UNIT 4.2: THE IRON AGE AND MONUMENTAL BUILDING

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LECTURE 9.1
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LECTURE OUTLINE

• Weekly Deadlines
• Stress and Strain

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STRESS AND STRAIN

• The Three Stages in the Deformation of a Material
• The Atomic Spring Model
• Stress and Strain, Calculations
• The Stress-Strain Curve
• The Meaning of Youngs Modulus

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THE THREE STAGES OF DEFORMATION
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HOOKES LAW
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ATOMIC SPRINGS I
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ATOMIC SPRINGS II
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STRESS AND STRAIN

• Stress Load/Area
• Strain Elongation/Original Length
• Youngs Modulus Stress/Strain

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STRESS AND STRAIN CALCULATIONS I
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STRESS AND STRAIN CALCULATIONS II

• a) A square metal bar of length 1,000 mm and
  width 40 mm is loaded in tension and begins to
  yield at 16,000 kg. Its length is now 1,010 mm.
• What is the yield stress?
• What is the strain at yield?
• Stress 16,000/40 x 40 10kg/mm2
• Strain 1,010 - 1,000/1,000 10 0.01

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STRESS AND STRAIN CALCULATIONS III

• Suppose that a second bar, of the same material
  and in the same condition, is 20 mm x 50 mm in
  cross-section and is 1,500 mm long. At what
  stress will this second bar yield, and at what
  elongation?
• Stress Load, 10/Area Load/20 x 50
• Load 10,000 kg
• Strain Elongation 0.01/Original Length ?/
  1,500
• Elongation 1500 x 0.01 15mm

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STRESS AND STRAIN CALCULATIONS IV

• What is the Youngs Modulus of the Material?
• Youngs Modulus Stress/Strain
• Youngs Modulus 10/0.01 1,000 kg/mm2

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THE STRESS-STRAIN CURVE
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YOUNGS MODULUS CERAMICS, METALS, AND POLYMERS
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STRESS-STRAIN CURVE OF A STAINLESS STEEL I
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STRESS-STRAIN CURVE OF A STAINLESS STEEL II
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ON STRENGTH AND STIFFNESS

• Lest there be any possible, probable, shadow of
  doubt, strength is not, repeat not, the same
  thing as stiffness. Stiffness, Young's modulus,
  is concerned with how stiff, flexible, springy or
  floppy a material is. Strength is the force or
  stress needed to break a thing. A biscuit is
  stiff but weak, steel is stiff and strong, nylon
  is flexible but strong, raspberry jelly is
  flexible and weak. The two properties together
  describe a solid about as well as you can
  reasonably expect two figures to do.
• J. E. Gordon, The New Science of Strong Materials