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Poor design originally. A (modern) joist hanger on the joists, jacked up tight to close the split, should solve the problem. If your joists are too thick for the joist hanger, use one for double joists and shim the thickness difference with short pieces of plywood or boards.

Here is a link that might be useful: Joist hanger

thanks bus driver.
The only problem is the joist rests on a sill and then notch rests on beam. Traditional hangers won't fit against beam due to sill. I honestly think I need to replicate notch an sister same 2x10. If joist was not a step fit I would be right with you. I'm not sure my replicant idea really works either. Unless I nail joist to beam with corner bracket.

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Maybe slip hanger under joist between sill while leveling?

Use two jacks. One under the joist about 6 inches away from the beam.Jack up the joist tightly but not to bulge the floor above. Then see if the hanger will slip in above the ledger strip. If not, cut away the ledger strip under the joist (while it is supported by the first jack), then place the hanger and put the second jack under it. When jacked up tight, nail the hanger with the specified fasteners.
If more detail is required, if your imagination/creativity cannot take over from here, then this job is beyond your capabilities.
I think that EVERY one of your joists needs this treatment.

This post was edited by bus_driver on Wed, May 14, 14 at 8:49

Thanks Bus Driver.

I'm on your page about removing the ledger strip.

In some cases I may need to pack LVL under old joists to confirm contact with hangers. All the while sistered to new joists (where possible). And yes, I would plan to do all joists, especially if the ledger board gets removed. Since this house is old, the challenge will be dealing with stapled up utilities, plumbing and HVAC.

While I obviously do not intend to solely perform this work.
I come here for the education and understanding on what should be done.

"cut away the ledger strip under the joist" Just two saw cuts required.
No one suggested removing the ledger strip for the full length.It was assumed that shop facilities for you are limited.I did one house the joists were very thick and I designed a shop-made hanger that would support both the joist and the ledger strip. Built the hangers myself. Some joists had problems out in the span and I jacked them up before sistering. Some were sistered on both sides and the hanger was made to support the triple combination. Jacking the hanger before fastening makes sure it is fully supporting the joist(s).
Slow progress, lots of work, great results.

Thanks.

Yes; leave the ledger alone besides cutting for hangers. I'm with you. In my experience the wood for the wall studs (real 2 x 4's) in my last home (same age) was boarderline petrified and ate sawzall blades for breakfast. I trust that same level of progress will happen here.

I actually have a true 2" on each joist, so hanger sizes will need to be considered in junction with sistering joists.

I'd be curious to see a sketch of your hanger design that incorperates both joist and ledger. Do you have a sketch or drawing on this?