Why Cantilever Beams Are Made Trapezoidal?

 

A cantilever beam is a horizontal, rigid structural component that is supported at one fixed end and free at the other. They bear load in the form of bending. When a horizontal force is applied to the free end in the cantilever, it transfers those forces to the column through the fixed end and then to the foundation and ultimately to beneath the ground, where those forces are re-distributed among the soil.

We often observe cantilever beam below our balcony, bridges, etc.

    Cantilever beams are made trapezoidal because of the bending moment acting on them. We should provide more depth to the structure where there is more bending moment acting upon. Otherwise, the structure will collapse due to more bending or turning effect of the structure.

1.      1.  When a point force is acted upon a Cantilever beam

Let us consider a weight (W) is acted upon a free end of the cantilever beam of length (l).

 For equilibrium, vertical forces are zero

                              ∑Fy =0

                             +w-Ry=0

                             Ry=W

W at free end tends to bend the beam downward. So, there is production of maximum bending moment in the fixed or support end. Hence to counter the maximum bending moment produced in the fixed end, more depth is provided in fixed end than in free end. Otherwise, the beam will collapse or shear off.

    From bending moment diagram as well, maximum bending moment (Wl) is acted upon the fixed end of the cantilever beam and zero bending moment is acted on the free end of the cantilever beam even though weight is applied to the free end of the beam.

Since the bending moment is maximum at the fixed end, more depth should be provided in the fixed end to avoid collapse of the structure due to the turning effect and minimum depth should be provided at the free end of the cantilever beam.

2.    When a uniformly distributed load is acted upon the beam

For uniformly distributed load as well, the maximum bending moment(WL^2/2) will be acted upon on the fixed end of the beam. So, the depth should be maximum on the fixed end of the cantilever beam.

We often see beams of rectangle shape as well. If we prefer on putting rectangle beams, then we must construct a beam of relatively more depth. Otherwise, due to the dead load on the free end, there is a high chance of collapse. Also, trapezoidal beams are more economical than rectangular beams. Rectangle beams only increases the cost of project. It does not have any significance. 

  

 

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