If you re working by yourself this can be done with a string level.
String level new floor joists.
Nailing two 2x4s together will work to span about three joists unless the sag is under a weight bearing wall.
Lay a new 3 4 plywood subfloor and bob s your uncle.
There is always the possibility in older properties that your floor joists have dropped at one end because the timber has become rotten and compressed.
Then set new joists same height as existing ones alongside the old.
Set the joist in with s 3 4 block sitting on top and raise until the block touches the string and drive a screw right below the string remove block and set go set the other end the same way.
A day until they re level.
Run a string line across perpendicular to the joists maybe an inch above where you want the joists to end up make sure it is perfectly level then you can quickly check the accuracy of the floor joist by measuring down from the string line.
Set a hydraulic jack and post under the beam and jack up the joists about 1 8 in.
Use floor glue it will stick.
Then a string line can be fixed to the top of these two new joists giving you the level for the joists in between.
If the floor is sagging the damaged joist and or a few neighboring joists may need to be jacked up slightly to straighten or raise the floor so the sister joist can be put into place.
You will have a level sound surface to lay your new floor on.
In some cases we will sink the subfloor between the joists on plywood ledges and on the other end of the room the sistered joist can raise it up to the desired level.
The string line would be fixed in position x in the diagram below.
If you have help this can be accomplished by laying the level on the beam and adjusting until its level.
Setting the joists perfectly level at the house is easy and the beam makes them fairly even near the front edge but the problem is in the middle.
Tie a string across the top of level 3 4 above the highest joist.
Just hammer a nail into the floor by the side of the room you want to be level then run the string out to the far end with the string level attached.
Even though we use 1 pt lumber the joists are often slightly warped or vary in depth at times causing adjacent joists to differ in height by as much as 1 2 inch or more.
Make the bottom edge of each of the new joists even with the strings all the way across.
Affix aluminum or wood joists alongside each of the existing joists with the new joists hanging lower than the original ones.
Secure the new joists to the old by shooting 2 1 2 inch wood screws through the sides of the new ones and into the old ones.
If you have an uneven floor you may need to think about leveling floor joists with shims.
The new sister joist is cut to the same length or slightly shorter as the old joist and is inserted into the joist cavity and snugged up against the old joist.