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Ut Tensio, Sic Vis
As the extension, so the force – Robert Hooke
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Solid Mechanics
1. Introduction
Tensor Notation
Kronecker Delta
2nd Order Tensor Transformations
Trace, Scalar Product, Eigenvalues
2. Strain
Strain Tensors
Volume and Area Change
Polar Decomposition
3. Rates of Deformation
Rate of Deformation and Spin Tensors
Other Rates of Change (Volume and Area)
4. Stress
Cauchy Equation of Motion
Alternative Measures of Stress
Principal Stresses
Von Mises Failure Criterion
5. Superimposed Rotation
6. Hyperelasticity
Phenomenological and Micromechanical Models
Tabulated and Calibrated Models
7. Rate-Form Constitutive Expressions
Hypoelasticity (Jaumann)
Time-Stepping Algorithm
8. Linear Infinitesimal Elasticity
Elastic Modulii and Poisson Ratio
Navier and Beltrami-Michell Equations
Final Words
Appendix
Prestressed Concrete
1. Pre-tensioning vs. Post-tensioning
2. Basic Concept Method
3. Load Balancing Method
4. Required Section Moduli
5. Post-Tensioning Friction & Anchor Set Losses
6. Working Stress Design Tables and Examples
7. Choosing the Appropriate Section Shape
8. Beam Design Example
9. Slab Design Example
10. Shear
11. Strut and Tie Methodology Regarding Shear
12. Anchorage Zone
13. Deep Beams
Classical Structural Analysis
1. Conjugate Beam Method
2. Unit Load Method
3. Method of Least Work
4. Unit Load Method (indeterminate)
5. Method of Least Work (indeterminate)
6. Axial/Bending “composite” (indeterminate)
7. Moment Distribution Method (indeterminate)
a. Modified stiffness
b. Treatment of joint translations
8. Slope Deflection Method (indeterminate)
Mechanics of Materials
1. Hooke’s Law
2. Statically Indeterminate Structure (axial)
3. Poisson’s Ratio
4. Torsion
5. Statically Indeterminate Structure (torsion)
6. Bending
7. Shear
8. Shear flow
9. Principal stresses
10. Mohr’s Circle
11. Beam deflections and rotations
12. Statically Indeterminate Structure (bending)
13. Connections
Statics
1. Force Equilibrium
2. Moments
3. Moment Couple
4. Equivalent Force
5. Static Equilibrium
6. Trusses
7. Equilibrium of components
8. Distributed Loading
9. Beams
10. Friction
11. Redundancy
4. Equivalent Force
An overview of the concept of “equivalent force” (statics) is located
HERE
