Raising a floor joist is a process which many homeowners can tackle if the damages are not too extreme, and the initial causes aren't pervasive. Before undergoing any substantial changes to the structure of the house, be sure you consult a contractor or other professional. Understanding how the entire residential structure fits together is key when significantly altering one portion of the foundation.
Only lift the floor 1/8th of an inch per day. By going slowly the structure of the house has time to adjust to the lifting and not receive too much stress. If you lift the floor too quickly there can be serious structural damage. Wood tends to give slightly and using only an 1/8th of an inch you can work with the natural give within the wood, rather than causing buckling. If buckling seems to be occurring even at 1/8th of an inch, or damage is suspected slow to 1/16th of an inch per day.
Choose the Right Kind of Jack
In certain instances a hydraulic jack might be better than an adjustable and vice versa. Hydraulic jacks can be temperamental in older houses due to the inability of extremely fine control. In such instances screw jacks would be better so only minute motions are made. Consult the local home improvement store for specific needs of the individual situation. In either case, the jack needs to be adjustable in order to proceed in the slowest possible manner. If there is no basement and only a crawl space, a house jack will be needed and support structures (either pyramid or cribbing) will need to be constructed for the jack to sit on a level surface. A rental company which supplies jacks should be able to provide the structural timbers necessary for the project.
Multistory homes may have identical issues on both the first and second story because the issue is directly related. In such instances, leveling the first floor might result in leveling the second at the same time. Such issues can come from many places. Some of the most common causes are a settling or weakening in a load bearing wall or the underlying concrete slab has cracked/tilted due to unstable ground. In such instances, be careful to watch as you raise the lower level. Frequently check the upper story to make sure the leveling isn't buckling between the floors or creating damages on the ceiling of the lower story.
If the correction is minor - only a 1/4 inch over an 8-foot span - using shims between the floor joist and the subflooring can often rectify it without the need to raise the floor joist with a jack. Wooden shims are often used to work out squeaks and stabilize spongy areas, but they can also be used for slight adjustments to specific places within the flooring where joists might have settled slightly. The same can be used with the girders, though often problems with girders occur where splices are pieced together rather than where the girder meets the joist.