Ceiling – How to fix drooping ceiling tiles

I want to add on to ben's answer. You will always have sag with a 14 foot header. If it is a metal i-beam maybe 1/100th of an inch... Your wood/LVL will sag much more.

What you are describing is ultra typical when there is a point load above and they used LVL. I don't know why cities keep allowing the use of LVL for anything more than 10 feet. It will look great and then year 2-3 it starts sagging... year 4-5 you get cracks and notice it... It is not unsafe because the LVLs will have to be seriously sagging before anything would happen. 5/8" is just enough to disturb the finish and annoy you. You can either install a beam in the middle of the room or put in a better header.

I can tell you I bought quite a few houses with sagging rooms for a huge discount. It is really an easy fix. You support each side of the room with a temp frame job, cut out LVL, and install metal i-beam. This is a one day job if you have a couple helpers. The main thing is to jack the metal beam slightly higher than level and support that level during install.

Presuming the place is built right or something close to normal & expected. You would drill a small hole (drinking straw or pencil sized) in the dripping area of the ceiling so an Endoscope Camera could be inserted to catch the leak in action. This would be repeated probably just 2 more times until the leaking pipe is found.

When drilling the hole you'd want a bucket underneath to catch any puddled water up there or just have towels on the floor around a bucket & insert a short bent piece of wire to direct the water down into the bucket.

Then, you rip out the entire ceiling & permanently fix the pipe & that means DO NOT use some screw-on piece of garbage that fake plumbers have been pushing for decades. The Landlord must be involved in all of this & must be the one to have the above performed by a Real Professional Plumber.