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The Dungeon Master's Guide has the following rule for objects (p.246):

Damage Threshold. Big objects such as castle walls often have extra resilience represented by a damage threshold. An object with a damage threshold has immunity to all damage unless it takes an amount of damage from a single attack or effect equal to or greater than its damage threshold, in which case it takes damage as normal. Any damage that fails to meet or exceed the object's damage threshold is considered superficial and doesn't reduce the object's hit points.

Are there any published examples of objects with damage thresholds?

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Page 119 in the DMG has damage thresholds (and other statistics) for Airborne and Waterborne Vehicles.

\$\begin{array}{|l||c|} \hline \textbf{Ship} & \textbf{...} & \textbf{Damage Threshold} \\ \hline \text{Airship} & \text{...} & \text{—} \\ \text{Galley} & \text{...} & 20 \\ \text{Keelboat} & \text{...} & 10 \\ \text{Longship} & \text{...} & 15 \\ \text{Rowboat} & \text{...} & \text{—} \\ \text{Sailing ship} & \text{...} & 15 \\ \text{Warship} & \text{...} & 20 \\ \hline \end{array} \$

Beyond that, the core books don't talk about damage specific thresholds of any objects. Which puts the rest of objects squarely in the DM's purview.

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    \$\begingroup\$ If a wooden ship has threshold 20, a castle wall should have threshold >=40. \$\endgroup\$ – GreySage May 11 '16 at 16:52
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    \$\begingroup\$ It's handy to know that damage thresholds should start around the 10+ range, at least. \$\endgroup\$ – Sebkha May 12 '16 at 0:57
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    \$\begingroup\$ My personal rule: Think of which giant do you think should be able to batter your castle/wall/building down and check the damage it can do with its boulder attack. The threshold should be just a little less than the max. \$\endgroup\$ – pokep May 12 '16 at 14:26
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The Storm King's Thunder adventure states on p. 38 ("B1. Outer Gates") that the town gates of Bryn Shander (to the north, east, and southwest) have a damage threshold of 10 when barred shut.

Each of the two sets of doors at the Goldenfields gatehouse, mentioned on p. 46 ("G1. Gatehouse"), also has a damage threshold of 10.

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    \$\begingroup\$ Welcome to RPG.SE. Please take the tour and visit the help center to see how this Q&A site works. Thanks for the answer, and for providing a published source as asked for in the question. \$\endgroup\$ – KorvinStarmast Aug 22 '18 at 17:39
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    \$\begingroup\$ It might be worth expanding this answer with a summary of the numerous other damage thresholds mentioned in the adventure (for certain trees, altars, statues, vehicles or parts thereof, and other large objects). Feel free to use spoiler-tag formatting if needed. \$\endgroup\$ – V2Blast Nov 23 '18 at 4:45
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A submarine in the Waterdeep: Dragon Heist adventure has an overall damage threshold of 15 (p. 142, under "Submarine Features"). The doors of the submarine each have a damage threshold of 10.

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    \$\begingroup\$ Welcome to rpg.se! Take the tour and check out how to answer when you get a chance. You've provided a really good example but to make a fully answer you need to reference the source materials. It may also help to expand your post to be a more complete answer instead of just an example. Thanks for contributing and happy gaming! \$\endgroup\$ – linksassin Nov 23 '18 at 4:28

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