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Date : 2016-06-23 12:24:21

A CANTILEVER OF LENGTH CARRIES A CONCENTRATED LOAD 'W' AT ITS FREE END:

Draw shear force and bending moment.

 

Solution:

  • At a section a distance x from free end consider the forces to the left, then F = -W (for all values of x) -ve sign means the shear force to the left of the x-section are in downward direction and therefore negative
  • Taking moments about the section gives (obviously to the left of the section)
  • M = -Wx (-ve sign means that the moment on the left hand side of the portion is in the anticlockwise direction and is therefore taken as –ve according to the sign convention)
  • so that the maximum bending moment occurs at the fixed end i.e. M = -W l
  • From equilibrium consideration, the fixing moment applied at the fixed end is Wl and the reaction is W.
  • The shear force and bending moment are shown as,

Fig: SFD and BMD of Cantelever beam carrying load at its one end

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