chapter 2: topics in strain - union...
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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
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 6
Poisson’s Ratio
strainaxialstrainlateral
long
lat =−=εεν
Union CollegeMechanical Engineering
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
+−−=
−+−=
−−+=