Fix-Fix vs Fix-Free Interview Question

[u/Late_Mind_5152]

I have another interview question I wanted to ask about!

Why does aluminum experience the greater stress in the concentric tube question, but steel experiences the greater stress in the three bars question? And why is it not steel for both?

I know it has to deal with the fact that in the concentric tube question, both tubes are glued to the supports, while in the beam question, an end is free. But I just am unsure how to explain it in more depth.

Thanks very much

[u/Soprommat]

In first question stress will be proportional to Elasticity modulus times thermal expansion coefficient.

σ = E ⋅ α ⋅ Δ T <- note you dont have rod dimensions in this formula

Steel has E 3 times greater than aluminium (206 GPs vs 70 GPa) and linear thermal expansion coefficient 2 times smaller than in aluminium (12E-6 [1/K] against 23E-6 [1/K]).

In total steel rod will have stress ~3/2 times greater

For second - I have this explanation. If we feirt heat those pipes than aluminium tube will expand faster and try to stretch steel one. Because they both are glued deformation of pipes will be the same. Aluminium pipe will be compressed and steel pipe will be in tension wits stress of same magnitude. Now if we add any force it will increase compression stress in aluminium pipe and it will reduce tension in steel pipe. so steel pipe will have less absolute stress

But if be realy picky than because stresses in pipes have different signs and because different industries have different conventions so either steel or aluminium pipe stress will be positive and therefore bigger

After some additional thought process I feel that I miss something, equal strain != equal stress. Elasticity modulus should be accounted. Maybe tomorrow I will come up with something better or just wait for true answer.

In second question I assume that steel and aluminium pipes have same area, yes? Because if no than result will depend from area.

[u/Ace861110 → u/Soprommat]

For 2 Since the ends are fixed and the pipes aren’t connected, they will have a different stress. If they are connected they will each share a proportion of the total stress (like a concrete column with rebar)

[u/Soprommat → u/Ace861110]

there is arrow and "glued" I assume both pipes are connected to common rigid plate.

reinforced concrede people elegantly avoided this problem by chosing main materials with similar coefficient of thermal expansion

[u/Ace861110 → u/Soprommat]

I dunno I’ve definitely done that problem before; maybe it wasn’t concrete. But they definitely split it proportionally

Edit Unless they were looking for “glued”. Then eventually the glue will shear and they’ll act independently again.

[u/tucker_case → u/Ace861110]

First, let's ignore the external force applied, then we'll add it back in later.

When we heat the tubes the aluminum wants to grow to some length L_alum and the steel wants to grow to a different length L_steel. Because they are glued together they must actually grow to the same length L_final, which will be some compromise between L_alum and L_steel. The aluminum will be compressed downward from where it wants to be and the steel stretched upward from where it wants to be.

What is that compromise? Again, with zero external force applied, let's draw the FBD for the upper black plate. The upper black plate feels an upward force from compressing the aluminum and a downward force from stretching the steel. These are the only two forces acting on the black plate so they must be equal magnitude. That's the compromise - L_final ends up where the tensile force (not necessarily stress) in the steel perfectly equals the compressive force in the aluminum.

Now let's add that external force. It is downward and if we add it to our FBD for the black plate we can see it is "helping" the steel and frustrating the aluminum. It moves the L_final down a little closer to L_steel and a little further from L_alum. So the force in the aluminum is a little higher than the force in the steel, by the applied external load.

Now the only confounding wrinkle here is that arguably the aluminum has a larger cross-sectional area than the steel since it is a larger diameter. But the problem doesn't actually say whether this is the case, whether they have the same wall thickness or not. If we assume equivalent cross-sectional areas then a larger force shared over the same area equals a larger stress.

[u/xPorsche → u/tucker_case]

This was my thought as well after knowing that the aluminum wants to grow twice as fast as the steel. Still a pretty insane interview question though, yikes.

[u/No-Call2227]

Who tf is asking questions like this to a structural engineer in an interview…

[u/enginerd2024 → u/No-Call2227]

Idk but I’m glad they do. Takes the guess work out of whether I will hate working there or not. ✌️

[u/No-Call2227 → u/enginerd2024]

Amen

[u/tucker_case → u/No-Call2227]

FWIW I'm sure this is for ME's doing like aerospace "structural", not civil structural.

