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Mechanics

Mechanics. Loadings. 3 Basic Types of Loadings Static Dynamic Environmental. Constant. Applied Stress. t. Static Loadings. Slowly applied Sustained for period of time Slowly removed Classifications Dead Loads Live Loads. Periodic. Applied Stress. Amplitude. t. Applied

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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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