How do you sort 'should have [obligation]' and 'should have [expectation]'?

Question

He should have been there.

means that "I think he had a duty to go there, but failed", doesn't it?

He should have been there by yesterday.

and this implies "I think he might have arrived there at least not later than yesterday".

Then, how do you make a sentence which means "I think he had a duty to go there not later than yesterday, but failed" using with should've? This would seem kinda stupid question, but I'm struggling... please teach me.

Answer 1

It can mean either one or both depending on the context of the conversation.

If I was complaining to someone that the plumber hadn't come to fix a leak yet I would say, "He should have been here an hour ago," meaning he should have been there by obligation and by a certain time.