Note: This is not a conspiracy thread or anything of that sort so please refrain from turning it into that.
To my knowledge, the towers were made up of practically 100% steel when it came down to structural support and whatnot and yet the speed in which the buildings came down still defies any type of logic and it still makes me shiver to this day.

hno:
So basically my question is simple: Were the towers actually safe when it came down to structural support and strength of the steel which supported the structure?
I suppose the answer to that question has to be 'no'. Clearly, you can't say that a building is safe if over 2,000 of its occupants lost their lives due to its collapse.
It really depends on how you define 'safe'. No building is totally safe - all that we can ask is that it be as safe as reasonably practicable. That means that we have to think about whether the designers back in the late 60s should have foreseen the possibility that their building would have airplanes deliberately crashed into them by terrorists who were prepared to lose their own lives in pursuit of their goals.
Since the disaster eleven years ago, a huge amount of investigation has been carried out by structural engineers into just how the building behaved following the crashes and how the towers eventually collapsed. This has involved frame by frame analysis of thousands of images of the towers backed up by computer analysis. Much of this analysis is in the public domain for anyone who cares to look and so your statement that the collapse 'defies any type of logic' has been well and truly refuted.
Whilst a lot of the analysis is pretty complicated, the basic reasons for the collapse are fairly simple and are just elementary physics.
As Quantum X described, the towers had a 'shell and core' type construction with the central core, composed of steel columns, taking the vertical load of the structure and the external skin, composed of fabricated steel sections also taking its share of the vertical load but also the bending load due to wind load on the towers.
This design allowed a large area of column free office space to be provided on each floor, important in a modern building, and it is also believed that the heavyweight cladding of the exterior, with its narrow windows, appealed to the Japanese architect who suffered from vertigo and hated the huge expanses of glass with their vertiginous views common in many skyscrapers.
The floors also played an important role in the structure as, apart from the obvious function of supporting the loads from people and office furniture, they also acted as large diaphragms effectively bracing both the external skin and the central core.
Structural engineers are largely of the opinion that the floors were the reason for the buildings eventual collapse. Whilst adequate to support all ordinary loading, they were of relatively flimsy (lightweight steel truss with concrete topping) construction and with weak connections to the core and external skin.
Another problem with the shell and core design, which was especially notable in the case of Tower No. 2 was that the concentration of building services in the centre of the building, meant that the escape stairs were very close to each other and the plane impact effectively closed off all means of escape for the people above the crash zone. Had stairs been located at each corner of the building, many of the people above may have survived.
When the planes hit the towers, they caused massive damage to the external skin, which is clear from all the photos and videos of the event. About two thirds of the columns on one side of the tower were knocked out by the impact. What is less clear, but which has been proved by computer analysis is that several of the internal floors and some of the columns of the central core would have been knocked out.
The reason that the towers didn't collapse right away following the destruction of so many load bearing members is down to the fact that the designers had incorporated a huge structural steel truss into the roofs. So, following the impact, the external wall of the building and the floors that it supported, effectively hung from this truss and the load was distributed into the damaged central core.
The towers remained stable for some time after the crashes but the heat of the fire caused by the airliners fuel (backed up by that due to the paper, timber and plastic etc in the building) caused the exposed steel members to lose their strength (steel does this at temperatures well below that at which it melts). This effect was made worse by the fact that the brittle sprayed-on fireproofing of the building had been blown off by the impact explosion.
In addition, the failure of the floors meant that the steel columns of the building, overloaded by the load transfer, damaged by the impact and weakened by the intense heat also lost the propping effect of the floors (steel members subject to compressive loads need to be held in position at regular intervals to stop them from buckling). With that combination, collapse became inevitable.
Although the causes were the same, the two towers collapsed in different ways. Tower 2, the first to fall, did so due to the failure of its external skin. Tower 1 failed due to the failure of its central core.
As soon as the collapse was initiated, the speed of that collapse is not remarkable. The towers, I believe, weighed about half a million tonnes each, which means that the weight of the sections above the collapse zone would have been something like 100,000 to 200,000 tonnes - heavier than a fully laden supertanker. Once that started moving, only a massively strong structure could have stopped it or slowed it down. Effectively, the towers 'unzipped', the huge mass of the top section forced its way through the bottom section with the relatively flimsy floors offering little resistance and the external skin (just bolted together) being pushed out of the way. The central core probably lasted longer but the removal of its lateral restraint as the floors surrounding it collapsed meant that it could no longer support its own weight.
The idea that the towers were designed to withstand plane crashes is true but has been distorted by the conspiracy theorists.
In carrying out the design of structures such as this, you have to take into account the possibility that a plane could be flown into the building and, at the time of the design, that was not that extraordinary as a plane did fly into the Empire State Building during World War II. That was an accident caused by the pilot losing his direction in low cloud and it resulted in some structural damage to the building and the deaths of some people inside it.
By the 60s, planes were a lot bigger and faster and so the worst scenario considered by the designers was that a Boeing 707 would get lost and accidentally hit one of the towers. The most realistic scenario imagined at the time would be that a plane, coming into land at one of New York's airports would be flying low and accidentally collide with a tower.
The difference between that scenario and what happened on 911 was that the planes were deliberately flown at 400mph into the towers, as opposed to the maximum 200 mph of a plane on its landing approach (planes never normally fly at such speeds so close to the ground).
That makes a huge difference because, as anyone who is familiar with dynamics knows, the energy contained by a moving object is proportional to the square of its speed and so, the planes may have hit the towers at twice the envisaged speed but will have imparted four times the energy.
There is another factor as well. Both planes were at the beginning of cross-continental journeys and were, therefore, carrying their maximum fuel load as opposed to a landing plane that would normally have much less fuel on board. Not only did that add to the volume of fuel and hence the intensity of the fire but it also meant that the wings, where the fuel is stored, acted like battering rams and, instead of being shredded by the steel columns were heavy enough to smash them out of the way.
Leslie Robertson, the structural engineer responsible for the World Trade Center, stated that he was not aware just how a building could be protected against a massive fuel fire and that had probably not been taken into account in the design of the fire-proofing.
The investigation into the WTC collapse did result in a large number of recommendations, not all of which have yet been implemented.
Structurally, it was realised that more structural continuity was required in skyscrapers to guard against progressive collapse - highlighting the failure of the floors within the WTC.
Means of escape were also investigated and, apart from the need to have widely spaced escape routes, as I mentioned above, the need to have protected lifts to prevent people being faced with the need to climb down 100 storeys to get to a place of safety was recognised.
The inadequacies of fire-proofing in the WTC has led to the requirement either to embed structural steel members in concrete or use some blast-resistant material such as intumescent paint (which swells to form a protective coating when subject to) heat.
So, probably the towers were as safe as they probably could be given the level of knowledge back in the 60s but modern towers should be a lot safer.