Armor dama?

[Zaebos]

Armor can be damaged in a number of ways.

Should you roll a natural one on a save, a piece of your equipment may take damage. (DMG page 214 Damaging Magic Items; PH Page 177 Saving Throw-Automatic Faliures and Successes).

Also, some monsters damage equipment as well...Rust Monster and Bebilith come to mind.

 

[Zaebos]

Is there a limit to how much damage a suit of armor, let's say studded leather, can take before it is rendered useless?

Table 9-8 and 9-9 answers this question in the PH.

Studded leather has a hardness of 2 and 15 hitpoints (armor bonus x5). You might want to increase the hardness since Studded Leather does have metal bits, anywhere from 2-5 hardness I would find acceptable, but that is just me.