The three-sided shape of towers was chosen for a very specific and practical purpose: to prevent the towers being blown over like a pack of cards.
No one had attempted before to build blocks of flats as high as those in the Barbican which are 43 or 44 storeys heigh. The danger of what is called “overturning moments due to wind” increases with the square of the height of the building. So the effects of wind are four times as great for a 30 storey block as for a 15 storey block. If you have a building where all structural walls were lined up in one direction – which you might have if it is in the shape of a square or a rectangle – strong wind against one long wall can blow the building over, unless it is sufficiently strongly built. Having structural walls which are not parallel means that they can’t be blown over like a deck of cards.
One approach to the “overturning” risk would have been to have a steel-frame construction; but the architects and the City Corporation preferred to construct the estate in reinforced concrete.
Other methods of achieving extra wind stability which the structural engineers and the architects considered were the installation of diagonal braces between the columns and bolting on external framing in the form of a triangular lattice work. But those would have severely obstructed views from the flat, so they were rejected.
The solution they chose was to have walls in two or more non-parallel planes. From whichever direction winds might blow, they would be exerting force down the length of some structural walls, not against their faces. The stability is provided by internal structural walls of reinforced concrete. These are the walls between the flats for the most part. And this construction has also helped with insulation against noise between flats and fire resistance.
So, the requirement to achieve stability in high winds was one of the major factors for the ‘triangular’ shape of the tower blocks. (Strictly speaking, they are ‘polygonal’. The shape of the towers is more complicated than a pure triangle.)
“Overturning moments due to wind” was still a concern with some of the earlier designs for the towers which were in the shape of shallow triangles. This would have meant that there would be occasions when the wind pressure would all be on one of the largest wall surfaces where the depth of the building behind it was the least, and therefore the resistance to overturning the least. So the architects substituted a more equal-sided ‘triangular’ structure.