Learn Hardcore Croatian: U uredu je zabranjeno pušiti. - Smoking is forbidden in the office.

je is the verb “to be” (3rd person singular) that links the predicate: it makes a full sentence.
In signs/labels, it’s often omitted: Zabranjeno pušiti. or Zabranjeno pušenje. That’s elliptical style.
In normal speech/writing, keep je: U uredu je zabranjeno pušiti.

Why is zabranjeno neuter and not zabranjen?

Neuter zabranjeno is the impersonal predicative form used when there’s no explicit subject or when the subject is a neuter noun like pušenje.
Compare:
- Pušenje je zabranjeno. (neuter noun, so neuter adjective)
- Ulaz je zabranjen. (masculine noun ulaz, so masculine zabranjen)
- Vožnja je zabranjena. (feminine noun vožnja, so feminine zabranjena)
In Zabranjeno je pušiti, there’s no overt subject; neuter is the default.

Why is pušiti an infinitive? Could I use pušenje instead?

Yes, both are fine:

U uredu je zabranjeno pušiti. (infinitive; natural in speech)
Pušenje u uredu je zabranjeno. / U uredu je zabranjeno pušenje. (verbal noun; a bit more formal)
Signs often use the short noun phrase: Zabranjeno pušenje.

Why uredu and not ured?

Because u + static location takes the locative case. ured in the locative singular is uredu.

Static: Radim u uredu. (in the office; locative)
Motion into: Idem u ured. (to the office; accusative)

Why u and not na?

Use u for being inside enclosed spaces (rooms, buildings): u uredu, u školi. na is for surfaces/events/areas: na stolu, na koncertu, na poslu. You wouldn’t say na uredu.

Is the word order fixed, or can I move things around?

You can reorder for emphasis (keeping clitic placement in mind):

U uredu je zabranjeno pušiti. (neutral)
Pušenje u uredu je zabranjeno. (topic = smoking)
Zabranjeno je pušiti u uredu. (focus on the ban)
Sign style: Zabranjeno pušiti u uredu. (elliptical)

Why does je come after U uredu? Where do clitics go?

Clitics like je, se, ga prefer the second position in the clause. The first chunk is U uredu, so je comes right after it: U uredu je zabranjeno… If you start differently, je still tries to be second: Pušenje u uredu je zabranjeno.

Could I say Ne smije se pušiti u uredu? Is that the same?

Yes: Ne smije se pušiti u uredu. = It’s not allowed to smoke in the office.

smjeti = to be allowed/permitted.
This is very common and natural; zabranjeno sounds a bit more formal/sign-like.

How do I say it’s allowed to smoke in the office?

U uredu se smije pušiti.
U uredu je dopušteno/dozvoljeno pušiti.

I’m confused by u uredu vs u redu. Are these different?

Yes:

u uredu = in the office (u
- locative of ured).
u redu = OK/all right; or “in order/row.” Example contrast: U uredu je zabranjeno pušiti. vs U redu, zabranjeno je pušiti.

How do you pronounce the double u in u uredu?

Say two u’s smoothly without adding a consonant: [u u-re-du]. They can blend slightly, or you can make a tiny pause. Write it as two words: u uredu.

Could I use kancelarija instead of ured?

You’ll hear kancelarija in Serbian and colloquially. In standard Croatian, ured is preferred. If you use kancelarija, inflect it: u kancelariji (locative).

Is pušiti the right aspect here? What about popušiti?

Use imperfective pušiti for general prohibitions. Perfective popušiti means completing the act (“smoke up”) and is not used in bans.

How would I say this in the plural, like In offices, smoking is prohibited?

U uredima je zabranjeno pušiti.
Or: Pušenje u uredima je zabranjeno.