Robert Louis Stevenson uses several structural elements to create and build suspense and intrigue in The Strange Case of Dr. Jekyll and Mr. Hyde. Some of these structural elements follow.
1. Stevenson starts Chapter 1 with a detailed description about a character--actually two characters--other than Dr. Jekyll or Mr. Hyde, the namesakes of the story. The reader expects to meet first Dr. Jekyll and then Mr. Hyde but instead Mr. Utterson and Mr Enfield are offered up.
2. He then introduces a narrative of an experience told by a participant--Mr. Enfield--in a horrible event centering on Mr. Hyde's inhuman behavior.
3. Next Mr. Utterson intimates that he has knowledge of the signatory of the bank check and of the physical relationship of the person's home with the building with the strange door entered by the vile Hyde.
All these structural elements create an instant suspense by (1) creating an interesting and intriguing and trustworthy point of view (or focalizer) into the story (Mr. Utterson) and by (2) setting up a string of questions that inspire the reader to search for answers by turning the pages.
Stevenson continues in this vein of introducing characters or gradually deepening details about the characters and introducing puzzling events, such as Jekyll's peculiar will and Jekyll's that Utterson give Hyde help when Jekyll would be no longer there, as the conflict deepens and the plot unfolds.
The pivotal device for building and heightening intrigue and suspense is the introduction in Chapter 4 of the horrific murder of Sir Danvers Carew. Two things are accomplished at the point. First, the reader wants to know how it comes about that Hyde is tracked down and caught and whether he is made to pay for his crime. At the same time, the reader is horrified for the fate of Dr. Jekyll who at all times is presented as a sympathetic, although flawed and perhaps deluded, character.
Finally, Stevenson explores the emotional and psychological (combined emotional and cognitive) suffering of certain characters, particularly Jekyll and Hyde and Lanyon. All these elements--and the distance from Jekyll that is created by having the narrator tell the story through Utterson's experience of it instead of Jekyll's experience of it--contribute to the sense of intrigue and suspense in The Strange Case of Dr. Jekyll and Mr. Hyde.