Poissons Ratio

1
(No Transcript)
2

• Poissons Ratio
• Shear Stress-Strain
• Creep
• Fatigue

3
Bar in Compression
Under compression, height shrinks, girth thickens
4
Poissons Ratio
5

• Poissons Ratio
• Shear Stress-Strain
• Creep
• Fatigue

6
Shearing Strain
Shear strain,? The change in angle from an
original right angle, in radians.
Hookes Law for Shear
7
Example

• SOLUTION
• Determine the average angular deformation or
  shearing strain of the block.

• Apply Hookes law for shearing stress and strain
  to find the corresponding shearing stress.

A rectangular block of material with modulus of
rigidity G 90 ksi is bonded to two rigid
horizontal plates. The lower plate is fixed,
while the upper plate is subjected to a
horizontal force P. Knowing that the upper plate
moves through 0.04 in. under the action of the
force, determine a) the average shearing strain
in the material, and b) the force P exerted on
the plate.

• Use the definition of shearing stress to find the
  force P.

8
G 90 ksi
9
Relation Among E, n, and G

• An axially loaded slender bar will elongate in
  the axial direction and contract in the
  transverse directions.

• An initially cubic element oriented as in top
  figure will deform into a rectangular
  parallelepiped. The axial load produces a normal
  strain.

• If the cubic element is oriented as in the bottom
  figure, it will deform into a rhombus. Axial load
  also results in a shear strain.

10

• Poissons Ratio
• Shear Stress-Strain
• Creep
• Fatigue

11
Creep

• Time-dependent permanent deformation
• Usually over a long time period
• Can be accelerated by heat

No Load
Same Load P, Left on Over Time
Deformation after Load P
12

• Poissons Ratio
• Shear Stress-Strain
• Creep
• Fatigue

13
Fluctuating Loads
Fluctuating forces may lead to fatigue failure.
14
Fatigue
(http//www.egr.msu.edu/classes/me471/thompson/han
dout/class13_2005SFatigue.pdf)
15
Rotating Beam Fatigue Testing
(http//www.egr.msu.edu/classes/me471/thompson/han
dout/class13_2005SFatigue.pdf)
16
Typical Fatigue Test Data Plot (Steel)
(http//www.egr.msu.edu/classes/me471/thompson/han
dout/class13_2005SFatigue.pdf)
17
Fatigue Data Plots
(http//www.egr.msu.edu/classes/me471/thompson/han
dout/class13_2005SFatigue.pdf)
18
Fatigue
S

• Fatigue properties are shown on S-N diagrams.

• A member may fail due to fatigue at stress levels
  significantly below the ultimate strength if
  subjected to many loading cycles.

Stress at Failure (ksi)
N

• When the stress is reduced below the endurance
  limit, fatigue failures do not occur for any
  number of cycles.

19
Other Fatigue Testing Modes
(http//www.egr.msu.edu/classes/me471/thompson/han
dout/class13_2005SFatigue.pdf)