Plastic lumber doesn't have enough strength to be used for studs; wood and steel are far stronger. While you could size up plastic lumber so it would reach the same strength of wood and steel, it would then be too large to work well as a framing material.
Yes, plastics can be used structurally for outdoor applications, plastic decking being the most popular. Other structural applications include fences, playgrounds, ramps, outdoor furniture, and landscaping elements.
On the house exterior, though, plastics are not just recommended but indispensable for fascia, soffits, and corner boards.
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Fascias are the long boards just under your roofline that you hang your Christmas lights from.
Fascia boards rot like crazy because they are so exposed to the elements and they get dripped on from the roof. When gutters are clogged and begin to overflow, the problem is magnified.
Unless you are a complete stickler for historical detail, it makes complete sense to install fascia boards in expanded cellular polyvinyl chloride (PVC). This board comes in a wide variety of attractive colors (as the sales literature might say), and this color is "baked in." This means that the color is inherent with the materials--much like adding a drop of food color to a cookie dough mix.
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Soffits are the boards underneath the part of the roof that juts out from the sides. Soffits are another perfect candidate for plastic building materials because they can get weathered (though not nearly as much as fascia boards).
Soffits tend to collect lots of insect-borne gunk: spider webs, cocoons, wasp's nests, etc. It's advantageous to have soffits made of waterproof materials such as PVC so that you can spray them down annually.
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House corners get beat up in two distinct ways. First, like fascia boards, they are vertically-exposed to weather. At least fascia boards are elevated from the ground at least 8 feet; house corners, since they run the height of a house, are both elevated and ground-level. Drip and mud splatter continually strike house corners. Secondly, corners get physical abuse: lawn mowers, rakes, brooms, wheelbarrows, children.
It's possible to buy PVC corners that form a solid "L" shape, giving them greater structural stability. Why would you want to buy two separate boards and join them? Well, it's cheaper--but you undo your well-laid plans of having tough-and-unbreakable house corners. Make the investment in the integrated corners; you won't regret it.