"I didn't design the layout of Brasilia. I just did its architecture.
And it's a place where the buildings count for a lot. The city is flat.
The horizon stretches away endlessly."
- Oscar Niemeyer
Misc. notes on architecture
Re, the Modernist affinity for geometric simplicity, and the flat roof. Boxes with lids on them, more or less.
Granted, the flat-roofed structure has been around since time immemorial, being the direct descendent of the most rudimentary of architectural configurations, the post-and-lintel affair. Due to this lineage, one might describe it as "classic" in a sense. But perhaps only classic by default, by base necessity, since the prior mode of default mostly meant scouting out caves and the like. Post and lintel basically meaning walls and roof -- support and shelter. The rudiments.
The lintel element being -- by extension -- the flat roof. Which would become the basic structural feature thereafter, especially for buildings that served the most basic purposes -- be they domestic or institutional. Such things lack grandeur, speak in too humble of terms.
SO: The flat roof being a matter of default throughout the ages. Until the twentieth century, when High Modernism brought it back into style, made it a matter of preference. Modernism, with its guiding principle of purity and all that -- banishments of ornament and excess, form following function for the sake of improving (and aestheticizing) the built environment. That sense of purism extending to the reductivist basics of modular geometrical volumes -- permutations of the square and rectangle; the rectitude of -- as Le Corbusier would put it -- the right (i.e., 90-degree) angle.
All of that aside, there are inherent disadvantages to the flat roof, the sort that pose issues for the longevity of the building. One of course is the simple matter of water; which can collect in puddles along the plane of the roof, causing leaks which thereby incrementally shortening the integrity of the structure (not to mention adding to all sorts of laborious, expensive, and continual maintenance).
From an engineering point of view, the sloped roof has its upsides (no pun intended); mainly because it channels a lot of the gravitational taxation out towards the corners, where the corner beams could divert said forces right back down into the earth. But you lose that with a flat roof. Especially if its ceiling is low, and the structure sprawls. In which case it requires -- like the sort that covers any vast acreage (a factory, say) -- an optimum of load-bearing supports within. Basic physics, really. The more weight put upon a roof (be it the heavy accumulation of seasonal snows, a recreational deck or helipad, or the simple stacking of additional storeys), the more it needs to be reinforced from within, and extensively throughout. Stress-points have to be diffused – equally dispersed.
Such pragmatic considerations aside, there were plenty of other reasons to beat up on Modern architecture; and plenty of critics have lined up to do so in recent decades. Much of the criticism extending beyond considerations about form, focusing instead on issues of functionality. In this respect, it sometimes adopts the posture of a type of Adolf Loos-ish civic-virtues sanctimonious blowholing; which at times comes across as disingenuous, the anti-"purity" puritanism often hanging on the speaker as smartly as a second-hand suit.
At any rate, Le Corbusier is the favorite target for critics of Modern architecture; particularly his "Radiant City," which is overwhelmingly cited as the ultimate in bloodlessly "rational," dystopia-via-utopian urban planning. And yes, to look at the drawings and the model, one can't argue with that assessment. But it was never built or realized, if only because it was unbuildable and unrealizable, which is undoubtedly for the better. But there’s always Brasília, which was built and exists as an actualization of a similar plan. Like Corbu’s scheme, it's been described as inhumanly sprawling and impersonal, too aesthetically elitist and "absolute" in its grandeur. Similarly, it’s also been assailed for being too organized around the culture of roadways and the automobile; its expanses exceedingly unfriendly to pedestrian traffic and difficult to reach or navigate on foot. So while on one level – as a series of containers for administrative and bureaucratic activity – the city serves its function. But on another level, a much more logistical and symbolic level, one might argue it fails to fulfill its purpose.
Or so it’s said. Perhaps, dunno. I'm neither an architect nor an engineer, and I imagine this sort of thing is better left to those with the requisite expertise. What's more, I’ve never been to Brasília. But from appearances, the structure seems to be bearing up fairly well. Not only that, but it's still looking quite grand at the same time.