chapter 2: topics in strain - union...

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 1

Chapter 2:Topics in Strain

Thermal ExpansionPoisson’s RatioGeneralized Stress v. Strain Relationships

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 2

Thermal Expansion Coeficient

Deformation Due to Thermal Loading

Thermal Strain

( ) LTT ⋅Δ⋅=αδ

( )TLT

T Δ⋅== αδε

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 3

Indeterminate ProblemsAdditional external load is appliedSuperposition is applies

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 4

Example 1Consider a circular shaft shown. The shaft is made of steel with the following properties.

E-200GPaν=0.3α=11.7x10-6 C-1

In addition to the loading shown, the shaft is heated from 25C to 125C. Determine the reactions at A and C.

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 5

Poisson’s Ratio

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ESC023: Mechanics of Materials 6

Poisson’s Ratio

strainaxialstrainlateral

long

lat =−=εεν

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ESC023: Mechanics of Materials 7

For Axial Loading of a Bar

E

EAP

xzy

xxx

σνεε

σεσ

⋅−==⇒

=⇒=

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 8

Example 2

Given the steel bar shown. If an axial force p=80kN is applied , determine the change in the dimensions of its cross section.

E=200GPaν=0.32

Union CollegeMechanical Engineering

ESC023: Mechanics of Materials 9

Generalized Hooke’s Law

EEE

EEE

EEE

zyxz

zyxy

zyxx

σνσνσε

νσσνσε

νσνσσε

+−−=

−+−=

−−+=