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Table legs

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Currently made of lead, cast iron, steel, composites - a strange diversity! ... g. axial springs, leaf springs, helical springs, spiral springs, torsion bars, etc. ... – PowerPoint PPT presentation

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Title: Table legs


1
Materials Selection Without Shape - Case Studies
  • Table legs
  • Flywheels
  • Springs
  • Pressure vessels
  • Precision Devices
  • Buildings

2
Materials for Table Legs
Aim cylindrical legs as light and thin as
possible constraint resistance to
buckling first eliminate r and get for
slenderness
3
Materials Selection for Table Legs
4
Materials Selection for Table Legs
5
Materials for Flywheels
  • Flywheel store energy.
  • Currently made of lead, cast iron, steel,
    composites - a strange diversity!
  • Aim highest stored energy per unit weight,
    without failing
  • Stored energy
  • Mass of flywheel disk

6
Materials for Flywheels
  • The quantity to be maximized
  • The maximum principle stress in a spinning disk
    of uniform thickness
  • Eliminating R? gives

7
Materials Selection for Flywheels
8
Materials Selection for Flywheels
9
Materials for Springs
  • Spring is a device for storing energy
  • Springs come in many shapes and have many
    purposes, e.g. axial springs, leaf springs,
    helical springs, spiral springs, torsion bars,
    etc.

10
Materials for Springs
  • Maximum energy stored in axial spring
  • For torsion bars
  • For leaf springs (bending deformation)
  • The geometry and form of the spring is immaterial
    to the objective function
  • For efficient small spring
  • For efficient light spring

11
Materials Selection for Efficient Small Spring
12
Materials Selection for Efficient Small Spring
13
Materials Selection for Efficient Light Spring
14
Materials Selection for Efficient Light Spring
15
Materials for Safe Pressure Vessels
  • Daily examples aerosol can, boiler, etc.
  • Small vessels are designed to yield before
    break the distortion easy to detect and the
    pressure released safely.
  • Large vessels are designed to leak before
    crack i.e. critical crack length for unstable
    propagation is larger than vessel wall thickness
    leak is easily detected and releases pressure
    gradually

16
Materials for Safe Small Pressure Vessels
  • The hoop stress of a thin-wall spherical vessel
    of radius R is
  • If the vessel contains no cracks or flaws of
    diameter greater than 2ac, then the stress
    required for crack propagation is
  • For yield before crack

17
Materials for Safe Large Pressure Vessels
  • Number and sizes of cracks in large pressure
    vessels changes with time due to corrosion and
    cyclic loading but NDT cannot be done very
    frequently, therefore the leak before crack
    strategy.
  • Through-thickness crack must still be stable
  • The wall thick enough for the pressure without
    yielding
  • Eliminate t, gives
  • Maximize p means

18
Materials for Safe Pressure Vessels
19
Materials for Safe Pressure Vessels
20
Materials to Minimize Thermal Distortion in
Precision Devices
  • The precision of measuring device is limited by
    its stiffness and the dimensional change or
    distortion caused by temperature gradients.
  • Elastic deflection of the Force Loop is allowed,
    provided natural vibration frequencies are high!
  • Expansion is permissible of the Force Loop,
    provided distortion does not occur!

21
Materials to Minimize Thermal Distortion in
Precision Devices
  • The temperature can be equalized by heat
    conduction
  • The strain related to temperature is
  • The strain gradient (distortion)
  • Distortion is minimized by maximizing
  • To reduce sensitivity to external vibration, the
    natural frequencies must be high

22
Materials to Minimize Thermal Distortion in
Precision Devices
23
Materials to Minimize Thermal Distortion in
Precision Devices
24
Structural Materials for Buildings
  • Roughly half the cost of a house is the cost of
    materials of which it is made (?HK300/sq. ft in
    Hong Kong)
  • The quantities is very large, e.g. around 20000
    tonnes for a large apartment block
  • Structural materials must be stiff, strong and
    cheap
  • The critical components in building are loaded
    either in bending or as columns

25
Structural Materials for Buildings
26
Structural Materials for Buildings
27
Structural Materials for Buildings
28
Summary
  • The case studies illustrate how the choice of
    materials is narrowed
  • Most designs make certain non-negotiable demands
    on the material, e.g. operation temperature,
    corrosion resistance, etc.
  • The choice is further narrowed by maximizing
    performance.
  • Final choice also depends on more detailed
    information of properties, manufacturing
    processes, joining, finishing, etc.
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