I am currently designing a plane that will have a 75 inch wingspan and use a wood spar rib combination wing. I am having trouble determining the cross sectional spar size needed. I plan to use spruce for the spar. I have calculated that a bending moment of 2,714 lb-in will be felt at the root of the wing. I am modeling the wing as a simple cantilever beam. I am getting extremely large amounts of stress present with this bending moment, which far exceeds the strength of spruce. How can I accurately determine the spar cross sectional area required?

Thanks

I think your calculations may be a bit high. For reference the last two giant scale airplanes that I owned with built up wings a Cap 232 97" had spruce spars of 3/8" square and a Reed Falcon ( Pitts Special type ) 72" has spruce 3/8"X1/4". Both used 3/32 vertical grain balsa for shear webbing. For some added strength you could also add trailing edge spars with shear webbing.

My calculations may very well be a bit high. However my plane will weigh 33 lbs with cargo and has a wing area of roughly 980 in^2. Its an unusual plane being designed for a competition. How do you justify the choice of spar size mathematically?

My examples were kits that were produced by others. Specifically they are Unlimited aerobatic airplanes that are both powered by 70cc engines. Most R/C aircraft have not been run through stress analysis, in most cases it's just not nessesary. We typically overbuild based on experience of what we know works.

Why the need to build an airplane with such a high wing loading?

I'm guessing this is for the SAE heavy lift contest? My club in Fort Worth hosts it every other year.
Where are you calculating the load to be? If you are doing the math as if the load is on the wingtip, your numbers are going to be way over. But wing loading is distributed along the wing's length, not evenly exactly, but fairly close. You can probably get close enough by calculating the stress in the middle of the wing half, but that may not be accurate enough for your professor.
Here's a paper on the topic written by the Aggies. Aside from that hideous maroon and white color scheme they always do, they've showed up with some decent planes over the years. To my knowledge, they've at least never folded a wing.
atmeh_paper.pdf