# Bending of a cantilever beam

How is the bending of a cantilever beam negative when, some of the statics methods say otherwise, assuming I am applying them correctly?

1. When I used the singularity functions method, I obtained a positive bending at the fixed end.
2. Again, using the equilibrium equations, I found out that bending at the fixed end is positive.

Now observing the concept, bending assumed to be positive whenever it develops compression at the upper fibers of the beam and tension in the lower fibers of the beam and vice versa.

1. Considering the deflected shape of the cantilever beam, it is evident that the upper fibers of the beam get elongated while lower fibers get shortened. Hence, bending must be negative.
2. Furthermore, when using the graphical method, the bending starts positive, assuming the approach I took is correct, but how can it equal zero at the free end if the difference (obtained from the area of the SFD is positive? In other words, [+Ma +(+difference)] should be positive value, not zero.
3. Lastly, analyzing the concept that BMD is the integral of the SFD, when integrating the SFD, or the curve, it must be a positive result not a negative.

A possible interpretation I got is that I assumed an opposite sense of the moment reaction.