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Techniques of Structural Analysis and Design, Spring 2003
Lecture Notes
Mathematica software
is required to run the .nb files in this section.
Unit #1
Notes (
PDF
)
Concept Questions
Concept Question 1 (
PDF
)
Mathematica Notebooks
Beam 1 Degrees of Freedom (
NB
)
Beam 3 Degrees of Freedom (
NB
)
Spring System (
NB
)
Unit #2
Notes (
PDF
)
Concept Questions
Concept Question 2 (
PDF
)
Concept Question 3 (
PDF
)
Concept Question 4 (
PDF
)
Concept Question 5 (
PDF
)
Math Aside (
PDF
)
Unit #3
Reading Assignments
Textbook, Section 3.3: Kinematics of Deformation
Notes (
PDF
)
Concept Questions
Concept Question 6 (
PDF
)
Mathematica Notebooks
Comparison of Linear and Nonlinear Strain (
NB
)
Unit #4
Reading Assignments
No Reading Assignment for this Unit
Notes (
PDF
)
Concept Questions
Concept Question 7 (
PDF
)
Unit #5
Reading Assignments
Textbook, Section 3.4: Constitutive Equations
Notes (
PDF
)
Concept Questions
Concept Question 8 (
PDF
)
Concept Question 9 (
PDF
)
Unit #6
Reading Assignments
No Reading Assignments for this Unit
Notes (
PDF
)
Unit #7
Reading Assignments
Textbook, Section 4.1: Work and Energy
Textbook, Section 4.2: Strain Energy and Complementary Strain Energy
Notes (
PDF
)
Concept Questions
Concept Question 10 (
PDF
)
Concept Question 11 (
PDF
)
Examples
Application to Beam Theory (
PDF
)
Unit #8
Reading Assignments
Textbook, Section 4.3 and 5.1: Principle of Virtual Displacements
Notes (
PDF
)
Concept Questions
Concept Question 12 (
PDF
)
Concept Question 13 (
PDF
)
Unit #9
Reading Assignments
Textbook:
Calculus of Variations
: Section 4.4.1 to 4.4.7, Section 4.3 and 5.1
Notes (
PDF
)
Unit #10
Reading Assignments
Textbook:
Principle of Total Potential Energy
, Section 5.2
Notes (
PDF
)
Concept Questions
Concept Question 14 (
PDF
)
Concept Question 15 (
PDF
)
Mathematica Notebooks
Example of Application of Castigliano's 1st Theorem (
NB - 1.2 MB
)
Unit #11
Reading Assignments
Textbook:
Principle of Virtual Forces and Maximum Complementary Potential Energy, Reciprocity Theorems
, Section 5.3, 5.4 and 5.5
Mathematica Notebooks
Unit #12
Reading Assignments
Textbook:
Direct Variational Methods
, Section 7.1
Section 7.2 (Optional)
Section 7.3 Ritz Method
Notes (
PDF
)
Notes (cont'd) (
PDF
)
Concept Questions
Concept Question 16 (
PDF
)
Concept Question 17 (
PDF
)
Mathematica Notebooks
Application of Ritz Method to Beam Theory (
NB
)
Application of Ritz Method to a Bar with Variable Cross Section (
NB - 1.1 MB
)
Unit #13
Reading Assignments
Textbook:
The Finite Element Method
, Chapter 9
Section 9.1
Section 9.2
Notes (Part I) (
PDF - 1.2 MB
)
Notes (Part II) (
PDF - 1.4 MB
)
Notes (Part III) (
PDF - 1.1 MB
)
Notes (Part IV) (
PDF
)
Concept Questions
Concept Question 18 (
PDF
)
Concept Question 19 (
PDF
)
Concept Question 20 (
PDF
)
Mathematica Notebooks
Making Progress Towards the Finite Element Method (
NB
)
Formulation of Finite Element Matrices for 1D Problems (
NB
)
Unit #14
Reading Assignments
Section 9.3
Notes (
PDF
)
Concept Questions
Concept Question 21 (
PDF
)
Mathematica Notebooks
Formulation of Euler Beam Finite Element (
NB
)
Unit #15
Notes (
PDF - 1.1 MB
)
Notes (Part II) (
PDF
)
Concept Questions
Concept Question 22 (
PDF
)
Concept Question 23 (
PDF
)
Mathematica Notebooks
Formulation of Linear Square Elasticity Element (
NB
)
Formulation of Quadratic Square Elasticity Element (
NB - 1.3 MB
)
Formulation of Isoparametric 4-Node Elasticity Element (
NB
)
Unit #16
Notes (
PDF
)
Concept Questions
Concept Question 24 (
PDF
)
Concept Question 25 (
PDF
)
Mathematica Notebooks
Motivation for Numerical Integration (
NB
)
Gauss Quadrature Integration Rules (
NB
)
Unit #17
Notes (
PDF
)