Mechanics

Computer simulation of structural behaviour is the motivation behind a good part of the material posted on this website. However, before getting to such simulations it is necessary to understand the mechanics that governs the problem. The top portion of this page covers the boundary value problems that I address in CIVL 435.  I address the subsequent material, analysis of trusses and frames and dynamics, in CIVL 332. The elasticity and plasticity theory at the bottom of the page is material for both CIVL 435 and CIVL 509.


MEMBERS AND CROSS-SECTIONS
Notes
Truss Members
Euler-Bernoulli Beams
Timoshenko Beams
Beams with Axial Force
Beams on Elastic Foundation
St Venant Torsion
Warping Torsion
Lateral Torsional Buckling
Kirchhoff and Mindlin Plates
Catenary Cables
Beam examples
Fixed-roller Beam with Point Load
Beam with Prescribed End Displacements
Beam on Elastic Foundation
Cantilever in Torsion
Plate examples
Naviers Plate Solution for Uniform Load
Naviers Plate Solution for Point Load
Levys Plate Solution for Uniform Load
Plate with Edge Moments
Cross-section examples
I Cross-section
Channel Cross-section
Closed Rectangular Cross-section
Closed Cross-section with Flanges
Two-cell Cross-section
Python
Plot Beam Diagrams (Screenshot)
TRUSSES AND FRAMES
Notes
Degree of Static Indeterminacy
Overview of Methods
Analysis of 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
Energy Methods
Examples
Determinate Portal Frame
Collection of Statically Determinate Structures
T Frame
Beam with Pretensioned Undertruss
Three-member Buttress Frame
Deflection and Buckling of Simply Supported Deep Beam
Curved Beam
Buckling of Arch
DYNAMICS
Notes
Vibration of Single Mass
Vibration of Distributed Mass
Energy Methods in Dynamics
Examples
Mass Subject to Ground Motion
Python
trapezoidalRecordIntegration()
sdofNewmark()
SDOF Dynamic Analysis (Screenshot)
Ground Motion Files
GroundAccelerationX.txt
GroundAccelerationY.txt
GroundAccelerationZ.txt
THEORY OF ELASTICITY
Notes
2D Elasticity Theory
3D Elasticity Theory
Stress Transformations, Principal Stress, and Mohr’s Circle
Examples
Generic 2D Stress Distributions
2D Cantilevered Beam
THEORY OF PLASTICITY
Notes
Stress-based Failure Criteria
Uniaxial Plasticity
Multiaxial Plasticity