Cook barley in medium saucepan of boiling salted water until tender, about 30 minutes. Drain; cool. Transfer to large bowl.
Cook beans in large pot of boiling salted water until crisp-tender, about 4 minutes. Drain. Transfer beans to bowl of ice water to cool. Drain well. Pat beans dry with paper towels. Cut half of beans into 2-inch pieces. Transfer to bowl with barley. Mix in corn kernels. Coarsely chop 2 bunches arugula; add to bowl with barley mixture.
Whisk olive oil, vinegar, shallots, thyme and Dijon mustard in small bowl to blend. Pour enough dressing over barley mixture to coat. Season salad to taste with salt and pepper.
Arrange remaining 2 bunches arugula around edge of large platter. Arrange remaining whole beans in spoke pattern atop arugula. Mound salad in center of platter. Sprinkle with goat cheese. Drizzle any remaining dressing over arugula and beans and serve.
