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Mechanics

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  1. Mechanics

  2. Loadings 3 Basic Types of Loadings • Static • Dynamic • Environmental CE 336

  3. Constant Applied Stress t Static Loadings • Slowly applied • Sustained for period of time • Slowly removed Classifications • Dead Loads • Live Loads CE 336

  4. Periodic Applied Stress Amplitude t Applied Stress t to Transient Applied Stress t Dynamic Loadings • Impulse or Shock • Vibration • Random • Transient • Periodic CE 336

  5. Environmental Loadings • Physical • Chemical Many Classifications • Thermal, Moisture… • Abrasion, Hydraulic… • Oxidation, Acid, Base… CE 336

  6. Static Forces and Stresses • Flexure Stress,  = Mc/I • Bending Shear  = VQ/It • Direct Compression Stress,  = -P/A • Direct Tension Stress,  = P/A • Torsional Shear  = Tr/Ip CE 336

  7. Review of Mechanics • Equilibrium (internal vs. external) • Combined Stresses • Yield, (0.2% offset) • Elastic Limit, • Proportional Limit, • Limitations of elastic theory CE 336

  8. Stress vs. Strain Linear  Non-Linear ult y ult y  0.002 CE 336

  9. Overview of Mechanics • Modulus of Elasticity • tangent • secant • chord • Shear Modulus CE 336

  10. Overview of Mechanics • Elastic • Plastic • Ductility • Toughness • Resilience • Hardening CE 336

  11. Elasticity • Ability to store energy and recover strain when unloaded Perfectly elastic materials return to their original geometry when fully unloaded. CE 336

  12. Plasticity • Ability to absorb energy upon loading Perfectly plastic materials maintain the deflected shape after loading is removed. CE 336

  13. Ductility • The ability to sustain plastic deformation without fracture  = ult/y CE 336

  14. Toughness • Toughness: Mechanical measure of total absorbed and stored energy at fracture CE 336

  15. Resilience • Resilience: Mechanical measure of storing energy at yield CE 336

  16. Review of Mechanics • Deformations and Strains, = E • Flexural, Mx/EI =  • (plane sections remain plane) • Compression and Tensile, /L =  • Shear deformations G(distortions) • Poisson Strains l = x CE 336

  17. Review of Mechanics • Poisson ratio concrete = 0.15 steel = 0.25 • Dilatation (cubical dilation) e = (V’-V)/V e = ex(1-2) CE 336

  18. Generalized Hooke’s Law CE 336

  19. y y  Elastic vs. Plastic Behavior Linear Non-Linear CE 336

  20. Environmental/Mechanical Strain • Coefficient of Thermal Expansion • Creep, • Shrinkage, • Relaxation • Chemical Resistance CE 336

  21. Review of Mechanics • Stiffness: Load necessary to cause a unit deformation • Modulus • Shape, I, J, L, e.g. EI/L or AG • Restrain Conditions • Distribution of Forces according to Stiffness CE 336

  22. Review of Mechanics • Material Compatibility in composite • Material Compatibility in environments CE 336

  23. Ductility and Fracture Characteristics • Ductile Behavior Advantages and Disadvantages • Brittle Behavior Advantages and Disadvantages CE 336

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