Special Cases of Bending

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Special Cases of Bending

• Composite Beams
• Reinforced Concrete Beams

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Composite Beams

• Beams constructed of two or more materials
• Wood beams with steel straps
• Concrete beams with steel reinforcing rods
• Designed to be more efficient in carrying loads
  that single material beams

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Transformation Process

• Flexure formula based on homogenous material
• Need to transform beam into one that meets
  formula requirements
• Need planes to remain plane, strains to vary
  linearly from neutral axis

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Transformation Process

• Convert beam into single material
• Modify the width on one material so that it
  carries the same load as if it were made of the
  other material
• Establish a transformation factor

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Transformation

• Transformation factor
• Where E1 is the modulus of elasticity of the
  stiffer material and E2 is for the other material
• The other material flange becomes b2 nb wide
  and the stress found is transformed to s ns2
• The beam can be converted into stiffer or other
  material

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Reinforced Concrete Beams

• One of the assumptions we made for the flexure
  formula was same E for tension and compression.
  Not true of concrete.
• Concrete has little strength in tension and is
  prone to cracking in tension

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Reinforced Concrete Beams

• In concrete beams strength gained by tensile
  loading of concrete is neglected
• Strength based on concrete in compression and
  steel reinforcing rods
• Modified transformation method used

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Reinforced Concrete Beams

• To find the neutral axis
• Where n Est /Econc
• Solve for h the location of the neutral axis and
  proceed in the usual manner

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