LE 4

• Beam


  Structural member used to support loads applied at different points along its length
• Statically Determinate Beam


  Beam whose support reactions can be solved using its current FBD and the three equilibrium equations (number of unknowns is equal or less than the number of equations)
• Internal Force


  Force developed within the body due to external forces (e.g. Shear Force)
• Shear Diagram


  Representation of how applied forces and loads perpendicular to a beam are transmitted along the length of the beam
• Bending Moment Diagram


  Representation of how applied forces and loads perpendicular to a beam create a moment variation along the length of the beam
• Change-of-Load Points


  Points along the beam where there are support reactions, concentrated forces, couple moments, and endpoints of distributed loads
• Distributed Load


  Load applied along a specific length of a beam that is equivalent to a single concentrated load/force with magnitude equal to the area of the distributed load
• Statically Determinate Beams (FBDs with three unknowns or less)

  • Simply-supported Beam
  • Double-overhanging Beam
  • Cantilever Beam (Beam with fixed support)
• Statically Indeterminate Beam (FBDs with more than three unknowns)


  • Fixed Beam
  • Continuous Beam
  • Fixed at one end, simply supported at the other end
• When a statically indeterminate beam has an internal hinge, the beam may become statically determinate when dismembered into two beams using the hinge as a point of dismemberment
• Types of Applied Load

  • Concentrated Load
  • Uniformly Distributed Load
  • Uniformly Varying Distributed Load
  • Non-Uniformly Distributed Load
• Conversion of Distributed Loads to Concentrated Loads

  • Magnitude - area of the distributed load
  • Location of the Concentrated Load - centroid of the area of the distributed load
• Internal Forces


  • Normal Force (N)
  • Shear Force (V)
  • Bending Moment (M)
• In beam analysis, resistance to shear and bending is more important than resistance to normal force
• In ENSC 11's context, Vertical Forces induce shear forces, horizontal forces induce normal/axial forces, while angled forces induce both shear and normal/axial forces
• Usually, only vertical forces or forces perpendicular to the beam are considered in the beam analysis
• Drawing Shear and Bending Moment Diagrams

  1. Method of Sections

  2. Area Method
• Area Method is preferable when the beam contains many change-of-load points which imply many sectioning to be done
• Point of zero shear contains an extremum of Bending Moment (highly positive or highly negative) but not necessarily contains the absolute maximum Bending Moment
• Point of internal hinge will always yield zero bending moment
• Shear and Bending Moment Diagrams of a body under equilibrium will always start and end at zero
• When either method is used from left to right, in Shear Diagram, upward forces are positive while downward forces are negative. In Bending Moment Diagram, counterclockwise moments are negative while clockwise moments are positive