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An interesting video: youtube video - Railroad tank car vacuum implosion
But how is it possible for a metal tank to implode? Even if one can vacuum it, it is subjected to 1 external atmospheric pressure maximum which is around 1 bar or 14.6 psi. How could 14.6 psi crush a metal tank? Please correct me if I am wrong.
Atmospheric pressure is equivalent to supporting a weight of 10 tonnes (about 10 average cars) per metre squared. Put like that, it's not surprising that those metal tanks crumple.
However, in the comments you raise the point that you pump your bike tyres to 40 psi (about 3 atm) and yet they don't explode. I think this gets to the crux of your confusion.
The crumpling of that tank involves the metal undergoing some fairly insignificant bending. The energy required to bend metal (which, by the way, is naturally pretty soft) is not that great. Whereas the energy required to rip it (or your bike tyres) apart requires significantly more energy. This is because the former case involves simply relocating atomic-scale dislocations while the latter involves breaking atomic bonds. Two very different processes.
To illustrate this point, it's easy to compress an empty can of coke. But do you think you could tear a hole in the can?
Indeed, if you reversed the situation so that the tank contained 1 atm of pressure, and the outside was instead the vacuum, then it would not explode.
First of all, as mentioned, atmospheric pressure can exert very high loads when integrated over significant areas. As an example, an overpressure of just 2psi is sufficient to destroy many houses and can kill people. That's about 13% of atmospheric pressure.
Secondly there is an important scale question. You give an example of a bike tyre: a road bike tyre is often inflated to 8 bar or more: if you inflated a car tyre to 8 bar ... well, don't. The reason for this is that the tension in the structure of the tyre goes like $\mathrm{pressure}\times\mathrm{radius}$: so larger tyres have linearly more tension for the same pressure, and would therefore have to have linearly thicker walls to withstand the same pressure.
Finally and most importantly there is an enormous difference between the behaviour of structures (as opposed to materials) under compression and under tension. This is really a huge engineering area but even physicists can see why it's true. Consider for instance a steel rod 2mm in diameter and a metre long: you could easily hang from such a rod, because it's very strong in tension. But if you tried to stand on it then it would collapse immediately. This happens because when the rod is in tension it's in stable equilibrium -- if it bends a bit then the tension pulls it straight -- while if it's in compression then the equilibrium is much less stable -- if it bends a bit then there is an enormous lever which causes it to bend further and it can abruptly collapse. The details of this are complicated and engineers spend a lot of time working out how to design structures which are strong in compression and bending and what the stresses are in them, but the principles are easy to understand.
So tyres, for instance, are nearly pure tension structures: a tyre would not support even a tiny positive pressure outside it. Designing structures which work in compression, such as submarine hulls, is really hard, and they are vulnerable to catastrophic collapse when their design strength is exceeded. Similarly a railway car is designed to support a (small) internal pressure which places its structure in tension, but when it is in compression it will collapse immediately.
A tank is shaped for pressure from the inside, not the outside. The hull of the tank is convex. Pressure on the inside will cause the hull to assume a shape maximizing the volume per surface which leads to spherical or cylindrical shapes. This does not need much rigidity: balloons come in similar shapes. Pressure on the outside instead will maximize surface per volume. Which basically means crumpling the tank: there is no stable shape to assume. You can easily crumple a thin plastic bottle by sucking on it (and it may even break in the process). But good luck exploding it by blowing into it.
Drawing a vacuum in the tank puts the tank walls under a compressive load. The ability of a structure to take compressive load depends on its stability. For a tank car, if we ignore the end caps, compressive loads are acting in two directions - lengthwise and radial. The cylindrical tank will be very stable in lengthwise compression - any buckling forces are distributed over a large amount of material. However, it will not be anywhere near as stable under radial compression, because in that mode the tank wall simply acts as a flat sheet and will easily buckle either inward or outward because there is nothing to resist it. As soon as such a buckling starts, it changes the tank shape; no longer a cylinder, forces become unbalanced and collapse progresses.
If the tank wall is thick enough, it will remain stable under a full vacuum. If the tank wall is too thin, any unevenness in stress (maybe just from the way it is supported on its wheels) may be enough to initiate buckling. Likewise if there is any defect or dent in the tank wall.
If you look at the tank from its circular side you could see how it has to perform like an arch to support the load of atmospheric pressure. Let's imagine we cut a section 1 meter long of this cylinder and cut the bottom part off to have a nice round arch and inspect how it works.
It is roughly 3 meters diameter so it has to support a load of 3 x 1 meters x 10 tons = 30 tons which wants to turn the arch flat by bending the two side walls and pushing them laterally out.
This bending stress has to be resisted by thin wall of the tank (6-8 millimeters), 4 millimeter out half under tension and 4 millimeter in under compression. I did a fast estimate and it boils down to a 22.5 tons meters of momentum which is much higher then the 3 tons meter (the rough sigma x I/H of the tank wall).
There are two questions: "Why does vaccum crush the steel tank?" and Why the tank implode?"
lemon's answered the first question perfectly - multiply the 1 atm pressure by the surface area of the tank and you will get the force, that crushed it.
The second answer is not that simple. The tank walls are designed to transform the pressure forces (perpendicular to the surface) to plain tension/compression (parallel to the surface).
That's theory.
In reality the shape is not perfect, material is not homogenoeus and the atmospheris pressures are not the only forces involved. When the material is in tension the major forces tend to anticipate the instabilities. When in compression the major forces amplify the instabilities.
When the tank is inflated, the tension and bending modulus anticipate the random deformation of the shape (only radius is changing). When evacuated there is only bending modulus anticipates the deformation. For low vacuum this modulus is high enough to stabilise the system but it is quite easy to overcome. Then little distortion in the equilibirum causes all the accumulated energy to release.
Depends on the wall thickness, for example you can collapse a plastic bottle sucking with your mouth but you can't with a glass bottle. There is an Asme code to calculate the minimum wall thickness of a steel tank. The code for external pressure is diferent for internal pressure because geometry of the vessel is very important. Flat and convexe geometry tends to collapse more than concave or spherical.
