Bringing a Real World Problem to Elasticity Advanced Strength of Materials

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Bringing a Real World Problem to Elasticity
(Advanced Strength of Materials)

• Autar Kaw, Glen Besterfield, Sanjeev Nichani
• ASEE 2003 National Conference Exposition
• June 25, 2003

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Modernizing Elasticity

• Symbolic Algebra (1994)
• Real-Life Problems (2001)
• Approximate Methods (2003)

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Why incorporate real-life problems and research?

• Train graduate students in state-of-the-art
  research in emerging technologies.
• Real world application of course work increase
  comprehension.
• Encourage that education and research are of
  equal value and are complementary parts of an
  integrative engineering and science education
  enterprise.

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BRIDGEof LIONS (1927)
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Bascule Bridge THG
Hub
Trunnion
Girder
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Trunnion-Hub-Girder Assembly Procedure Problems
Step1. Trunnion immersed in liquid
nitrogen Step2. Trunnion warm-up in
hub Step3. Trunnion-Hub immersed in liquid
nitrogen Step4. Trunnion-Hub warm-up into girder
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Trunnion-Hub-Girder Assembly
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Interpreting Strain Gage Reading
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Problem 1Calculate Strains Stresses

• Given strains from a rosette in the hub when the
  trunnion-hub is immersed into liquid nitrogen,
  calculate
• Strains in x-y co-ordinates
• Stresses in x-y co-ordinate
• Principal Strains and Stresses

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Failure in Hub

• Cracks developed radially near the inner diameter
  of the hub. So we need to apply failure theories
  to predict if failure took place

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Problem2 Failure Theories

• Apply six failure theories and fracture mechanics
  to predict failure at the inner diameter of the
  hub when the trunnion-hub is immersed in liquid
  nitrogen.

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Interference Fits
FN2 fit tolerances
Trunnion
Hub
Range of Diametric Interference
0.004249ltdlt0.007720
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Problem3Axisymmetric Stresses
Range of Stresses in Axisymmetric Problems
Comparison of Steady-State Hoop Stress at Hub
Inner Diameter
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Trunnion Stuck in Venetian Causeway Bridge

• When the trunnion was inserted into the hub, the
  trunnion got stuck before it could be fully
  inserted.

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Thermal Expansion Coefficient Variation with
Temperature
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Problem4 Estimating Contraction Thermal
Strains
Change in diameter ?D by cooling it in liquid
nitrogen is given by
D outer diameter ?(T) instantaneous
thermal expansion coefficient Ta ambient
temperature, Tc boiling temperature of
liquid nitrogen.
overestimates the thermal contraction by 28
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Square Plate with a Hole
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Problem 5Square Plate with Hole

• Find displacement and stress field in a square
  plate with hole, where the hole is subjected to a
  uniform radial displacement

Hole with Uniform Radial Displacement
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Resources for Instructors

• http//www.eng.usf.edu/kaw/class/elasticity.
• http//www.eng.usf.edu/besterfi/bascule.

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Conclusions

• A single real-life problem was been successfully
  implemented in a course in Elasticity.
• The breadth of topics covered included
• transformations of stresses,
• failure theories,
• fracture mechanics,
• axisymmetrically loaded problems,
• effect of temperature dependent thermoelastic
  properties,
• stresses in plates with circular holes.