ME 101: Materials and Stresses

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ME 101Materials and Stresses

• Chapter 5

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Job of Mechanical Engineer

• Design Hardware/Components
• Must not fail when loaded with expected forces
• Must be reliable
• Must be safe
• What is failure?
• Break/fracture
• Distortion?

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Component Failure

• What causes failure?
• Excessive loads for given geometric dimensions
• Forces, moments, pressures, impacts, etc.
• How do we design to avoid failure?
• Dimensions of component
• Stresses intensity of forces applied over an
  area
• Material selection
• Strength ability of material to support and
  withstand applied stresses
• If strength gt stress, no failure?
• Not always (repeated loading cycle fatigue)

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Case Study

• The DeHavilland Comet - the worlds first jet
  airliner (1952)

• Aircraft and
• company
• destroyed by
• stress fractures
• study of
• Solid Mechanics
• and Strength of
• Materials

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Mechanics

• Statics and Dynamics
• Treat bodies as rigid do not change when forces
  are applied
• Real bodies are not rigid and will deform and/or
  fracture
• Solid Mechanics
• Study of the deformation of solid structures
• Consider different materials under loads
• Consider how body deforms and if it will fail
• Strength of materials

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Deformation
Elastic Deformation not permanent, return to
original shape/dimensions when force is
removed Plastic Deformation permanent, when
force is removed shape/dimensions remain changed
Consider a paper clip
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Axial Stress
To be in equilibrium, force must be carried by
the rod at each cross section
Note s is perpendicular to area A
Depicted as a concentrated force, but influence
is assumed to be equally distributed over cross
sectional area
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Tension and Compression
F
F
Tension
F
F
Compression
Units?
or
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Unit Prefixes and Conversions

• kilo (k) mega (M) giga (G)
• 103 106 109

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Example

• A 6 steel rod, 1/4 in diameter is used as the
  shaft to support a 500 lb load
• What is the stress in the rod?

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Strain
F
F
Lo
Lf
Units?
Typically very small (0.005 or 0.5for example)
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Stress and Strain
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Hookes Law
k
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Stress-Strain Curve
(Elastic Modulus or Youngs Modulus)
Unit of force per unit area Physical material
property (slope of stress-strain curve)
Frequently used Esteel 210 GPa
(30Mpsi) Ealuminum 70 GPa (10Mpsi)
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Lateral (Diameter) Effects
P
P
P
P
Diameter will contract/enlarge with
tension/compression. Cross-sectional effect
known as Poissons contraction or expansion
represents dimensional change that occurs
perpendicular to the direction of applied force.
Material property to quantify contraction/expansio
n Poissons ratio, ?
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Poissons Ratio
Tension typically reduces diameter Compression
typically increases diameter

• Typical values for Poissons ratio are 0.25 to
  0.35
• Steel and most metals 0.29
• Granite 0.25
• Rubber 0.5

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What About the Plastic Region?
Below A Elastic with stress and strain
proportional Between A and B - Elastic but stress
and strain not proportional Beyond B - Permanent
deformation starts occurring Beyond D - Material
cannot sustain stress and material deteriorates
until fracture
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Yielding to Fracture
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Example

• d 10 mm, tensioned to 4kN
• Draw FBD and calculate ?

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Example

• d 10 mm, L 325mm, ? 50.9MPa, E 210GPa
• Calculate ?, ?L, and ?d of U-bolt