Example of Limit State Design Method

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Bolted joint failure modes
F. Matthews, in Handbook of Polymer Composites
for Engineers
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Lay-up 1 45,0,-45,0,90,0,45,0,-45,0s Lay-up
2 45,-45,02,45,90,-45,03s Lay-up
3 45,-45,45,-45,90,05s Lay-up
4 45,-45,02,90,0,45,-45,02s Lay-up
5 45,-45,05,45,-45,90s
Effect of blocked laminate stacking sequence on
bearing strength
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Simplified procedures for designing composite
bolted joints

• from CC Chamis, J Reinf Plast Comp.,vol 9,
  pp614-626

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Basic bolt geometry
F
y
x
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1. Bearing (compression) failure
F
At failure, F d t sxc
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2. Tension failure
F
At failure, F (w-d) t sxT
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3. Wedge splitting(due to lateral pressure of
bolt)
F/2
F
At failure, F ½(2e - d) t syT
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4. Shear out
F
At failure, F 2 e t txy
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5. Combined tension and shear
F
At failure, F ½ t (w - d)sxT 2 e txy
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Example failure analysis

• High strength carbon/epoxy laminate.
• Layup 0,45,0,90s - 10 plies at 0.125 mm per
  ply.
• Fibre volume fraction 60
• Strength values
• long. tension (sxT) 546 MPa
• trans. tension (syT) 343 MPa
• long. compression (syT) 550 MPa
• in-plane shear (txy) 267 MPa

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Example failure analysis

• Bolt diameter (d) 6 mm
• Laminate thickness (t) 1.25 mm
• Joint width, or bolt spacing (w) 25 mm
• Edge distance (e) 25 mm
• Applied load (F) 5000 N

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1. Bearing (compression)

• Compressive stress is
• sxc F / d t 5000 / (6 x 1.25) 667 MPa
• This is greater than the compressive strength of
  the laminate, so bearing failure occurs.
• The maximum load would be
• 550 x 6 x 1.25 4125 N

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2. Tension

• Tensile stress is
• sxT F / (w - d) t 5000 / (19 x 1.25) 211
  MPa
• This is less than the tensile strength of the
  laminate, by a factor of 2.6.

And so oneach failure mode is considered
separately, and a margin of safety calculated.
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Geometrical aspects

• It is straightforward to use a spreadsheet to
  examine the dependence of overall strength and
  failure mode on bolt geometry.
• The following example takes the laminate
  information given above, and calulates failure
  loads for the 5 different modes as a function of
  bolt diameter

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- shear failure load is independent of bolt
diameter- bearing failure occurs for d lt 12
mm- strongest joint has d between 12 and 13 mm,
where several failure modes are likely (for this
laminate)
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Multi-bolt joints

• from CC Chamis, J Reinf Plast Comp.,vol 9,
  pp614-626

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Example analysis of multi-bolt joint

• Connection required between composite panel and
  metal plate.
• Assume that all bolts share load equally.
• Bolts are designed for the composite - we
  assume the metal plate is strong enough.
• High strength carbon/epoxy laminate, as defined
  previously.

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Example analysis of multi-bolt joint

• Design tensile load (P) 400 N/mm
• Bolt diameter (d) 6 mm
• Bolt spacing (p) 6 bolt diameters 36 mm
• Edge distance (e) 4 bolt diameters 24 mm

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Load carried per bolt

• F bolt spacing x load per unit width
• 36 mm x 400 N/mm
• 14400 N
• 14.4 kN

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Number of bolts per row

• 1. Assuming bearing failure mode
• n F / d t sxc
• 14400 / (6 x 1.25 x 550)
• 3.5
• so 4 bolts are required to avoid bearing failure.

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Number of bolts per row

• 2. Assuming tension failure mode
• n F / (p - d) t sxT
• 14400 / (36 - 6) x 1.25 x 546)
• 0.7
• so only 1 bolt is required to avoid tensile
  failure.

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Check other failure modes for edge and centre
bolts

• 3. Check first row centre bolt in shear-out
• Each bolt takes 14400 / 4 3600 N
• Shear stress 3600 / (2 e t) 60 MPa
• Compare with shear strength of laminate
• 60 lt 267 MPa, so OK.

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Check other failure modes for edge and centre
bolts

• 4. Check first row centre bolt in wedge
  splitting
• Transverse tensile stress
• 2 x 3600 / (2e - d) t 137 MPa
• Compare with transverse tensile strength of
  laminate
• 137 lt 343 MPa, so OK.

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Check other failure modes for edge and centre
bolts

• 5. Check corner bolt in tension/shear-out
• Force required to cause failure
• F ½ t (p - d)sxT 2 e txy
• 18248 N
• This is much greater than the actual load on this
  bolt (3600 N), so OK.

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Other factors not included in preliminary design

• Bypass load
• Friction effects
• Cyclic loading and laminate degradation
• Thermal and moisture effects
• Biaxial loads
• Flat-wise compression