Notes

The following files are PDF documents created in Word, with figures created in PowerPoint. Beyond the basic notes on mathematics there are two main themes: structural analysis and probabilistic analysis. This means that the notes are meant to provide support for the structural analysis courses CIVL 332 and CIVL 435, and the probabilistic course CIVL 518.

MATHEMATICS
Notation
Fractions
Functions
Calculus
Quadrature
Combinations
Series Expansions
Complex Analysis
Nonlinear Equations
Differential Equations
Vectors and Geometry
Matrices and Linear Algebra
SOLID MECHANICS
Stress and Strain
3D Elasticity Theory
Stress Transformations
Stress-based Failure Criteria
PLANE TRUSSES AND FRAMES
Symbols
Idealization of Structures and Loads
Assumptions, Theories, Methods
Stability and Indeterminacy
Forces in Determinate Structures
Moment-Area Method
Conjugate Beam Method
Unit Virtual Load Method
Flexibility Method
Slope Deflection Method
Moment Distribution Method
Stiffness Method
Influence Lines
Approximate Methods
Elasto-plastic Analysis
STRUCTURAL BOUNDARY VALUE PROBLEMS
Truss Members
Euler-Bernoulli Beams
Timoshenko Beams
St Venant Torsion
Warping Torsion
Beams with Axial Force
Beams on Elastic Foundation
Lateral Torsional Buckling
2D Continuum Problems
Kirchhoff and Mindlin Plates
Curved Beams and Arches
STRUCTURAL INITIAL VALUE PROBLEMS
SDOF Oscillators
Oscillating Strings and Beams
Oscillating Plates
MDOF Dynamics
ENERGY METHODS
Virtual Work and Variational Principles
Calculus of Variations
Work and Energy Expressions
COMPUTATIONAL STRUCTURAL ANALYSIS
Computational Stiffness Method
Finite Element Fundamentals
Inelastic and Dynamic Analysis
Response Sensitivity Analysis
The Truss Element
The Linear Frame Element
The Displacement-based Nonlinear Frame Element
The Force-based Nonlinear Frame Element
The CST Element
The Q4 Element
The M4 Element
FATIGUE
Stress Concentrations
SN Curves and Miners Rule
Rainflow Count of Cycles
Fracture Mechanics
BASIC PROBABILISTIC ANALYSIS
Uncertainty and Risk
Set Theory
Probability Theory
PROBABILISTIC MODELS
Discrete Random Variables
Continuous Random Variables
Extreme Value Models
Multivariate Distribution Models
Linear Regression Models
Logistic Regression Models
Damage Accumulation Models
Size Effect Models
Fragility Models
Bayesian Network Models
Bayesian Hierarchical Models
Bernoulli Sequences
Poisson Point Processes
Poisson Pulse Processes
Continuous Stochastic Processes
Discounting Models
PROBABILISTIC METHODS
Analysis of Functions
Probability Transformations
Reliability Analysis
MVFOSM
FORM
SORM
Sampling
System Reliability
Load Combination
Stochastic Dynamics
Stochastic Fatigue
DECISIONS UNDER UNCERTAINTY
How Humans Make Decisions
Calibration to Past Practice
Calibration to Target Safety
Expected Cost Theory
Expected Utility Theory
Prospect Theory
LQI and SWTP
Decision Trees
TECHNICAL WRITING
Why Write Well
Good Habits of Technical Writing
Grammar
Mini Dictionary

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