Steel structure

106. Design Examples of Plate  Girders Steel structure  Plate Girders  4 0’   40’   40’   2 nd   3rd   4th  R oof