CTC / MTC 222 Strength of Materials

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CTC / MTC 222Strength of Materials

• Chapter 1
• Basic Concepts

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Strength of Materials

• A natural follow-up to the study of statics
• Statics the study of forces acting on rigid
  bodies at rest
• Strength of materials the study of the
  relationships between external forces acting on
  elastic bodies and the internal stresses and
  strains caused by these forces

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Strength of Materials

• In statics, the bodies analyzed are assumed to be
  rigid
• Deformations or deflections of the bodies are
  neglected
• In strength of materials, the bodies analyzed are
  considered deformable
• Deformations and deflections of the bodies are
  important considerations

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Course Objectives

• To provide students with the necessary tools and
  knowledge to analyze forces, stresses, strains,
  and deformations in mechanical and structural
  components.
• To help students understand how the properties of
  materials relate the applied loads to the
  corresponding strains and deformations.

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Course Objectives

• To provide students with a portion of the
  knowledge necessary to design (or analyze) a
  product, machine or structure that is safe and
  stable under the loads exerted on it.
• Three modes of failure must be considered
• Failure by fracture
• Excessive deflection or deformation
• Instability or buckling
• Principles of strength of materials are required
  to ensure the component is safe with regard to
  strength, rigidity and stability.

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Chapter Objectives

• Use units from the SI metric unit system and the
  U.S. Customary unit system correctly
• Define mass and weight and use these terms
  correctly
• Define stress, direct normal stress, direct shear
  stress and bearing stress
• Define single shear and double shear
• Define strain, normal strain and shearing strain
• Define Poissons ratio, modulus of elasticity in
  tension and modulus of elasticity in shear

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Basic Unit Systems

• U.S. Customary Units
• Length foot (ft) or inch (in)
• Mass slug (lb-s2 / ft)
• Force pound (lb), or kip
• Time - seconds (s)
• SI Metric Units
• Length meter (m) or millimeter (mm)
• Mass kilogram (kg)
• Force newton (N) (kgm / s2 )
• Time - seconds (s)

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Unit Conversions

• Convert all lengths in an equation to the same
  unit, all masses to the same unit, all forces to
  the same unit, all measures of time to the same
  unit, etc.
• Avoid mixed units
• To convert from one unit to another, multiply by
  a factor whose denominator in the first unit is
  equal to the numerator in the second unit.
• To convert 10 meters to feet, multiply by 3.281
  feet/1 meter
• 10 m x (3.281 ft / 1 m) 32.81 ft
• To convert 10 feet to meters, multiply by 1
  meter/3.281 feet
• 10 ft x (1 m / 3.281 ft) 3.048 m
• Conversion factors listed in Appendix A-26

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Mass, Force and Weight

• Mass the amount of substance in a body
• Absolute, not dependent on location
• A scalar quantity has magnitude only
• Force a push or pull exerted on a body by an
  external source
• A vector quantity has magnitude and direction
• Weight the force exerted on a body by gravity
• Relative, dependent on location

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Mass, Force and Weight

• Mass, force, and weight are related by Newtons
  2nd Law
• Force mass x acceleration
• F ma, or m F / a
• When the force is the force of gravity, this can
  be expressed as
• W mg, or m W / g
• g is the acceleration due to gravity
• g 9.81 m / s2 in SI units
• g 32.2 ft / s2 in US units
• Units of mass kg in SI Units, slugs (-
  s2/ft)in US units
• Units of weight N (kg-m/s2) in SI Units, lbs in
  US units

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Density and Specific Weight

• Density the amount of mass per unit volume
• Units slugs / ft3, kg / m3
• Specific Weight the amount of weight per unit
  volume
• Units lbs / ft3, N / m3

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Stress

• Stress the internal resistance to an external
  force offered by a unit area of the material from
  which a member is made, or, more simply, force
  per unit area
• Stress force / area F / A
• Units in US Customary system
• Pounds / in2 (psi), kips / in2 (ksi)
• Units in SI system
• Newtons / m2 , Newtons / mm2 , Kilonewtons / m2
• Also expressed in pascals (Pa), or more commonly,
  megapascals (MPa)
• 1 Pa 1 N / m2
• 1MPa 1x 106 N / m2 1x 103 KN / m2 1 N / mm2

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Direct Normal Stress

• Normal Stress a stress which acts perpendicular
  (or normal) to the cross section of the member
• Direct Normal Stress a normal stress which is
  also uniform across the resisting area
• Units in US Customary system
• Pounds / in2 (psi), kips / in2 (ksi)
• Units in SI system
• Newtons / m2 , Newtons / mm2 , Kilonewtons / m2
• Also expressed in pascals (Pa), or more commonly,
  mega pascals (MPa)
• 1 Pa 1 N / m2
• 1 MPa 1x 106 N / m2 1x 103 KN / m2 1 N / mm2

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Direct Normal Stress, ?

• Compressive Stress
• Tends to crush the material
• Shortens the member
• Tensile Stress
• Tends to pull the material apart
• Elongates the member
• s Applied Force/Cross-sectional Area F/A
• Area A is perpendicular to the line of action of
  the force

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Direct Shear Stress, ?

• Shear a cutting action
• Direct Shear Stress
• Shear force is resisted uniformly by the area of
  the part in shear
• Shear stress is uniform across the area
• ? Applied Force/Shear Area F/As
• Single shear applied shear force is resisted by
  a single cross-section of the member
• Double shear applied shear force is resisted by
  two cross-sections of the member

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Bearing Stress, sb

• Bearing Stress - developed when one body rests on
  another and transfers a load normal to it,
  tending to crush the supporting material
• sb Applied Load/Bearing Area F/Ab
• Area Ab is the area over which the load is
  transferred
• For flat surfaces in contact, Ab is the area of
  the smaller of the two surfaces
• For a pin in a close fitting hole, Ab is the
  projected area, Ab Diameter of pin x material
  thickness

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Contact Stress, sc

• A type of bearing stress developed when a load is
  transmitted between two surfaces over a very
  small area. Examples
• A cylindrical roller on a flat plate
• A sphere on a flat plate
• Area of bearing is theoretically zero.
• Due to elasticity of materials actual bearing
  area is very small
• Detailed analysis of these stresses, sometimes
  called Hertz stresses is beyond the scope of this
  course.

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Stress Elements

• Stress element a free body diagram of an
  infinitesimal portion of a member
• 3D element is a cube
• 2D element is a rectangle
• If faces are unit areas, forces represent
  stresses (force per unit area)
• Overall body is in equilibrium, therefore stress
  element is in equilibrium
• Tensile and compressive stresses are
  perpendicular to face
• Shear stresses are parallel to face

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Strain, e

• An applied load causes a load-carrying member to
  deform
• This deformation can be measured. It can also be
  calculated.
• Strain unit deformation, calculated by dividing
  the total deformation by the original length
• Strain e total deformation / original length
• Units
• Could be considered dimensionless
• Preferably reported as in/in, or mm/mm

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Shearing Strain, g

• Shearing action on parallel faces of stress
  element tend to deform it angularly
• The angle g measured in radians is the shearing
  strain