BIOMEDE 231, Fall 2019

[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.


  1. Introductions
    1. Introduction to class and logistics
    2. Introduction to ourselves
    3. Introduction to basic concepts
      1. Space
      2. Time
      3. Mass
      4. Force
      5. Particle
      6. Rigid body
    4. Newton’s laws
    5.  Vectors
      1. Definition
      2. Sums, subtractions
      3. Dot product (parallelity)
      4. Cross product (perpendicularity)
        1. Right hand rule
        2. Determinants
        3. Varignon’s theorem
    6. Trigonometry (a few basic rules)
  1. Forces
    1. Types of forces
      1. Body force
      2. Surface force
      3. Tensile v. compressive
    2. Modeling forces
      1. External v. internal effects
      2. What and why
    3. Free-body diagrams
    4. Principle of transmissibility
    5. General approach to problems
    6. Action of forces
    7.  Supports
      1. Cable / rope / spring
      2. Smooth frictionless surface / wheel / roller
      3. Rough surface
      4. Frictionless slider
      5. Frictionless pulley
      6. Fixed support
      7. Pinned support
  1. Moments
    1. Torque
    2. Moments about a line
    3. Couples
    4. Supports
      1. Wheel
      2. Pin
      3. Fixed support
      4. Collar
      5. Principle of moments (extension of Varignon’s theorem)
  1. Equilibriums
    1. Equivalent systems
    2. Resultant forces
    3. Static equilibrium
      1. In 2D
      2. In 3D
    4. Special cases of equilibrium
    5. Indeterminancy
    6. Stability
  2. Structures
    1. Two force members
      1. Trusses
      2. Analysis of trusses
        1. Method of joints (if interested in every force/member)
          1. Free body diagram
          2. Static equilibrium
          3. Draw a FBD of each joint, assume outward forces from all connected elements
          4. Apply statics equations
        2. Method of sections (if interested in just one, few)
          1. Free body diagram
          2. Static equilibrium
          3. Make cuts through members (no more than 3 and expose forces in each member
          4. Apply statics equations
    2. Three force members
      1. Frames
      2. Machines
  3. Centers
    1. Of area (Centroids)
      1. Basic concept
      2. Composite areas
    2. Of mass
    3. Of gravity
      1. Volumes
    4. Resultants at centers
      1. Choose reference point and move all forces to that point
      2. Sum forces and couples
      3. Find resultant force’s new line of action
    5. Moment of inertia (second moment of area)
    6. Parallel axis theorem
  1. Beams
    1. Types of loads
      1. Point (concentrate)
      2. Distributed
      3. Continuous
      4. Discontinous
    2.  Analysis
      1. Equilibrium of beam as a whole (statics)
      2. Internal forces (mechanics of materials)
    3. Shear force / bending moment diagrams
      1. Cut to expose internal forces
        1. Axial loads
        2. Shear forces
        3. Bending moments
        4. Torsion
      2. Steps for analysis
        1. Step 1, conversion
          1. Convert distributed loads to point loads
          2. Redraw FBD (include external + reaction forces)
          3. Statics
        2. Step 2, identification
          1. Continuous loads (single cut)
          2. Discontinuous (each discontinuity is a boundary)
        3. Step 3, for each cut
          1. Redraw FBD
          2. Determine distributed load
          3. Assign assumed positive V and M
          4. Statics
        4. Step 4, draw diagrams
          1. Optional table with equations and values
          2. Make diagrams
          3. Double check
  2. Kinematics (motion without force)
    1. Translation and rotation
    2. Metrics needed to describe object in motion
      1. Displacement
      2. Velocity
      3. Acceleration
    3. Objects in contact
    4. Relative motion
      1. Velocity
      2. Instantaneous center of zero velocity (rotation)
      3. Acceleration
      4. Rotating axes
    5. General motion equations
  1. Kinetics (motion with force)
    1. Acceleration methods
      1. Mass moment of inertia
      2. Moment about different point / axis (parallel axis theorem)
    2. Work-energy methods
      1. Work
        1. Linear motion
        2. Power
        3. Rotation
      2. Energy
        1. Potential
        2. Kinetic
      3. Conversion of energy
        1. Conservative forces only
        2. Non-conservative forces
    3. Impulse-momentum methods
      1. Momentum
      2. Impulse
      3. Impulse-momentum theorem
      4. Angular momentum
      5. Collisions and impacts
        1. Coefficient of restitution
  2. Mechanics of materials I 
    1.  Loading
      1. Tension
      2. Compression
      3. Shear
      4. Torsion
      5. Deformations in general
        1. Magnitude of an applied load
        2. Direction of an applied load
        3. Material properties
    2. Stress
    3. Strain
    4. Elastic materials
      1. Homogeneity v. heterogeneity
      2. Isotropy v. anisotropy
      3. Linear v. nonlinear
      4. Time (in)dependence / viscoelasticity
    5. Stiffness, strength, and stability
    6. Poisson ratio
    7. Safety factor
    8. Prismatic bars (constant cross-sectional area)
    9. Non-prismatic bars (non-constant cross-sectional area
      1. Cylindrical beams
      2. Non-cylindrical beams
    10.  Torsion
      1. Stresses
      2. Strains
      3. Oblique cuts
    11. Thermal effects
  1. Mechanics of materials II
    1. Tensors
      1. Stress tensors
        1. Principal stresses
        2. Stress transformations
        3. Plane stresses
        4. Maximum shear stress along arbitrary planes
        5. General strategy
          1. Make a list of parameters
          2. Find the planar angle
          3. Figure out principal stresses
          4. Find maximum shear
          5. Draw the transformed situation
      2. Strain tensors
        1. Plain strain
        2. Strain transformations
          1. Strain gauges
          2. Principal strains
      3. Stress and strain relationship
      4. Lame’s constant