How far out do you expect a tape measurer to extend before it begins to fall? What type of failure mode does this encompass?

Hint: What cantilever beam diagram can be drawn from this application.

Additional:

  1. Does flipping the tape measurer up/down have an effect on how far it can extend?
  2. What is causing the tape measurer to fail?

The hunt to find a logical answer was quite the thrill, so I’ll share my thoughts below.

When you extend a tape measurer out like this, my first interpretation was to think of it just as distributed load acting downward against simply supported cantilever beam. This would be the case where the fixed end is supported at the wall, but instead it’s just as the user supporting it with your hand as it extends out. See images below as a reference:

Taking a section view of the tape measurer, the cross-section has a concave shape like this:

image

What’s very cool about the cross-section of this shape is that it’s intentionally designed! Thinking about a distributed load being applied, the top surface is being put in tension, while the bottom surface is in compression.

My theory about tape measurers is that the actual material used has greater tensile strength than compression strength, allowing the tape to extend further out when held at the correct orientation.

Proof can be seen below with the tape measurer being extended out at the same distance, and the measurer only buckling with the cross-section flipped over. This proves that the top surface has a greater tensile strength than compressive strength.

For the actual failure mode of the tape measurer, it’s akin to a beam buckling. The tape measurer does not fracture or experience plastic deformation, as it’ll always return to the same elastic shape as before.

Much of the engineering intuition here revolved first around thinking about similar structures we have in the world, and that’s where I came to thinking of arches. Some resources I read as a guide are referred to here:

Open to more discussion from the community as well. :slight_smile:

Found an interesting paper linked in The Prepared Newletter that describes in technical depth how arches work: