The internal structure of Chapter 4 of The Hobbit can be analyzed using the traditional Freytag's pyramid structure. Though it's not a perfect fit since this is just one chapter in a bigger story, it still works.
Chapter 4 begins with a description of the Misty Mountains and how the party feels confident in traversing them due to the advice of Gandalf and Elrond. This introductory section of the chapter operates much like exposition, giving the reader a good feel for the setting and the characters' state of mind as they continue their adventure.
The action rises when a thunderstorm hits, forcing the party into a cave for shelter. Then the horses and party members (with the exception of Gandalf) are captured by the Goblins who live within the mountain. When the party is brought before the angry Great Goblin, the suspense rises further, leaving the reader to wonder if Bilbo and the dwarfs will be eaten.
Like any longer narrative, the chapter also has a climax. The climax occurs when the Great Goblin attempts to kill Thorin after he recognizes his sword as one infamous for slaying goblins, but Gandalf comes to the rescue. The falling action occurs when the party runs out of the mountain with the goblins on their trail.
There isn't a proper resolution to Chapter 4, as the group is pursued by the goblins and Bilbo is ultimately knocked unconscious before the transition to Chapter 5. Until the reader progresses to the following chapter, the fate of the heroes is uncertain.