at 9:42:23 AM
1 5/8" deflection is quite substantial!
The first concern is to see if any renovation has been done on the second floor that may have redirected the load path above or created a point load somewhere in the midspan of the joists. This should be verified before any repair begins. Another common problem is that the joists have been compromised by cutting or notching for utilities, particularly plumbing in bathrooms. Look closely for this.
If that is not the case, you can open the ceiling below and temporarily remove the electrical, plumbing and HVAC. At this point you can temporarily and slowly jack up the sagging joists. Once they are as close to straight and level as possible you can "sister" a new joist beside each existing joist using construction adhesive and nails or screws. The number and pattern of fasteners will be prescribed in the Ontario Building Code 2006.
It is important to note that unless these "sistered" joists bear on both bearing points (typically the outside wall and an interior load bearing wall) they are NOT increasing the strength of the floor but are simply re-establishing a level floor and greatly stiffening the existing framing. If you can get full length joists from bearing point to bearing point you will be increasing the strength of the floor above.
This will be all dependent on the load above, and while sagging is common in older structures it can never be simply dismissed as "an old structure". Something is causing the sagging and that should definitely be identified and addressed first.
This is one of the more involved and potentially dangerous (possibly catastrophically) jobs to tackle in a home as it often involves all of the mechanical trades as well as major structural aspects of the building.
If you are not well versed in building sciences I would urge you to retain the services of a professional contractor in your area or a Structural Engineer (P.Eng) yourself if you plan on attempting the repair.
That 1 5/8" deflection is cause for concern.
I hope this helps.
The Cedarbrook Group