# Why do two simply supported beams stacked on top of each other deflect more than a single beam of twice the thickness?

If the thickness of each beam in the stacked configuration is 't', the thickness of the single beam is '2t'.

Explanations in terms of Euler Bernoulli beam theory, or any other explanation that is understandable for a Mechanical Engineering major, would be helpful.

Why do two simply supported beams stacked on top of each other deflect more than a single beam of twice the thickness?

Because the mating surfaces slide. The result is that you don't have the same tension on the underside and don't have the same compression on the top side.

If you look at the stress distribution in a bending beam it is zero at the neutral axis, and increases linearly as you approach the surface.

M / I = σ/y = E / R is the important equation, if you rearrange it to MR = EI then for a given M and E, R is proportional to I that is the curvature is less as I increases.

I for a beam width b and thickness t is 1/12 bt3, so two of them would be 1/6bt3, whereas for your double thickness beam it is 1/12b(2t)3, 2/3bt3.

So E is much greater for the double thickness beam, so its radius is greater, so it bends less.

• I understand everything, except why we can add the I for the stacked beams individually about their own neutral axes. What does it physically mean to add them together? Don't they need a common axis to add them about, something like a parallel axis theorem? Aug 15, 2023 at 15:22
• I see what you are getting at. This pure beams in bending, if you were to space the beams apart vertically axial forces come into play as well. Aug 15, 2023 at 22:47