The pillars are most probably subject complement to the semi-predicate “to be”. Object complement might not be entirely indefensible, but I think subject complement is by far the better analysis.
In “I want you to be happy”, we call “happy” an object complement, because “want” is active, and “happy” is a complement to “you”, which is object to “want”.
The type of sentence you brought up is this: she is said to be cruel.
The main verb “is said” is passive. This is a special passive construction, which attracts an infinitive (here “to be”). “To be” is a copula, i.e. a verb that can have a subject complement. When a copula is nested within a passive construction, we say that the copula gets a subject complement (cruel), since “cruel” is a complement to the subject “she”.
If you have object + verb that can have object complement (there aren’t that many) + noun or adjective that fits the object, you have an object complement. Such verbs are “to find” (I find you gross), “to consider” (I consider you my enemy), “to make” (I make you mad), “to have” (we had the house built by her), “to paint” (we painted her black), “to leave” (I left her crying), and some more. You can see that “consider” and “find” are of the same type, just as “paint” and “make” are of the same type; of each type, there are more, and probably some others that do not fit a type.
As an alternative, you have an object complement in a sentence of the type “I want you to be happy” as mentioned above.
“Beaten” as separate from a finite verb / verb phrase, as a semi-adjective, means “having been beaten”: “the beaten kid” means the kid that has been / was beaten; that is, the beating is over.
The passive verb phrase “is beaten” is just the passive of “beats”: it is in the present tense, there is no sense of the beating’s being over. “John is beaten every day at school”.
Only in its semi-adjective meaning can a participle be used as a complement, which is not very common; if it does not have its adjectival meaning, it must be part of the verb phrase / finite verb, which is usually the case.