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Axial Tension
Maximum Size of Bolt Holes
Nominal Bolt Diameter
(in.)
Standard Hole Diameter
(in.),
Oversize Hole Diameter
(in.)
Short-Slotted Hole
(in.)
Long-Slotted Hole
(in.)
d < 1/2d + 1/32d + 1/16(d + 1/32) by (d + 1/4)(d + 1/32) by (2.5d)
d ≥ 1/2d + 1/16d + 1/8(d + 1/16) by (d + 1/4)(d + 1/16) by (2.5d)
Tension Member Design


Gross area
  Ag = Gross area of cross section.

Net Area
  Net area An of a member is the sum of the products of the thickness and the net width of each element.
    For a part in any diagonal or zigzag line, the additional quantity is:   s2.t / (4g)

  s = longitudinal center-to-center spacing (pitch) of any two consecutive holes.
  g = transverse center-to-center spacing (gage) between fastner gage lines.

Effective Net Area, Reduction-Shear Lag Coefficient (U)

  Bolts:
    Ae = An . U

  For angle members having two and more bolts in the line of force:    U = 1 - 1.2 x/L < 0.9,   but >= 0.4

  For channel members having two and more bolts in the line of force:    U = 1 - 0.36 x/L < 0.9,   but >= 0.5

  x - distance from shear plane to centroid of the cross section
  L - length of the connection in the direction of loading

  Welds:
  (a) When the tension load is transmitted only by longitudinal welds or by longitudinal welds in combination with transverse welds:
    Ae = Ag . U

  U - reduction coefficient = 1 - x/L <= 0.9
  Ag - gross area of member

  (b) When the tension load is transmitted only by transverse welds:
    Ae = A . U

  U = 1.0
  A - area of directly connected elements

  (c) Otherwise:

  for angle members:    U = 1 - 1.2 X/L < 0.9 but U >= 0.4

  for channel members:    U = 1 - 0.36 X/L < 0.9 but U >= 0.5

   x - distance from shear plane to centroid of cross section
   L - length of longitudinal weld

Design Strength for Tension Members:

  Yielding in the gross section: (Eq. C2-1)
     fTn = f.Fy.Ag= 0.90 Fy.Ag   LRFD

     Ta = Fy.Ag / Ot = Fy.Ag/1.67  ASD

  Fracture in the net section: (Eq. C2-2)
     fTn = f.Fu.Ae= 0.75 Fu.Ae  LRFD

     Ta = Fu.Ae / Ot = Fu.Ae/2.0  ASD

Design Rupture Strength:

  Shear Rupture Strength: (Eq. E5.1-1)
     fVn = f(0.6).Fu.Anv= 0.75 (0.6) Fu.Anv  LRFD

     Va = (0.6).Fu.Anv / O = (0.6) Fu.Anv/2.0   ASD

  Tension Rupture Strength for Welded Connection: (Eq. E2.7-1)
     fPn = f.Fu.Ae= 0.6 Fu.Ae  LRFD

     Pa = Fu.Ae / O = Fu.Ae/2.5  ASD

  Tension Rupture Strength for Bolted Connection: (Appendix A, E3.2)

  a) For flat sheet connections not having staggered hole patterns:

    1)   for washers are provided under both the bolt head and the nut
    fPn = f. Ft. An   LRFD
    Pa = Ft. An / O   ASD
     for single bolt, Ft =(0.1 + 3d/s)Fu <= Fu
     for multiple bolts, Ft = Fu
      f = 0.65 for double shear, 0.55 for single shear

       O = 2.0 for double shear, 2.22 for single shear

    2)   for washers are NOT provided under both the bolt head and the nut

    fPn = f. Ft. An   LRFD
    Pa = Ft. An / O   ASD
     for single bolt, Ft = (2.5 d/s)Fu <= Fu
     for multiple bolts, Ft = Fu
      f = 0.65

       O = 2.0

  b) For flat sheet connections having staggered hole patterns:

     fPn = f. Fu.An
      f = 0.65   LRFD

     Pa = Fu.An/ O
       O = 2.22   ASD

  c) For other than flat sheet:

     fPn = f. Fu.(An.U)
      f = 0.65   LRFD

     Pa = Fu.(An.U) / O
       O = 2.22   LRFD

    d - nominal bolt diameter
    s - sheet width divided by number of bolt holes in cross section

  Block Shear Rupture Strength: (Eq. E5.3-1, E5.3-2)
     The lesser of following:

    LRFD
     fRn = f [0.6 Fy.Agv + Fu.Ant]
     fRn = f [0.6 Fu.Anv + Fu.Ant]

    ASD
     Ra = [0.6 Fy.Agv + Fu.Ant]/ O
     Ra = [0.6 Fu.Anv + Fu.Ant]/ O

    f = 0.65 for bolted connections, 0.6 for welded connections
     O = 2.22 for bolted connections, 2.5 for welded connections

    Ant = net area subject to tension
    Anv = net area subject to shear
    Agv = gross area subject to shear

Reference: AISI S100-2007


  Combined Bending and Tension C5.1.2

  ASD
    1).        Ob .Mx / Mnxt + Ob .My / Mnyt + Ot .T / Tn < = 1.0

    2).        Ob .Mx /Mnx + Ob .My / Mny - Ot .T / Tn < = 1.0
  LRFD
    1).        Mux / (fb .Mnxt)+ Muy / (fb .Mnyt) + Tu / (ft. Tn) < = 1.0

    2).        Mux / (fb .Mnx)+ Muy / (fb .Mny) - Tf / (ft. Tn) < = 1.0

      Mx - Required allowable flexural strength about axis X
      My - Required allowable flexural strength about axis Y
      T - Required allowable axial strength

       Ob = 1.67
       Ot = 1.67


      Mux - Required flexural strength about axis X
      Muy - Required flexural strength about axis Y
      Tu - Required axial strength

      Mnxt = Sftx . Fy - Nominal flexural strength about axis X
      Mnyt = Sfty . Fy - Nominal flexural strength about axis Y
      Sftx - Section modulus of full unreduced section relative to extreme tension fibre about axis X
      Sfty - Section modulus of full unreduced section relative to extreme tension fibre about axis Y

      Mnx - Nominal flexural strength about axis X
      Mny - Nominal flexural strength about axis Y
      Tn - Nominal tensile strength

      fb = 0.9 - resistance factor for bending
      ft = 0.95 - resistance factor for shear