chapter 2: topics in strain - union...
TRANSCRIPT
![Page 1: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/1.jpg)
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 1
Chapter 2:Topics in Strain
Thermal ExpansionPoisson’s RatioGeneralized Stress v. Strain Relationships
![Page 2: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/2.jpg)
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
![Page 3: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/3.jpg)
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 3
Indeterminate ProblemsAdditional external load is appliedSuperposition is applies
![Page 4: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/4.jpg)
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.
![Page 5: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/5.jpg)
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 5
Poisson’s Ratio
![Page 6: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/6.jpg)
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 6
Poisson’s Ratio
strainaxialstrainlateral
long
lat =−=εεν
![Page 7: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/7.jpg)
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 7
For Axial Loading of a Bar
E
EAP
xzy
xxx
σνεε
σεσ
⋅−==⇒
=⇒=
![Page 8: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/8.jpg)
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
![Page 9: Chapter 2: Topics in Strain - Union Collegeminerva.union.edu/bucinelr/mer214/LectureNotes/MER21… · · 2008-09-22Union College Mechanical Engineering ESC023: Mechanics of Materials](https://reader033.vdocuments.net/reader033/viewer/2022051407/5ae446927f8b9a90138eb8bb/html5/thumbnails/9.jpg)
Union CollegeMechanical Engineering
ESC023: Mechanics of Materials 9
Generalized Hooke’s Law
EEE
EEE
EEE
zyxz
zyxy
zyxx
σνσνσε
νσσνσε
νσνσσε
+−−=
−+−=
−−+=