Per the listing and IRC: listed firestops at each floor level or every 10 feet vertically. Most mfrs. state must use a listed intermediate support section of chimney once over about 32ft of chimney. Again, this is per each listed instruction. Most mfrs. will allow the use of plumbers strapping or drives screwed to the outer wall of the chimney as long as the screws do not penetrate the inner section. While not required by the listing, you can install sheetmetal screws in each joint to reinforce it. You should be putting 3-4 screws per joint in all elbows and the offset sections.

HTH,
Bob

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Keep the fire inside the fireplace!
IAFCI Regional Director & Certified Fireplace Inspector
Certified Master Hearth Professional & HPBA BoD