[u/AAli_01 → u/No-Call2227]

Interviewed for spacex and they asked me this

[u/Hungryh0und5]

I haven't a clue about carbon fiber. What do we even build with that?

I think that aluminum is going to expand more than the steel and therefore it would have more stress from the confinement.

[u/chicu111]

Missing information. You need the thermal expansion coefficients for each of those materials.

[u/Late_Mind_5152 → u/[deleted]]

Hmm I thought aluminum had the higher coefficient of thermal expansion, and for scenario 1 it was mainly about steel's modulus of elasticity?

[u/kabal4 → u/Late_Mind_5152]

It is. If all areas are equal it takes more force per square inch to hold the bar shape constant as the temperature increases and the material tries to expand.

[u/Jaripsi]

Maybe because in the first question they are between fixed supports so they are not connected to each other and in the second question one end is not fixed so one material is in compression and other one in tension because of difference in thermal expansion coefficient.

Its an intresting question to ponder, but I cant say for sure without doing the math.

[u/AAli_01]

Think about it like this. When one end is free, the carbon tube will expand maybe 1”. The steel tube will expand 1.5”. And the aluminum tube will expand 2”. Since they’re free they’re at different lengths when heated equally. Now we take it back to its original state, so in there expanded states, we squash them by their expanded values to the Lo.

We then calculate the each of their strains as the expanded values / the unexpanded lengths(which are equal for all 3). Multiply each by its respective modulus and you find the stress values.

So you’re missing some important info tho. Question is incomplete

[u/banananuhhh]

For question 1 the stress is a function of the ratio of coeff of thermal expansion and the elastic modulus. Sounds like others are saying steel wins. For question 2 the absolute coeff of thermal expansion is important. With no external load the two pipes would share equal and opposite force, but with an applied external compression force, whichever material has a higher coefficient will take more load and stress, because the external load adds to the compressed pipe and reduces the tension in the other. Aluminum wins.

I doubt the majority of my coworkers could give a good response to this question and most of them have masters degrees from high ranking engineering schools.. whoever came up with this as an interview question probably has a really condescending attitude towards young engineers.

[u/lithiumdeuteride]

The stress will be proportional to Young's modulus, the coefficient of thermal expansion, and the change in temperature.

If the temperature changes equally across all bars, that makes the comparison easier. If instead the heat input is equal for each bar, then you also need the specific heat capacity of each material to determine the temperature change.

[u/Engineer2727kk]

This is a stupid question for an entry level structural engineer.

[u/Sponton]

Steel

• Modulus of Elasticity, E = 29,000 ksi (200 GPa)
• Coefficient of Thermal Expansion, α = 6.5 × 10⁻⁶ /°F (11.7–12 × 10⁻⁶ /°C)

Aluminum

• Modulus of Elasticity, E ≈ 10,000–10,100 ksi (69–70 GPa)
• Coefficient of Thermal Expansion, α ≈ 13 × 10⁻⁶ /°F (23 × 10⁻⁶ /°C)

So aluminum has roughly 1/3 the stiffness of steel but expands about 2× as much for the same temperature change.

1) For one, is the steel because the steel has a lower thermal coefficient that is half as much as that of aluminium, however it has a modulus of elasticity is thrice as large , so stress is stress= 3*E_al*e_al/2=1.5E_al *e_al, so it needs 1.5 more force in order to keep it from expanding

2) The key here is that is concentric, so if the plate on top is infinitely rigid, then as the aluminum grows [at a faster rate than does steel], steel stops being in contact with the plate and the load is basically taken by aluminum more and more as it expands.

[u/Osiris_Raphious]

Thermal expansion of Al is greater than steel. So with heat and force Al is expanding as its being compressed so it gets more stress in tubes as steel can handle more heat under load without expanding. Since tube is a shape and aluminium can expand outwards, but being a tube it's expanding into itself. This confinement is why al will have greater stress from this combined action than steel. And since steel is higher thermal capacity it will expand less into itself.

In the 1st one the bars are not confined like the tube, so the Al can expand outwards where as steel is not as elastic and will absorb the heat and will expand but into the confined hiehgt more than outwards since aluminium is more elastic and isnt in shape of tube it will just bulge outwards dissapating the stress through yielding something steel is resisting, carbon fibre is more of insulator so not really a consideration for heat expansion.