Problem # 27

Deflection of Cantilever Beam : Bracket Function.

Use bracket functions and the x-coordinate as shown in the figure to find the deflection of the beam at its left end.

Consider as given :
Length of beam : L
Distance : a
Moment of inertia of cross-section :
Young's modulus : E
Force : P

  1. Determine the moment equation M(x) using bracket functions. Include a sketch of the relevant Free Body Diagrams you are using.
  2. Integrate to find the deflection curve.
  3. What are the conditions from which to determine the integration constants ?
  4. Determine the equation for the deflection at the left end of the beam.