[THIS IS A DRAFT. IT IS NOT TO BE RELIED UPON DURING THE FALL 2019 SEMESTER.]
A generally unpolished outline of the material hopefully included in this class. Subject to change without notice.
- Introductions
- Introduction to class and logistics
- Introduction to ourselves
- Introduction to basic concepts
- Space
- Time
- Mass
- Force
- Particle
- Rigid body
- Newton’s laws
- Vectors
- Definition
- Sums, subtractions
- Dot product (parallelity)
- Cross product (perpendicularity)
- Right hand rule
- Determinants
- Varignon’s theorem
- Trigonometry (a few basic rules)
- Forces
- Types of forces
- Body force
- Surface force
- Tensile v. compressive
- Modeling forces
- External v. internal effects
- What and why
- Free-body diagrams
- Principle of transmissibility
- General approach to problems
- Action of forces
- Supports
- Cable / rope / spring
- Smooth frictionless surface / wheel / roller
- Rough surface
- Frictionless slider
- Frictionless pulley
- Fixed support
- Pinned support
- Types of forces
- Moments
- Torque
- Moments about a line
- Couples
- Supports
- Wheel
- Pin
- Fixed support
- Collar
- Principle of moments (extension of Varignon’s theorem)
- Equilibriums
- Equivalent systems
- Resultant forces
- Static equilibrium
- In 2D
- In 3D
- Special cases of equilibrium
- Indeterminancy
- Stability
- Structures
- Two force members
- Trusses
- Analysis of trusses
- Method of joints (if interested in every force/member)
- Free body diagram
- Static equilibrium
- Draw a FBD of each joint, assume outward forces from all connected elements
- Apply statics equations
- Method of sections (if interested in just one, few)
- Free body diagram
- Static equilibrium
- Make cuts through members (no more than 3 and expose forces in each member
- Apply statics equations
- Method of joints (if interested in every force/member)
- Three force members
- Frames
- Machines
- Two force members
- Centers
- Of area (Centroids)
- Basic concept
- Composite areas
- Of mass
- Of gravity
- Volumes
- Resultants at centers
- Choose reference point and move all forces to that point
- Sum forces and couples
- Find resultant force’s new line of action
- Moment of inertia (second moment of area)
- Parallel axis theorem
- Of area (Centroids)
- Beams
- Types of loads
- Point (concentrate)
- Distributed
- Continuous
- Discontinous
- Analysis
- Equilibrium of beam as a whole (statics)
- Internal forces (mechanics of materials)
- Shear force / bending moment diagrams
- Cut to expose internal forces
- Axial loads
- Shear forces
- Bending moments
- Torsion
- Steps for analysis
- Step 1, conversion
- Convert distributed loads to point loads
- Redraw FBD (include external + reaction forces)
- Statics
- Step 2, identification
- Continuous loads (single cut)
- Discontinuous (each discontinuity is a boundary)
- Step 3, for each cut
- Redraw FBD
- Determine distributed load
- Assign assumed positive V and M
- Statics
- Step 4, draw diagrams
- Optional table with equations and values
- Make diagrams
- Double check
- Step 1, conversion
- Cut to expose internal forces
- Types of loads
- Kinematics (motion without force)
- Translation and rotation
- Metrics needed to describe object in motion
- Displacement
- Velocity
- Acceleration
- Objects in contact
- Relative motion
- Velocity
- Instantaneous center of zero velocity (rotation)
- Acceleration
- Rotating axes
- General motion equations
- Kinetics (motion with force)
- Acceleration methods
- Mass moment of inertia
- Moment about different point / axis (parallel axis theorem)
- Work-energy methods
- Work
- Linear motion
- Power
- Rotation
- Energy
- Potential
- Kinetic
- Conversion of energy
- Conservative forces only
- Non-conservative forces
- Work
- Impulse-momentum methods
- Momentum
- Impulse
- Impulse-momentum theorem
- Angular momentum
- Collisions and impacts
- Coefficient of restitution
- Acceleration methods
- Mechanics of materials I
- Loading
- Tension
- Compression
- Shear
- Torsion
- Deformations in general
- Magnitude of an applied load
- Direction of an applied load
- Material properties
- Stress
- Strain
- Elastic materials
- Homogeneity v. heterogeneity
- Isotropy v. anisotropy
- Linear v. nonlinear
- Time (in)dependence / viscoelasticity
- Stiffness, strength, and stability
- Poisson ratio
- Safety factor
- Prismatic bars (constant cross-sectional area)
- Non-prismatic bars (non-constant cross-sectional area
- Cylindrical beams
- Non-cylindrical beams
- Torsion
- Stresses
- Strains
- Oblique cuts
- Thermal effects
- Loading
- Mechanics of materials II
- Tensors
- Stress tensors
- Principal stresses
- Stress transformations
- Plane stresses
- Maximum shear stress along arbitrary planes
- General strategy
- Make a list of parameters
- Find the planar angle
- Figure out principal stresses
- Find maximum shear
- Draw the transformed situation
- Strain tensors
- Plain strain
- Strain transformations
- Strain gauges
- Principal strains
- Stress and strain relationship
- Lame’s constant
- Stress tensors
- Tensors