Let’s say aluminum didn’t exist. Same goes for other lightweight metals (magnesium, etc.). The only metal you have is steel. Would it be possible to build a full-size aircraft using steel where aluminum is now used?
Steel has been used for high strength components of aircraft. A tubular steel structure can be used to make the fuselage or wing structure. Think of the old birdcage race cars, or look at steel tube bicycles. You can make very strong lightweight steel structures. You still have to cover the structure, and you won’t be using steel sheet for that. Back to doped canvas perhaps 
OTOH, you could imagine going to a very different construction regime - perhaps pressurised vessels, or pre-stressed skins. One is reminded that the early Atlas rocket was mainly stainless steel, and relied upon internal pressure to maintain structural integrity. I doubt that lack of aluminium would be a deal breaker for the development of modern aircraft, although the construction methods would likely be significantly different. It isn’t as if aluminium is a perfect material itself. It comes with a whole raft of its own headaches.
Given enough power, they say, anything will fly. So yes. You could,
There actually have been aircraft made primarily of steel, mostly around the 1930’s. Aluminum is more typical, true, but it hasn’t always been readily available or has at times been very expensive. The Beechcraft Staggerwing was a steel airplane in that it used steel for the metal bits, it also used wood and fabric as well. Later models of Beechcraft also incorporated a lot of steel in their construction and despite being in the “light aircraft” category they’re pretty heavy for their size. They later move to more typical aluminum use. The Budd RB Conestoga cargo plane was stainless steel. At the time of its design, WWII, there were concerns about aluminum shortages impacting aircraft construction.
If those materials were not available, it does not mean that steal is the only alternative, Wood has been used successfully, along with fabric.
The XB-70 Valkyrie was designed to cruise at Mach 3 and so couldn’t use aluminum. It used stainless steel and titanium.
Yes. Steel tubing was used in WWI, for example on the Fokker D.VII. The Hawker Hurricane of WWII had its rear fuselage made of tubular steel covered with linen. Even into the '50s some airplanes were made with fabric-covered steel tubing (e.g., Piper Super Cub and Tri Pacer). The American Champion (formerly Bellanca) Champion/Citabria/Decathlon line is still made that way (though the wing spars are now metal). Welded steel structures are fairly popular in many homebuilt aircraft.
IIRC, western intelligence was surprised to find the MiG-25 was constructed with a lot of steel when they got hold of the one Victor Belenko used to defect. That also accounted for the ridiculously huge engines, which were needed for all of that weight.
This is not to say the plane was badly constructed or designed. The U.S. wouldn’t have built a plane that way because we had access to better materials and facilities. There was actually some clever engineering on the MiG-25, given the circumstances of its provenance and the conditions under which it would likely operate. But in the end, the weight required some brute force in the form of huge engines.
That’s sort of Soviet engineering in a nutshell, there. Use the best materials and technology you’ve got, and when that’s lacking, make up for it with lots and lots of brute force.
As mentioned, steel tube structure with fabric or wood covering was seen even in parts of high performance military a/c up to WWII. That method is still used in some kit airplanes now.
All steel construction was much less common but not unheard of. The first all metal a/c, the Junkers J1 (E.1) of 1915, was mainly made of steel: steel tube structure covered by very thin steel sheeting. But Junkers soon adopted their trademark corrugated aluminum skin (over aluminum tube) construction as for the J9 (D.1) of 1918, the first operational all metal fighter.
Pfft. Steel is easy. Try concrete instead.
The Budd Conestoga was made from stainless steel.
Gives a whole new meaning to “having the Glide slope of a brick”.
Quite right.
The largest aircraft ever flown, the Hughes H-4 (‘Spruce Goose’) was made from wood (but birch, not spruce).
That record of largest plane that flew may be broken next year if the Strato-launcher flies.
My favorite sea plane is Stainless steel skinned.
I once went to a little talk by Bob Hammer, who was building new Me262s (and restoring a Navy-owned one), and he said the 262 was basically a steel airplane, due to material shortages in the Reich during the war.
The nose section of approximately the first 2 meters was made mainly of steel, at least that was true of the Me 262 B-1a w.nr. 110639 owned by the USN, according to “Me 262” by Smith and Creek Vol 4.
Here’s a detailed description of Me 262’s structure with similar info, although it seems construction varied, for example the Me 262 B1a/U1 in the South African National War Museum has wooden construction at the least at the very tip of the nose
Also the main wing spars were a composite of steel and aluminum, and there were steel reinforcing plates in various places. But the structure was mainly aluminum.
The other aspect of the Me 262 and steel was that jet engine hot section components that were made of high temperature alloy steel in contemporary British and US jet engines were plain carbon steel in German ones for lack of the alloying materials. Which is why production 262’s engines had such a short operational life.
The second German jet fighter the He-162 was made of more steel and wood than aluminum, but unless a country ran out of suitable wood and glue, plywood made more sense particularly for the outer skin of an a/c than steel.
Toward the end, German glue really was bad and its wooden airplanes did fall apart. Some speculation is that the slave labor they increasingly depended upon got better at sabotage.
Somehow, I don’t think the Birch Bitch would… fly, publicity-wise.