Course Content
The course content is organized in two ways: by topic and by lecture. The organization by topic shows the relations among the various lectures, while the organization by lecture shows the progression of topics during the semester. Note: this material is still subject to change as circumstances require -- topics may be added or deleted, and the order of topics may be modified.
By Topic:
I. Stress Analysis
A. Basic Concepts
1. The Stress Vector
2. The Stress Matrix
3. Relationship between Stress Vector and Stress Matrix
B. States of Stress
1. Terminology
2. Relationship to the Stress Resultants
C. Transformation of Stress
1. 2D Case
2. 3D Case
D. Principal Stresses
1. Definition and Properties
2. Examples
E. Mohr's Circle
1. 2D Case
2. 3D Case
II. Failure Criteria
A. Yielding Failure
1. Maximum Shearing Stress Criterion
2. Distortion Energy Criterion
B. Brittle Fracture
1. Maximum Principal Stress Criterion
2. Coulomb-Mohr Theory
III. Strain Analysis
A. Displacements and Strains
1. Rigid Displacements
2. Deformations
a. Normal Strains
b. Shearing Strains
3. Compatibility of Strains
B. Properties of the Strain Matrix
IV. Stress-Strain Relations
A. Terminology for Constitutive Theory
B. Generalized Hooke's Law
1. Definition
2. Consequences of Material Symmetry
3. Elastic Moduli
V. Energy Methods
A. Strain Energy
1. Definition of Strain Energy and Complementary Strain Energy
2. Calculation of Strain Energy for Standard Loads
B. Energy Method Theorems
1. Castigliano's 1st Theorem
2. Complementary Energy Theorem
3. Castigliano's 2nd Theorem
4. Application of Theorems
5. Rayleigh/Rayleigh-Ritz Method
VI. Elasticity
A. Background
1. Relationship of Elasticity to Mechanics of Materials
2. Fundamental Ideas and Equations
B. 2D Problems in Rectangular Coordinates
1. Plane Stress
2. Plane Strain
3. Airy's Stress Function
4. Solutions for Rectangular Coordinates
C. 2D Problems in Polar Coordinates
1. Governing Equations in Polar Coordinates
2. Michell/Flaumant Problem
3. Contact Stresses
4. Circular Hole in Infinite Plate
VII. Torsion
A. Torsion of General Shafts
1. Prandtl Stress Function
2. Torsion of Elliptical Cross Sections
3. Torsion of Rectangular Cross Sections
B. Membrane Analogy
1. Explanation of the Analogy
2. Torsion of Thin-Walled Members
3. Torsion of Thin-Walled Tubes
VIII. Unsymmetric Beams
A. Bending Problems
B. Bending-Torsion Problems
1. Shear Center
2. Calculation of Transverse Shear Stresses
By Lecture:
|
Lecture # |
Date |
Topic |
Reading |
|
1 |
Aug 21 |
Stress Vector |
Sections 1.0-1.2 |
|
2 |
Aug 23 |
Stress Matrix |
Section 1.3 |
|
3 |
Aug 25 |
Relation between Stress Vector and Stress Matrix |
Section 2.1.4 |
|
4 |
Aug 28 |
Terminology and Relations to Stress Resultants |
Appendix I |
|
5 |
Aug 30 |
2D and 3D Transformations |
Sections 2.0-2.1.2 |
|
6 |
Sep 1 |
Definition and Properties of Principal Stresses |
Section 2.1.5 |
|
7 |
Sep 6 |
Principal Stress Examples |
--- |
|
8 |
Sep 8 |
2D and 3D Mohr's Circle |
Section 2.1.3,2.1.6-2.1.7 |
|
9 |
Sep 11 |
Mohr's Circle Examples |
--- |
|
10 |
Sep 13 |
Maximum Shearing Stress Criterion |
Section 7.0-7.3.2 |
|
11 |
Sep 15 |
Distortion Energy Criterion |
Section 7.3.3-7.3.4 |
|
12 |
Sep 18 |
Maximum Principal Stress Criterion and Coulomb-Mohr Theory |
Section 7.3.5-7.3.6 |
|
13 |
Sep 20 |
Normal Strains and Shearing Strains; Rigid Displacements |
Section 1.4.1-1.4.2, 1.5 |
|
14 |
Sep 22 |
Strain
Compatibility and the Strain Matrix |
Section 2.2, 2.5 |
|
15 |
Sep 25 |
Constitutive
Theory; Generalized Hooke's Law; Material Symmetry |
Section 2.3 |
|
16 |
Sep 27 |
Elastic Moduli |
--- |
|
17 |
Sep 29 |
Definition of
Strain Energy and Complimentary Strain Energy |
Section 6.0-6.2 |
|
18 |
Oct 2 |
Calculation for
Standard Loads |
Section 6.3 |
|
19 |
Oct 4 |
Castigliano's
1st Theorem |
Section 6.4 |
|
20 |
Oct 6 |
NO LECTURE |
--- |
|
21 |
Oct 11 |
Complementary
Energy Theorem |
Section 6.5 |
|
22 |
Oct 13 |
Castigliano's
2nd Theorem |
Section 6.6 |
|
23 |
Oct 16 |
Applications of
Energy Methods |
Section 6.8 |
|
24 |
Oct 18 |
Rayleigh &
Rayleigh-Ritz Methods |
Section 6.11-6.12 |
|
25 |
Oct 20 |
Relation of
Elasticity to M.O.M./ |
Section 2.4 |
|
26 |
Oct 23 |
Plane Stress and
Plane Strain |
Section 4.0-4.1 |
|
27 |
Oct 25 |
Airy's
Stress Function |
Section 4.2.1 |
|
28 |
Oct 27 |
Solutions in
Rectangular Coordinates |
--- |
|
29 |
Oct 30 |
Governing Equations
in Polar Coordinates |
Section 4.2.2 |
|
30 |
Nov 1 |
Michell/Flaumant
Problem |
Section 4.2.5 |
|
31 |
Nov 3 |
Contact Stresses |
Section 5.9.1 |
|
32 |
Nov 6 |
Circular Hole in
Infinite Plate |
Section 4.2.4 |
|
33 |
Nov 8 |
Prandtl
Stress Function |
Section 4.3.1 |
|
34 |
Nov 10 |
NO LECTURE |
--- |
|
35 |
Nov 13 |
Torsion of Elliptic
Cross Sections |
--- |
|
36 |
Nov 15 |
Torsion of
Rectangular Cross Sections |
Section 4.3.2 |
|
37 |
Nov 17 |
Membrane Analogy:
Explanation and Examples |
--- |
|
38 |
Nov 20 |
Torsion of
Thin-Walled Tubes |
Section 5.1-5.2.1 |
|
39 |
Nov 27 |
Bending of Unsymmetric Beams |
Section 5.3 |
|
40 |
Nov 29 |
Shear Center |
Section 5.4.1-5.4.2 |
|
41 |
Dec 1 |
Calculation of
Transverse Shear Stresses |
Section 5.4.3 |
|
42 |
Dec 4 |
To Be Announced |
--- |
|
43 |
Dec 6 |
To Be Announced |
--- |
|
44 |
Dec 8 |
To Be Announced |
--- |
Last modified:Monday, 25-Sep-06 11:44:11 EDT