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Long Time User - First time Poster (renovating 90 yr old community center with detached garage. Some garage joists ENDS are rotten and others are compromised.)

Are the joist sizes acceptable and are there better solutions for this issue?

Brick garage o/d 23'w x 24'2"d. Walls 13" thick. Brick parapet aluminum roof enclosed on all 4 sides w 2 scuppers on back side. Concrete floor slopes = 4". Leaks like a sieve on one side wall at front and back corners where joists were inserted into cavities in the brick wall. Existing construction (all lumber dimensions are true dimensions): lower row of joists are 2"x6.5"x24' spanning the width of the building w/o center supports (yet only minimal sag over the years); these are notched 6" on each end; the 6" notch sits in a 3"wx4"hx6"d cavity left in the brick wall (23' exposed joist plus 6" notches on each end = 24'); these are installed level, 24" on center, a min 9' from floor to bottom of joist. To create a slope for the roof, on the high end 2"x6.5"x20h" 'supports' are aligned with and secured vertically near the ends of each lower joist; the lengths of each pair of 'supports' diminishes by 1.5" from one joist to the next. A second joist 2"x6.5"x23' (no notch) is secured to the "supports" directly above the lower first joist. 1" decking above that and aluminum roofing above that. Over the years the notches of two of the lower first joists have rotted away (the furthest front and furthest back joists - the ones closest to the front and back wall) and dropped, causing the attached 'supports' and second joists to follow. This is only on one wall. The notches of the other joists appear to be only compromised but still supporting the weight of the roof.

Solution: I install a beam perpendicular to the existing joists and 6" away from the leaking side wall side. I anchor three post supports into the concrete floor - 1' from the front and back walls with the third centered. To each I screw a 4"x4" posts (treated for strength OR two 2"x4"s sistered). Using a post saddle I attach a beam to the top of the post to support the lower first joists. I propose for this 23' beam, two 2"x8"s sistered (actually, each of the 23's would be a 14'8" butting a 7'4"). Should these be 2"x10"s? Should the beam be a single 2x sitting in a notch in the top of the post? When completed, the beam will be carrying the load of only the two joists which have rotten notches; however, eventually the other notches will rot and I want this beam to be able to support all the joists as that rot occurs.

Yes, I intend to install an identical beam 6" from the other side wall and a third down the center; I will be sure that the ends of the beam are protected from any moisture from the brick wall; I will use ties to secure the beam to the lower first joists, the lower first joists to the 'supports', and the 'supports' to the second joists; add a rubber membrane to the roof and to the inside and top of the parapet walls; and repair any other leaks found.

(Hope I've described this clearly with no construction or grammatical errors - don't want any stinging replies on my first post....) :vs_no_no_no:
 

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Does your location not require a building permit and an on site inspection for this type work?
 
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