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

Bar in Compression

Under compression, height shrinks, girth thickens

Poissons Ratio

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

Shearing Strain

Shear strain,? The change in angle from an

original right angle, in radians.

Hookes Law for Shear

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.

G 90 ksi

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.

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

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

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

Fluctuating Loads

Fluctuating forces may lead to fatigue failure.

Fatigue

(http//www.egr.msu.edu/classes/me471/thompson/han

dout/class13_2005SFatigue.pdf)

Rotating Beam Fatigue Testing

(http//www.egr.msu.edu/classes/me471/thompson/han

dout/class13_2005SFatigue.pdf)

Typical Fatigue Test Data Plot (Steel)

(http//www.egr.msu.edu/classes/me471/thompson/han

dout/class13_2005SFatigue.pdf)

Fatigue Data Plots

(http//www.egr.msu.edu/classes/me471/thompson/han

dout/class13_2005SFatigue.pdf)

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.

Other Fatigue Testing Modes

(http//www.egr.msu.edu/classes/me471/thompson/han

dout/class13_2005SFatigue.pdf)

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