A CANTILEVER OF LENGTH CARRIES A CONCENTRATED LOAD 'W' AT ITS FREE END:
Draw shear force and bending moment.
- 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