0
$\begingroup$

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.

enter image description here

$\endgroup$

1 Answer 1

0
$\begingroup$

"...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."

From the statement above, we conclude the bending moment on a cantilever beam can only be positive, or negative, because the deflected shape of a cantilever typically forms a "single curvature", for which the sign remains constant throughout its length.

Note, that the "coordinate system" may twist the results and gives different signs to the moment. But, no confusion should result if using a consistent coordinate system and sticking with the sign convention stated in the very beginning.

enter image description here

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.