Unit 2: Mechanics

• Mechanics

  A branch of engineering that studies the status of objects at rest or in motion
• Forces


  Actions applied to an object that can cause it to change its state of rest or motion
• Moments

  Actions applied to an object that can cause it to rotate
• Fields in mechanics

  • Statics (equilibrium of bodies)
  • Dynamics (motion of bodies)
• Components of dynamics

  • Kinematics (displacement, velocity, acceleration)
  • Kinetics (forces and moments causing motion)
  • Energetics (work and energy)
• Classical laws of mechanics


  Mathematical conditions governing rest and motion
• Internal loads


  Loads generated within the material of a body that maintain equilibrium
• Stresses

  Internal loads that develop within a body
• Strains


  Geometric changes induced by stresses in a solid body
• Elastostatics


  Field that studies stresses and strains in solid bodies
• Particle

  Representation of a solid with considerable mass but negligible size
• Rigid body

  Representation of a solid with considerable mass and size, capable of translation and rotation
• Free body diagram (FBD)

  Sketch of all efforts applied to a body responsible for its present status
• Mechanics is based on a few laws of nature which have an axiomatic character, based on numerous observations and regarded as being known from experience
• Axiom I: Principle of equilibrium


  When a body is at rest or moving with constant velocity and subjected to a balanced system of forces, it will maintain its original status
• Trailer connected to a truck

  • Weight W
  • Normal reaction N
  • Traction force T
• Axiom II: Principle of inertia

  If a body is subjected to an unbalanced system of forces, it will move with an acceleration proportional to the resultant force and inversely proportional to its mass
• Axiom III: Principle of action and reaction

  When two particles interact, they apply onto each other a force of equal magnitude but opposite direction
• Book resting on a table


  • Weight of book
  • Normal reaction of table
• Scalar

  An algebraic quantity designated exclusively by a positive or negative value
• Vector

  A geometric element representing a physical quantity and consisting of a segment portion of a straight line with a specific orientation
• Force


  An action exerted by a body on another neighboring body, applied by direct contact or at a specified distance
• Force


  • Defined by point of application, direction, sense, and magnitude
• Weight

  Force applied by the gravity field of an object, equal to the product of its mass and the gravitational acceleration
• External force

  Force applied by a component surrounding the system, either directly or at a distance
• Internal force

  Force applied by a neighbor component belonging to the same global system
• Concentrated force

  Force applied to a region of a body that is very small relative to the overall size of the body
• Distributed force

  Loading applied along a considerable space of the body and not at any specific points
• Concurrent forces

  Concentrated forces with a common point of application
• Resultant

  Theoretical force that combines a group of physical forces acting on a body having the equivalent effect as the original group of forces combined
• Resultant


  The vector sum of all the forces acting on a particle or rigid body
• Finding resultant of multiple forces

  Apply parallelogram rule between first two forces, then with third force, and so on
• Cartesian formulation method

  Alternative method to find direction and magnitude of resultant by calculating scalar components along x, y, z axes
• Direction cosines must satisfy cos^2α + cos^2β + cos^2γ = 1
• Decomposition of a force

  Replacing a single force with two or three other forces (components) by projecting along predefined directions
• Equilibrium of particles

  All forces applied on a particle are concurrent at the particle itself, providing the possibility of an "exclusive" translational motion in case the resultant of those forces is not zero
• Couple

  A pair of two parallel vector forces, opposite in sense, equal in magnitude, and separated by a distance d called "arm"
• Moment of a force about an axis

  A physical quantity measuring the ability of a force to produce rotation about a point or axis

  
• Parallel forces


  A system of forces where none of their lines of action intersect at any point
• Bearing

  A physical member connected to the main rigid body to prevent its motion along one or many directions