1. Mechanics

2. Loadings
3 Basic Types of Loadings
Static
Dynamic
Environmental
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3. Static Loadings Slowly applied Sustained for period of time
Slowly removed
Classifications
Dead Loads
Live Loads
Static loading comprise most of the loadings on buildings and are often used to model loadings for simple engineering systems.
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4. Dynamic Loadings Impulse or Shock Vibration Classifications Random
Transient
Periodic
Transient Loads – Cars, Trucks, Cranes,
Periodic Loads - Rotating Motors
Random – Blast, Earthquake,
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5. Environmental Loadings
Physical
Chemical
Many Classifications
Thermal, Moisture…
Abrasion, Hydraulic…
Oxidation, Acid, Base…
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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
There are certain stress formula that every engineer should know before discussing the specific materials by which structures are designed. Beams are subjected to flexural stress and bending shear. Pedestals are typically subjected to direct compression. Cables are subjected to direct tension stress. Shafts are subjected to torsional shear.
Most structural elements are subjected to a combination of two or more of these stresses, e.g. building columns are subjected by flexural stress, bending shear and direct compression stress. These combined stresses can be added together using the principles of strength of materials (Mohr’s circle, transformation equations, stress-strain diagram addition).
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7. Review of Mechanics Equilibrium (internal vs. external)
Combined Stresses
Yield, (0.2% offset)
Elastic Limit,
Proportional Limit,
Limitations of elastic theory
In engineering mechanics, the topics of physics(Newton’s laws), statics and strength of materials can be used to balance material properties vs. applied stresses. This equilibrium is a basic concept of engineering design.
As the stress in a material reaches yield point, the equilibrium equations and concepts change from elastic to plastic theory.
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8. Stress vs. Strain Linear  Non-Linear ult y ult y  0.002 CE 336
Materials have the same yield stress and strain, as well as, the same ultimate stress and strain. However, the behavior is very different.
ult y 
0.002
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9. Overview of Mechanics Modulus of Elasticity tangent secant chord
Shear Modulus
Tangent Modulus of Elasticity is typically measured at =0 or 0.05 max but may be measured at any level of stress of interest for intermediate loading ranges.
Secant modulus of elasticity is typically measured at 0.4 max or 0.45 max
Chord modulus is used when the stress in a given range is needed. The secant modulus can be thought of a special case of the chord modulus of elasticity.
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10. Overview of Mechanics Elastic Plastic Ductility Toughness Resilience
Hardening
Defining the performance of a material of structural element is not always as easy as defining its elastic stresses. The fracture of the material is often the only failure considered by non-engineers. However, experienced engineers know that failure is a much broader concept. If a member deflects too much, it is often unserviceable (e.g. causes mechanical equipment to malfunction, create an uncomfortable condition for building occupants, redistributes loads to yield other parts of the structure). Safety of structure often requires ductility to provide a warning of impending failure and to redistribute loads to provide redundancy in structural elements. Toughness and Resilience are sometimes needed when structures are required to absorb energy (e.g. blast loadings, earthquakes, impacts). Finally, hardness is often a requirement to prevent a change in geometry or wear resistance.
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11. 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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12. Plasticity Ability to absorb energy upon loading
Perfectly plastic materials maintain the deflected shape after loading is removed.
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13. Ductility
The ability to sustain plastic deformation without fracture
 = ult/y
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14. Toughness & Resilience
Toughness: Mechanical measure of total absorbed and stored energy at fracture
Resilience: Mechanical measure of storing energy at yield
Resilience is the energy stored upon loading to the yield point.
Toughness is the total energy necessary to fracture the material
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15. 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
Deformations are important in nearly all civil engineering endeavor. Dams, pipelines, buildings and bridges are all build to tight deformation characteristics. These deformations are often used as predictors of problems or measures of successful designs.
From strength of materials, the modulus of elasticity, the shear modulus and poisson’s ratio are basic material constants in predicting failure.
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16. Review of Mechanics concrete = 0.15 steel = 0.25 e = ex(1-2)
Poisson ratio
concrete = 0.15
steel = 0.25
Dilatation (cubical dilation)
e = (V’-V)/V
e = ex(1-2)
Poisson’s ration and dilatation are used to calculate the lateral deformation and the volumetric changes in any material. These properties allow engineers to verify designs and avoid undesirable deformations.
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17. Generalized Hooke’s Law
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18. Elastic vs. Plastic Behavior  y y
Linear
Non-Linear
Materials have the same yield stress and strain, as well as, the same ultimate stress and strain. However, the behavior is very different.
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19. Environmental/Mechanical Strain
Coefficient of Thermal Expansion
Creep,
Shrinkage,
Relaxation
Chemical Resistance
Thermal expansion, creep, relaxation and creep occur in nearly all civil engineering materials. Each develops or relieves stresses in building elements. Pipes, beams, columns, tanks, walls, etc all are affected by the strains caused by these environmental and mechanical factors.
Chemical resistance is strictly related to the environmental factors. The corrosion or deterioration of a material from chemical means usually diminishes the load carrying capacity of an element or embrittles the element.
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20. 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
Statics and Strength of Materials introduced the concepts of stiffness and flexibility. These terms will be further reinforce in CE 240, structural analysis. The relationship between materials properties and stiffness is clearly explained by Hooke’s Law and determinate and indeterminate structural analysis.
As you become more aware of structural analysis, you will appreciate stiffness and flexibility more.
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21. Review of Mechanics Material Compatibility in composite
Material Compatibility in environments
Composites are materials that are connected to carry structural load in a shared manner. Composite materials are typically created to optimize the properties of multiple materials.
For Example
A steel beam with a concrete compression flange uses the tensile strength of the the steel in the tension face of flexure, and the compressive strength of the concrete in the compressive face of flexure.
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22. Ductility and Fracture Characteristics
Ductile Behavior
Advantages and Disadvantages
Brittle Behavior
Ductile Behavior
Elastic energy is stored Plastic energy is consumed
Warning Loss of Toughness
Energy Abs Lower Strength
Brittle Behavior
On-Off Switch Sudden Collapse
Higher Strength Lower Toughness
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