Thinner than 1/8? Do you think 2"x2" @ 1/4" thick is sufficient?

EDIT: In my lunchtime haste, I overlooked a key piece of information: Stress equals Mc/I where M is your moment (caused by your loading), c is half of your section depth, and I is your moment of inertia. Because these have different section depths, you really need to compare the ratios of the c/I (the lower the better). I also added the weights to make it easier to follow (hopefully).

The capacity is a function of the wall thickness AND the depth. Basically, you want the section with the highest moment of inertia which for a rectangle is (1/12)(width)(depth)^3. Because this is a hollow section, the void is subtracted out. As you can see the depth gets cubed, so you get a lot more strength from a deeper section (i.e. more bang for your buck) as shown below. From my steel manual, the moment of inertias for the shapes discussed are shown below. For the rectangular sections, these are oriented with the long side vertical.

HSS2x2x1/8: I = 0.486, c = 1", c/I = 2.06, weight = 3.04 lb/ft

HSS2x2x1/4: I = 0.747, c = 1", c/I = 1.34, weight = 5.38 lb/ft

HSS3x2x1/8: I = 1.30, c = 1.5", c/I = 1.15, weight = 3.90 lb/ft

HSS3x2x3/16: I = 1.77, c = 1.5", c/I = 0.85, weight = 5.59 lb/ft

HSS3x2x1/4: I = 2.13 , c = 1.5", c/I = 0.70, weight = 7.08 lb/ft

HSS4x2x1/8: I = 2.65 , c = 2.0", c/I = 0.75, weight = 4.75 lb/ft

The last two sections are comparable strength-wise, but the 4" section is lighter and should cost less. Both are about twice as strong as the 2x2x1/4 section (1.34 vs 0.70/0.75). Compared to the 2x2x1/4, the 4x2x1/8 is also lighter and should be cheaper.

Additionally, you could consider buying a higher grade of steel which would allow you to go smaller. I don't know if you have the option, but a grade 50 steel will be stronger than a grade 36. I don't know the cost differential.

Lastly, as others pointed out, the span of your ramps is also a factor. You are talking about 5' ramps, but others have 8' ramps with supports. Even if the logs are the same weight, it would be tough to compare directly since they result in different bending stresses. As someone pointed out, there are calculators available online that can help you out with this.

I know it is a lot of information and jargon, but ultimately the deeper the section, the better. I hope this helps.