You have a stool with four legs identical in size. Two legs are made from aluminum, while the other legs are made from steel. If a load is placed on the stool's seat, will the legs take equal load or not?

Mechanical Engineering Mechanical Design
4

Did you figure it out?

Since the stool has legs with identical geometry, but different material, we need the deflection of each leg under an applied load to remain constant.

δ = \frac{PL}{AE}

Now we know that we want to keep the following parameters constant while we apply a vertical load to this stool seat:

  • A – cross-sectional area of the stool leg
  • δ – displacement length of each leg
  • L – length of each stool leg

We can set the leg deflections equal to each other as follows:

δ_1 = δ_2

\frac{P_1L}{AE_1} = \frac{P_2L}{AE_2}

\frac{E_2}{E_1} = \frac{P_2}{P_1}

Since we know steel typically has a Young’s Modulus of 200 GPa compared to 70 GPa for aluminum, we can derive this relationship:

\frac{E_2}{E_1} = \frac{200}{70} > 1

∴\frac{P_2}{P_1} > 1

Solution
From the relationship above, we see that the steel legs will take a higher load than the aluminum legs in this situation. This makes intuitive sense since the stiffer material supports the larger load.

Extra Practice
If you thought this question was interesting, check out another one about stools!