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Mechanics

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CE 336 Loadings 3 Basic Types of Loadings Static Dynamic Environmental

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CE 336 Static Loadings 1. Slowly applied 2. Sustained for period of time 3. Slowly removed Classifications Dead Loads Live Loads

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CE 336 Dynamic Loadings 1. Impulse or Shock 2. Vibration Random Transient Periodic t Applied Stress Amplitude Periodic Applied Stress Transient t toto t Applied Stress

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

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CE 336 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/I p

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

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CE 336 Stress vs. Strain 0.002 yy ult ult yy Linear Non-Linear

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CE 336 Overview of Mechanics Modulus of Elasticity tangent secant chord Shear Modulus

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CE 336 Overview of Mechanics Elastic Plastic Ductility Toughness Resilience Hardening

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

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

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CE 336 Ductility The ability to sustain plastic deformation without fracture = ult / y

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CE 336 Toughness & Resilience Toughness: Mechanical measure of total absorbed and stored energy at fracture Resilience: Mechanical measure of storing energy at yield

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CE 336 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

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

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CE 336 Generalized Hooke’s Law

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CE 336 Elastic vs. Plastic Behavior Linear Non-Linear yy yy

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

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CE 336 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

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CE 336 Review of Mechanics Material Compatibility in composite Material Compatibility in environments

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CE 336 Ductility and Fracture Characteristics Ductile Behavior Advantages and Disadvantages Brittle Behavior Advantages and Disadvantages

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