floor joists, header splice, old house

huangyhg

floor joists, header splice, old house
i have come across a strange configuration in my first floor joist layout.
1) the joists on each side of the basement stairwell are not doubled. the stairwell parellels the floor joists.
2) four joists parallel to the stairwell on one side are connected midway to a perpendicular doubled header.
3) the doubled header goes between the (not doubled) joist on the basement stairwell and another not-doubled joist.
4) the full length joists for this part of the structure extend from a center beam, where they are notched and resting on a 2x2 ledger board, to a concrete block outside wall.
5) the spliced joists are also attached to the center beam, are notched and rest on the same 2x2 ledger board. they are attached to the midway header the same way--on both sides--then extend to the same concrete block outside wall.
6) there is a spliced joist next to the single stairwell joist with a poorly constructed supporting (?) wall underneath it, and a wall above it.
7) there is a wall above the midway header, and a wall above the other not-doubled joist, parellel to the stair well.
8) basement floor is concrete slab.
my question: is this structurally sound (i doubt it), and what is the best way to resolve the situation without putting a second full length supporting wall.
thank you.
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further information about span, joist size, floor deck, joist species (if known) is required to answer your questions.
floor decking is 1/2" plywood (1970 era)
full length joists are 15'10" x (2" x 10")
sliced joist are divided midway @7'10"
joist spacing from stairwell is:
full joist @ 0", 6', 6'6", 7'10", 8'2", then 16" oc.
spliced joists are sistered to full joists at 0" and 6'.
spliced joists are also at: 1'0", 2'0", 3'4" and 4'8"
joists are white pine (wp)3  the stamp also says 9-dry and eagle lake.
it doesn't sound safe because the splices joists do not appear to have a means to transfer tension across the splice. actually, this is hardly called a splice, so much as joists bearing on a transfer beam.
two solutions, both requiring some analysis, would be :
put columns below each end of the double header.pretty simple. can you stand the columns? will the columns crack the slab.
scab a piece of plywood to the bottom of the cut(or spliced) joists to transfer the tension across them. more difficult, but no loss of floor space. you'll need to shore up the whole area prior to nailing on the plywood. is there a means of shear transfer? what is the nailing req'd to transfer the tension?
i personally favor the 2nd. but them, i'm an engineer and enjoy that type of analysis.
would i assume that the double header (transfer beam) is a cantilever beam to make the calculation?
the load for the 6' x 16' section 14 psf dead + 40 psf residential code live load (54psf total).
would the plywood be 8' x 3' in two sections, with 1/8" expansion space?  i'm not sure how the load transfer would occur across the "double header".
nailing would be calculated for shear in the same manner as a shear wall?
thank you in advance.
it sounded like the dbl header is simple span from the first post. what would it be cantilevering over? do you expect much expansion over a 6 foot width of floor? if not, then probably a single piece would suffice.
the plywood would only need to be long enough to transfer the tension forces. this will be dictated by the nailing requirements.
nail calculations would be similar to that of a shear wall in regards to mode of failure /nail strength. the tension forces would be approximate wl^2/8 *[12]/d(of the joist). remember the nails will actually be in shear, not tension. the allowable tension will need to be checked for the plywood. be conservative. the moment arm will actually be less the the depth of the joist, since compression (to counter the tension) will occur over a depth near the top of the joist.
this will of course result in higher tension/compression forces.
_________   __________<---subfloor above
         | |
         | |        <--joists(dbl hdr between
_________| |__________         joists)
___________________  
                ^------plywood
maybe this limited sketch will help.