The Corruption of Frodo

[Nurumaiel]

Why did he want to put Frodo through that?

I highly doubted that Gandalf wanted to put Frodo through anything. This is what I feel:

As Boromir88 said, Gandalf couldn't take the Ring himself. He said as much himself. That leaves, as Lyta pointed out, the choice of Bilbo or Frodo. Bilbo was already having difficulties with the Ring, and I feel that if he hadn't let it go when he did he never would have. Frodo was the only one left.

And then, of course, the main focus then was to take the Ring to Rivendell. The problem of bearing the Ring to Mordor to destroy it did not wholly arise until the Council of Elrond, and it was then that Frodo chose to take the Ring. 'I will take the Ring, though I do not know the way,' he said.

So what we have is this:

1- Gandalf could not have taken the Ring (see Boromir88's post).
2- It would be best if Bilbo did not take the Ring (see Lyta's post)
3- The objective then was to take the Ring to Rivendell, not all the way to Mordor

So considering the first two points, Frodo would be the only logical choice. Considering the third, the danger was not terribly immense. Gandalf had intended to go to Frodo to help him, but he was imprisoned in Isengard and detained. I don't believe he expected such sufferings to befall Frodo. By the time danger was pretty much inevitible, Frodo chose to take the Ring.