Hello Mohammed,
You're welcome,I'm glad if you've found my post useful in any way.
As to the sentence you've given, I think that how you analyse the sentence is the right way it should be parsed. By uttering quoted sentence the focus is being placed on the state of the chair and not on the action of its breaking. The past participle "broken" is a participial adjective by its form and functionaly it is a subject complement and modifies the noun "chair" .
If the focus is to be set on the action and we're supposed to convey the breaking of the chair as a new information to someone than we would say :
The chair has been broken.
In this case "broken" is the past participle form of the verb "break" and it is part of the verb phrase " has been broken" .
I understand it like I've put it above,still it would be better to ask a native speaker to get a hundred percent accurate answer.
Best regards
Velimir