Wk1 – Lecture 1 Dana R. Swalla PhD, PE

Lecture 1: Normal stress/strain

1

• Intro to Mechanics of Materials• Normal Stress• Normal Strain/Deformation• Units• Homework and Problem solving format• Example problems• Homework assignment

Wk1 – Lecture 1 Dana R. Swalla PhD, PE 2

Intro• Mechanics of Materials requires:

– Equilibrium– Constitutive Laws– Compatibility

• Examples of solid bodies we will study– Bar with axial load

– Shafts in torsion

– Beams in bending

– Columns in compression

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Normal Stress• Definition: Force per unit area, or intensity of the forces distributed over a given section.

• Sign Convention: Tension (+) Compression (-) • Units:

Area

Force

Ref 2

• F vs P vs P’ (‘force’ vs ‘load’):

• Centric vs eccentric loading:

• Effect of distribution:2

3

23

10

10_1

in

lbfpsi

lbfkip

m

NkPa

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Definition of Normal Strain

•Strain vs Deformation: Strain is the deformation of the member per unit length and is a dimensionless quantity. However, the original units are often kept (m/m, in/in, etc).

•Effect of Geometry:

Ref 1Constant cross section

Variable cross section

L

dx

d

xx

lim0

A load, 2P, is required to produce the same deformation in a rod of the same length, but with an area, 2A

Note, however, that the stress and strain are the same.

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Homework Format, posting, etc

• See LMS

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Example 1:

Ref 2

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Example 2:

Ref 2

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References

Ref 1

Ref 2

Ref 3

Ref 4