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MECHANICS OF MATE

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OUTLINE REVIEW

STRESS

NORMAL STRESS

SHEAR STRESS

BEARING STRESS

PUNCHING STRESS

STRAIN

NORMAL STRAIN

SHEAR STRAIN

MATERIAL PROPERTIES

STRESS-STRAIN DIAGRAM AND HOOKES LAW

STRAIN ENERGY

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Average Normal Stress Distributio

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Normal Stress

An element subjected to a normal stress must have an opposite

normal stress. UNIAXIAL STRESS P is equivalent to the volume under the stress diagram

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Maximum Average Normal Stres

Sometimes, a member experiences multiple loads. This would mdifferent sections, different internal forces are induced.

It is very important to find the section where P/A is maximum

Axial or Normal Force Diagram

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Average Shear Stress

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Single Shear

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Double Shear

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Bearing Stress

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Punching Shear Stress

Punching Shear:

=P/Area ResistingPunching Shear

Punching Shear ArePerimeter of hole Thickness

Link ABC:

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Link ABC:- Upper portion: 3/8 in th- Lower portion: 1/4 in t- Upper and lower portio

are glued @ B

Pin A: 3/8 in diameterPin C: 1/4 in diameter

Find:a) Shear stress in pin A

b) Shear stress in pin Cc) Largest normal stress

link ABCd) Average shear stress i

glued arese) Bearing stress in link a

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STDeformations: Shape/a

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DEFORMATIONS

Changes in the shape and size of a body that is subjected to an force or temperature change

Can either be highly visible or practically unnoticeable

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Normal Strain,

Can be defined as:

The change in length of a line per unit le

Dimensionless

Elongation (+)

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Shear Strain,

Change in angle between two previously perpendicular lines

If is less than pi/2, (+)

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Small Strain Analysis

For small strains

Sin = , Cos = 1, Tan =

Paths of deformed member can be approximated as straight lines

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A rigid lever is attached to a cable. A force P makes the lever 0.05degrees. Determine the strain on the cable.

D t i th Sh St i t E if id CD i di l d b

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Determine the Shear Strain at E if side CD is displaced b

shown.

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MATERIAL PROPERSTRESS-STRAIN DIAGRAM,HOOKES LAW,ST

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TENSILE TEST (video)

http://www.cyberphysics.co.uk/topics/forces/young_modulus.htm

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STRESS-STRAIN DIAGRAM (Stee

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Types of Stress-Strain Diagrams:

1. Conventional Stress-Strain Diagram uses

the original dimensions of a material

2. True Stress-Strain Diagram uses theactual dimensions of a material at the instantthe load is applied

Stress-Strain Diagram

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STRESS-STRAIN DIAGRAM (Stee

Elastic Region

Upon removal of load, material returns

to its original shape

Plastic Region Material has permanent deformation upon

increase of load

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STRESS-STRAIN DIAGRAM (Stee

Proportional Limit

Stress is proportional to strain

Elastic Limit

Material still returns to its original shape

beyond the proportional limit

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STRESS-STRAIN DIAGRAM (Stee

Yield stress

Stress at the region where material deforms

without any increase in load

Ultimate Stress Maximum stress achieved upon increase of load

after the material yields

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STRESS-STRAIN DIAGRAM (Stee

Necking

decrease in the cross-sectional area in

a localized region

Rupture

Point where material breaks or fails

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STRESS-STRAIN DIAGRAM (Concr

http://www.diracdelta.co.uk/science/source/s/t/stress-strain%20diagram/source.html#.U9F0lPmSxrs

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Ductile vs Brittle

http://www.cyberphysics.co.uk/topics/forces/young_modulus.htm

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HOOKES LAW

=

E- Modulus of Elasticity/Youngs Modulus

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STRAIN ENERGY Energy that is stored in a material due to its deformation

Strain-Energy Density

=

Modulus of resilience

Modulus of toughness

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Modulus of Resilience (ur)

- Amount of energy a material can take beforeexperiencing permanent deformation.

- It is the area under the stress-strain diagramwhere stress is proportional to strain.

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Modulus of Toughness (ut)

- Amount of energy a material can take before it

fractures/ breaks.

- Represents the entire area under the stress-straindiagram