This is one of the shorter tales in the Grimm’s first edition. Later variations tell an extended story about why these three left on their journey. It’s also one of those that doesn’t seem to have any real, deeper meaning so there’s not a whole lot to do in the way of analysis. I’ll go ahead and post the whole story and y’all can decide for yourselves if there’s a message here.
A straw, a coal, and a bean came together and wanted to take a great journey. They had already gone through many countries when they reached a brook without a bridge and couldn’t cross. Finally, straw came up with a good idea.
He laid himself across the brook, and the others were to cross over him, first coal, then bean. Coal took wide steps and slowly crossed the straw, while bean toddled after. When coal got to the middle of straw, however, straw began to burn and burned through and through. Coal fell fizzling into the water and died. Straw broke into two pieces and flowed away.
Bean, who was somewhat behind, slipped and fell into the water but managed to help herself a little by swimming. Finally, bean had to drink so much water that she burst and was driven to shore in this condition. Fortunately, a tailor was sitting there. He was resting while taking a hike in the woods. Since he had a needle and thread in his sack, he sewed bean together. Ever since this time all the beans have a seam.
Grimm, Jacob; Grimm, Wilhelm. The Original Folk and Fairy Tales of the Brothers Grimm: The Complete First Edition (p. 56). Princeton University Press. Kindle Edition.