Learn Spanish (Latin America): La nueva estructura fue construida por los albañiles. - The new structure was built by the masons.

In the analytical passive voice, the past participle functions like an adjective describing the subject. Because the subject receiving the action is La nueva estructura (feminine singular), the participle must agree with it, becoming construida.

Why use the preterite fue instead of the imperfect era?

We use the preterite fue because the building process is viewed as a fully completed event in the past. If you used the imperfect era construida, the sentence would focus on the ongoing process, meaning something closer to the structure was being built.

Since the passive se is so common in Spanish, could I say se construyó por los albañiles?

No, that would sound very unnatural. While the passive se is heavily used in Spanish, it is almost never used when you explicitly name the agent (the person doing the action). Because this sentence names the builders with por los albañiles, you must use the analytical passive voice (fue construida).

Is there a subtle difference between saying nueva estructura and estructura nueva?