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Trying to span 20 feet with rafters on 8 foot spacings is a very hard problem. Go into any big box store and look up. You will see the size of the beams they use for such a situation. A typical assumption for your area might be snow load of 30 lbs per square foot, with a dead load of 10 lbs per square foot. This makes 40 lbs per square foot. Figure 8 feet of supported roof per foot of beam and we get 320 lbs per foot. By my calculations, 2x1.75x14 LVL is only slightly overkill for this loading. Fb comes out at 1800 PSI. A ordinary sawn lumper 2x12 is hopeless -- peak bending stress exceeds 6000 PSI. I get a free span of only about 10 feet possible with a 2x12 on 8 foot spacings. You might be able to cheat on the snow load, but you shouldn't design any building roof to less than 25 lbs live plus 5 lbs dead loading, and that isn't much less than the 40 psf Menard's probably was working with. I suspect something like a set of purpose-built half scissors trusses might be more economical than the LVLs.
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